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In condensed matter physics, a time crystal is a quantum system of particles whose lowest-energy state is one in which the particles are in repetitive motion. The system cannot lose energy to the environment and come to rest because it is already in its quantum ground state. Time crystals were first proposed theoretically by Frank Wilczek in 2012 as a time-based analogue to common crystals – whereas the atoms in crystals are arranged periodically in space, the atoms in a time crystal are arranged periodically in both space and time.[1] Several different groups have demonstrated matter with stable periodic evolution in systems that are periodically driven.[2][3][4][5] In terms of practical use, time crystals may one day be used as quantum computer memory.[6]

The existence of crystals in nature is a manifestation of spontaneous symmetry breaking, which occurs when the lowest-energy state of a system is less symmetrical than the equations governing the system. In the crystal ground state, the continuous translational symmetry in space is broken and replaced by the lower discrete symmetry of the periodic crystal. As the laws of physics are symmetrical under continuous translations in time as well as space, the question arose in 2012 as to whether it is possible to break symmetry temporally, and thus create a "time crystal"[1]

If a discrete time-translation symmetry is broken (which may be realized in periodically driven systems), then the system is referred to as a discrete time crystal. A discrete time crystal never reaches thermal equilibrium, as it is a type (or phase) of non-equilibrium matter. Breaking of time symmetry can occur only in non-equilibrium systems.[5] Discrete time crystals have in fact been observed in physics laboratories as early as 2016. One example of a time crystal, which demonstrates non-equilibrium, broken time symmetry is a constantly rotating ring of charged ions in an otherwise lowest-energy state.[6]

Concept

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Ordinary (non-time) crystals form through spontaneous symmetry breaking related to spatial symmetry. Such processes can produce materials with interesting properties, such as diamonds, salt crystals, and ferromagnetic metals. By analogy, a time crystal arises through the spontaneous breaking of a time-translation symmetry. A time crystal can be informally defined as a time-periodic self-organizing structure. While an ordinary crystal is periodic (has a repeating structure) in space, a time crystal has a repeating structure in time. A time crystal is periodic in time in the same sense that the pendulum in a pendulum-driven clock is periodic in time. Unlike a pendulum, a time crystal "spontaneously" self-organizes into robust periodic motion (breaking a temporal symmetry).[7]

Time-translation symmetry

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Main article: Time-translation symmetry

Symmetries in nature lead directly to conservation laws, something which is precisely formulated by Noether's theorem.[8]

The basic idea of time-translation symmetry is that a translation in time has no effect on physical laws, i.e. that the laws of nature that apply today were the same in the past and will be the same in the future.[9] This symmetry implies the conservation of energy.[10]

Broken symmetry in normal crystals

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Main articles: Crystal symmetry and spontaneous symmetry breaking
Normal process (N-process) and Umklapp process (U-process). While the N-process conserves total phonon momentum, the U-process changes phonon momentum.

Common crystals exhibit broken translation symmetry: they have repeated patterns in space and are not invariant under arbitrary translations or rotations. The laws of physics are unchanged by arbitrary translations and rotations. However, if we hold fixed the atoms of a crystal, the dynamics of an electron or other particle in the crystal depend on how it moves relative to the crystal, and particle momentum can change by interacting with the atoms of a crystal—for example in Umklapp processes.[11] Quasimomentum, however, is conserved in a perfect crystal.[12]

Time crystals show a broken symmetry analogous to a discrete space-translation symmetry breaking. For example,[citation needed] the molecules of a liquid freezing on the surface of a crystal can align with the molecules of the crystal, but with a pattern less symmetric than the crystal: it breaks the initial symmetry. This broken symmetry exhibits three important characteristics:[citation needed]

  • the system has a lower symmetry than the underlying arrangement of the crystal,
  • the system exhibits spatial and temporal long-range order (unlike a local and intermittent order in a liquid near the surface of a crystal),
  • it is the result of interactions between the constituents of the system, which align themselves relative to each other.

Broken symmetry in discrete time crystals (DTC)

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Time crystals seem to break time-translation symmetry and have repeated patterns in time even if the laws of the system are invariant by translation of time. The time crystals that are experimentally realized show discrete time-translation symmetry breaking, not the continuous one: they are periodically driven systems oscillating at a fraction of the frequency of the driving force. (According to Philip Ball, DTC are so-called because "their periodicity is a discrete, integer multiple of the driving period".[13])

The initial symmetry, which is the discrete time-translation symmetry () with , is spontaneously broken to the lower discrete time-translation symmetry with , where is time, the driving period, an integer.[14]

Many systems can show behaviors of spontaneous time-translation symmetry breaking but may not be discrete (or Floquet) time crystals: convection cells, oscillating chemical reactions, aerodynamic flutter, and subharmonic response to a periodic driving force such as the Faraday instability, NMR spin echos, parametric down-conversion, and period-doubled nonlinear dynamical systems.[14]

However, discrete (or Floquet) time crystals are unique in that they follow a strict definition of discrete time-translation symmetry breaking:[15]

  • it is a broken symmetry – the system shows oscillations with a period longer than the driving force,
  • the system is in crypto-equilibrium – these oscillations generate no entropy, and a time-dependent frame can be found in which the system is indistinguishable from an equilibrium when measured stroboscopically[15] (which is not the case of convection cells, oscillating chemical reactions and aerodynamic flutter),
  • the system exhibits long-range order – the oscillations are in phase (synchronized) over arbitrarily long distances and time.

Moreover, the broken symmetry in time crystals is the result of many-body interactions: the order is the consequence of a collective process, just like in spatial crystals.[14] This is not the case for NMR spin echos.

These characteristics makes discrete time crystals analogous to spatial crystals as described above and may be considered a novel type or phase of nonequilibrium matter.[14]

Thermodynamics

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Time crystals do not violate the laws of thermodynamics: energy in the overall system is conserved, such a crystal does not spontaneously convert thermal energy into mechanical work, and it cannot serve as a perpetual store of work. But it may change perpetually in a fixed pattern in time for as long as the system can be maintained. They possess "motion without energy"[16]—their apparent motion does not represent conventional kinetic energy.[17] Recent experimental advances in probing discrete time crystals in their periodically driven nonequilibrium states have led to the beginning exploration of novel phases of nonequilibrium matter.[14]

Time crystals do not evade the second law of thermodynamics,[18] although they spontaneously break "time-translation symmetry", the usual rule that a stable object will remain the same throughout time. In thermodynamics, a time crystal's entropy, understood as a measure of disorder in the system, remains stationary over time, marginally satisfying the second law of thermodynamics by not increasing.[19][20]

History

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Nobel laureate Frank Wilczek at University of Paris-Saclay

The idea of a quantized time crystal was theorized in 2012 by Frank Wilczek,[21][22] a Nobel laureate and professor at MIT. In 2013, Xiang Zhang, a nanoengineer at University of California, Berkeley, and his team proposed creating a time crystal in the form of a constantly rotating ring of charged ions.[23][24]

In response to Wilczek and Zhang, Patrick Bruno (European Synchrotron Radiation Facility) and Masaki Oshikawa (University of Tokyo) published several articles stating that space–time crystals were impossible.[25][26]

Subsequent work developed more precise definitions of time-translation symmetry-breaking, which ultimately led to the Watanabe–Oshikawa "no-go" statement that quantum space–time crystals in equilibrium are not possible.[27][28] Later work restricted the scope of Watanabe and Oshikawa: strictly speaking, they showed that long-range order in both space and time is not possible in equilibrium, but breaking of time-translation symmetry alone is still possible.[29][30][31]

Several realizations of time crystals, which avoid the equilibrium no-go arguments, were later proposed.[32] In 2014 Krzysztof Sacha at Jagiellonian University in Kraków predicted the behaviour of discrete time crystals in a periodically driven system with "an ultracold atomic cloud bouncing on an oscillating mirror".[33][34]

In 2016, research groups at Princeton and at Santa Barbara independently suggested that periodically driven quantum spin systems could show similar behaviour.[35] Also in 2016, Norman Yao at Berkeley and colleagues proposed a different way to create discrete time crystals in spin systems.[36] These ideas were successful and independently realized by two experimental teams: a group led by Harvard's Mikhail Lukin[37] and a group led by Christopher Monroe at University of Maryland.[38] Both experiments were published in the same issue of Nature in March 2017.

