We show the possible excitation of a phonon laser instability in an ultra-cold atomic gas confined in a magneto-optical trap. Such an effect results from a negative Landau damping of the collective density perturbations in the gas, leading to the coherent emission of phonons. This laser instability can be driven by a blue-detuned laser superimposed to the usual red-detuning laser beams which usually provide the cooling mechanism. Threshold conditions, instability growth rates and saturation levels are derived. This work generalizes, on theoretical grounds, the recent results obtained with a single-ion phonon laser, to an ultra-cold atomic gas, where real phonons can be excited. Future phonon lasers could thus adequately be called phasers.We show the possible excitation of a phonon laser instability in an ultra-cold atomic gas confined in a magneto-optical trap. Such an effect results from a negative Landau damping of the collective density perturbations in the gas, leading to the coherent emission of phonons. This laser instability can be driven by a blue-detuned laser superimposed to the usual red-detuning laser beams which usually provide the cooling mechanism. Threshold conditions, instability growth rates and saturation levels are derived. This work generalizes, on theoretical grounds, the recent results obtained with a single-ion phonon laser, to an ultra-cold atomic gas, where real phonons can be excited. Future phonon lasers could thus adequately be called phasers.

arXiv:0911.4916Europhysics Letters (EPL)Aug 1, 201027 citations

Single-ion phonon laser in the quantum regime

Dong Yuanzhang, He Siwen, Deng Zhijiao +3 more

The quantum phonon laser state is a vibrational state generated by phonon coherent amplification based on quantum mechanics. Its core is coherent excitation and manipulation of phonon quantum states by controlling phonon dynamics. This technology breaks classical limits of traditional phonon lasers, offering new methods for quantum information. Previous research on quantum phonon lasers focused on quantum van der Pol oscillators. As typical nonlinear quantum systems, they show significant value in trapped-ion systems. These breakthroughs extend nonlinear dynamics into the quantum domain and provide platforms for exploring quantum nonlinear phenomena. Although realized in two-ion systems, practical applications remain challenging. This paper explores how a single trapped ion generates quantum phonon laser states using a three-level model. By solving the quantum master equation numerically, steady-state characteristics are analyzed, focusing on quantum statistics including the Wigner function and second-order correlation function. An experimental scheme is proposed based on a single trapped 40Ca+ ion, using bichromatic blue-sideband and red-sideband lasers to generate quantum phonon laser states. By introducing the characteristic function of motional states, precise quantum state tomography is achieved. Additionally, a two-level model discusses the phonon laser threshold effect. However, the three-level model shows significantly different thresholds and more accurately describes the quantum phonon laser's physical mechanisms.The quantum phonon laser state is a vibrational state generated by phonon coherent amplification based on quantum mechanics. Its core is coherent excitation and manipulation of phonon quantum states by controlling phonon dynamics. This technology breaks classical limits of traditional phonon lasers, offering new methods for quantum information. Previous research on quantum phonon lasers focused on quantum van der Pol oscillators. As typical nonlinear quantum systems, they show significant value in trapped-ion systems. These breakthroughs extend nonlinear dynamics into the quantum domain and provide platforms for exploring quantum nonlinear phenomena. Although realized in two-ion systems, practical applications remain challenging. This paper explores how a single trapped ion generates quantum phonon laser states using a three-level model. By solving the quantum master equation numerically, steady-state characteristics are analyzed, focusing on quantum statistics including the Wigner function and second-order correlation function. An experimental scheme is proposed based on a single trapped 40Ca+ ion, using bichromatic blue-sideband and red-sideband lasers to generate quantum phonon laser states. By introducing the characteristic function of motional states, precise quantum state tomography is achieved. Additionally, a two-level model discusses the phonon laser threshold effect. However, the three-level model shows significantly different thresholds and more accurately describes the quantum phonon laser's physical mechanisms.

