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Physical Review A

Improving the cooling of a mechanical oscillator in a dissipative optomechanical system with an optical parametric amplifier

Sumei Huang, Aixi Chen

Published Dec 12, 2018• 45 citations
Publisher

Abstract

The ground-state cooling of a macroscopic mechanical oscillator is a crucial prerequisite for implementing the quantum manipulation of the mechanical oscillator. Here we show that a degenerate optical parametric amplifier (OPA) can significantly improve the cooling of the mechanical membrane in the purely dissipative coupling system in the unresolved sideband regime. In the presence of the OPA with a parametric phase $\ensuremath{\pi}/2$, the mechanical membrane can be cooled from room temperature 293 K to 10 mK, a factor of 112 lower than that in the absence of the OPA. If the mechanical oscillator is precooled to 0.1 K, the mechanical membrane can be cooled into the microkelvin regime.

DOI
10.1103/physreva.98.063818

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The ground-state cooling of a macroscopic mechanical oscillator is a crucial prerequisite for implementing the quantum manipulation of the mechanical oscillator. Here we show that a degenerate optical parametric amplifier (OPA) can significantly improve the cooling of the mechanical membrane in the purely dissipative coupling system in the unresolved sideband regime. In the presence of the OPA with a parametric phase \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/2, the mechanical membrane can be cooled from room temperature 293 K to 10 mK, a factor of 112 lower than that in the absence of the OPA. If the mechanical oscillator is precooled to 0.1 K, the mechanical membrane can be cooled into the microkelvin regime.
Abstract Quantum manipulation of mechanical oscillators has important applications in fundamental physics and quantum information processing. Ground-state cooling of the mechanical oscillators is the prerequisite for these applications. In this paper, we propose a scheme for cooling double mechanical oscillators simultaneously, in which the parametric processes induced by a degenerate optical parameter amplifier (OPA) change the statistical properties of the cavity field, resulting in the lower average phonon numbers. However, it is worth noting that two mechanical modes with the same frequency cannot be cooled due to destructive interference between the two cooling processes. While two mechanical oscillators with different frequencies can be simultaneously cooled to near their ground-state, and the cooling efficiency can be improved by increasing the parametric gain of OPA.
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 demonstrate that an especially tuned degenerate optical parametric amplifier (OPA) inside a cavity can lead to the momentum squeezing of a moving membrane in a dissipative optomechanical system. The momentum squeezing of the membrane depends on the parametric gain and the parametric phase of the OPA, the power of the external laser driving the cavity, and the temperature of the environment. The best achievable momentum squeezing is about 2.53 dB, which is limited by the OPA. Moreover, we show that the momentum squeezing of the membrane can be detected by directly measuring the cavity output field. In addition, we find that the mechanical squeezing can be enhanced to about 10.36 dB under the joint effect of the OPA and an input broadband squeezed vacuum field.
The generation of quantum entanglement in macroscopic systems remains a longstanding challenge. In this paper, we study theoretically the stationary entanglement of the two remote mechanical oscillators in a two-cascaded-cavity optomechanical system with a degenerate optical parametric amplifier (OPA) inside the first cavity. The two cavity modes in each cavity are driven at the red- and blue-sideband frequencies. The logarithmic negativity is used to quantify the amount of the stationary mechanical entanglement. We find that the stationary mechanical entanglement depends on the parametric gain and phase of the OPA, the input laser powers, the cavity decay rates, and the temperature of the environment. We show that it is possible to enhance the stationary mechanical entanglement by the use of the OPA, and the optimal enhancement of the stationary mechanical entanglement happens at the parametric phase 𝜋 / 2 of the OPA. At lower temperatures, the OPA exhibits a more significant improvement effect on the stationary mechanical entanglement.
We propose a method to break the dark mode of two degenerate mechanical resonators (MRs) in optomechanical systems via the Coulomb interaction. Two degenerate MRs can be cooled to their ground-state simultaneously beyond the resolved sideband regime using the Coulomb interaction and an optical parametric amplifier (OPA). We show that strong and robust mechanical squeezing beyond 3 dB can be generated using the OPA and mechanical parametric amplification (MPA) introduced by the Coulomb interaction. Our results manifests that robust bipartite and genuine tripartite entanglement can be produced in a degenerate optomechanical system.
Abstract We investigate the effect of a degenerate optical parametric amplifier (OPA) placed inside an optomechanical cavity on the steady-state entanglement of two cavity modes, which jointly interact with a mechanical resonator. Two cavity modes are, respectively, driven at the red and blue sideband associated with the mechanical resonator, which generates entanglement between them in the limit of resolved sideband. The OPA gives rise to single-mode squeezing of the cavity fields, which results in significant improvement of the two-mode entanglement. It is found that an optimal nonlinear gain of the OPA exists, depending on the system temperatures, which yields the maximum entanglement. The improvement is particularly remarkable for the system at cryogenic temperatures.