Later, time crystals in open systems, so-called "dissipative time crystals," were proposed in several platforms breaking a discrete [39][40][41][42] and a continuous[43][44] time-translation symmetry. A dissipative time crystal was experimentally realized for the first time in 2021 by the group of Andreas Hemmerich at the Institute of Laser Physics at the University of Hamburg.[45] The researchers used a Bose–Einstein condensate strongly coupled to a dissipative optical cavity and the time crystal was demonstrated to spontaneously break discrete time-translation symmetry by periodically switching between two atomic density patterns.[45][46][47] In an earlier experiment in the group of Tilman Esslinger at ETH Zurich, limit cycle dynamics[48] was observed in 2019,[49] but evidence of robustness against perturbations and the spontaneous character of the time-translation symmetry breaking were not addressed.

In 2019, physicists Valerii Kozin and Oleksandr Kyriienko proved that, in theory, a permanent quantum time crystal can exist as an isolated system if the system contains unusual long-range multiparticle interactions. The original "no-go" argument only holds in the presence of typical short-range fields that decay as quickly as r−α for some α > 0. Kozin and Kyriienko instead analyzed a spin-1/2 many-body Hamiltonian with long-range multispin interactions, and showed it broke continuous time-translational symmetry. Certain spin correlations in the system oscillate in time, despite the system being closed and in a ground energy state. However, demonstrating such a system in practice might be prohibitively difficult,[50][51] and concerns about the physicality of the long-range nature of the model have been raised.[52]

Experiments

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In October 2016, Christopher Monroe at the University of Maryland claimed to have created the world's first discrete time crystal. Using the ideas proposed by Yao et al.,[36] his team trapped a chain of 171Yb+ ions in a Paul trap, confined by radio-frequency electromagnetic fields. One of the two spin states was selected by a pair of laser beams. The lasers were pulsed, with the shape of the pulse controlled by an acousto-optic modulator, using the Tukey window to avoid too much energy at the wrong optical frequency. The hyperfine electron states in that setup, 2S1/2 |F = 0, mF = 0⟩ and |F = 1, mF = 0⟩, have very close energy levels, separated by 12.642831 GHz. Ten Doppler-cooled ions were placed in a line 0.025 mm long and coupled together.

The researchers observed a subharmonic oscillation of the drive. The experiment showed "rigidity" of the time crystal, where the oscillation frequency remained unchanged even when the time crystal was perturbed, and that it gained a frequency of its own and vibrated according to it (rather than only the frequency of the drive). However, once the perturbation or frequency of vibration grew too strong, the time crystal "melted" and lost this subharmonic oscillation, and it returned to the same state as before where it moved only with the induced frequency.[38]

Also in 2016, Mikhail Lukin at Harvard also reported the creation of a driven time crystal. His group used a diamond crystal doped with a high concentration of nitrogen-vacancy centers, which have strong dipole–dipole coupling and relatively long-lived spin coherence. This strongly interacting dipolar spin system was driven with microwave fields, and the ensemble spin state was determined with an optical (laser) field. It was observed that the spin polarization evolved at half the frequency of the microwave drive. The oscillations persisted for over 100 cycles. This subharmonic response to the drive frequency is seen as a signature of time-crystalline order.[37]

In May 2018, a group in Aalto University reported that they had observed the formation of a time quasicrystal and its phase transition to a continuous time crystal in a Helium-3 superfluid cooled to within one ten thousandth of a kelvin from absolute zero (0.0001 K).[53] On August 17, 2020 Nature Materials published a letter from the same group saying that for the first time they were able to observe interactions and the flow of constituent particles between two time crystals.[54]

In February 2021, a team at Max Planck Institute for Intelligent Systems described the creation of time crystal consisting of magnons and probed them under scanning transmission X-ray microscopy to capture the recurring periodic magnetization structure in the first known video record of such type.[55][56]

In July 2021, a team led by Andreas Hemmerich at the Institute of Laser Physics at the University of Hamburg presented the first realization of a time crystal in an open system, a so-called dissipative time crystal using ultracold atoms coupled to an optical cavity. The main achievement of this work is a positive application of dissipation – actually helping to stabilise the system's dynamics.[45][46][47]

In November 2021, a collaboration between Google and physicists from multiple universities reported the observation of a discrete time crystal on Google's Sycamore processor, a quantum computing device. A chip of 20 qubits was used to obtain a many-body localization configuration of up and down spins and then stimulated with a laser to achieve a periodically driven "Floquet" system where all up spins are flipped for down and vice-versa in periodic cycles which are multiples of the laser's frequency. While the laser is necessary to maintain the necessary environmental conditions, no energy is absorbed from the laser, so the system remains in a protected eigenstate order.[20][57]

Previously in June and November 2021 other teams had obtained virtual time crystals based on floquet systems under similar principles to those of the Google experiment, but on quantum simulators rather than quantum processors: first a group at the University of Maryland obtained time crystals on trapped-ions qubits using high frequency driving rather than many-body localization[58][59] and then a collaboration between TU Delft and TNO in the Netherlands called Qutech created time crystals from nuclear spins in carbon-13 nitrogen-vacancy (NV) centers on a diamond, attaining longer times but fewer qubits.[60][61]

In February 2022, a scientist at UC Riverside reported a dissipative time crystal akin to the system of July 2021 but all-optical, which allowed the scientist to operate it at room temperature. In this experiment injection locking was used to direct lasers at a specific frequency inside a microresonator creating a lattice trap for solitons at subharmonic frequencies.[62][63]

In March 2022, a new experiment studying time crystals on a quantum processor was performed by two physicists at the University of Melbourne, this time using IBM's Manhattan and Brooklyn quantum processors observing a total of 57 qubits.[64][65][66]