quant-pharXiv:2603.01585Mar 3, 2026

Phonon Propagator

Fabrizio Tafuri, C. A. Perroni, G. De Filippis

UNITEXT for physicsJan 1, 20260 citations

Finite-Time Electrometry with a Quantum-Regime Single-Ion Phonon Laser

Pei-Dong Li, Yuan-Zhang Dong, Zhuo-Zhu Wu +6 more

The phonon laser realized in a trapped ion, i.e., a self-sustained mechanical oscillator, has demonstrated the unique characteristics in practically detecting externally applied electric signals without the prerequisite of sideband cooling. Entering the quantum regime via sideband cooling is expected to further improve its sensing performance. Here we report the first experimental realization of a quantum-regime single-ion phonon laser ( $\bar{n}<10$ ) using a trapped $^{40}\mathrm{Ca}^+$ ion and demonstrate electrometry based on its phase-space symmetry-breaking response to weak resonant electric fields. By tuning the phonon-laser parameters, we reveal that the sensing performance is fundamentally governed by the finite-time relaxation dynamics of the underlying open quantum system. We find that a slow Liouvillian relaxation, correlated with the finite experimental interaction window, effectively enhances the dynamic susceptibility while maintaining the structural robustness of the limit cycle. This regime, when applied to the detection of electric fields, produces a shot-noise-limited peak sensitivity of $14.15 \pm 0.77~μ\mathrm{V/m}/\sqrt{\mathrm{Hz}}$ and a minimum detectable field variation of $δE_{\mathrm{min}} \approx 1.83~μ\mathrm{V/m}$ . Our results establish quantum phonon lasers as a practical platform for advanced sensing and highlight the central role of Liouvillian dynamics in non-equilibrium electrometry.The phonon laser realized in a trapped ion, i.e., a self-sustained mechanical oscillator, has demonstrated the unique characteristics in practically detecting externally applied electric signals without the prerequisite of sideband cooling. Entering the quantum regime via sideband cooling is expected to further improve its sensing performance. Here we report the first experimental realization of a quantum-regime single-ion phonon laser ($\bar{n}<10$) using a trapped $^{40}\mathrm{Ca}^+$ ion and demonstrate electrometry based on its phase-space symmetry-breaking response to weak resonant electric fields. By tuning the phonon-laser parameters, we reveal that the sensing performance is fundamentally governed by the finite-time relaxation dynamics of the underlying open quantum system. We find that a slow Liouvillian relaxation, correlated with the finite experimental interaction window, effectively enhances the dynamic susceptibility while maintaining the structural robustness of the limit cycle. This regime, when applied to the detection of electric fields, produces a shot-noise-limited peak sensitivity of $14.15 \pm 0.77~μ\mathrm{V/m}/\sqrt{\mathrm{Hz}}$ and a minimum detectable field variation of $δE_{\mathrm{min}} \approx 1.83~μ\mathrm{V/m}$. Our results establish quantum phonon lasers as a practical platform for advanced sensing and highlight the central role of Liouvillian dynamics in non-equilibrium electrometry.

quant-pharXiv:2606.21068Jun 22, 20260 citations

Pulsed phonon lasing in trapped ions

Yi Xie, Wei Wan, Hao Wu +3 more

Optical laser pulses play important roles in various fields, and the phononlike analog, i.e., phonon laser pulses, should also be very useful. We show the possibility of pulsed phonon lasing in trapped ions based on our observation that coherent phonon pulses are generated and then transferred between transverse dimensions due to nonlinear resonance once the oscillation amplitude of the trapped ions is larger than a threshold. We study the pulsed phonon output with the multiple-scale method using the first-order nonlinear differential equations which govern time evolution of the amplitudes and phases of the interacting modes. We also discuss the feasibility of $Q$ -switched pulsed phonon lasing and the potential application.Optical laser pulses play important roles in various fields, and the phononlike analog, i.e., phonon laser pulses, should also be very useful. We show the possibility of pulsed phonon lasing in trapped ions based on our observation that coherent phonon pulses are generated and then transferred between transverse dimensions due to nonlinear resonance once the oscillation amplitude of the trapped ions is larger than a threshold. We study the pulsed phonon output with the multiple-scale method using the first-order nonlinear differential equations which govern time evolution of the amplitudes and phases of the interacting modes. We also discuss the feasibility of $Q$-switched pulsed phonon lasing and the potential application.

Physical Review AMay 6, 201313 citations

\bar{n}<10

) using a trapped

^{40}\mathrm{Ca}^+

ion and demonstrate electrometry based on its phase-space symmetry-breaking response to weak resonant electric fields. By tuning the phonon-laser parameters, we reveal that the sensing performance is fundamentally governed by the finite-time relaxation dynamics of the underlying open quantum system. We find that a slow Liouvillian relaxation, correlated with the finite experimental interaction window, effectively enhances the dynamic susceptibility while maintaining the structural robustness of the limit cycle. This regime, when applied to the detection of electric fields, produces a shot-noise-limited peak sensitivity of

14.15 \pm 0.77~μ\mathrm{V/m}/\sqrt{\mathrm{Hz}}

and a minimum detectable field variation of

δE_{\mathrm{min}} \approx 1.83~μ\mathrm{V/m}

. Our results establish quantum phonon lasers as a practical platform for advanced sensing and highlight the central role of Liouvillian dynamics in non-equilibrium electrometry.

Q

-switched pulsed phonon lasing and the potential application.