In a sequence of single spins interacting longitudinally with a mechanical oscillator, and using the micromaser model with random injection, we show that after an appropriate postselection of each spin, a phonon laser analog with Poisson statistics is created with nearly perfect coherence, evidenced by the second order coherence function that goes asymptotically to one. The nonlinear gain of the system depends crucially on the properly postselected spin state as well as the pump. Our model and results suggest that the mechanism of interaction followed by a postselected state or partial trace (common in laser and maser theory) of the spins may create the coherent vibrational radiation. However, for situations where the mechanical losses are high and it is impossible to decrease these, then the heralded postselection can be the only resource to get phonon lasing if compared to the partial trace operation. These ideas and results may be useful for further theoretical and technical developments.
In a sequence of single spins interacting longitudinally with a mechanical oscillator, and using the micromaser model with random injection, we show that after an appropriate postselection of each spin, a phonon laser analog with Poisson statistics is created with nearly perfect coherence, evidenced by the second order coherence function that goes asymptotically to one. The nonlinear gain of the system depends crucially on the properly postselected spin state as well as the pump. Our model and results suggest that the mechanism of interaction followed by a postselected state or partial trace (common in laser and maser theory) of the spins may create the coherent vibrational radiation. However, for situations where the mechanical losses are high and it is impossible to decrease these, then the heralded postselection can be the only resource to get phonon lasing if compared to the partial trace operation. These ideas and results may be useful for further theoretical and technical developments.
Quantum mechanical oscillators operating at frequencies up to the GHz regime have been predicted to support phonon lasing -- self-sustained coherent vibrational motion emerging when the effective gain exceeds intrinsic losses. Current phonon-laser proposals face two key limitations, namely: they lack scalability and rely on coupling all oscillators to a common field, which significantly restricts flexibility and prevents selective, on-demand phonon lasing at specific locations. Given that numerous applications and theoretical insights naturally emerge from scalable many-body systems, addressing these limitations is timely. In this Letter, we demonstrate how scalable arrays of individually addressable phonon lasers can be generated through local driving in a quantum many-body Ising-like spin chain. We rigorously establish the resonance conditions under which mechanical oscillators transition from thermal motion to sustained coherent self-oscillation. Unlike previous approaches that rely on a common coupling bus, our proposal employs purely local driving, resulting in an inherently modular and scalable architecture ideally suited for integration into large-scale quantum systems. Additionally, our approach enables on-demand lasing of individual mechanical oscillators at specific sites by simply switching the spin-mechanical coupling interaction on and off, provided specific resonance conditions are satisfied. Notably, our phonon laser array is robust against resonance mismatches and naturally exhibits both pairwise self-organized synchronization and global phase locking near resonance. Finally, we outline an experimental implementation within current experimental capabilities.
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.
Macroscopic quantum superposition states are fundamental to test the classical-quantum boundary and present suitable candidates for quantum technologies. Although the preparation of such states has already been realized, the existing setups commonly consider external driving and resonant interactions, predominantly by considering Jaynes-Cummings-like and beam-splitter-like interactions, as well as the nonlinear radiation pressure interaction in cavity optomechanics. In contrast to previous works on the matter, we propose a feasible probabilistic scheme to generate a macroscopic mechanical qubit, as well as phononic Schr\"odinger's cat states with no need of any energy exchange with the macroscopic mechanical oscillator. Essentially, we investigate an open dispersive spin-mechanical system in the absence of any external driving under nonideal conditions, such as the detrimental effects due to the oscillator and spin energy losses in a thermal bath at nonzero temperature. In our work, we show that the procedure to generate the mechanical qubit state is solely based on spin postselection in the weak to moderate coupling regime. Finally, we demonstrate that the mechanical superposition is related to the amplification of the mean values of the mechanical quadratures as they maximize the quantum coherence.
Applied Physics
Optomechanical systems typically consist of a mechanical oscillator or cantilever that can be driven by the optical radiation pressure of light. The light can either amplify the motion of the cantilever or be used to reduce the amount of vibration and effectively cool it. Recent work has demonstrated cooling to the extent that the number of vibrations, or phonons, in an oscillator can be quantized, even reaching the quantum-mechanical ground. Galland et al. introduce a method to introduce a single phonon into their mechanical oscillator. Starting off in the quantum-mechanical ground, they pump the system with a laser pulse that generates an entangled phonon-photon pair. Detection of the photon then heralds that a single-phonon state has been induced into the oscillator. The ability to deterministically control the number of vibrational quanta in such an optomechanical system has important implications for the likes of quantum information processing and quantum enhanced sensing applications.
Phys. Rev. Lett. 112 , 143602 (2014).
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.
We present a theory which can explain the micromaser as well as its optical counterpart, the microlaser, for appropriate values of dissipative parameters. We show that, in both the the cases, the cavity radiation fields can have sub-Poissonian photon statistics. We further analyse if it is possible to attain a Fock state of the radiation field. The microlaser is precluded for such analysics due to the damping of its lasing levels making transitions at optical frequencies. Hence, we focus our attention on the micromaser and our exact simulation of the dynamics shows that it is not possible to generate a Fock state of the cavity radiation field.