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Quantum logic clock
Quantum logic clock
Quantum logic clock
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A quantum clock is a type of atomic clock with laser cooled single ions confined together in an electromagnetic ion trap. Developed in 2010 by physicists at the U.S. National Institute of Standards and Technology, the clock was 37 times more precise than the then-existing international standard.[1] The quantum logic clock is based on an Al spectroscopy ion with a logic atom.

Both the Al-based quantum clock and the Hg-based optical atomic clock track time by the ion vibration at an optical frequency using a UV laser, that is 100,000 times higher than the microwave frequencies used in NIST-F1 and other similar time standards around the world. Quantum clocks like this are able to be far more precise than microwave standards.

Accuracy

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A NIST 2010 quantum logic clock based on a single aluminum ion

The NIST team are not able to measure clock ticks per second because the definition of a second is based on the standard NIST-F1, which cannot measure a machine more precise than itself. However, the aluminum ion clock's measured frequency to the current standard is 1121015393207857.4(7) Hz.[2] NIST have attributed the clock's accuracy to the fact that it is insensitive to background magnetic and electric fields, and unaffected by temperature.[3]

In March 2008, physicists at NIST described an experimental quantum logic clock based on individual ions of beryllium and aluminum. This clock was compared to NIST's mercury ion clock. These were the most accurate clocks that had been constructed, with neither clock gaining nor losing time at a rate that would exceed a second in over a billion years.[4]

In February 2010, NIST physicists described a second, enhanced version of the quantum logic clock based on individual ions of magnesium and aluminium. Considered the world's most precise clock in 2010 with a fractional frequency inaccuracy of 8.6 × 10−18, it offers more than twice the precision of the original.[5] [6] In terms of standard deviation, the quantum logic clock deviates one second every 3.68 billion years, while the then current international standard NIST-F1 Caesium fountain atomic clock uncertainty was about 3.1 × 10−16 expected to neither gain nor lose a second in more than 100 million years.[7] [8] In July 2019, NIST scientists demonstrated such a clock with total uncertainty of 9.4 × 10−19 (deviates one second every 33.7 billion years), which is the first demonstration of a clock with uncertainty below 10−18.[9][10][11]

Quantum time dilation

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"Two clocks are depicted as moving in Minkowski space. Clock B is moving in a localized momentum wave packet with average momentum pB, while clock A is moving in a superposition of localized momentum wave packets with average momentum pA and p0A. Clock A experiences a quantum contribution to the time dilation it observes relative to clock B due to its nonclassical state of motion."[12]

In a 2020 paper scientists illustrated that and how quantum clocks could experience a possibly experimentally testable superposition of proper times via time dilation of the theory of relativity by which time passes slower for one object in relation to another object when the former moves at a higher velocity. In "quantum time dilation" one of the two clocks moves in a superposition of two localized momentum wave packets,[further explanation needed] resulting in a change to the classical time dilation.[13][14][12]

Other accurate experimental clocks

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The accuracy of quantum-logic clocks was briefly superseded by optical lattice clocks based on strontium-87 and ytterbium-171 until 2019.[9][10][11] An experimental optical lattice clock was described in a 2014 Nature paper.[15] In 2015 JILA evaluated the absolute frequency uncertainty of their latest strontium-87 429 THz (429228004229873.0 Hz[16]) optical lattice clock at 2.1 × 10−18, which corresponds to a measurable gravitational time dilation for an elevation change of 2 cm (0.79 in) on planet Earth that according to JILA/NIST Fellow Jun Ye is "getting really close to being useful for relativistic geodesy".[17][18][19] At this frequency uncertainty, this JILA optical lattice optical clock is expected to neither gain nor lose a second in more than 15 billion years.[20]


