Steady-state mechanical squeezing in a hybrid atom-optomechanical system with a highly dissipative cavity.

Wang DY, Bai CH, Wang HF, Zhu AD, Zhang S - Sci Rep (2016)

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f4: The variance of the displacement quadrature X relates to the effective detuning Δeff by solving the master equation numerically.Here Δeff can be tuned individually by varying Δc, the average phonon number is set to be 1, 10, and 50 respectively, and the other parameters are chosen to be the same as in Fig. 2.
Mentions: In this section, we solve the master equation numerically to calculate the steady-state variance of the mechanical displacement quadrature X. Firstly, we show the numerical results for the time evolution of the variance with the Hamiltonian HL and Heff as shown in Fig. 3. We can find that the variance will be stable after time evolution. The relationship between the steady-state variance and effective detuning is shown in Fig. 4. One can see from Fig. 4 that the minimum value of variance can be achieved at the optimal detuning point of , which comes from the standard cavity cooling Hamiltonian in Eq. (15) under the transformed frame. The change rate of variance on the effective detuning increases with increasing the average phonon number . In the process of numerical simulation, the parameters are set to be ωm/(2π) = 5 MHz, ωa/(2π) = 500 THz, δa = 400 ωm, Δc = −0.9 ωm, G0 = 6.3 ωm, g = 10−3 ωm, η = 10−4 ωm, κ = 10 ωm, γc = 0.1 ωm, γm = 10−6 ωm, , and respectively, which satisfy the conditions , and . The average phonon number corresponds to the temperature T = 12 mK. At the optimal detuning point , the steady-state variance of the displacement quadrature is 〈δX2〉 = e−2ζ = 0.65. However, one can see from Fig. 4 that we need a more precise control for Δeff to achieve the optimal steady-state squeezing of the mechanical resonator with the temperature rising constantly.

Bottom Line: Quantum squeezing of mechanical resonator is important for studying the macroscopic quantum effects and the precision metrology of weak forces.The validity of the scheme is assessed by simulating the steady-state variance of the mechanical displacement quadrature numerically.The scheme is robust against dissipation of the optical cavity, and the steady-state squeezing can be effectively generated in a highly dissipative cavity.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, College of Science, Yanbian University, Yanji, Jilin 133002, China.

ABSTRACT
Quantum squeezing of mechanical resonator is important for studying the macroscopic quantum effects and the precision metrology of weak forces. Here we give a theoretical study of a hybrid atom-optomechanical system in which the steady-state squeezing of the mechanical resonator can be generated via the mechanical nonlinearity and cavity cooling process. The validity of the scheme is assessed by simulating the steady-state variance of the mechanical displacement quadrature numerically. The scheme is robust against dissipation of the optical cavity, and the steady-state squeezing can be effectively generated in a highly dissipative cavity.

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