Quantum Cheshire cat

In quantum mechanics, the quantum Cheshire cat is a quantum phenomenom that suggests that a particle's physical properties can take a different trajectory from that of the particle itself. The name makes reference to the Cheshire Cat from Lewis Carroll's Alice's Adventures in Wonderland, a feline character which could disappear leaving only its grin behind. The effect was originally proposed by Yakir Aharonov, Daniel Rohrlich, Sandu Popescu and Paul Skrzypczyk in 2012.

In classical physics, physical properties cannot be detached from the object associated to it. If a magnet follows a given trajectory in space and time, its magnetic moment follows it through the same trajectory. However, in quantum mechanics, particles can be in a quantum superposition of more than one trajectory previous to measurement. The quantum Cheshire experiments suggests that previous to a measurement, a particle may take two paths, but the property of the particle, like the spin of a massive particle or the polarization of a light beam, travels only through one of the paths, while the particle takes the opposite path. The conclusion is only obtained from an analysis of weak measurements, which consist in interpreting the particle history previous to measurement by studying quantum systems in the presence of small disturbances.

Experimental demonstration of the quantum Cheshire cat have already been claimed in different systems, including photons and neutrons. The effect has been suggested as a probe to study properties of massive particles by detaching it from its magnetic moment in order to shield them from electromagnetic disturbances. A dynamical quantum Cheshire cat has also been proposed as a counterfactual quantum communication protocol.

Neutrons are uncharged subatomic particles that have a magnetic moment, with two possible projections on any given axis.

A beam of neutrons, with all with their magnetic moments aligned to the right, enters a Mach–Zehnder interferometer coming from the left-to-right. The neutrons can exit the interferometer into a right port, where a detector of neutrons with right magnetic moment is located, or upwards into a dark port with no detector (see picture).

The neutrons enter the interferometer and reach a beam splitter. Each neutron that passes through, enters into a quantum superposition state of two different paths, namely A and B. This initial state is referred to as the preselected state. As the neutrons travel the different paths, their wave functions reunites at a second beam splitter, causing interference. If there is nothing in the path of the neutrons, every neutron exits to the interferometer moving to the right and activates the detector. No neutron escapes upwards into the dark port due to destructive interference.

One can add different components and filters in one of the paths. By adding a filter that flips the magnetic moment of the neutron in path B (lower branch), it leads to a new superposition state: neutron taking path A with a magnetic moment pointing right, plus the neutron taking path B with the magnetic moment flipped pointing to the left. This state is called a postselected state. As the states can no longer interfere coherently due to this modification, the neutrons can exit through the two ports, either to the right reaching the detector or exiting towards the dark port.

In this configuration, if the detector clicks, it is only because the neutrons had a magnetic moment oriented in to the right. By means of this postselection, it can be confidently stated that the neutron that reached the detector passed through path A, which is the only path to contains neutron magnetic moments oriented to the right. This effect can be easily demonstrated by putting a thin absorber of neutrons in the path. By placing the absorber in path B, the rate of neutrons that are detected remains constant. However, when the absorber is positioned in path A, the detection rate decreases, providing evidence that detected neutrons in the postselected state travel only through path A.