See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Quantum logic clock

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A quantum logic clock is an optical that employs to interrogate the narrow intercombination transition in a single trapped , such as ^{27}\mathrm{Al}^{+}, achieving fractional uncertainties below 10^{-18}. This technique pairs the clock ion with a secondary "logic" ion, like ^{25}\mathrm{Mg}^{+}, for sympathetic and state readout, as the clock transition in aluminum is optically inaccessible directly. Developed at the National Institute of Standards and Technology (NIST), the clock operates at optical frequencies around 1.1 \times 10^{15} Hz, offering stability orders of magnitude superior to traditional cesium clocks at 9.2 \times 10^9 Hz. The concept emerged from advancements in and in the early 2000s, with NIST demonstrating the first quantum logic clock in 2005 using a single ^{27}\mathrm{Al}^{+} co-trapped with a ^{9}\mathrm{Be}^{+} logic . By 2010, an enhanced version surpassed all other atomic clocks in precision, neither gaining nor losing a second over 3.7 billion years. Ongoing refinements, including improved ion traps to minimize micromotion and sensitivities, have pushed performance further; in 2019, NIST reported a systematic uncertainty of 9.4 \times 10^{-19}. In July 2025, NIST's upgraded quantum logic clock set a new world record with a systematic of 5.5 \times 10^{-19}, accurate to 19 decimal places and 41% more precise than prior benchmarks, while exhibiting 2.6 times greater stability than other clocks. This enables applications in fundamental physics, such as testing through quantum time dilation effects and monitoring variations in the fine-structure constant. Relativistic , where height differences alter clock rates by approximately 10^{-16} per meter, also benefits from its precision.

History

Early Development

The direct readout of narrow optical transitions in single trapped ions poses significant challenges, particularly for clock transitions that are electric dipole forbidden, such as the 1S0→3P0^1S_0 \to ^3P_0 transition in 27^{27}Al+^+, which exhibit extremely low spontaneous emission rates and prevent efficient fluorescence-based state detection without disturbing the quantum state. This limitation motivated the development of quantum logic techniques to enable indirect, high-fidelity readout of the internal states of such "spectroscopy" ions by coupling them to a co-trapped "logic" ion with accessible optical transitions. The use of quantum logic gates between co-trapped ions to map the internal state of the ion onto the logic ion for detection via was proposed by David J. Wineland and colleagues at NIST in 2001 and experimentally demonstrated in a seminal publication. This approach leverages established trapping and laser manipulation techniques to perform entangling operations, allowing non-destructive measurement of otherwise inaccessible states. Early experiments conducted at NIST in demonstrated quantum logic operations between 9^9Be+^+ and 27^{27}Al+^+ ions, achieving state detection fidelities exceeding 96% through a controlled-NOT gate that transfers the aluminum ion's state to the beryllium ion for readout. Building on this, follow-up work in 2006–2007 resolved the narrow clock transition in 27^{27}Al+^+ using the same mixed-species setup, with the first use of 9^9Be+^+ as the logic ion to control and indirectly detect the 27^{27}Al+^+ clock ion states via on the beryllium ion. These prototypes marked the foundational step toward practical clocks, confirming the viability of the method for precision .

Key Milestones

In March 2008, researchers at the National Institute of Standards and Technology (NIST) demonstrated the first experimental quantum logic clock using a single 27^{27}Al+^+ ion as the clock qubit sympathetically cooled and read out via a co-trapped 9^9Be+^+ logic ion, achieving a fractional frequency uncertainty of approximately 5.2×10−175.2 \times 10^{-17} in comparison to the mercury-ion standard, which rivals the precision of the then-leading Hg+^+ optical clock. In 2010, NIST scientists published results on an improved Al+^+ quantum logic clock with a fractional frequency inaccuracy of 8.6×10−188.6 \times 10^{-18}, equivalent to a time deviation of 1 second every 3.68 billion years, led by key researchers including Chin-Wen Chou, David B. Hume, and others, with contributions to metrology from James J. McFerran in related optical clock comparisons. By July 2019, advancements in trap design and electric field compensation enabled an Al+^+ clock with a systematic reduced to 9.4×10−199.4 \times 10^{-19}, corresponding to a deviation of 1 second every 33.7 billion years, as reported by Samuel M. Brewer and collaborators at NIST. From 2020 to 2025, quantum logic clocks reached accuracy levels at 10−1910^{-19}, with measurements stable to the 19th decimal place; notably, in July 2025, NIST achieved a systematic of 5.5×10−195.5 \times 10^{-19} through enhancements to the optical trap, including reduced excess micromotion via modified wafer electrodes and improved systems for longer operation.

