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arXiv:1003.4048 · New Journal of Physics

Achieving ground state and enhancing optomechanical entanglement by recovering information

Haixing Miao, S. L. Danilishin, H. Müller‐Ebhardt, Yanbei Chen

Published Aug 12, 2010• 28 citations
arXivHTMLPDF

Abstract

For cavity-assisted optomechanical cooling experiments, in order to achieve the quantum ground state of the mechanical oscillator, the cavity bandwidth needs to be smaller than the mechanical frequency. In the literature, this is the so-called resolved-sideband or good-cavity limit, and this is based on an understanding of optomechanical dynamics. We provide a different but physically equivalent explanation of such a limit: that is, information loss due to finite cavity bandwidth. With an optimal feedback control to recover the information in the cavity output, we can surpass the resolved-sideband limit and achieve the quantum ground state. In addition, recovering this information can also significantly enhance the entanglement between the cavity mode and the mechanical oscillator. Especially when the environmental temperature is high, such optomechanical entanglement will either exist or vanish critically depending on whether information is recovered or not. This provides a vivid example of a quantum eraser in the optomechanical system.

DOI
10.1088/1367-2630/12/8/083032

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For cavity-assisted optomechanical cooling experiments, in order to achieve the quantum ground state of the mechanical oscillator, the cavity bandwidth needs to be smaller than the mechanical frequency. In the literature, this is the so-called resolved-sideband or good-cavity limit, and this is based on an understanding of optomechanical dynamics. We provide a different but physically equivalent explanation of such a limit: that is, information loss due to finite cavity bandwidth. With an optimal feedback control to recover the information in the cavity output, we can surpass the resolved-sideband limit and achieve the quantum ground state. In addition, recovering this information can also significantly enhance the entanglement between the cavity mode and the mechanical oscillator. Especially when the environmental temperature is high, such optomechanical entanglement will either exist or vanish critically depending on whether information is recovered or not. This provides a vivid example of a quantum eraser in the optomechanical system.
Ground-state cooling of mechanical resonators is a prerequisite for the observation of various quantum effects in optomechanical systems and thus has always been a crucial task in quantum optomechanics. In this paper, we study how to realize ground-state cooling of the mechanical mode in a Fano-mirror optomechanical setup, which allows for enhanced effective optomechanical interaction but typically works in the (deeply) unresolved-sideband regime. We reveal that for such a two-sided cavity geometry with very different decay rates at the two cavity mirrors, it is possible to cool the mechanical mode down to its ground state within a broad range of parameters by using an appropriate single-sided coherent feedback. This is possible even if the total optical loss is more than seven orders of magnitude larger than the mechanical frequency and the feedback efficiency is relatively low. Importantly, we show that a more standard double-sided feedback scheme is not appropriate to cooperate with a Fano-mirror system.
Mechanical oscillators which respond to radiation pressure are a promising means of transferring quantum information between light and matter. Optical–mechanical state swaps are a key operation in this setting. Existing proposals for optomechanical state swap interfaces are only effective in the resolved sideband limit. Here, we show that it is possible to fully and deterministically exchange mechanical and optical states outside of this limit, in the common case that the cavity linewidth is larger than the mechanical resonance frequency. This high-bandwidth interface opens up a significantly larger region of optomechanical parameter space, allowing generation of non-classical motional states of high-quality, low-frequency mechanical oscillators.
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.
Preparing macroscopic mechanical resonators close to their motional quantum groundstate and generating entanglement with light offers great opportunities in studying fundamental physics and in developing a new generation of quantum applications. Here we propose an experimentally interesting scheme, which is particularly well suited for systems in the sideband-unresolved regime, based on coherent feedback with linear, passive optical components to achieve groundstate cooling and photon-phonon entanglement generation with optomechanical devices. We find that, by introducing an additional passive element – either a narrow linewidth cavity or a mirror with a delay line – an optomechanical system in the deeply sideband-unresolved regime will exhibit dynamics similar to one that is sideband-resolved. With this new approach, the experimental realization of groundstate cooling and optomechanical entanglement is well within reach of current integrated state-of-the-art high-Q mechanical resonators.
Preparing macroscopic mechanical resonators close to their motional quantum groundstate and generating entanglement with light offers great opportunities in studying fundamental physics and in developing a new generation of quantum applications. Here we propose an experimentally interesting scheme, which is particularly well suited for systems in the sideband-unresolved regime, based on coherent feedback with linear, passive optical components to achieve groundstate cooling and photon-phonon entanglement generation with optomechanical devices. We find that, by introducing an additional passive element - either a narrow linewidth cavity or a mirror with a delay line - an optomechanical system in the deeply sideband-unresolved regime will exhibit dynamics similar to one that is sideband-resolved. With this new approach, the experimental realization of groundstate cooling and optomechanical entanglement is well within reach of current integrated state-of-the-art high-Q mechanical resonators.
Dissipation and the accompanying fluctuations are often seen as detrimental for quantum systems since they are associated with fast relaxation and loss of phase coherence. However, it has been proposed that a pure state can be prepared if external noise induces suitable downwards transitions, while exciting transitions are blocked. We demonstrate such a refrigeration mechanism in a cavity optomechanical system, where we prepare a mechanical oscillator in its ground state by injecting strong electromagnetic noise at frequencies around the red mechanical sideband of the cavity. The optimum cooling is reached with a noise bandwidth smaller than but on the order of the cavity decay rate. At higher bandwidths, cooling is less efficient as suitable transitions are not effectively activated. In the opposite regime where the noise bandwidth becomes comparable to the mechanical damping rate, damping follows the noise amplitude adiabatically, and the cooling is also suppressed. Sideband cooling is a well-known technique exploiting coherent pumping for cooling a quantum system, and recent theoretical work suggested that even broadband noise might be used to the same effect. Here, the authors demonstrate this by cooling a mechanical oscillator in its ground state using synthetic noise.