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arXiv:2501.14645 · Communications in Theoretical Physics

Dynamics and spectral response of linear-quadratic optomechanical interaction: effects of pure dephasing

Alejandro R. Urzúa

Published Apr 22, 2025• 1 citation
arXivHTMLPDF

Abstract

Abstract In this paper, the decoherence dynamics and spectral response of an optomechanical system, with linear and quadratic couplings, is addressed. The decoherence considered arises from pure dephasing, described by the Milburn stochastic evolution of the Schrödinger equation. In the first part of this paper, it is shown how the decoherence rate influences the evolution of the number of phonons, and the quadrature of the mechanical resonator. In the second part of the paper, an attempt to look at the spectral response of the mechanical part of the system is given using non-stationary spectroscopy. The response of the resonator in its equilibrium position is emphasized when the single-photon regime is considered. Coherent states in the cavity field and the mechanical resonator are also represented. Results and discussion comparing the inclusions of the linear, quadratic, and linear-quadratic couplings are given, regarding the influence of the dephasing in the decoherence mechanism.

DOI
10.1088/1572-9494/adcf09

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Abstract In this paper, the decoherence dynamics and spectral response of an optomechanical system, with linear and quadratic couplings, is addressed. The decoherence considered arises from pure dephasing, described by the Milburn stochastic evolution of the Schrödinger equation. In the first part of this paper, it is shown how the decoherence rate influences the evolution of the number of phonons, and the quadrature of the mechanical resonator. In the second part of the paper, an attempt to look at the spectral response of the mechanical part of the system is given using non-stationary spectroscopy. The response of the resonator in its equilibrium position is emphasized when the single-photon regime is considered. Coherent states in the cavity field and the mechanical resonator are also represented. Results and discussion comparing the inclusions of the linear, quadratic, and linear-quadratic couplings are given, regarding the influence of the dephasing in the decoherence mechanism.
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We study theoretically the dynamics of multiple mechanical oscillators coupled to a single cavity field mode via linear or quadratic optomechanical interactions. We focus specifically on the strong-coupling regime where the cavity decays much faster than the mechanical modes, and the optomechanical coupling is comparable to or larger than the mechanical frequency, so that both the optical and mechanical systems operate in the deep quantum regime. Using the examples of one and two mechanical oscillators, we show that the system can classically exhibit bistability and bifurcations, and we explore how these manifest themselves in interference, entanglement, and correlation in the quantum theory, while revealing the impact of decoherence of the mechanical system due to cavity fluctuations and coherent driving.
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.
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 the field of cavity optomechanics, proposals for quantum nondemolition (QND) measurements of phonon number provide a promising avenue by which one can study the quantum nature of nanoscale mechanical resonators. Here we investigate these QND measurements for an optomechanical system whereby quadratic coupling arises due to shared symmetries between a single optical resonance and a mechanical mode. We establish a relaxed limit on the amount of linear coupling that can exist in this type of system while still allowing for QND measurements of mechanical Fock states. The ability to perform optomechanical QND measurements of this nature would allow one to probe the decoherence of these mesoscopic states, providing an experimental test bed for quantum collapse theories.