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arXiv:2109.05338 · Physical Review A

Cavity mode dephasing via the optomechanical interaction with an acoustic environment

Qidong Xu, M. P. Blencowe

Published Dec 13, 2021• 7 citations
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Abstract

We consider an optomechanical system comprising a single cavity mode and a dense spectrum of acoustic modes and solve for the quantum dynamics of initial cavity mode Fock (i.e., photon number) superposition states and thermal acoustic states. The optomechanical interaction results in dephasing without damping and bears some analogy to gravitational decoherence. For a cavity mode locally coupled to a one-dimensional elastic string-like environment or two-dimensional elastic membrane-like environment, we find that the dephasing dynamics depends respectively on the string length and membrane area---a consequence of an infrared divergence in the limit of an infinite-sized string or membrane. On the other hand, for a cavity mode locally coupled to a three-dimensional bulk elastic solid, the dephasing dynamics is independent of the solid volume (i.e., is infrared finite), but dependent on the local geometry of the coupled cavity---a consequence of an ultraviolet divergence in the limit of a ``pointlike'' coupled cavity. We consider as possible respective realizations for the cavity-coupled one- and two-dimensional acoustic environments an $LC$ oscillator capacitively coupled to a partially metalized strip and a cavity light mode interacting via light pressure with a membrane.

DOI
10.1103/physreva.104.063509

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We consider an optomechanical system comprising a single cavity mode and a dense spectrum of acoustic modes and solve for the quantum dynamics of initial cavity mode Fock (i.e., photon number) superposition states and thermal acoustic states. The optomechanical interaction results in dephasing without damping and bears some analogy to gravitational decoherence. For a cavity mode locally coupled to a one-dimensional elastic string-like environment or two-dimensional elastic membrane-like environment, we find that the dephasing dynamics depends respectively on the string length and membrane area---a consequence of an infrared divergence in the limit of an infinite-sized string or membrane. On the other hand, for a cavity mode locally coupled to a three-dimensional bulk elastic solid, the dephasing dynamics is independent of the solid volume (i.e., is infrared finite), but dependent on the local geometry of the coupled cavity---a consequence of an ultraviolet divergence in the limit of a ``pointlike'' coupled cavity. We consider as possible respective realizations for the cavity-coupled one- and two-dimensional acoustic environments an LCLCLC oscillator capacitively coupled to a partially metalized strip and a cavity light mode interacting via light pressure with a membrane.
Decoherence in macroscopic quantum systems arises mainly from interactions with the environmental bath, offering key insights into the quantum-classical boundary. In this paper, we study the acoustic-environment-induced effects in a circuit quantum electrodynamics system, where an LC oscillator is optomechanically coupled to a long mechanical strip and capacitively coupled to a superconducting qubit. The mechanical strip functions as an acoustic environment, comprising a continuum of bath modes. The qubit population, serving as a probe of acoustic-environment-induced dephasing (AEID), exhibits collapse and revival dynamics in its Rabi oscillations. The AEID effect is extracted using a Ramsey-like interference scheme, manifesting as a dynamical decay in amplitude and a modification in the oscillation frequency. Our scheme opens avenues for studying the mechanisms of decoherence introduced by acoustic environments and to explore the optomechanically induced nonlinearity by collective acoustic bath modes.
In this dissertation, I theoretically investigate the open system dynamics of cavity optomechanical systems in the quantum limit, where a mechanical resonator couples to a cavity mode via radiation pressure force. Recent developments in nano-fabrication and cooling techniques make it possible to optically control and manipulate the motion of micro- and nano-mechanical resonator. Several experiments have demonstrated the possibility of preparing macroscopic mechanical resonators into their quantum ground state, which makes optomechanical systems an ideal candidate for studying the quantum behavior of macroscopic objects. One important direction in quantum optomechanics is the study of the decoherence of optomechanical system due to the interaction with their external environments. This dissertation explores the decoherence effects by considering the influence of the radiation pressure coupling on the interaction between optomechanical system and its environments. Because the effects of the nonlinear interaction vary with the optomechanical coupling strength, three different interaction regimes are fully studied here: the weak coupling, the intermediate coupling and the strong coupling.
In this work, we theoretically study a finite and undamped two-mode optomechanical model consisting of a high quality optical cavity containing a thin, elastic, and dielectric membrane. The main objective is to investigate the precursors of quantum phase transition in such a model by studying the behavior of some observables in the ground state. By controlling the coupling between membrane and modes, we find that the two lowest energy eigenstates become degenerate, as is indicated by the behavior of the mean value of some operators and by other quantifiers as a function of the coupling. Such degenerate states are characterized by a coherent superposition of eigenstates describing one of the two modes preferentially populated and the membrane dislocated from its equilibrium position due the radiation pressure (Schrödinger's cat states). The delocalization of the compound system photons+membrane results in an increase in fluctuations as measured by Robertson-Schrödinger uncertainty relations.
In the field of optomechanics, one typically studies the interaction of a single mechanical resonator and a single optical cavity mode. In this thesis, we investigate collective quantum effects in optomechanical systems with two or more optical and mechanical modes. First, we study the generation and destruction of entanglement between two mechanical resonators effected by optical cavity fields. We also describe how the optomechanical interaction can be employed to mediate strong coherent coupling and entanglement between a micromechanical membrane and a single atom. Secondly, we show that a configuration with two optical and a single mechanical mode can lead to enhanced nonlinear interactions, which can be exploited for quantum non-demolition measurements of the phonon and photon numbers. Finally, we explore the quantum many-body dynamics of optomechanical arrays. In particular, we research into the transition from a disordered state due to quantum noise to a state with phasecoherent mechanical oscillations. As an intermediate step towards this study, we also investigate the nonlinear classical dynamics of single- and multi-mode optomechanical setups and compare theoretical predictions to experimental data.
Abstract Recent advancements in strong single-photon optomechanical coupling also demand a deeper understanding of environmental interactions in this regime. In this regime the standard Lindblad master equation, which is derived in the eigenbasis of the bare optical and mechanical modes, misassigns the dephasing rate. We therefore use the dressed-state master equation, which is formulated in the eigenbasis of the strongly coupled photon–phonon Hamiltonian, the dressed states of the system. This work investigates the impact of squeezed vacuum and thermal reservoirs on the decoherence of cavity photon Fock states in the strong coupling regime. We demonstrate that decoherence can be effectively controlled by tuning reservoir parameters, with the control mediated through a cavity dephasing term that becomes significant at high temperatures. The findings presented provide critical insights into reservoir engineering for precise control of quantum decoherence, advancing the understanding of strongly coupled optomechanical systems in engineered environments.
Recent advancements in strong single-photon optomechanical coupling also demand a deeper understanding of environmental interactions in this regime.In this regime the standard Lindblad master equation, which is derived in the eigenbasis of the bare optical and mechanical modes, misassigns the dephasing rate. We therefore use the Dressed-State Master Equation (DSME), which is formulated in the eigenbasis of the strongly coupled photon-phonon Hamiltonian, the dressed states of the system. This work investigates the impact of squeezed vacuum and thermal reservoirs on the decoherence of cavity photon Fock states in the strong coupling regime. We demonstrate that decoherence can be effectively controlled by tuning reservoir parameters, with the control mediated through a cavity dephasing term that becomes significant at high temperatures. The findings presented provide critical insights into reservoir engineering for precise control of quantum decoherence, advancing the understanding of strongly coupled optomechanical systems in engineered environments.