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In trapped ion systems, single-ion phonon lasers based on the van der Pol oscillator mechanism have been applied in fields such as weak electric field measurement and weak force detection. As a coherent source analogous to photon lasers, phonon lasers precisely control the vibrational states of the ions through sideband excitation and cooling techniques, aiming to further extend their applications to areas such as continuous-variable quantum computing, quantum nonlinear dynamics, and quantum precision measurement. This paper presents a theoretical study of single-ion phonon laser in the quantum regime using a three-level model. By solving the master equation, we obtain the steady-state phase diagram for generating the phonon laser and analyze the system's Wigner quasi-probability distribution and second-order correlation properties. Based on the ion trap system, this paper proposes an experimental scheme, namely, using a bichromatic light field composed of a blue-sideband laser and a red-sideband laser acting on a trapped40Ca+ ion, thereby generating a phonon laser in the quantum regime. The vibrational quantum state is then characterized using the characteristic function measurement method.
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Keywords:
- Trapped ions /
- Wigner function /
- phonon laser
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