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arXiv:2301.08156 · Physical Review Letters

Phonon Laser in the Quantum Regime

Tanja Behrle, Thanh Long Nguyen, Florentin Reiter, D. Baur, Brennan de Neeve, M. Stadler, Matteo Marinelli, F. Lancellotti, Susanne F. Yelin, Jonathan Home

Published Jul 28, 2023• 36 citations
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Abstract

We demonstrate a trapped-ion system with two competing dissipation channels, implemented independently on two ion species cotrapped in a Paul trap. By controlling coherent spin-oscillator couplings and optical pumping rates we explore the phase diagram of this system, which exhibits a regime analogous to that of a (phonon) laser but operates close to the quantum ground state with an average phonon number of n[over ¯]<10. We demonstrate phase locking of the oscillator to an additional resonant drive, and also observe the phase diffusion of the resulting state under dissipation by reconstructing the quantum state from a measurement of the characteristic function.

DOI
10.1103/physrevlett.131.043605

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We demonstrate a trapped-ion system with two competing dissipation channels, implemented independently on two ion species cotrapped in a Paul trap. By controlling coherent spin-oscillator couplings and optical pumping rates we explore the phase diagram of this system, which exhibits a regime analogous to that of a (phonon) laser but operates close to the quantum ground state with an average phonon number of n[over ¯]<10. We demonstrate phase locking of the oscillator to an additional resonant drive, and also observe the phase diffusion of the resulting state under dissipation by reconstructing the quantum state from a measurement of the characteristic function.
We demonstrate a trapped-ion system with engineered competing dissipation channels, implemented independently on two ion species co-trapped in a Paul trap. We use control of the spin-oscillator couplings via motional sideband drives and engineered decay rates via optical pumping to explore the phase diagram of this system, which is analogous to that of a (phonon) laser. Reconstruction of the phonon distribution via the readout of the motional sideband oscillation allows us to show the phase transition from a dark to the bright and coherent lasing phase. In contrast to earlier work [1] our laser works close to the quantum ground state with average phonon numbers below ten. In the lasing phase, we demonstrate phase locking of the oscillator to an additional resonant drive. We use readout of the characteristic function [2] to show symmetry breaking of the Wigner function when locked. We also observe the intrinsic phase diffusion of the lasing process starting from a displaced coherent state. The readout of the characteristic function once again shows washing out of the initial asymmetry. The toolbox of techniques is extensible to squeezed laser systems through the use of additional laser drives, is predicted to offer advantages in sensing [3], and provides methods for the general use of the mixed-ion-species platform in the simulation of dissipative spin-boson systems.
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.
We explore trapped ions as a setting to investigate nonequilibrium phases in a generalized Dicke model of dissipative spins coupled to phonon modes. We find a rich dynamical phase diagram including superradiantlike regimes, dynamical phase coexistence, and phonon-lasing behavior. A particular advantage of trapped ions is that these phases and transitions among them can be probed in situ through fluorescence. We demonstrate that the main physical insights are captured by a minimal model and consider an experimental realization with Ca+ ions trapped in a linear Paul trap with a dressing scheme to create effective two-level systems with a tunable dissipation rate.
Cooling of atoms and ions using a red-detuned laser has had a profound impact on science and technology. In this work simultaneous laser cooling and blue-detuned laser pumping of a Mg+ ion in a Paul trap is studied. Blue-detuned pumping is conventionally referred to as the heating regime, and in early work, remarkably complex behaviors (bistability and limit cycles) have been associated with this regime. These behaviors have so far not been fully explained. Here, it is shown that blue-detuned pumping, as opposed to heating, causes stimulated emission of center-of-mass phonons, leading to coherent oscillatory motion of the ion in analogy with a laser. Mechanical amplification is calculated as well as the threshold pumping condition for oscillation. A single ion in a linear radio-frequency trap is studied to verify these predictions. Blue-detuned pumping of the magnesium D2 transition at 279.6 nm provides amplification along the long axis of the ion trap so as to excite only axial oscillations. A slightly off-axis, red-detuned beam cools the center-of-mass motion to approximately 1 mK.
In this article we present a comprehensive theoretical investigation of phonon lasing with mixed-species trapped ions, as demonstrated in [T. Behrle, Phys. Rev. Lett. 131 (2023)], employing both a semi-classical mean-field description and a full quantum theory. We derive an analytic expression for the second-order coherence function, confirming the experimental observation of the system's lasing behaviour above threshold. Building on the successful implementation of the two-ion lasing scheme, we propose a novel approach for achieving phonon lasing with a single trapped ion, offering significant experimental advantages and making the implementation of multiple phonon lasers within a single setup feasible. Furthermore, we explore lasing in a squeezed basis and in different regimes of the Lamb-Dicke approximation, highlighting the potential to produce non-classical states with promising applications in precision sensing. Our analysis of a sensing protocol based on squeezed states, using experimentally feasible parameters, shows a sensitivity enhancement of up to two orders of magnitude.
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 QQQ-switched pulsed phonon lasing and the potential application.