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Journal of the Optical Society of America B

Generation of the mechanical Schrödinger cat state in a hybrid atom-optomechanical system

Najmeh Etehadi Abari, M. H. Naderi

Published Jun 2, 2020• 9 citations
Publisher

Abstract

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.

DOI
10.1364/josab.393352

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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.
The generation of a superposition state of a single-mode or two-mode coherent state is always an attractive topic. We propose schemes to generate the Schrödinger cat state and entangled coherent state of a mechanical oscillator in a hybrid optomechanical system. By introducing time-dependent coupling between the atom and photon, an effective Hamiltonian is deduced, where a tripartite interaction with time-dependent coupling is achieved. The effect of relatively high free energy can be cancelled so that we can obtain a relatively large average phonon number. Including dissipation, we derive an analytic solution of the system and further discuss the decoherence and disentanglement. In addition, a steady phonon laser can be reached.
Abstract In this study, we propose an experimental scheme to generate macroscopic quantum cat states of a mechanical oscillator within a hybrid atom-optomechanical system. The system consists of a mechanical oscillator harmonically coupled to an optical cavity, where the atom-cavity interaction operates in the ultrastrong-coupling regime described by the Rabi–Stark model. The cavity photon and atom state measurements project the mechanical mirror into cat states, with the process enhanced by Fock-state initialization, nonlinear atom-field coupling and modulated mechanical tuning. Wigner-function analysis confirms nonclassicality. The key findings are: (1) higher initial photon number n increases coherent-state amplitudes and separations of the cat states; (2) smaller detuning improves distinguishability; (3) both the nonlinear atom-photon coupling term and stronger optomechanical coupling accelerate the generation of cat states. This approach provides a parameter-tunable framework for quantum coherence control.
We propose a scheme to generate the macroscopic entangled Schrödinger cat state of two mechanical resonators in a hybrid optomechanical system by introducing modulated photon-hopping interaction between two cavities. We show that the obtained entangled cat state possesses large average phonon number and the two base vectors of which are nearly orthogonal, thus causing the high degree of entanglement. To justify the robust of the scheme, the dissipation of the system and the noise from the environment are considered. It shows that the high fidelity between the obtained state and the target state can be achieved in the presence of dissipation and thermal noise within our parameter regions, which suggests that our state-generation proposal is feasible.
A theoretical scheme for the realization of the sphere-coherent motional states in an optomechanical cavity in the presence of a two-level atom is proposed. To this end, the analogy between an atom-assisted optomechanical cavity and a laser-driven trapped-ion system is used. This analogy provides us with a theoretical tool to show how sphere-coherent states (SCSs) can be generated for the motional degree of freedom of the macroscopic mechanical oscillator (MO) from atom-field-mirror interactions in a multimode optomechanical cavity. Some nonclassical properties of the generated state of the MO, including the degree of quadrature squeezing and the negativity of the Wigner distribution, are studied. We also examine the effects of the dissipation mechanisms involved in the system under consideration, including the atomic spontaneous emission and the damping of the motion of the MO, on the generated motional SCSs.
Abstract We propose a model for controlling and enhancing the entanglement between the two cavity fields and mirror with a hybrid optomechanical system consisting of Λ-type three-level 85Rb atomic ensembles driven by two externally modulated laser fields. When one (another) cavity mode is driven at the red (blue) mechanical sideband and both cavity modes are blue-detuned by the mechanical frequency to the respective atomic resonant transitions, the dynamic coupling control of the cavity field and mirror can be realized by periodically modulating the amplitudes of the two incident laser fields. Compared to the unmodulated case, the periodic modulation of the laser fields in a cavity-optomechanical system embedded with a small number of atoms has the capability to enhance the entanglement between the two cavity fields and mirror. This scheme provides a new approach to the generation and control of entanglement in cavity-optomechanical systems.
We present a systematic study on the effects of dynamical transfer and steady-state synchronization of quantum states in a hybrid optomechanical network consisting of two cavities, which carry atoms inside and interact via a common moving mirror such as the mechanical oscillator. It is found that a high fidelity transfer of Schrödinger’s cat and squeezed states between two cavities modes is possible. On the other hand, we demonstrate the synchronization effect of the cavity modes in a steady squeezed state with its high fidelity realized by the mechanical oscillator that intermediates the generation, transfer and stabilization of the squeezing. In this framework, we also study the generation and evolution of bipartite and tripartite entanglement and find its connection to the effects of quantum state transfer and synchronization. Particularly, when the transfer occurs at the maximal fidelity, any entanglement is almost zero, so the different cavity modes are disentangled. However, these modes become entangled when the two bosonic modes are synchronized in a stationary squeezed state. The results provided by the current study may find applications in quantum information technologies, in addition to the setups for metrology, where squeezed states are essential.