In June 2022, the observation of a continuous time crystal was reported by a team at the Institute of Laser Physics at the University of Hamburg, supervised by Hans Keßler and Andreas Hemmerich. In periodically driven systems, time-translation symmetry is broken into a discrete time-translation symmetry due to the drive. Discrete time crystals break this discrete time-translation symmetry by oscillating at a multiple of the drive frequency. In the new experiment, the drive (pump laser) was operated continuously, thus respecting the continuous time-translation symmetry. Instead of a subharmonic response, the system showed an oscillation with an intrinsic frequency and a time phase taking random values between 0 and 2π, as expected for spontaneous breaking of continuous time-translation symmetry. Moreover, the observed limit cycle oscillations were shown to be robust against perturbations of technical or fundamental character, such as quantum noise and, due to the openness of the system, fluctuations associated with dissipation. The system consisted of a Bose–Einstein condensate in an optical cavity, which was pumped with an optical standing wave oriented perpendicularly with regard to the cavity axis and was in a superradiant phase localizing at two bistable ground states between which it oscillated.[67][68][69][70]

In February 2024, a team from Dortmund University in Germany built a time crystal from indium gallium arsenide that lasted for 40 minutes, nearly 10 million times longer than the previous record of around 5 milliseconds. In addition, the lack of any decay suggests the crystal could have lasted even longer, stating that it could last "at least a few hours, perhaps even longer".[71][72][73][74][75]

In March 2025, researchers at TU Dortmund University observed complex nonlinear behavior in a semiconductor-based time crystal made of indium gallium arsenide. By periodically driving the system with laser pulses, they uncovered transitions from synchronized oscillations to chaotic motion. The system exhibited structures such as the Farey tree sequence and the devil's staircase—patterns never before seen in semiconductor time crystals—offering new insights into dynamic phase transitions and chaos in driven quantum systems.[76]

References

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Time crystal

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A time crystal is a phase of matter in which spontaneous symmetry breaking occurs with respect to time-translation invariance, resulting in perpetual, periodic oscillations in time without net energy absorption, analogous to how ordinary crystals exhibit periodic structure in space by breaking spatial translation symmetry. This phenomenon represents a novel nonequilibrium state that challenges classical notions of equilibrium thermodynamics and symmetry in physics. The concept of time crystals was first proposed by physicist in 2012, inspired by the idea of extending crystalline order from space to time in . Wilczek envisioned continuous time crystals in closed, equilibrium systems where the ground state would exhibit intrinsic temporal periodicity. However, subsequent theoretical analysis revealed no-go theorems prohibiting such continuous time crystals in isolated, equilibrium many-body systems due to constraints from and the . This led to the reformulation of time crystals as discrete variants in periodically driven, or Floquet, systems, where an external periodic drive imposes discrete , and the system's response features a subharmonic period that breaks this symmetry spontaneously. Experimental realization of discrete time crystals was achieved in 2017 through independent efforts using diverse quantum platforms, including a chain of trapped ions at the University of Maryland, where laser pulses induced periodic flips in spin states with doubled periodicity. Similar observations followed in nitrogen-vacancy centers in and superconducting qubits, confirming the robustness of this phase against decoherence and disorder. These milestones validated the Floquet framework and opened avenues for studying nonequilibrium phases of matter. Beyond discrete time crystals, research has advanced toward continuous time crystals in open, dissipative systems, where interactions with an environment stabilize temporal order without periodic driving. A landmark 2022 experiment using a of rubidium-87 atoms demonstrated such a phase, with oscillations persisting indefinitely under continuous . Recent developments as of 2025 include visible macroscopic time crystals in arrays, observable to the as rippling patterns, and explorations of time crystals emerging from in interacting systems. These structures hold promise for applications in quantum sensing, , and computing, leveraging their exceptional coherence times for precise timekeeping and stable qubits.

Fundamental Concepts

Time-translation symmetry

refers to the fundamental principle in physics that the laws governing natural phenomena remain unchanged under arbitrary shifts in time, meaning the form of the is invariant if time is translated by a constant amount. This underpins much of classical and , ensuring that physical processes do not depend explicitly on the choice of time origin. A cornerstone of this concept is , which establishes a direct link between continuous symmetries of the action in and corresponding conservation laws. Specifically, implies the , as the theorem dictates that invariance under time shifts leads to a associated with the system's total , typically represented by the Hamiltonian in conservative systems. Emmy Noether's original paper formalized this relationship, showing that for systems where the Lagrangian does not explicitly depend on time, the energy is a constant of motion. In everyday physics, manifests in scenarios where holds without external time-varying influences. For instance, a undergoing uniform motion in empty space maintains constant indefinitely, as its remains unchanged over time. Similarly, in conservative systems like a orbiting a star under gravitational forces, the motion follows periodic orbits with fixed periods and conserved total , illustrating how the preserves dynamical stability. From a quantum mechanical perspective, time-translation symmetry arises when the Hamiltonian operator H^\hat{H} is independent of time, leading to stationary states that are eigenstates of H^\hat{H} with definite energy eigenvalues. These states evolve under the time-dependent Schrödinger equation solely through a phase factor e−iEt/ℏe^{-iEt/\hbar}, where EE is the energy and ℏ\hbar is the reduced Planck's constant, without altering probabilities or expectation values. Mathematically, this is represented by the absence of explicit time dependence in H^\hat{H}, ensuring that [H^,T^]=0[\hat{H}, \hat{T}] = 0, where T^\hat{T} is the time-translation operator generating shifts in the system's temporal evolution.

Symmetry breaking in time

Spontaneous symmetry breaking (SSB) occurs when the or of a physical system lacks the present in its governing Hamiltonian or driving protocol. This phenomenon arises in many-body systems where selects a particular configuration from a degenerate set, leading to an ordered phase. A paradigmatic example is the ferromagnet below its , where the isotropic spin-rotation of the Hamiltonian is broken by the of a net aligned along a specific direction, despite no external favoring that orientation. In the context of time crystals, SSB is applied to , resulting in a state that exhibits perpetual, coherent without requiring continuous energy input to sustain the motion. Unlike equilibrium phases, this temporal ordering manifests as a subharmonic response, where the period of the system's is longer than that of any external periodic drive, such as in Floquet-engineered systems. This breaking implies that the system's dynamics repeat with a timescale incommensurate with the drive, distinguishing time crystals from trivially driven oscillators. A rigorous definition of this temporal SSB requires that the expectation value of a local operator O^\hat{O} in the oscillates periodically with a ω\omega that is not a of the driving , capturing the emergence of temporal long-range order. Mathematically, this order parameter can be expressed as ⟨O^(t)⟩=Re⁡[ψeiωt],\langle \hat{O}(t) \rangle = \operatorname{Re} \left[ \psi e^{i \omega t} \right], where ψ\psi is a complex and ω≠mΩ\omega \neq m \Omega for mm and driving Ω\Omega. This formulation ensures the system's response breaks the discrete or continuous imposed by the Hamiltonian or periodic protocol. Time crystals differ fundamentally from machines of kind, which would violate of by extracting net work from a single . In time crystals, no net work is extracted because the oscillatory motion traces closed cycles in , with average power input from the drive balancing any in non-equilibrium realizations, preserving . This internal periodicity thus represents a novel nonequilibrium phase without thermodynamic prohibition.

