Ground-state cooling of mechanical resonator in double optical cavity
Authors: Liu Ni , Wang Jian-Fen , Liang Jiu-Qing ,   State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China
Published: December 2020

<sec>The ground-state cooling of mechanical resonator is one of the fundamental problems in cavity quantum photomechanics. The so-called ground-state cooling is to make the number of steady-state phonons of the mechanical resonator less than one. In this paper, we first propose an electromagnetically-induced-transparency-like cooling mechanism in a double-cavity optomechanical system to cool a mechanical resonator. In the double-optical cavity optomechanical system, the right additional cavity, which is directly coupled to a standard optomechanical system, contains an ultra-cold two-level atomic ensemble. By selecting the optimal parameters to meet the cooling process of the mechanical resonator corresponding to the maximum value of the optical fluctuation spectrum and the heating process of the mechanical resonator corresponding to the minimum value of the optical fluctuation spectrum, the mechanical resonator can be cooled by monitoring the phonon number. We also exert the effects of the atomic additional cavity on the quantum Langevin equations and optical fluctuation spectrum. We find that the atomic double-cavity system may have a better ground-state cooling than the double-cavity in certain parameters.</sec><sec>To date, the researchers have proposed a number of theoretical cooling schemes in order to achieve the ground-state cooling of mechanical resonator. As far as we know, the sideband cooling for just a standard optomechanical system is a most famous scheme and the mechanical resonator is coupled to the optical field via radiation pressure force. By the quantum theory of mechanical resonator’s sideband cooling, the optical fluctuation spectrum determines the transition rate of both cooling and heating process of the mechanical resonator. That’s to say, the optical fluctuation spectrum at a mechanical resonator frequency <i>ω</i><sub>m</sub> is corresponding to the cooling transition, whereas the optical fluctuation spectrum at –<i>ω</i><sub>m</sub> is corresponding to the heating transition. They respectively correspond to anti-Stokes and Stokes effect in physics. Under resolvable sideband conditions, the optical field’s decay rate (the half-width of the single Lorentzian peak of optical fluctuation spectrum) is less than the frequency of the mechanical resonator. So, the ground-state cooling of the mechanical resonator can be obtained by making the maximum and minimum value of the optical fluctuation spectrum respectively correspond to the cooling anti-Stokes process and heating Stokes process.</sec><sec>In this paper, we mainly observe the electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system with an ensemble of two-level atoms. By adjusting the maximum and minimum value of the optical fluctuation spectrum at the position of <i>ω</i> = <i>ω</i><sub>m</sub> and <i>ω</i> = –<i>ω</i><sub>m</sub>, the mechanical resonator could be cooled down approximately to the ground state. Even when there exists an ensemble of two-level atoms in the right additional cavity, the mechanical resonator can be better cooled than just a cavity. These results may be conducive to the ground-state cooling of the mechanical resonator in the future experiment.</sec>