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International Journal of Modern Physics D

MACROSCOPIC QUANTUM MECHANICS AND SINGLE-PHOTON MICHELSON INTERFEROMETRY

Yang Ran, Xuefei Gong, Shouyong Pei, Ziren Luo, Yun-Kau Lau

Published Sep 1, 2011• 0 citations
Publisher

Abstract

Single-photon Michelson interferometry as a probe to macroscopic quantum mechanics is considered. With dual output readout at both the bright and dark ports, it is shown that a nonlocal, linear superposition of two Schrödinger cats may be generated by the opto-mechanical coupling of a single photon with a movable macroscopic quantum mirror in one arm of the interferometer. With a balanced homodyne readout scheme, a CHSH inequality may be formulated and the violation of which serves to verify the nonlocality of the two spacelike separated Schrödinger cats. The relevance of this result in our understanding of possible wave function collapse dynamics is briefly touched upon. Macroscopic entangled state of two mirrors generated by opto-mechanical coupling and the associated CHSH inequality are also discussed.

DOI
10.1142/s0218271811020238

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Single-photon Michelson interferometry as a probe to macroscopic quantum mechanics is considered. With dual output readout at both the bright and dark ports, it is shown that a nonlocal, linear superposition of two Schrödinger cats may be generated by the opto-mechanical coupling of a single photon with a movable macroscopic quantum mirror in one arm of the interferometer. With a balanced homodyne readout scheme, a CHSH inequality may be formulated and the violation of which serves to verify the nonlocality of the two spacelike separated Schrödinger cats. The relevance of this result in our understanding of possible wave function collapse dynamics is briefly touched upon. Macroscopic entangled state of two mirrors generated by opto-mechanical coupling and the associated CHSH inequality are also discussed.
We suggest an all-optical scheme to generate entangled superposition of a single photon with macroscopic entangled states for testing macroscopic realism. The scheme consists of source of single photons, a Mach-Zehnder interferometer in routes of which a system of coupled-down converters with type-I phase matching is inserted, and a beam splitter for the other auxiliary modes of the scheme. We use quantization of the pumping modes, depletion of the coherent states passing through the system, and interference effect in the pumping modes in the process of erasing which-path information of the single-photon on exit from the Mach-Zehnder interferometer. We show the macroscopic fields of the output superposition are distinguishable states. This scheme generates macroscopic entangled state that violates Bell's inequality. Moreover, the detailed analysis concerning change of amplitudes of entangled superposition by means of repeating this process many times is accomplished. We show our scheme works without photon number resolving detection and it is robust to detector inefficiency.
Quantum entanglement and quantum superposition are fundamental properties of quantum mechanics, which underline quantum information and quantum computation. Preparing quantum states in the macroscopic level is both conceptually interesting for extending quantum physics to a broader sense and fundamentally important for testing the validity of quantum mechanics. In this dissertation, schemes of preparing macroscopic entanglement and macroscopic superposition states in cavity optomechanics are studied using the unitary evolution method in the nonlinear regime or Lyapunov equation in the linearized regime. Quantum entanglement and quantum superposition states can be realized using experimentally feasible parameters with the proposals in this dissertation.\nFirstly, a scheme of entangling two movable end mirrors in a Fabry-Perot cavity that are coupled to a common single photon superposition state is studied. It is shown that strong entanglement can be obtained either in the single-photon strong coupling regime deterministically or in the single-photon weak coupling regime conditionally.\nSecondly, a scheme of entangling two movable end mirrors, that are coupled to two-mode entangled fields generated from a correlated-emission laser is investigated. By tuning the input driving laser frequencies at the Stokes sidebands of the cavity, the radiation-pressure coupling can be linearized as an effective beam-splitter-like interaction. Hence entanglement can be transferred from the two-mode fields to the two mechanical mirrors. Macroscopic entanglement between macroscopic mirrors persists at temperature ~ 1K.\nThirdly, a scheme of creating macroscopic quantum superpositions of a mechanical mirror via periodically flipping a photonic qubit is proposed. Quantum superposition states of a mechanical mirror can be obtained via the nonlinear radiation coupling with a single-photon superposition state. However, the difference between two superposed mechanical states is very small due to the weak single-photon coupling rate available in experiment. By periodically flipping the photonic qubit state, the difference can be magnified. It is shown in detail that this scheme is experimentally feasible under current technology.
We show that the generation of entanglement of two heavily macroscopic mirrors is feasible with state of the art techniques of high-precision laser interferometry. The basis of such a demonstration would be a Michelson interferometer with suspended mirrors and simultaneous homodyne detections at both interferometer output ports. We present the connection between the generation of entanglement and the standard quantum limit (SQL) for a free mass. The SQL is a well-known reference limit in operating interferometers for gravitational-wave detection and provides a measure of when macroscopic entanglement can be observed in the presence of realistic decoherence processes.
We study the quantum dynamics of a Michelson interferometer with Fabry-Perot cavity arms and one movable end mirror, and driven by a single photon---an optomechanical device previously studied by Marshall et al. as a device that searches for gravity decoherence. We obtain an exact analytical solution for the system's quantum mechanical equations of motion, including details about the exchange of the single photon between the cavity mode and the external continuum. The resulting time evolution of the interferometer's fringe visibility displays interesting new features when the incoming photon's frequency uncertainty is narrower or comparable to the cavity's line width---only in the limiting case of much broader-band photon does the result return to that of Marshall et al., but in this case the photon is not very likely to enter the cavity and interact with the mirror, making the experiment less efficient and more susceptible to imperfections. In addition, we show that in the strong-coupling regime, by engineering the incoming photon's wave function, it is possible to prepare the movable mirror into an arbitrary quantum state of a multidimensional Hilbert space.
The fully entangled Schrodinger cat state obtained immediately upon measurement of a superposed two state quantum system by a detector is often said to paradoxically predict macroscopically different outcomes simultaneously. However, nonlocal interferometry experiments and their accompanying quantum theoretical analyses, testing momentum entangled photon pairs over the full range of phases, demonstrate that the cat state does not fit this description. This state instead represents two nonlocally coherent correlations between its subsystems. Even if the detector is a cat, this state is not paradoxical. Furthermore, standard quantum theory correctly predicts the experimentally observed nonparadoxical outcomes. Thus both quantum theory and quantum experiments show there is no Schrodinger cat paradox associated with measurement. This resolves the problem of definite outcomes and, with it, the measurement problem. Upon entanglement with a detector, superpositions collapse nonlocally and unitarily to one definite macroscopic outcome. No special collapse postulate is needed.
In recent years two fundamental aspects of quantum mechanics have attracted a great deal of interest, namely the investigation on the irreducible nonlocal properties of Nature implied by quantum entanglement and the physical realization of the 'Schroedinger Cat'. In the present work a macro - state consisting of about 3.5 x 10^4 photons in a quantum superposition and entangled with a far apart single - photon state is generated. Then, the non-separability of the overall micro-macro system is demonstrated and the corresponding Bell's inequalities are found to be violated. Precisely, an entangled photon pair is created by a nonlinear optical process, then one photon of the pair is injected into an optical parametric amplifier operating for any input polarization state, i.e. into a phase-covariant cloning machine. Such transformation establishes a connection between the single photon and the multi particle fields. We then demonstrate the non-separability of the bipartite system by adopting a local filtering technique within a positive operator valued measurement.