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Physica Scripta

Enhancing sideband cooling by initial photon-phonon correlation

Wei Niu, Wen-Quan Yang, Yonghong Ma, Chuan‐Cun Shu, Wen-Zhao Zhang

Published Jul 17, 2024• 0 citations
Publisher

Abstract

Abstract We propose an optimized sideband cooling protocol for an optomechanical system coupled to a mechanical non-Markovian reservoir, considering the presence of initial system correlations. By incorporating the effect of initial correlations in the Heisenberg equations, we derive a more stringent dependence on the initial conditions and time-dependent evolution of the phonon numbers. Our findings demonstrate that considering the initial correlations can significantly reduce the number of phonons during the cooling process. Moreover, by adjusting the strength and phase of the initial correlation, the ground-state cooling process can be accelerated. We observe a characterization of this cooling optimization process that resembles the phenomenon of entanglement death and revival. This work provides a promising platform for effectively manipulating phonons and facilitating quantum information processing in optomechanical systems.

DOI
10.1088/1402-4896/ad6488

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Abstract We propose an optimized sideband cooling protocol for an optomechanical system coupled to a mechanical non-Markovian reservoir, considering the presence of initial system correlations. By incorporating the effect of initial correlations in the Heisenberg equations, we derive a more stringent dependence on the initial conditions and time-dependent evolution of the phonon numbers. Our findings demonstrate that considering the initial correlations can significantly reduce the number of phonons during the cooling process. Moreover, by adjusting the strength and phase of the initial correlation, the ground-state cooling process can be accelerated. We observe a characterization of this cooling optimization process that resembles the phenomenon of entanglement death and revival. This work provides a promising platform for effectively manipulating phonons and facilitating quantum information processing in optomechanical systems.
An optimized sideband cooling in the presence of initial system correlations is investigated for a standard optomechanical system coupled to a general mechanical non-Markovian reservoir. We study the evolution of phonon number by incorporating the effects of initial correlations into the time-dependent coefficients in the Heisenberg equation. We introduce the concept of cooling rate and define an average phonon reduction function to describe the sideband cooling effect in non-Markovian regime. Our results show that the instantaneous phonon number can be significantly reduced by introducing either the parametric-amplification type or the beam-splitter type initial correlations. In addition, the ground state cooling rate can be accelerated by enhancing the initial correlation of beam-splitter type. By optimizing the initial state of the system and utilizing Q-modulation technology, a stable mechanical ground state can be obtained in a very short time. Our optimized cooling protocol provides an appealing platform for phonon manipulation and quantum information processing in solid-state systems.
A sideband cooling strategy that incorporates (i) the dynamics induced by structured (non-Markovian) environments in the target and auxiliary systems and (ii) the optimally time-modulated interaction between them is developed. For the context of cavity optomechanics, when non-Markovian dynamics are considered in the target system, ground state cooling is reached at much faster rates and at a much lower phonon occupation number than previously reported. In contrast to similar current strategies, ground state cooling is reached here for coupling-strength rates that are experimentally accessible for the state-of-the-art implementations. After the ultrafast optimal-ground-state-cooling protocol is accomplished, an additional optimal control strategy is considered to maintain the phonon number as close as possible to the one obtained in the cooling procedure. Contrary to the conventional expectation, when non-Markovian dynamics are considered in the auxiliary system, the efficiency of the cooling protocol is undermined.
We propose an alternative experimentally feasible approach to achieve high-efficiency ground-state cooling of a mechanical oscillator in an optomechanical system under the deeply unresolved sideband condition with the assistance of both intracavity and extracavity squeezing. In the scheme, a degenerate optical parametric amplifier is placed inside the optical cavity, generating the intracavity squeezing; in addition, the optical cavity is driven by the extracavity squeezed light, namely the extracavity squeezing. The quantum interference effect generated by intracavity squeezing and extracavity squeezing can completely suppress the nonresonant Stokes heating process while greatly enhancing the anti-Stokes cooling process. Therefore, the joint-squeezing scheme is capable of cooling the mechanical oscillators to their quantum ground state in a regime far away from the resolved sideband condition. Compared with other traditional optomechanical cooling schemes, the single-photon cooling rate in this joint-squeezing scheme can be tremendously enlarged by nearly three orders of magnitude. At the same time, the coupling strength required to achieve ground-state cooling can be significantly reduced. This scheme is promising for cooling large-mass and low-frequency mechanical oscillators, which provides a prerequisite for preparing and manipulating nonclassical states in macroscopic quantum systems and lays a significant foundation for quantum manipulation.
We theoretically study the dynamics of the ground-state cooling and the quantum entanglement in a modulated optomechanical system, where the frequency of the mechanical oscillator and the optical field or the strength of the driving laser is time dependent. In this paper, we focus mainly on the fact that the system works in the regime of blue detuning. It is found that in the long-time limit the steady-state phonon number can be decreased significantly so that the mechanical oscillator is cooled to the ground state by appropriately selecting the frequency and the amplitude of the modulation. Further, with the help of the dynamical modulation in the system, the time evolution of the entanglement preevaluation value displays the death and rebirth of quantum entanglement between the mechanical oscillator and the optical field, which correspond, respectively, to the increase and decrease of the effective phonon number of the mechanical oscillator. In particular, when the steady-state dynamics of the system is quasiperiodic, the dynamics of the entanglement preevaluation value exhibits a quasiperiodic behavior, which means that the quantum phenomena can be represented in nonlinear classical dynamics.
We solve the Lindblad master equation for the quantum state of a pumped optomechanical system coupled to a thermal bath. We show that the solution to the state in the linear pumping regime is a beam-split thermal state when pumped on the red sideband of cavity resonance and a two-mode squeezed thermal state when pumped on the blue sideband. The time dependence of each state is fully described by four coupled differential equations. Using this formalism, we describe a process of first cooling the mechanical mode via the red-sideband pump, then entangling that mode using the blue-sideband pump. We find that there is an optimal strength of blue-sideband pumping to drive the correlation variance between the two modes below a desired threshold for a maximum amount of time. This optimal value depends both on the loss rates and equilibrium temperatures of the two modes, and we provide an approximate analytic expression for this relationship. We show that a long entanglement time is achievable, even at relatively high temperatures, as long as the optical loss rate is much higher than the mechanical one.
Abstract Ground-state cooling of mesoscopic mechanical objects is still a major challenge in the unresolved-sideband regime. We present a frequency modulation (FM) scheme to achieve cooling of the mechanical resonator to its ground-state in a double-cavity optomechanical system containing a mechanical resonator. The mean phonon number is determined by numerically solving a set of differential equations derived from the quantum master equations. Due to efficient suppression of Stokes heating processes in the presence of FM, the ground-state cooling, indicated by numerical calculations, is significantly achievable, regardless of whether in the resolved-sideband regime or the unresolved-sideband regime. Furthermore, by choosing parameters reasonably, the improvement of the quantum cooling limit is found to be capable of being positively correlated with the modulation frequency. This method provides new insight into quantum manipulation and creates more possibilities for applications of quantum devices.