Photonics Research, 2023, 11 (9): A26, Published Online: Aug. 28, 2023  

Optomechanical preparation of photon number-squeezed states with a pair of thermal reservoirs of opposite temperatures

Author Affiliations
1 State Key Laboratory of Precision Spectroscopy, Department of Physics, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
2 Shanghai Branch, Hefei National Laboratory, Shanghai 201315, China
3 School of Physics and Astronomy, and Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
4 Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
5 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
Figures & Tables

Fig. 1. (a) Diagram of the population jump rates between neighboring Fock states. (b) Eigenvalues of the dissipation rate operators κn^± versus number n. (c) Number statistics distribution of the steady state. The probability Pn increases versus n in the region dominated by the negative-temperature dissipation and decays in the rest region dominated by the positive-temperature one, so a peak appears in the intermediate region.

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Fig. 2. (a) Cavity optomechanical scheme of feedback control. The optical cavity is coupled to the mechanical oscillator through dispersive and dissipative optomechanical interactions simultaneously. With the dispersive coupling, the oscillator undergoes a shift proportional to the radiation pressure force, i.e., to the photon number, and then changes the cavity dissipation rate κx^+ through the dissipative coupling. Except for the optomechanical dissipation, the cavity mode has a gain of rate κ induced by the negative-temperature reservoir, and the oscillator is subjected to Brownian thermal noise. The high frequency of the optical mode makes our near-zero temperature assumption reasonable. (b) Dissipation control protocol. The positive-temperature dissipation rate κx^+ is smaller than the negative-temperature one in the region x<L but increases rapidly and overtakes it in the region x>L. The steep change occurs mainly in a region of width d.

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Fig. 3. Steady-state photon number statistics obtained by approximate solution [Eq. (13)] and numerical simulation of the master equation [Eq. (7)]. (a) Photon number fluctuation Δn versus dissipation ratio γ/κ. The approximate solution is plotted in a red solid line, whereas, the numerical results are marked with a “+.” (b) Numerical results for the steady-state probability distribution of photon number for increasing γ/κ. All results for g0=7.07×102ωm, (κ0,κ,κv)=(101,102,103)ωm, and (d,L)=(14,7×104)xzpf.

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Table1. Experimental Parameters and Ideal Squeezing Degrees for Several Representative Optomechanical Systems

Setupmeff (kg)ωm/2π (Hz)g0/2π (Hz)x1 (nm)d (nm)L (nm)Δnn¯Δn2/n¯ (dB)
Micromirror [79]1.1×10109.7×103221.27×1082.48*50 [80]7×1034×109−19
SiN membrane [76]1×10101.03×1050.571×10112.48100 [81]2.5×1051×1013−22
Micro-disk [82]2×10152.5×107262.6×10110.040.02 [83]1.9×1047.7×108−3
Levitated particle [84]2.8×10183×1053 [85,86]6.3×1080.3*30 [87,88]1.1×1034.8×108−26
Photonic crystal [89]4×10164.9×1061.3×1053.5×106101008.4×1022.9×107−16
Cold atomic gases [90]2.4×10227×1043.5×1067025*25000.334.8−26


Baiqiang Zhu, Keye Zhang, Weiping Zhang. Optomechanical preparation of photon number-squeezed states with a pair of thermal reservoirs of opposite temperatures[J]. Photonics Research, 2023, 11(9): A26.

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