Analogy to spatial crystals

In conventional spatial crystals, atoms or molecules arrange themselves into a periodic lattice structure, spontaneously breaking the continuous translation of into a discrete set of translations corresponding to the lattice spacing. This results in a stable, repeating pattern that minimizes the system's energy in , as described in foundational . The of time crystals draws a direct analogy to this spatial order, but in the temporal domain. Just as a spatial crystal exhibits periodicity in position, a time crystal displays spontaneous periodicity in time, breaking the continuous of the laws of physics into a discrete temporal lattice. Frank Wilczek coined the term "time crystal" in 2012, inspired by the nomenclature of spatial crystals, to describe a phase of matter where the system's ground state evolves periodically without external input, akin to a "crystal in time." Visually, one can imagine atoms locked into a repeating geometric pattern across space in a diamond, versus the collective state of particles in a time crystal cycling through the same configuration repeatedly over time, like a perpetual clock embedded in the material itself. A key difference arises in their realization: while spatial crystals achieve their ordered state by minimizing energy in equilibrium, time crystals cannot exist in closed, equilibrium systems due to constraints from and symmetry principles, necessitating periodic external drives to sustain their temporal order and prevent thermalization. This non-equilibrium requirement highlights how time crystals extend the symmetry-breaking paradigm beyond static spatial structures into dynamic, oscillating behaviors.

Types of Time Crystals

Continuous time crystals

The original concept of continuous time crystals represents a proposed phase of matter in closed at equilibrium, where the exhibits spontaneous breaking of continuous , leading to periodic behavior in time despite the Hamiltonian remaining invariant under time shifts. However, subsequent no-go theorems have ruled out the existence of such equilibrium continuous time crystals in isolated systems, as they would contradict fundamental principles like energy conservation and thermal equilibrium stability. In such systems, the lowest-energy state is not stationary but oscillates with a period incommensurate with any intrinsic timescale of the Hamiltonian, analogous in concept to how spatial crystals break continuous to form periodic lattices. This notion poses significant theoretical challenges, as it appears to contradict the in isolated systems; without energy input would violate the s of equilibrium thermodynamics unless the is highly degenerate, allowing (SSB) to select a time-periodic configuration from a continuum of possibilities. Achieving SSB in the time direction requires the system to explore a manifold of degenerate ground states, where quantum tunneling or other mechanisms could in principle select a rotating or oscillating state, but stability against perturbations remains a core issue. Frank Wilczek introduced the concept in 2012, proposing models such as a single quantum rotor under a potential that allows the to develop a linearly increasing expectation value for the angular position, ⟨θ(t)⟩=ωt\langle \theta(t) \rangle = \omega t, effectively rotating indefinitely. He also considered coupled harmonic oscillators, where the collective mode breaks through a time-dependent phase in the , formalized as ψ(t)=∑nψne−i(En+Δ)t\psi(t) = \sum_n \psi_n e^{-i(E_n + \Delta) t}, with Δ\Delta an incommensurate frequency shift that induces periodicity without altering the energy spectrum. Subsequent analysis revealed fundamental obstacles to realization. In 2015, Masaki and Seiji Oshikawa established no-go theorems demonstrating that stable continuous time crystals cannot exist in gapped without extreme fine-tuning of parameters, as any such time-periodic would be unstable to excitations or in the . Their proofs apply to general Hamiltonians in the or , showing that the required degeneracy and SSB lead to either gapless excitations or restoration of , effectively ruling out robust equilibrium time crystals. Although equilibrium continuous time crystals in isolated systems are prohibited by these theorems, the concept has been extended and realized in open, dissipative , where coupling to an environment stabilizes spontaneous breaking of continuous without the need for periodic driving. In these nonequilibrium settings, balances energy input to sustain persistent oscillations, representing a distinct phase of . Recent theoretical advances, as of 2025, demonstrate that quantum fluctuations—random variations inherent in quantum systems—can facilitate time crystal formation in dissipative quantum many-body systems, such as two-dimensional lattices of particles in laser traps, by driving correlations that lead to collective rhythmic behavior without needing an external clock. A landmark experimental demonstration occurred in using a continuously pumped dissipative atom-cavity system, where emergent periodic oscillations in number broke continuous time . As of 2025, further advances include macroscopic continuous time crystals in films, exhibiting visible spatiotemporal patterns driven by topological solitons under ambient illumination, and dissipative time crystals coupled to mechanical modes. Additionally, classical analogues of time crystals, though less common, can exhibit Hamiltonian time-crystal behavior without quantum effects, such as in closed, knotted molecular rings where the complexity of knots enhances the time-crystalline nature.

Discrete time crystals

Discrete time crystals emerge in periodically driven , known as Floquet systems, where the system's response exhibits a subharmonic periodicity, meaning the period of the observable's motion is an integer multiple n>1n > 1 of the driving period TT. This phenomenon represents a spontaneous breaking of the discrete time-translation symmetry imposed by the periodic drive, leading to persistent collective oscillations that are not synchronized with the driving frequency. A defining characteristic of discrete time crystals is their rigidity against perturbations, where the subharmonic oscillations maintain their period and even under small changes to the driving parameters or internal disorder, without needing an external reference clock to sustain the rhythm after initial preparation. These oscillations persist indefinitely in the ideal case due to the system's inherent dynamics, showcasing a form of temporal order analogous to spatial rigidity in conventional crystals. A crucial ingredient for stability is many-body localization (MBL), a quantum phenomenon where strong disorder prevents particles from thermalizing or absorbing energy from the drive, thereby "freezing" the system in a localized state that allows the time-periodic behavior to stabilize without heating. Representative examples include one-dimensional spin chains under periodic magnetic field kicks, where period-doubling responses (n=2n=2) arise in interacting Ising models with disorder, and trapped ion systems subjected to periodic laser pulses that induce collective spin flips with subharmonic entanglement dynamics. In these setups, the time-crystalline behavior manifests as macroscopic magnetization oscillating at 2T2T despite the drive at TT. Mathematically, this is captured by the Floquet operator U(T)=Texp⁡(−i∫0TH(t′)dt′)U(T) = \mathcal{T} \exp\left(-i \int_0^T H(t') dt'\right), whose eigenstates have quasienergies ϵ\epsilon modulo 2π/T2\pi/T, and observables oscillate with period nTnT, n>1n > 1, reflecting the broken symmetry. The stability of discrete time crystals is ensured through dynamical symmetry breaking, allowing the phase to endure in non-equilibrium conditions without the need for complete isolation from the environment, as long as perturbations remain below a critical threshold.

Theoretical Foundations

At the core of time crystal theory is the breaking of time-translation symmetry, which, by Noether's theorem, corresponds to energy conservation in physics. Traditional symmetries like spatial translation conserve momentum, while time-translation symmetry conserves energy; a time crystal violates this by having a ground state that evolves periodically rather than remaining static. Initial proposals envisioned equilibrium time crystals in closed systems without external driving, but no-go theorems demonstrated this impossibility in thermal equilibrium, as observable properties must be time-independent and quantum correlations prevent stable periodicity. Viable time crystals thus emerge in non-equilibrium settings, particularly Floquet systems with periodic driving.

