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arXiv:1709.09851 · Physical Review A

Dual to the anomalous weak-value effect of photon-polarization separation

James Q. Quach

Published Nov 22, 2019• 4 citations
arXivHTMLPDF

Abstract

The quantum Cheshire cat (QCC) thought experiment proposes that a quantum object's property (e.g., polarization, spin, etc.) can be separated from its physical body. This conclusion arose from an argument that interprets a zero weak value (WV) of polarization as no polarization. We show that this argument is incomplete in the sense that a zero WV reading could equally be interpreted as linear polarization. Nevertheless, through a generalization of the QCC, we complete their argument by excluding the possibility of linear polarization as a consistent interpretation. We go further and introduce the dual of the generalized QCC. The dual QCC exhibits an intriguing effect, where a horizontally polarized interferometer with just one arm can give rise to interference which is vertically polarized. The interference appears to arise as the result of the phase difference between the physical arm and a phantom arm. This peculiar effect arises from the interplay between the preselected and postselected states, which characterize WVs. The QCC has not yet been unambiguously experimentally demonstrated. The QCC dual offers an alternative pathway to experimental realization.

DOI
10.1103/physreva.100.052117

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The quantum Cheshire cat (QCC) thought experiment proposes that a quantum object's property (e.g., polarization, spin, etc.) can be separated from its physical body. This conclusion arose from an argument that interprets a zero weak value (WV) of polarization as no polarization. We show that this argument is incomplete in the sense that a zero WV reading could equally be interpreted as linear polarization. Nevertheless, through a generalization of the QCC, we complete their argument by excluding the possibility of linear polarization as a consistent interpretation. We go further and introduce the dual of the generalized QCC. The dual QCC exhibits an intriguing effect, where a horizontally polarized interferometer with just one arm can give rise to interference which is vertically polarized. The interference appears to arise as the result of the phase difference between the physical arm and a phantom arm. This peculiar effect arises from the interplay between the preselected and postselected states, which characterize WVs. The QCC has not yet been unambiguously experimentally demonstrated. The QCC dual offers an alternative pathway to experimental realization.
The quantum Cheshire cat (QCC) thought experiment proposes that a quantum object's property (\textit{e.g} polarisation, spin, etc.) can be separated from its physical body or \textit{disembodied}. This conclusion arose from an argument that interprets a zero weak value (WV) of polarisation as no polarisation. We show that this argument is incomplete in the sense that a zero WV reading could equally be interpreted as linear polarisation. Nevertheless, through a generalisation of the QCC, we complete their argument by excluding the possibility of linear polarisation as a consistent interpretation. We go further, and introduce the dual of the generalised QCC. The dual QCC exhibits an intriguing effect, where a horizontally-polarised interferometer with just one arm, can give rise to interference which is vertically-polarised. The interference appears to arise as the result of the phase difference between the physical arm and a \textit{phantom} arm. This peculiar effect arises from the interplay between the pre-selected and post-selected states, which characterises WVs. The QCC has not yet been unambiguously experimentally demonstrated. The QCC dual offers an alternative pathway to experimental realisation.
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.
Abstract One of the common conceptions of nature, typically derived from the experiences with classical systems, is that attributes of the matter coexist with the substance. In the quantum regime, however, the quantum particle itself and its physical property may be in spatial separation, known as the quantum Cheshire cat effect. While there have been several reports to date on the observation of the quantum Cheshire cat effect, all such experiments are based on first-order interferometry and destructive projection measurement, thus allowing simple interpretation due to measurement-induced disturbance and also subject to trivial interpretation based on classical waves. In this work, we report an experimental observation of the quantum Cheshire cat effect with noninvasive weak quantum measurement as originally proposed. The use of the weak-measurement probe has allowed us to identify the location of the single photon and that of the disembodied polarization state in a quantum interferometer. The weak-measurement probe based on two-photon interference makes our observation unable to be explained by classical physics. We furthermore elucidate the quantum Cheshire cat effect as quantum interference of the transition amplitudes for the photon and the polarization state which are directly obtained from the measurement outcomes or the weak values. Our work not only reveals the true quantum nature of Cheshire cat effect but also sheds light on a comprehensive understanding for the counter-intuitive quantum phenomena.
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.
Abstract The quantum superposition principle implies that a particle entering an interferometer evolves by simultaneously taking both arms. If a non-destructive, minimally-disturbing interaction coupling a particle property to a pointer is implemented on each arm while maintaining the path superposition, quantum theory predicts that, for a fixed state measured at the output port, certain particle properties can be associated with only one or the other path. This phenomenon is known as the quantum Cheshire cat effect. Here we report the realization of this prediction through joint observation of the spatial and polarization degrees of freedom of a single photon in the two respective arms of an interferometer. Significant pointer shifts ( ~ 50 microns), corresponding to measured weak values, are observed in each arm. This observation, involving coupling distinct properties of a quantum system in spatially separated regions, opens new possibilities for quantum information protocols and for tests of quantumness for mesoscopic systems.
Weak measurements, which enable access to weak values with minimal disturbance to the quantum system, have significantly advanced the study of counterintuitive quantum phenomena, including the quantum Cheshire Cat (QCC). Building on this methodology, we report a single-path realization of the QCC effect by mapping the two interferometric arms onto orthogonal polarization states of a single photon within the orbital angular momentum (OAM) degree of freedom. This approach demonstrates that the pre- and post-selected quantum states yield weak measurement statistics consistent with the polarization and OAM observables behaving as although they are localized differently, effectively decoupling the OAM property from its polarization-encoded carrier. Using a polarization-addressed spatial light modulator, we implement two programmable weak couplings on the same hardware: a weak absorptive perturbation (probing particle-like localization) that yields the particle-detectability weak value from the slope of the normalized post-selection probability and a small OAM rotation (probing wave-like OAM) that yields the OAM-related weak value from the slope of the interference visibility—both operating within the linear weak-coupling regime. By comparing the statistics from these two measurements, we experimentally confirm the effective decoupling of the photon’s particle localization and its OAM. This pointer-free, single-platform architecture preserves full weak-value readout capability while substantially reducing alignment and stabilization complexity, offering a compact and resource-efficient route to QCC-based property separation well suited for high-dimensional quantum applications.