Operating Principle

Ion Trapping and Laser Cooling

Ion trapping in quantum logic clocks relies on linear radiofrequency (RF) electromagnetic traps, commonly known as Paul traps, to confine single or small numbers of ions in a high-vacuum environment. These traps generate a time-varying quadrupole electric field that dynamically stabilizes the ions against centrifugal forces, enabling long confinement times essential for high-precision measurements. The effective potential in a linear Paul trap approximates a for the ions' radial motion, described by the U(r)=qV024mΩ2r02(x2+y2),U(r) = \frac{q V_0^2}{4 m \Omega^2 r_0^2} (x^2 + y^2), where qq is the ion charge, V0V_0 is the RF , mm is the ion mass, Ω\Omega is the RF , and r0r_0 is a characteristic trap dimension related to the geometry. This potential confines ions along the radial directions (x and y), while static DC voltages provide axial confinement along z. To prepare the ions for , reduces their to near the motional . [Doppler cooling](/page/Doppler cooling) is achieved by illuminating the ions with a red-detuned resonant with an electronic transition, here using 313 nm lasers on 9^9Be+^+ ions to scatter photons and impart opposite to the ion's , reaching temperatures on the order of millikelvin. This exploits the Doppler shift to preferentially cool ions moving toward the . Following , resolved-sideband cooling further lowers the temperature to the microkelvin regime by addressing the motional sidebands of the electronic transition, sequentially removing phonons until the ions approach the vibrational of the trap. This technique uses pulses tuned to the first red , coupling internal electronic states to specific motional quanta for efficient . In quantum clocks, which typically involve a pair of dissimilar s—a clock ion insensitive to direct laser manipulation and a logic ion—sympathetic cooling is employed to indirectly cool the clock ion. The logic ion, such as 9^9Be+^+, is laser-cooled as described, and through their shared Coulomb-mediated motional modes in the trap, the cooling transfers to the clock ion, such as Al+^+, achieving near-ground-state temperatures for both without directly addressing the clock transition.

Quantum Logic Spectroscopy

The clock transition in quantum logic clocks is the narrow electric quadrupole (E2) transition between the ¹S₀ ground state and the ³P₀ metastable excited state in the ²⁷Al⁺ ion, occurring at a wavelength of 267 nm and a frequency of approximately 1.12 PHz. This transition has a natural linewidth of about 8 mHz due to the long lifetime of the ³P₀ state (lifetime ≈ 20 s), enabling high-frequency resolution. Both states have total angular momentum J=0, rendering the transition first-order insensitive to magnetic field fluctuations, which minimizes Zeeman shifts during interrogation. Quantum spectroscopy addresses the challenge of directly detecting the clock states in ²⁷Al⁺, which lack suitable cycling transitions for fluorescence readout, by co-trapping the clock ion with a logic , typically ²⁵Mg⁺ or ⁹Be⁺, that possesses detectable optical transitions. The technique employs two-qubit entangling gates, such as the Mølmer-Sørensen (MS) gate, to couple the internal electronic states of the clock to the motional modes shared with the logic , creating an entangled state that maps the clock 's phase information onto the logic . This entanglement enables quantum-non-demolition (QND) readout of the clock state via state-dependent phase shifts, followed by projective measurement of the logic through resonant excitation (e.g., at 280 nm for Mg⁺), achieving detection fidelities exceeding 99% after multiple repetitions without disturbing the clock . The MS gate, driven by bichromatic fields near the carrier and sideband transitions, imparts a proportional to the clock state, preserving coherence for repeated interrogations. In the Rabi interrogation scheme, the clock transition is probed using π-pulses from a laser tuned to 267 nm, which coherently flip the ²⁷Al⁺ between ¹S₀ and ³P₀ states over interrogation times up to 150 ms, achieving Rabi frequencies of several Hz for high contrast (>70%). Following each π-pulse, an MS gate applies a state-dependent phase shift to the logic ion, encoding the accumulated phase from the clock . The phase accumulation during interrogation is given by ϕ=2πνt,\phi = 2\pi \nu t, where ν\nu is the transition and tt is the interrogation time; the fractional frequency uncertainty scales as δν/ν≈1/(Nt)\delta \nu / \nu \approx 1/(\sqrt{N} t)
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