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Journal of Modern Optics

State transfer and entanglement of two mechanical oscillators in coupled cavity optomechanical system

Taha Yousif, Wenjun Zhou, Ling Zhou

Published Jun 16, 2014• 15 citations
Publisher

Abstract

We investigate coupled two-cavity optomechanical systems to show their potential usages by revealing the physical processes. Under two conditions, we deduce the correspondingly effective Hamiltonian with beam splitter type and nondegenerate parametric-down conversion type, respectively. Including the whole interactions, we show that the state transfer and the stationary entanglement between the two mechanical resonators can be achieved.

DOI
10.1080/09500340.2014.927016

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We investigate coupled two-cavity optomechanical systems to show their potential usages by revealing the physical processes. Under two conditions, we deduce the correspondingly effective Hamiltonian with beam splitter type and nondegenerate parametric-down conversion type, respectively. Including the whole interactions, we show that the state transfer and the stationary entanglement between the two mechanical resonators can be achieved.
Abstract Systems of coupled mechanical resonators are useful for quantum information processing and fundamental tests of physics. Direct coupling is only possible with resonators of very similar frequency, but by using an intermediary optical mode, non-degenerate modes can interact and be independently controlled in a single optical cavity. Here we demonstrate coherent optomechanical state swapping between two spatially and frequency separated resonators with a mass ratio of 4. We find that, by using two laser beams far detuned from an optical cavity resonance, efficient state transfer is possible. Although the demonstration is classical, the same technique can be used to generate entanglement between oscillators in the quantum regime.
Systems of coupled mechanical resonators are useful for quantum information processing and fundamental tests of physics. Direct coupling is only possible with resonators of very similar frequency, but by using an intermediary optical mode, non-degenerate modes can interact and be independently controlled in a single optical cavity. Here we demonstrate coherent optomechanical state swapping between two spatially and frequency separated resonators with a mass ratio of 4. We find that, by using two laser beams far detuned from an optical cavity resonance, efficient state transfer is possible. Although the demonstration is classical, the same technique can be used to generate entanglement between oscillators in the quantum regime.Coupled mechanical resonators where each mode can be separately controlled are a promising system for quantum information processing. Here, Weaver et al. demonstrate coherent swapping of optomechanical states between two separate resonators.
Quantum entanglement in mechanical systems is not only a key signature of macroscopic quantum effects but has wide applications in quantum technologies. Here we propose an effective approach for creating strong steady-state entanglement between two directly coupled mechanical oscillators (or a mechanical oscillator and a microwave resonator) in a modulated optomechanical system. The entanglement is achieved by combining the processes of a cavity cooling and the two-mode parametric interaction, which can surpass the bound on the maximal stationary entanglement from the two-mode parametric interaction. In principle, our proposal allows one to cool the system from an initial thermal state to an entangled state with high purity by a monochromatic driving laser. Also, the obtained entangled state can be used to implement the continuous-variable teleportation with high fidelity. Moreover, our proposal is robust against the thermal fluctuations of the mechanical modes under the condition of strong optical pumping.
This paper investigates a coupled cavity optomechanical system consisting of two Fabry-Perot cavities and the two cavities are coupled via an optical fiber.Every cavity is made of one fixed mirror and a movable mirror,and the movable mirror can be regarded as a mechanical oscillators.Meanwhile,the two cavity modes are driven by classical laser fields.So,the interaction is inevitable between cavities,cavity and moving mirror,cavity and classical field.Firstly,in order to eliminate the two cavity fields,an effective Hamiltonian of the two phonon modes is derived by means of picture transformation,adiabatic eliminating,and rotating wave approximation ignoring the high frequency items,etc.Secondly,if the two mechanical oscillators initially are in coherent states,the coupled mechanical oscillators can be used to transmit state.Finally,in order to verify the analytical result,the fidelity of quantum state is numevically simulated,the result shows that the quantum state can be transferred periodically between the two mechanical oscillators,which is the same as the analytical result.
We propose an approach for generating steady-state mechanical entanglement in a coupled optomechanical system. By applying four-tone driving lasers with weighted amplitudes and specific frequencies, we obtain an effective Hamiltonian that couples the delocalized Bogoliubov modes of the two mechanical oscillators to the cavity modes via beam-splitter-like interactions. When the mechanical decay rate is small, the Bogoliubov modes can be effectively cooled by the dissipative dynamics of the cavity modes, generating steady-state entanglement of the mechanical modes. The mechanical entanglement obtained in the stationary regime is strongly dependent on the values of the ratio of the effective optomechanical coupling strengths. Numerical simulation with the full linearized Hamiltonian shows that significant amount of mechanical entanglement can indeed be obtained by balancing the opposing effects of varying the ratio and by carefully avoiding the system parameters that may lead to amplified oscillations of the mechanical mean values detrimental to the entanglement generation.
We theoretically investigate interactions between nondegenerate mechanical oscillators mediated by a time-dependent cavity field. We obtain a reduced master equation valid for all optomechanical systems operating in the weak-coupling regime. This master equation includes all forms of decoherence and backaction due to the dissipation of the field mediating the interaction. We apply the master equation to study two resonant coupling schemes within a rotating-wave approximation: the beam-splitter Hamiltonian and the two-mode parametric amplifier. In both cases, the effective unitary interaction can be made arbitrarily strong compared to the decoherence due to dissipation of the mediating field by choosing appropriate detunings.