Floquet theory and periodic driving

provides the mathematical foundation for analyzing subject to periodic driving, which is essential for understanding discrete time crystals. The Floquet theorem addresses the time-dependent iℏ∂ψ∂t=H(t)ψ(t)i \hbar \frac{\partial \psi}{\partial t} = H(t) \psi(t), where the Hamiltonian H(t)H(t) is periodic with period TT, satisfying H(t+T)=H(t)H(t + T) = H(t). According to this theorem, the solutions take the form of Floquet states: ψ(t)=e−iεt/ℏϕ(t)\psi(t) = e^{-i \varepsilon t / \hbar} \phi(t), where ε\varepsilon is the quasi-energy and ϕ(t)\phi(t) is a quasi-periodic function with ϕ(t+T)=ϕ(t)\phi(t + T) = \phi(t). In the application to time crystals, enables the construction of an effective time-independent Hamiltonian in the stroboscopic sense, capturing the system's at discrete times nTnT. The one-period time- operator U(T)=Texp⁡(−i∫0TH(t′)dt′)U(T) = \mathcal{T} \exp\left(-i \int_0^T H(t') dt'\right), where T\mathcal{T} denotes time-ordering, can be expressed as U(T)=e−iHFT/ℏU(T) = e^{-i H_F T / \hbar}, with HFH_F the Floquet Hamiltonian. The eigenvalues of U(T)U(T) are e−iθke^{-i \theta_k}, with quasi-energies θk\theta_k modulo 2π2\pi. The full over nn periods follows as U(nT)=[U(T)]nU(nT) = [U(T)]^n, allowing the identification of periodic responses that differ from the driving period, such as subharmonic oscillations with period nTnT (n > 1). Periodic driving protocols in theoretical models for discrete time crystals typically involve square-wave pulses, where the Hamiltonian alternates between static values over subintervals of the period, or continuous modulations, such as sinusoidal variations in parameters like magnetic fields or interactions in quantum simulators. These protocols ensure the periodicity required by while tailoring the effective Hamiltonian to exhibit desired symmetry properties. A simple model is a one-dimensional chain of spins with alternating pulses: an imperfect global spin-flip (rotation by π+ϵ\pi + \epsilon) followed by nearest-neighbor interactions in a random magnetic field, with effective Hamiltonian H=∑iJiσizσi+1z+∑ihiσixH = \sum_i J_i \sigma_i^z \sigma_{i+1}^z + \sum_i h_i \sigma_i^x, where σ\sigma are Pauli matrices, JiJ_i couplings, and hih_i random fields. A key feature enabling stable discrete time crystals is the prethermal regime, arising from a separation of timescales in strongly driven . Here, the drive frequency sets a fast timescale, while the effective Hamiltonian governs a slower dynamics, suppressing resonant heating effects and allowing the to remain close to the Floquet eigenstates for exponentially long times before thermalization. This regime supports long-lived time crystals by stabilizing the broken phase against . This Floquet framework underpins the realization of discrete time crystals, where the periodic driving induces subharmonic responses in the observable dynamics.

Many-body localization

Many-body localization (MBL) is a phenomenon observed in disordered, interacting quantum many-body systems, where the system resists thermalization despite unitary evolution, thereby preserving memory of its initial conditions over arbitrarily long times. Unlike ergodic systems that explore the full and equilibrate to a state, MBL arises from strong disorder that localizes quasiparticles—often described as "l-bits" (localized bits)—inhibiting and entanglement spreading. This localization occurs even at finite temperatures, marking a violation of the () and leading to non-ergodic behavior. In the context of discrete time crystals (DTCs), MBL plays a crucial role by shielding the system's temporal order from dissipative processes and ergodic heating under periodic driving. Without MBL, Floquet drives would cause rapid absorption of , leading to thermalization and loss of coherence; however, MBL suppresses this heating, enabling the DTC to exhibit infinite-time-periodic responses with period twice that of the drive, even in the presence of interactions and disorder-induced decoherence. This protection arises because the localized quasiparticles cannot facilitate the of drive-induced excitations, maintaining the subharmonic oscillations indefinitely. Theoretical models of MBL-protected DTCs often employ one-dimensional spin chains under Floquet driving, such as the Heisenberg model with random . In this framework, the Hamiltonian alternates between interaction terms like ∑iJ⋅σi⋅σi+1\sum_i \mathbf{J} \cdot \mathbf{\sigma}_i \cdot \mathbf{\sigma}_{i+1} (where σ\mathbf{\sigma} are Pauli operators) and a drive term involving random longitudinal fields hiσizh_i \sigma_i^z with disorder strength WW, plus transverse kicks gσxg \sigma^x. For sufficiently strong disorder, the system enters an MBL phase where l-bits emerge, supporting robust DTC order. Similar models using gradient fields instead of random disorder have also demonstrated DTC behavior in Heisenberg chains, highlighting localization mechanisms beyond quenched randomness. Diagnostics for MBL in these DTC models include the imbalance parameter, defined as I(t)=1L∑i(⟨σiz(t)⟩−mˉ)2I(t) = \frac{1}{L} \sum_i \left( \langle \sigma_i^z(t) \rangle - \bar{m} \right)^2 (where LL is system size and mˉ\bar{m} the average magnetization), which remains finite and non-zero in the MBL phase due to suppressed transport, contrasting with decay to zero in ergodic regimes. Another indicator is the spectral form factor g(t)=1N2∣Tr[U(t)]∣2g(t) = \frac{1}{N^2} \left| \mathrm{Tr} [U(t)] \right|^2 (with U(t)U(t) the Floquet operator and NN the Hilbert space dimension), which plateaus at a value scaling as 1/N1/N in MBL-DTCs, reflecting localization rather than random-matrix-like decay. These probes confirm the persistence of temporal correlations without thermalization. The transition from the MBL-DTC phase to a delocalized, ergodically heating phase occurs at a critical disorder strength WcW_c, typically on the order of the interaction scale (e.g., Wc≈4JW_c \approx 4J in models), beyond which the system absorbs energy unboundedly and loses coherence. Below WcW_c, interactions delocalize the l-bits, driving the system toward thermalization; above it, the DTC phase is stable. This critical point separates localized protection of time-translation symmetry breaking from dissipative . In the MBL-DTC phase, the finite localization length ξ\xi (characterizing exponential decay of correlations, ⟨σizσjz⟩∼e−∣i−j∣/ξ\langle \sigma_i^z \sigma_j^z \rangle \sim e^{-|i-j|/\xi}) ensures area-law scaling of entanglement S∼O(1)S \sim O(1) for subsystems, underscoring the non-thermal, ordered nature of the state. S=−Tr[ρAlog⁡ρA]∼const.S = -\mathrm{Tr} [\rho_A \log \rho_A] \sim \mathrm{const.} where ρA\rho_A is the reduced density matrix of subsystem AA, contrasting with volume-law growth in thermal phases. Recent advances as of 2025 indicate that quantum fluctuations can facilitate time crystal formation in dissipative quantum many-body systems, such as two-dimensional lattices, by driving correlations that lead to collective rhythmic behavior without an external clock, shifting the view of fluctuations from disruptive noise to an engine for self-organized periodicity.

