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Journal of the Optical Society of America B

Experimental simulation of a decohering Schrödinger’s cat state in wave optics

Keisuke Nishimura, Makoto Takeuchi, Takahiro Kuga

Published Jan 24, 2018• 2 citations
Publisher

Abstract

The study of decoherence properties improves our understanding of the fundamental principles of quantum mechanics and advances the study of quantum information processing. Herein, we report a wave-optical experiment that can simulate the decoherence process of a Schrodinger’s cat state (SCS) by photon loss. The method is based on an analogy between image rotation in wave optics and a beam splitter in quantum optics. Experimental results show that the SCS rapidly decays into a statistical mixture of two Gaussian states with approximately 10% photon loss. This behavior can be well described within the framework of quantum optics.

DOI
10.1364/josab.35.000337

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The study of decoherence properties improves our understanding of the fundamental principles of quantum mechanics and advances the study of quantum information processing. Herein, we report a wave-optical experiment that can simulate the decoherence process of a Schrodinger’s cat state (SCS) by photon loss. The method is based on an analogy between image rotation in wave optics and a beam splitter in quantum optics. Experimental results show that the SCS rapidly decays into a statistical mixture of two Gaussian states with approximately 10% photon loss. This behavior can be well described within the framework of quantum optics.
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In this work we suggest four simple, realistic experiments in which existence of the quantum entanglement between single photon and photon trajectory detector (Schrodinger cat effect) can be definitely testified. Mentioned experiments represent different variations of the well-known experiment of single photon interference at beam splitter. Here photon trajectory (micro) detector is represented by two simple quantum two-level systems, practically two atoms (first in excited and second in ground state) placed at only one, e.g. reflected photon trajectory. In final experiment, after first interaction between photon (in superposition state which is result of the previous, first interaction between photon and beam splitter) and detector, photon is redirected back by two total mirrors. It implies new, second interaction between photon and detector and later between photon and beam splitter. If after mentioned first interaction photon-detector entanglement exists, then after second mentioned interaction there is only one outcome at beam splitter. But if, after mentioned first interaction statistical mixture of reflected and transmitted photon exists, then after second mentioned interaction there are two outcomes at beam splitter. Results of suggested experiments can have very important role in never ending Galileian dialogue on the quantum mechanics foundation problem.
Abstract Cat states are systems in a superposition of macroscopically distinguishable states; this superposition can be of either classically or quantum distinct states, regardless of the number of particles or modes involved. Here, we constructed an experimental model that simulates an optical cat state by engineering the classical orbital angular momentum of light, referred to here as an analogous cat state (a-CS). In our scheme, the behaviors of the a-CS in position space show many similarities to the quantum version of the optical cat state in phase space, for example, movement, rotation, and interference. Experimentally, the a-CS, which has two spatially localized Gaussian intensity lobes, can be evolved from “kitten” to “cat” by engineering the acquired phase hologram. Additionally, we simulated the “decoherence” of the a-CS influenced by atmospheric turbulence. The a-CS provides a reliable tool for visualizing and studying the behaviors of quantum cat states in phase space.
The Schrodinger and Heisenberg pictures are equivalent formulations of quantum mechanics. Here we use the Schrodinger picture to calculate the decoherence that occurs when an optical Schrodinger cat state is passed through a beam splitter. We find that an exponentially large amount of decoherence can occur even when there is a negligible change in the quadrature operator x(t) in the Heisenberg picture. Similar results have been observed in the decoherence produced by an optical amplifier, and we suggest that the usual quadrature operators in the Heisenberg picture do not provide a complete description of the output of optical devices.