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arXiv:2001.00669 · Physical Review A

Delayed choice of paths in the quantum paradox of separating different properties of a photon

Debmalya Das, Ujjwal Sen

Published Jan 29, 2021• 9 citations
arXivHTMLPDF

Abstract

The so-called quantum Cheshire Cat is a scenario where a photon, identified with a cat, and a component of its polarization, identified with the grin of that cat, are separated. We observe that the same techniques can be used to separate two orthogonal components of polarization of a photon, on an average. We identify these polarization components of the photon as the grin and snarl of the cat for ease of comprehension. A gedanken experiment is presented in which we simultaneously tune the input polarizations of the photon in the two arms of a Mach-Zehnder interferometer. It is noted that for two particular choices of photon polarization, the presence of the two components gets reversed in the two arms. This reversal of the grin and the snarl occurs before the polarization components even interact with the tuners, i.e., before the choice of which arm each should be in is made.

DOI
10.1103/physreva.103.012228

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The so-called quantum Cheshire Cat is a scenario where a photon, identified with a cat, and a component of its polarization, identified with the grin of that cat, are separated. We observe that the same techniques can be used to separate two orthogonal components of polarization of a photon, on an average. We identify these polarization components of the photon as the grin and snarl of the cat for ease of comprehension. A gedanken experiment is presented in which we simultaneously tune the input polarizations of the photon in the two arms of a Mach-Zehnder interferometer. It is noted that for two particular choices of photon polarization, the presence of the two components gets reversed in the two arms. This reversal of the grin and the snarl occurs before the polarization components even interact with the tuners, i.e., before the choice of which arm each should be in is made.
The so-called quantum Cheshire cat is a phenomenon in which an object, identified with a ``cat'', is dissociated from a property of the object, identified with the ``grin'' of the cat. We propose a thought experiment, similar to this phenomenon, with an interferometric setup, where a property (a component of polarization) of an object (photon) can be separated from the object itself and can simultaneously be amplified when it is already decoupled from its object. We further show that this setup can be used to dissociate two complementary properties, e.g., two orthogonal components of polarization of a photon and identified with the grin and the snarl of a cat, from each other and one of them can be amplified while being detached from the other. Moreover, we extend the work to a noisy scenario, effected by a spin-orbit-coupling--like additional interaction term in the Hamiltonian for the measurement process, with the object in this scenario being identified with a so-called confused Cheshire cat. We devise a gedanken experiment in which such a ``confusion'' can be successfully dissociated from the system, and we find that the dissociation helps in the amplification of signals.
We report an experimental realization of the quantum paradox of the separation of a single photon from one of its properties (the so-called "quantum Cheshire cat"). We use a modified Sagnac interferometer with displaced paths to produce appropriately pre- and postselected states of heralded single photons. Weak measurements of photon presence and circular polarization are performed in each arm of the interferometer by introducing weak absorbers and small polarization rotations and analyzing changes in the postselected signal. The absorber is found to have an appreciable effect only in one arm of the interferometer, while the polarization rotation significantly affects the signal only when performed in the other arm. We carry out both sequential and simultaneous weak measurements and find good agreement between measured and predicted weak values. In the language of Aharonov et al. and in the sense of the ensemble averages described by weak values, the experiment establishes the separation of a particle from one its properties during the passage through the interferometer.
Even the subtle and apparently strange quantum effects can sometimes survive otherwise lethal influence of an omnipresent decoherence. We show that an archetypal quantum Cheshire Cat, a paradox of a separation between a position of a quantum particle, a photon, and its internal property, the polarization, in a two-path Mach–Zehnder setting, is robust to decoherence caused by a bosonic infinite bath locally coupled to the polarization of a photon. Decoherence affects either the cat or its grin depending on which of the two paths is noisy. For a pure decoherence, in an absence of photon–environment energy exchange, we provide exact results for weak values of the photon position and polarization indicating that the information loss affects the quantum Cheshire Cat only qualitatively and the paradox survives. We show that it is also the case beyond the pure decoherence for a small rate of dissipation.
The phenomenon of the quantum Cheshire cat (QCC) and its interpretation by Aharanov et al. [ New J. Phys. 15 , 113015 ( 2013 ) NJOPFM 1367-2630 10.1088/1367-2630/15/11/113015 ], with the conjecture that any quantum entity can be disembodied from its physical attributes, has resulted in a heated debate leading to interpretational controversy as well as practical consequences. Here, we propose an experimentally testable and physically more realistic and logically plausible interpretation. We utilize a specifically engineered Mach–Zehnder-type interferometeric setup that is quite similar to the original QCC setup but with the slight difference that now a single-photon, bipartite entangled state traverses the interferometer such that each path is designated to a photon with different tags. With this specific setup, we demonstrate that the photon’s polarization is never physically separated from the photon itself. Rather, it becomes dormant and hence inaccessible along the designated interferometric path. We also generalize the schematics and show that any precisely oriented photon’s polarization that stands inaccessible or dormant re-emerges along the same spatially separated and isolated arm as we tune the polarization vector away from the selected angle. Thus our proposal persuasively proves that polarization is never stripped off the photon itself and instead becomes inaccessible along the interferometeric arm for a certain particularly selected orientation. The schematics further reveal that this inaccessibility of the photon’s polarization is not permanent, fixed, and universal, but rather it is entirely constrained to a specific orientation in the Hilbert space, governed by the particular pre- and post-selected state under two-state vector formalism.
We report an experiment with neutrons in a silicon perfect crystal interferometer, that realizes a quantum Cheshire Cat in a delayed choice setting. In our setup the quantum Cheshire Cat is established by spatially separating the particle and its property (i.e. the neutron and its spin) into the two different paths of the interferometer. The condition for a delayed choice setting is achieved by postponing the choice of path assignment for the quantum Cheshire Cat, i.e. which path is taken by the particle and which by its property, until the point in time when the neutron wave function has already split and entered the interferometer. The results of the experiment suggest not only the fact that the neutrons and its spin are separated and take different paths in the interferometer, but also quantum-mechanical causality is implied, insomuch that the behavior of a quantum system is affected by the choice of the selection at a later point in time.
In a recent work, Aharonov et al suggested that a photon could be separated from its polarization in an experiment involving pre- and post-selection (Aharonov et al 2013 New J. Phys. 15 113015 ). They named the effect 'quantum Cheshire Cat', in a reference to the cat that is separated from its grin in the novel Alice ' s Adventures in Wonderland . Following these ideas, Denkmayr et al performed a neutron interferometric experiment and interpreted the results suggesting that neutrons were separated from their spin (Denkmayr et al 2014 Nat. Commun. 5 4492 ). Here we show that these results can be interpreted as simple quantum interference, with no separation between the quantum particle and its internal degree of freedom. We thus hope to clarify the phenomenon with this work, by removing these apparent paradoxes.