Thermodynamic Aspects

Equilibrium constraints

In thermal equilibrium, quantum systems achieve a state that minimizes the free energy, resulting in stationary density matrices where expectation values of observables are time-independent and invariant under time translations. This fundamental principle of equilibrium thermodynamics precludes the existence of spontaneous symmetry breaking (SSB) in the time domain for continuous time crystals, as periodic motion would imply a non-stationary ground state or thermal state, akin to perpetual motion without energy dissipation. No-go theorems rigorously demonstrate that continuous time crystals cannot form in equilibrium. For instance, in systems with a gapped —typical for many-body Hamiltonians with local interactions—the is unique and non-degenerate, preventing the degenerate manifold required for time-periodic order parameters. Achieving such SSB would necessitate gapless modes or exquisite fine-tuning of parameters to maintain degeneracy, rendering the phase highly unstable to perturbations like disorder or interactions. These theorems extend to finite-dimensional Hilbert spaces per site, ruling out equilibrium time crystals even in the . At finite temperatures, further prohibits temporal order, as the yields a time-translation-invariant Gibbs state. excite quasiparticles across the energy spectrum, disrupting any potential long-range temporal correlations and driving the system toward , where no stable periodic behavior persists. Unlike spatial SSB, where breaking continuous translation in dimensions greater than one allows stable crystals with gapless Goldstone modes (e.g., phonons propagating deformations), time acts as a single dimension without analogous "spatial" extent for mode propagation. In non-relativistic , the time dimension forbids such SSB in equilibrium because the Hamiltonian spectrum is bounded below, and Goldstone-like temporal modes would require unbounded negative frequencies or relativistic invariance, which is absent. This dimensional distinction ensures that spatial crystals thrive in while temporal analogs cannot. A key mathematical constraint arises from the energy-time : for a exhibiting periodic with period τ\tau, the energy uncertainty must satisfy ΔE≥ℏτ\Delta E \geq \frac{\hbar}{\tau} to allow coherent oscillations. However, equilibrium stationary states, such as energy eigenstates or thermal mixtures thereof, possess definite or sharply peaked energies (ΔE≈0\Delta E \approx 0), leading to an irreconcilable conflict that precludes periodic motion without external driving or non-equilibrium conditions.

Non-equilibrium dynamics

In Floquet systems, periodically driven quantum many-body systems evolve toward non-equilibrium steady states characterized by periodic attractors rather than , enabling the emergence of time crystals through the spontaneous breaking of discrete . These steady states arise from the competition between coherent driving and intrinsic , allowing persistent subharmonic oscillations that persist indefinitely in the ideal case. Beyond discrete variants, continuous time crystals can emerge in open, dissipative systems without periodic driving, where coupling to an environment provides continuous input and to stabilize temporal order. A key example is the experimental realization in a quantum gas of atoms coupled to an , where self-sustained oscillations persisted indefinitely under continuous pumping and loss, demonstrating spontaneous breaking of continuous . Dissipation plays a crucial role in open quantum systems by coupling the system to external reservoirs, which stabilizes discrete time crystals (DTCs) without requiring infinite coherence times, as losses counteract decoherence while preserving the oscillatory order. In such setups, the interplay of drive-induced gain and controlled leads to self-sustained limit cycles, where the system settles into a robust non-equilibrium phase distinct from equilibrium constraints. Heating suppression in these systems occurs through prethermalization, where the dynamics evolve on timescales much slower than the driving period, preventing rapid ergodic heating and allowing the system to remain in a metastable state with time-crystalline order. This prethermal regime is particularly effective in high-frequency drives, where effective Hamiltonians govern the slow , suppressing absorption and maintaining coherence over exponentially long times. Representative examples include dissipative DTCs realized in (QED) systems, where atoms coupled to an exhibit subharmonic responses under periodic laser driving and photon loss, demonstrating stable oscillations with lifetimes exceeding hundreds of drive cycles. Similarly, in arrays with engineered , continuous pumping and radiative decay sustain time-crystalline phases in thermal gases, showcasing robustness against thermal noise. Stability metrics for these non-equilibrium DTCs reveal that oscillation lifetimes scale exponentially with the drive frequency or interaction strength, while remaining robust to variations in drive up to thresholds where the prethermal breaks down, as quantified by coherence times on the order of 10^3 to 10^4 drive periods in experimental realizations.

Historical Development

Initial theoretical proposal

The concept of time crystals originated from an extension of the (SSB) observed in spatial crystals, where atoms arrange into periodic lattices despite translational invariance of the underlying laws. In September 2012, proposed the idea during a lecture, drawing on traditions from where SSB leads to ordered phases like ferromagnets or crystals. He published the theoretical framework shortly thereafter, suggesting that could exhibit periodic behavior in time in their ground states, breaking continuous without external driving; Wilczek envisioned a system that "ticks" rhythmically without any external driving force, much like a perpetual motion machine but grounded in quantum mechanics. Wilczek's key models illustrated this temporal periodicity while preserving energy conservation. One simple example involved a ring of N charged particles interacting via Coulomb repulsion, confined by a harmonic potential and subject to a weak perpendicular magnetic field; the ground state forms a rotating density wave (a soliton) with a finite period T, where the expectation value of the charge density oscillates periodically despite zero total angular momentum. Another model considered a linear array of N coupled quantum harmonic oscillators with nearest-neighbor interactions, where the ground state displays coherent oscillations at frequency ω ≠ 0, breaking time-translation invariance through a non-zero expectation value for the time derivative of position operators. These constructions emphasized that the periodicity arises from interactions selecting a discrete subgroup of the continuous time-translation group, analogous to spatial SSB but in the temporal domain. The proposal immediately faced skepticism, primarily over potential violations of no-go theorems in equilibrium . Critics argued that periodic motion in the would imply , contradicting and the Mermin-Wagner theorem's implications for continuous symmetries in finite systems. In particular, Patrick Bruno demonstrated that Wilczek's ring model is actually translationally invariant and non-rotating, with any observed rotation corresponding to an rather than true SSB. Wilczek responded by clarifying that the models require careful tuning to avoid dissipation and ensure the periodic state is the unique , but the debate highlighted challenges in realizing continuous time crystals in closed systems. Early theoretical extensions addressed these issues by shifting to non-equilibrium settings with periodic driving. Foundational work on Floquet many-body localization, which would enable stable discrete time crystals, was developed in 2014 by Norman Y. Yao et al. in dipolar systems. These efforts laid groundwork for subsequent proposals of discrete time crystals in systems of interacting spins.

Key theoretical milestones

The theoretical development of time crystals shifted focus to discrete formulations after the initial proposal of continuous variants. Earlier critiques included a 2013 no-go theorem by Patrick Bruno, which specifically ruled out spontaneously rotating time crystals in equilibrium systems. A pivotal advancement came in 2015 with the no-go theorem by Watanabe and Oshikawa, which rigorously proved that continuous time crystals cannot exist in the ground state or thermal equilibrium of generic quantum systems due to the absence of spontaneous breaking of continuous time-translation symmetry in closed Hamiltonians. Their argument, based on thermodynamic constraints and symmetry considerations, ruled out equilibrium realizations and prompted a pivot to nonequilibrium, periodically driven (Floquet) systems where discrete time-translation symmetry could be broken. Building on this, the first proposals for discrete time crystals emerged in 2016. Else, Bauer, and Nayak formulated discrete time crystals as Floquet systems where is spontaneously broken, leading to persistent subharmonic oscillations protected by (MBL) in disordered spin chains. In these MBL-protected discrete time crystals (DTCs), interactions and disorder suppress thermalization, enabling rigid, long-lived periodicity that is robust against perturbations, as demonstrated through analytical arguments and numerical simulations in one-dimensional Ising models. Concurrently in 2016, Khemani, Lazarides, Moessner, and Sondhi introduced prethermal DTCs, showing that even without strong disorder, a separation of timescales between driving frequency and local relaxation rates can sustain time-crystalline order for exponentially long durations before eventual heating to an infinite-temperature state. This prethermal regime arises in clean, interacting Floquet systems, where high-frequency driving creates an effective Hamiltonian with approximate symmetries that stabilize the phase, providing a pathway to observe DTCs in less disordered setups. In , work on open-system DTCs by Iadecola and collaborators incorporated dissipative processes, demonstrating that coupling to an environment can stabilize robust time-crystalline phases in Floquet systems by balancing drive-induced heating with targeted that preserves subharmonic coherence. This extension highlighted how open dynamics could enhance stability in realistic, noisy quantum platforms. By 2018, theoretical progress included classifications distinguishing fragile prethermal DTCs, which rely on timescale separation and degrade under strong perturbations, from robust MBL-protected variants that maintain order indefinitely due to localization. These milestones from 2015 to 2018 established the core framework for DTCs as viable nonequilibrium phases.

Experimental Realizations

Pioneering experiments (2016–2020)

The pioneering experimental demonstrations of discrete time crystals occurred nearly simultaneously in late 2016, with the first report appearing in October from the University of Maryland group led by . Using a chain of 10 trapped ytterbium-171 ions confined in a linear Paul trap, the team subjected the ions to periodic laser kicks to flip their spins, resulting in period-doubled oscillations that lasted for more than 50 drive cycles with high fidelity. Disorder was introduced through inhomogeneous magnetic fields and spin-dependent squeezing to realize an interacting spin chain under , preventing thermalization and allowing the time-crystalline order to emerge. This proof-of-principle realization highlighted the subharmonic frequency locking and exponential sensitivity to drive parameters as hallmarks of the phase. In 2017, this experiment was detailed in a publication observing robust 2T oscillations in the trapped ions with laser-driven flips and programmable disorder. Almost concurrently, the group led by reported their observation in late 2016 (published in March 2017). Using an ensemble of approximately 10^6 nitrogen-vacancy (NV) centers in a sample, the team applied periodic microwave pulses to drive the electron spins, observing a subharmonic response where the spin polarization oscillated at twice the driving period, indicative of broken . This response persisted robustly for over 100 drive cycles without decay, enabled by careful tuning of disorder via an external gradient to suppress heating and maintain . The experiment confirmed key signatures of a discrete time crystal, including rigidity against perturbations and stability in a disordered dipolar spin system, with observations of both 2T and 3T responses leveraging natural disorder. Subsequent confirmations in 2017 built on these results, with the Harvard team replicating and extending the NV-center experiment to demonstrate longer coherence times exceeding 100 cycles under refined pulse sequences and disorder optimization. These early setups emphasized the role of periodic and disorder in stabilizing the non-equilibrium phase, achieving coherence on the order of hundreds of cycles while avoiding dissipative heating through precise control of interactions. By 2018, simulations of discrete time crystal signatures in arrays of superconducting qubits were explored by groups including researchers, modeling period-doubling responses in driven qubit chains to predict experimental feasibility, though full realizations awaited later hardware advances. These initial experiments established the viability of discrete time crystals in diverse quantum platforms, with key metrics like ~100-cycle lifetimes underscoring their robustness against decoherence.

Advanced observations (2021–2025)

In 2021, researchers in the Lukin group at demonstrated discrete time-crystalline (DTC) order in arrays of neutral Rydberg atoms, protected by (MBL) mechanisms, using a programmable to observe coherent revivals and subharmonic responses under periodic driving. This experiment highlighted how quantum many-body scars could stabilize temporal order in interacting systems, enabling control over entanglement dynamics without rapid thermalization. In 2021–2022, a time crystal was simulated on a quantum processor by the Google Sycamore team, demonstrating time-crystalline eigenstate order in a driven many-body system, confirming theoretical predictions in a programmable superconducting qubit array. Advancing into photonic platforms, experiments in 2022 realized all-optical dissipative DTCs in Kerr-nonlinear optical microcavities, where periodic modulation induced robust subharmonic oscillations manifesting as visible temporal patterns in the cavity output. These photonic time crystals exhibited stability against noise, with the temporal periodicity directly observable through interference and intensity fluctuations, paving the way for integrated optical implementations. Breakthroughs from 2024 to 2025 expanded the diversity of time crystal realizations. In driven-dissipative Rydberg gases, multiple coexisting time crystals were observed, each with distinct periods emerging from nonlinear interactions and feedback, as reported in experiments achieving bifurcation into complex temporal phases. In , quantum chaos-born continuous time crystals were theoretically and numerically demonstrated in dissipative quantum systems, where chaotic correlations unexpectedly stabilized rhythmic oscillations, revealing a novel phase beyond equilibrium constraints. Visible naked-eye time crystals were created using liquid crystals under ambient illumination, producing persistent rippling patterns of molecular twists observable for hours without external input, marking the first macroscopic, directly visible manifestation. Additionally, time crystals in spin maser systems were observed via retarded feedback interactions in hybrid setups, showing phase transitions to rigid periodic states at . In 2025, advancements included the realization of quantum dissipative continuous time crystals, where quantum fluctuations in open systems facilitated stable periodic behavior without external driving, as shown in theoretical and experimental work on dissipative many-body systems. Similarly, continuous time crystals coupled to mechanical modes were observed in optomechanical setups, demonstrating synchronization between quantum and classical oscillations stabilized by dissipation. The Joint Quantum Institute (JQI) identified key ingredients for a new phase enabling scalable DTCs in solid-state systems, including tunable disorder and protocols in arrays, which support long-lived coherence and integration with existing quantum hardware. These developments collectively advanced time crystal coherence times beyond 1000 driving cycles in Rydberg and photonic setups, enabled room-temperature operations in and spin systems, and explored stacking configurations for prototype , where layered temporal patterns encode information with high stability. Despite these advances, experimental realizations face significant challenges, including scalability due to the small size of current systems, decoherence from environmental noise that disrupts oscillations, and the need for cryogenic conditions in most setups, although room-temperature operations have been achieved in select platforms like liquid crystals and spin masers.

Potential Applications

Quantum computing and simulation

Time crystals probe deep questions in physics by challenging equilibrium thermodynamics and illuminating non-equilibrium phase transitions, where they enable the study of ergodicity breaking and persistent ordered states in driven systems. Discrete time crystals (DTCs) have emerged as promising resources for due to their inherent stability and resistance to decoherence, functioning as long-lived s in periodically driven systems. In trapped platforms, DTC phases enable the storage of with extended coherence times, as the spontaneous breaking of discrete time-translation symmetry protects the system from environmental noise and thermalization. For instance, proposals for space-time crystals in ion traps demonstrate how collective oscillations can maintain qubit integrity without net energy absorption, potentially surpassing traditional quantum memories limited by exponential decoherence. Beyond , DTCs serve as powerful platforms for non-equilibrium many-body physics, capturing phenomena that are computationally intractable on classical hardware. These phases allow quantum processors to model disordered, interacting systems where particles remain localized despite periodic driving, revealing insights into breaking and Floquet engineering. Recent scalable demonstrations in superconducting qubits have validated DTC simulations of , providing a benchmark for verifying theoretical predictions in driven quantum matter. The temporal order in DTCs further enhances quantum error correction by integrating topological protection within driven frameworks, where higher-form symmetries and quantum codes stabilize information against local errors. Topologically ordered time crystals combine spatial anyons with temporal periodicity, enabling fault-tolerant operations through bulk-boundary correspondence in Floquet systems. This synergy offers a pathway to robust , as the intrinsic rigidity of DTC oscillations suppresses error propagation in non-equilibrium settings, while also supporting stable qubits against noise. Additionally, time crystals hold promise for energy storage through lossless oscillations and synchronization in communication networks. A landmark example is the 2021 realization of a DTC on Google's Sycamore processor, where a 20-qubit chain exhibited subharmonic response over hundreds of cycles, simulating a many-body-localized phase inaccessible to classical methods. Looking to 2025 prospects, DTCs are poised to improve quantum computer frequency standards, providing ultra-stable references for and gate calibration, as highlighted in recent analyses of their potential in hybrid quantum architectures.

