Creation, storage, and retrieval of an optomechanical cat state

Abstract

We analyze a method for the creation, storage and retrieval of optomechanical Schrödinger cat states, in which there is a quantum superposition of two distinct macroscopic states of a mechanical oscillator. In the quantum memory protocol, an optical cat state is first prepared in an optical cavity, then transferred to the mechanical mode, where it is stored and later retrieved using control fields. We carry out numerical simulations for the quantum memory protocol for optomechanical cat states using the positive-P phase space representation. This has a compact, positive representation for a cat state, thus allowing a probabilistic simulation of this highly non-classical quantum system. It is essential to use importance sampling to carry out the simulation effectively. To verify the effectiveness of the cat-state quantum memory, we consider several cat-state signatures and show how they can be computed. We also investigate the effects of decoherence on a cat state by solving the standard master equation for a simplified model analytically, allowing us to compare with the numerical results. Focusing on the negativity of the Wigner function as a signature of the cat state, we evaluate analytically an upper bound on the time taken for the negativity to vanish, for a given temperature of the environment of the mechanical oscillator. We show consistency with the numerical methods. These provide exact solutions, allowing a full treatment of decoherence in an experiment that involves creating, storing and retrieving mechanical cat states using temporally mode-matched input and output pulses. Our analysis treats the internal optical and mechanical modes of an optomechanical oscillator, and the complete set of input and output field modes which become entangled with the internal modes. The model includes decoherence due to thermal effects in the mechanical reservoirs, as well as optical and mechanical losses.

Dynamics of transient cat states in degenerate parametric oscillation with and without nonlinear Kerr interactions

“…A positive-valued Wigner function gives δ = 0 while δ is nonzero in the presence of any negative values in a Wigner function. The Wigner functions W + and W − for the even cat-state and odd cat-state respectively are given by [89] W ± (α, α * ) = 2 π N 2 ± {exp [−2 (α * − α * 0 ) (α − α 0 )] +exp [−2 (α * + α * 0 ) (α + α 0 )]…”

Generating a Squeezed‐Coherent‐Cat State in a Double‐Cavity Optomechanical System

“…We consider a system which consists of two coupled cavities [29] with modulation time-dependent jumping rate. [27,28,30] The two mode cavities share a common movable mirror which couples to the first and second cavity with a linear and quadratical coupling [46,47] respectively.…”

“…[15][16][17][18][19][20][21][22][23][24][25][26] Most recently, generating cat state of mechanical oscillator has caught people's attention. [27][28][29][30] Liao proposed a scheme to create macroscopically mechanical superposition states in a twomode optomechanical system by introducing modulated sinusoidal photon hopping between the two cavity modes. [27,28] Teh [29] showed that an optical cat state could be transferred to the DOI: 10.1002/andp.201900196 mechanical mode, where it was stored and later retrieved using control fields.…”

“…[27][28][29][30] Liao proposed a scheme to create macroscopically mechanical superposition states in a twomode optomechanical system by introducing modulated sinusoidal photon hopping between the two cavity modes. [27,28] Teh [29] showed that an optical cat state could be transferred to the DOI: 10.1002/andp.201900196 mechanical mode, where it was stored and later retrieved using control fields. Different from the superposition of coherent of cavity field, [14,31,32] the superposition of the coherent state of the mechanical oscillator is real Schrödinger cat state since the mechanical oscillator is macroscopic or mesoscopic massive object.…”

Optomechanical generation of a mechanical catlike state by phonon subtraction

“…Here we propose a scheme for preparation of a mechanical catlike state in quantum optomechanics that does not rely on nonlinear coupling [38,40,41] or on external generation and transfer of the nonclassical state [44,57]. An established technique for preparation of catlike states is subtraction of one or several quanta from a squeezed vacuum state [58,59].…”