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Physical Review A

Macroscopic quantum coherence and mechanical squeezing of a graphene sheet

Xiyun Li, Wenjie Nie, Aixi Chen, Yueheng Lan

Published Dec 14, 2017• 28 citations
Publisher

Abstract

We theoretically investigate the macroscopic quantum coherence and the mechanical squeezing of a mechanical oscillator in a hybrid optomechanical system consisting of a suspended graphene sheet and an ultracold atomic ensemble trapped inside a Fabry-P\'erot cavity. In the study the vacuum is used to mediate an effective optomechanical coupling between the graphene oscillator and the cavity field driven by an external laser beam. We find that in the presence of this coupling, the macroscopic quantum coherence and the mechanical squeezing of the graphene sheet can be attained in a certain range of driving power. In particular, the quantum coherence in the optomechanical system can be transferred from the optical field to the mechanical oscillator. We also investigate in detail the spectrum and the squeezing of the output field and the attained results may be used to study the mechanical squeezing of a graphene sheet.

DOI
10.1103/physreva.96.063819

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We theoretically investigate the macroscopic quantum coherence and the mechanical squeezing of a mechanical oscillator in a hybrid optomechanical system consisting of a suspended graphene sheet and an ultracold atomic ensemble trapped inside a Fabry-P'erot cavity. In the study the vacuum is used to mediate an effective optomechanical coupling between the graphene oscillator and the cavity field driven by an external laser beam. We find that in the presence of this coupling, the macroscopic quantum coherence and the mechanical squeezing of the graphene sheet can be attained in a certain range of driving power. In particular, the quantum coherence in the optomechanical system can be transferred from the optical field to the mechanical oscillator. We also investigate in detail the spectrum and the squeezing of the output field and the attained results may be used to study the mechanical squeezing of a graphene sheet.
We present a hybrid optomechanical scheme to achieve dynamical squeezing of position quadrature of a mesoscopic mechanical oscillator, that can be externally controlled by classical fields. A membrane-in-the-middle setup is employed, in which an atom in $\mathrm{\ensuremath{\Lambda}}$ configuration is considered to be trapped on either side of the membrane inside the cavity. We show that a considerable amount of squeezing (beyond the 3-dB limit) can be achieved and maintained at a transient time scale that is not affected by the spontaneous emission of the atom. Squeezing depends upon the initial preparation of atomic states. Further, a strong effective coupling (larger than the relevant decay rates) between the atom and the oscillator can be attained by using large control fields that pump the atom and the cavity. The effects of cavity decay and the phononic bath on squeezing are studied. The results are supported by the detailed analytical calculations.
This thesis concentrates on generating and measuring non-classical states of mechanical oscillators by coupling them to atomic and molecular quantum systems. We start with a discussion of what novel physics can be explored by mechanical systems operating in the quantum regime. We then discuss one technique making it a possibility- cavity optomechanics, particularly optomechanical cooling. We investigate the limits of optomechanical cooling and review how the coupling of mechanical oscillators to external heat baths limits the minimum attainable phonon occupation number. As a possible alternative for circumventing clamping losses, we consider an all-optical approach where the mechanical element (in this case, a Bragg mirror) is suspended via optical forces, and discuss some limitations of this approach. We explore several schemes aimed at the generation of quantum states in mechanical oscillators. We consider specifically two examples: one in which the mechanical oscillator is coupled to polar molecules via dipole-dipole interaction, and another where it is magnetically coupled to a Bose condensate. The first example emphasizes that such an interaction can generate parametric squeezing and entanglement. The second scheme demonstrates that the back action of BEC spin measurements can be used to generate quantum states of motion of a mechanical oscillator. We then discuss possible methods for measuring the entire density matrix of a mechanical oscillator. The first method achieves the tomographic reconstruction of the mechanical Wigner function by coupling it simultaneously to a classical optical oscillator and a qubit. The second approach involves a state transfer scheme between momentum excitations of a bose-condensate in a cavity and a moving mirror of the cavity that is entirely mediated by the light field. We conclude with a discussion of the broader implications of this work, and some future research directions.
In this paper, we investigate theoretically the quantum state transfer in a laser-driven hybrid optomechanical cavity with two Duffing-like anharmonic movable end mirrors containing an ensemble of identical two-level trapped atoms. The quantum state transfer from the Bogoliubov modes of the two anharmonic oscillators to the atomic mode results in the atomic quadrature squeezing beyond the standard quantum limit of 3 dB, which can be controlled by both the optomechanical and atom-field coupling strengths. Interestingly, the generated atomic squeezing can be made robust against the noise sources by means of the Duffing anharmonicity. Moreover, the results reveal that the presence of the Duffing anharmonicity provides the possibility of transferring strongly squeezed states between the two mechanical oscillators in a short operating time and with high fidelity.
In this paper, we propose a new theoretical scheme for generating a macroscopic Schrödinger cat state of a mechanical oscillator in a hybrid optomechanical system where a beam of two-level atoms passes through the cavity. In the model under consideration, the cavity field couples to the macroscopic mirror through the optomechanical interaction while it couples to the atom through a generalized Jaynes–Cummings interaction that involves the cavity-mode structure. The motion of the mirror modifies the cavity-mode function and therefore modulates the atom-field interaction, leading to the three-mode atom-field-mirror coupling or, equivalently, polariton-mirror coupling in a dressed picture. This interaction induces a controllable anharmonicity in the energy spectrum of the mechanical oscillator, which provides the possibility of generating a superposition of two time-dependent coherent states of the mechanical oscillator just by performing a conditional measurement on the internal states of the atoms exiting the optomechanical cavity. We also investigate the tripartite atom-field-mirror entanglement, which is controllable by adjusting the parameters of the system. In addition, we explore the effects of the mechanical dissipation and thermal noise on the tripartite quantum correlation in the system as well as the generated mechanical superposition state.
We report on the realization of a hybrid optomechanical system in which ultracold atoms are coupled to a micromechanical membrane. The atoms are trapped in the intensity maxima of an optical standing wave formed by retroreflection of a laser beam from the membrane surface. Vibrations of the membrane displace the standing wave, thus coupling to the center-of-mass motion of the atomic ensemble. Conversely, atoms imprint their motion onto the laser light, thereby modulating the radiation pressure force on the membrane. In this way, the laser light mediates a long-distance coherent coupling between the two systems. When the trap frequency of the atoms is matched to the membrane frequency, we observe resonant energy transfer. Moreover, we demonstrate sympathetic damping of the membrane motion by coupling it to laser-cooled atoms. Theoretical investigations show that the coupling strength can be considerably enhanced by placing the membrane inside an optical cavity. This could lead to quantum coherent coupling and ground-state cooling of the membrane via a distant atomic ensemble.
We investigate a hybrid system consisting of an optomechanical resonator and an optical cavity containing a quantum well. The system is coupled to a squeezed vacuum reservoir. We analyze the effect of the injection of squeezed photons inside the cavity on the intensity spectrum. The system reaches a regime of hybrid resonance where mechanical, excitonic and cavity modes are intermixed. Despite that the optomechanical interaction is the source of the nonlinearity in the system, the optimum squeezing is obtained at the hybrid resonance frequencies. However, when the squeezed vacuum is applied, at these frequencies the minimum squeezing is realized as well as an increase of fluctuations is observed. We show that the squeezed vacuum transforms the coherent states into highly squeezed states of light, and offers a great flexibility to obtain maximal squeezing. Furthermore, a perfect squeezing is predicted.