Sensing and metrology

Time crystals offer significant potential in sensing and due to their robust periodic oscillations, which provide enhanced stability and sensitivity beyond conventional methods, including precision sensing of weak fields. The discrete time crystal (DTC) phase in Floquet-driven systems exhibits ultra-stable oscillations that can serve as quantum clocks with potentially improved long-term frequency stability. These oscillations arise from spontaneous breaking of , enabling persistent coherence without net energy absorption after initialization. In DTCs, weak external fields perturb the temporal period of oscillations, leading to measurable shifts that amplify detection signals through many-body responses. This sensitivity stems from the system's rigidity, where small perturbations propagate across the ensemble, enhancing signal-to-noise ratios for (AC) fields. Boundary time crystals, in particular, demonstrate quantum-enhanced precision in estimating field parameters, achieving Heisenberg-limited scaling in dissipative environments. Applications in include precision sensing of mechanical displacements, where continuous time crystals coupled to mechanical resonators detect minute perturbations via magnon-oscillator interactions. For magnetic field imaging, DTCs realized in nitrogen-vacancy (NV) centers within leverage ' dipolar interactions to map local fields with nanoscale resolution and . These NV-based DTCs maintain temporal order under magnetic perturbations, enabling precise readout of field gradients. Recent 2025 advances feature spin time crystals, observed in hybrid systems with delayed feedback, exhibiting self-sustained oscillations robust to perturbations and suitable for precision frequency . These structures maintain stable spin dynamics, potentially supporting temperature-resilient measurements in spintronic devices. Figures of merit, such as Allan deviation in Floquet DTCs, reveal sub-shot-noise precision, with stability improving as σy(τ)∝τ−1\sigma_y(\tau) \propto \tau^{-1} for interrogation times τ\tau, outperforming classical limits in noisy environments. As of October 2025, demonstrations of linked time crystals have further opened pathways for enhanced interfaces in quantum sensing applications.

References

  1. https://iopscience.iop.org/article/10.1088/1361-6633/aa8b38
  2. https://www.annualreviews.org/doi/10.1146/annurev-conmatphys-031119-050658
  3. https://www.nature.com/articles/nature21413
  4. https://www.science.org/doi/10.1126/science.abo3382
  5. https://www.nature.com/articles/s41563-025-02344-1
  6. https://doi.org/10.1103/PhysRevLett.133.113401
  7. https://www.aalto.fi/en/news/time-crystals-could-power-future-quantum-computers
  8. https://www.eftaylor.com/pub/symmetry.html
  9. https://www.quantamagazine.org/how-noethers-theorem-revolutionized-physics-20250207/
  10. https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_%28Goergi%29/01%253A_Harmonic_Oscillation/1.03%253A_Time_Translation_Invariance
  11. https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/e50659071ed2c74e975e72b70d473ee3_MIT8_321F17_lec18.pdf
  12. https://physics.leima.is/quantum/symmetries.html
  13. https://arxiv.org/abs/1909.01820
  14. https://arxiv.org/abs/1202.2539
  15. https://arxiv.org/abs/1603.08001
  16. https://scipost.org/SciPostPhysLectNotes.11/pdf
  17. https://link.aps.org/doi/10.1103/PhysRevLett.109.160401
  18. https://link.aps.org/doi/10.1103/PhysRevLett.114.251603
  19. https://arxiv.org/abs/1410.2143
  20. https://link.aps.org/doi/10.1103/PhysRevLett.135.110404
  21. https://www.nature.com/articles/s41467-025-XXXXX
  22. https://arxiv.org/abs/2005.00586
  23. https://link.aps.org/doi/10.1103/PhysRevLett.117.090402
  24. https://arxiv.org/abs/1608.02589
  25. https://link.aps.org/doi/10.1103/PhysRevLett.111.070402
  26. https://link.aps.org/doi/10.1103/PhysRev.138.B979
  27. https://link.aps.org/doi/10.1103/PhysRevX.7.011026
  28. https://link.aps.org/doi/10.1103/RevModPhys.91.021001
  29. https://link.aps.org/doi/10.1103/PhysRevB.101.115303
  30. https://www.science.org/doi/10.1126/science.abg8102
  31. https://arxiv.org/abs/1807.09884
  32. https://www.nature.com/articles/s41467-025-64488-7
  33. https://www.wired.com/2013/04/time-crystals/
  34. https://link.aps.org/doi/10.1103/PhysRevLett.113.243002
  35. https://link.aps.org/doi/10.1103/PhysRevLett.116.250401
  36. https://arxiv.org/abs/1703.02547
  37. https://www.nature.com/articles/nature21426
  38. https://link.aps.org/doi/10.1103/PhysRevLett.127.090602
  39. https://www.nature.com/articles/s41586-021-04257-w
  40. https://www.nature.com/articles/s41467-022-28462-x
  41. https://www.sciencedaily.com/releases/2025/10/251015032309.htm
  42. https://www.colorado.edu/today/2025/09/05/physicists-have-created-new-time-crystal-it-wont-power-time-machine-could-have-many
  43. https://www.nature.com/articles/s42005-025-02117-x
  44. https://www.nature.com/articles/s41467-025-64673-8
  45. https://jqi.umd.edu/news/time-crystal-research-enters-new-phase
  46. https://iopscience.iop.org/article/10.1088/1361-6633/aa9d0f
  47. https://link.aps.org/doi/10.1103/PhysRevLett.109.163001
  48. https://www.optica-opn.org/home/newsroom/2022/february/a_step_toward_practical_time_crystals/
  49. https://www.science.org/doi/10.1126/science.abk0603
  50. https://www.nature.com/articles/s41467-024-54086-4
  51. https://arxiv.org/abs/2105.09694
  52. https://thequantuminsider.com/2025/10/17/is-it-time-for-time-crystals-researchers-report-time-crystals-could-power-future-quantum-computers/
  53. https://arxiv.org/abs/2505.08276
  54. https://link.aps.org/doi/10.1103/PhysRevA.109.L050203
  55. https://www.nature.com/articles/s42005-023-01423-6
  56. https://pmc.ncbi.nlm.nih.gov/articles/PMC5349499/
  57. https://phys.org/news/2025-05-crystal-maser.html
  58. https://link.aps.org/doi/10.1103/PhysRevB.111.125159
  59. https://interestingengineering.com/innovation/time-crystal-quantum-computing-europe
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