What Would Happen if a Quantum Cheshire Cat Were to Visit the Leisure Hive?
Happy Holidays, Everyone! Today’s article, just in time for your New Year’s Eve party, is on something extremely cool. It has to do with a paradox that is completely unintuitive and that is only revealed by weak measurements. A particle and its properties can be in different locations!
In the classic Doctor Who episode Leisure Hive, a so-called “science of tachyonics” serves as the basis for entertaining guests at a resort. A person enters a booth and their head and limbs are seemingly separated from their body, yet remain animated and are then harmlessly reattached.
That is, of course, full-fledged science fiction. However, a quantum particle such as a photon, an electron, or an atom, apparently can have its properties located in a position separate from the particle itself.
Recent theoretical and experimental work has invigorated the search for “quantum Cheshire cats”. Before I continue, however, I want to stress that the reference to cats is strictly metaphorical. Just as with the case of Schrödinger’s cat (Decoherence and the Quantum to Classical Transition; or Why We Don’t See Cats that are Both Dead and Alive), decoherence prevents macroscopic objects from displaying these quantum mechanical properties.
In Search of a Quantum Cheshire Cat
The authors of Quantum Cheshire Cats (also available here) define a “quantum Cheshire cat” as a photon that is in one location while its circular polarization is in another. The metaphor comes from the Cheshire cat in the story of Alice in Wonderland, whose smile persists independent of the cat:
The “cat” is the photon and its “smile” is the photon’s circular polarization state. The photon is in one of two possible locations, the left or right side of a modified Mach-Zehnder interferometer. Using weak measurements, including cleverly chosen pre-selected and post-selected states, leads to a sample of events where the photon went through the left arm with certainty. However, a polarization detector in the right arm can still see a signal!
“We seem to see what Alice saw—a grin without a cat! We know with certainty that the photon went through the left arm, yet we find angular momentum in the right arm.”
The paradox is removed if conventional, strong measurements of position and polarization are performed. The inevitable and apparent wave function collapse occurs and the photon’s position and angular momentum are found to be co-located. This is analogous to directly measuring which slit the particle goes through in a double slit experiment, which prevents an interference pattern from forming. Strong measurements are analogous to turning the light on and letting the cockroaches quickly scurry into hiding. Everything looks normal. But, weak measurements are like peering at what is going on in the dark, without scaring the roaches away.
Using weak measurements (The Strength of Weak Measurements in Quantum Physics), the disturbance on the state of the system can be reduced by accepting less precision. Then, the measurement is repeated many, many times to achieve the desired accuracy. This reveals that the circular polarization was in fact in the right leg of the interferometer while the photon was in the left, for certain pre- and post-selected events.
What Do We Do With a Quantum Cheshire Cat Once We Catch One?
Conventional wisdom is that when you look at, or measure, a quantum system, the wave function collapses into something that makes sense from a classical level. That is to say, strange or apparently contradictory paradoxes disappear. However, that assumes strong measurements. Until weak measurements were explored theoretically and experimentally in recent years, the distinction between strong and weak measurements was not appreciated.
Contemplating the implications of quantum Cheshire cats opens up several mind-boggling possibilities and opportunities. Separating physical properties, such as mass, energy, charge, magnetic moment, etc., from what we conventionally understand to be a particle could lead to new and more precise measurements, new technologies, new materials… Additionally, it has profound implications for our conceptual understanding of quantum physics and what a quantum system is up to between measurements or between interactions. Scientists will be exploring this amazing field for many years to come.
In Quantum Cheshire Cats, the authors discuss a couple modifications (beyond the reach of existing technology, but should be possible eventually), where the signature of a quantum Cheshire cat should be unambiguous; ensembles of electrons, for example.
Proposed modifications to the setup discussed above, i.e. using entangled pre- and post-selected states to allow the linear as well as the circular polarization states to be separated from the photon, are discussed in The Complete Quantum Cheshire Cat.
Possible hints of the metaphorical quantum Cheshire cat have been seen: Observation of a quantum Cheshire Cat in a matter wave interferometer experiment “…using a neutron interferometer… The experimental results suggest that the system behaves as if the neutrons went through one beam path, while their spin travelled along the other.”
The quantum Cheshire cat is an example of an interaction free measurement. Another example is the Elitzur–Vaidman bomb tester, also known as a quantum mechanical bomb tester. Also see Using quantum mechanics to detect bombs.
Masters student Catherine Holloway lectures on the science behind a quantum bomb detector at the Quantum Cryptography School for Young Students, held at the Institute for Quantum Computing, University of Waterloo: