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arXiv:1511.04859 · Physical Review A

Nonclassical non-Gaussian state of a mechanical resonator via selectively incoherent damping in a three-mode optomechanical system

Kang-jing Huang, Yan Yan, Jia‐pei Zhu, Yun‐Feng Xiao, Gao‐xiang Li

Published Mar 18, 2016• 3 citations
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Abstract

In this paper we propose a scheme for the generation of a nonclassical non-Gaussian motional state of a mechanical resonator (MR) in the three-mode optomechanical system in which two linearly coupled single-mode cavities interact dispersively with the mechanical oscillator simultaneously. With one cavity driven by a weak laser field and by properly tuning the driving frequency, a desirable phononic Liouvillian superoperator can be obtained by engineering the selective interaction Hamiltonian confined to Fock subspaces. It is shown that the MR can be driven dissipatively into a steady non-Gaussian nonclassical state, which possesses sub-Poisson statistics, although its Wigner function is positive. The present scheme can be useful for obtaining single phonons.

DOI
10.1103/physreva.93.033832

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We propose a scheme for generation of a nonlinear coherent state (NCS) of a mechanical resonator (MR) in an optomechanical micro-cavity, in which a two-level quantum dot (QD) and the microcavity are respectively driven by a strong laser and a weak laser. This microcavity can be engineered within a photonic band-gap (PBG) material. By properly tuning the frequency of the weak driving field, two-photon blockade phenomenon occurs. The QD-cavity subsystem can evolve into a dark state due to the damping of the microcavity and the elimination of the decay rate of the QD at selected frequencies in the PBG material. In this situation, the phonon mode of the MR can be prepared into a NCS, which is a non-classical state and possesses the sub-Poisson statistics. We also demonstrate the Wigner function of the NCS, which negativity implies its non-classicality.
We study an optomechanical system for the purpose of generating a nonclassical mechanical state when a mechanical oscillator is quadratically coupled to a single-mode cavity field driven by a squeezed optical field. The system corresponds to a regime where the optical dissipation dominates both the mechanical damping and the optomechanical coupling. We identify that multiphonon processes emerge in the optomechanical system and show that a mechanical oscillator prepared in the ground state will evolve into an amplitude-squared squeezed vacuum state. The Wigner distribution of the steady state of the mechanical oscillator is non-Gaussian exhibiting quantum interference and fourfold symmetry. This nonclassical mechanical state, generated via reservoir engineering, can be used for quantum correlation measurements of the position and momentum of the mechanics below the standard quantum limit.
We propose a scheme for preparing nanomechanical oscillators in nonclassical steady states, characterized by a pronounced negative Wigner function. In our optomechanical approach, the mechanical oscillator couples to multiple laser-driven resonances of an optical cavity. By lowering the resonance frequency of the oscillator via an inhomogeneous electrostatic field, we significantly enhance its intrinsic geometric nonlinearity per phonon. This causes the motional sidebands to split into separate spectral lines for each phonon number and transitions between individual phonon Fock states can be selectively addressed. We show that this enables the preparation of the nanomechanical oscillator in a single-phonon Fock state. Our scheme can, for example, be implemented with a carbon nanotube dispersively coupled to the evanescent field of a state of the art whispering gallery mode microcavity.
In this paper, we propose a driven-dissipative scheme for generating non-Gaussian entangled mechanical states and consider the remote preparation of motional Schr\"odinger cat states via mechanical entanglement. The system under our study consists of a cavity optomechanical setup with two frequency-mismatched mechanical oscillators simultaneously coupled to a bichromatically driven cavity field. We show that under appropriate conditions, an effective Hamiltonian for nondegenerate parametric down-conversion involving the two mechanical oscillators and the cavity field can be engineered. We demonstrate analytically and numerically that the cavity dissipation drives the mechanical oscillators into a steady-state non-Gaussian entangled state. The properties of the mechanical state, including non-Gaussianity, Wigner negativity, entanglement, and quantum steering, are investigated in detail. We further reveal that through the non-Gaussian mechanical entanglement, the remote preparation of the Schr\"odinger cat states of one mechanical oscillator can be achieved by coupling the other one to an auxiliary probe cavity and homodyning the output of the probe cavity. We also discuss the robustness of the mechanical states against thermal fluctuations. Our scheme provides a feasible approach for the dissipative and remote preparation of non-Gaussian mechanical nonclassical states.
We present a proposal to prepare the macroscopic superposition states of a mechanical oscillator in an optomechanical system with quadratic coupling. By coherently driving the optomechanical cavity with an external field, a Kerr-type interaction among phonons is induced. The macroscopic mechanical superposition can be generated by exploiting the Kerr nonlinearity in the mechanical oscillator, just as the generation of a nonclassical state of light in a Kerr medium. One merit of our proposal is that the Kerr nonlinearity can be strongly enhanced by adjusting the amplitude of the driving field. The influence of the system damping on the realization of mechanical non-Gaussian state is discussed by the negativity of the Wigner function. The results show that the macroscopic superposition states are robust against the mechanical thermal noise.
We put forward a deterministic dissipative protocol to prepare phonon Fock states in nonlinear quantum optomechanical devices. The system is composed of a mechanical mode interacting with an optical field via radiation pressure, whereas the light mode is laser driven in the resolved blue-sideband regime. To keep our results tractable, we switch to an interaction picture in a displaced basis, where the effective Hamiltonian exhibits the selective photon-phonon interaction explicitly. After proper parameter adjustment and similarly to cavity-cooling schemes, the quantum evolution allows steering of the mechanical degree of freedom to the desired Fock state by directing the optical excitations dynamically towards the target phonon state. The numerical results, including decoherence on both the mechanical and the optical degrees of freedom, prove to be quite robust in the good- and bad-cavity regimes, with fidelities exceeding 95%. Finally, characterization of the achieved nonclassicality, as well as the limitations and feasibility of our protocol under experimental parameters, is also discussed.