The system of a trapped ion translationally excited by a blue-detuned near-resonant laser, sometimes described as an instance of a phonon laser, has recently received attention as interesting in its own right and for its application to non-destructive readout of internal states of non-fluorescing ions. Previous theoretical work has been limited to cases of two-level ions. Here, we perform simulations to study the dynamics of a phonon laser involving the $\Lambda$ -type $^{138}\mbox{Ba}^{+}$ ion, in which coherent population trapping effects lead to different behavior than in the previously studied cases. We also explore optimization of the laser parameters to maximize amplification gain and signal-to-noise ratio for internal state readout.The system of a trapped ion translationally excited by a blue-detuned near-resonant laser, sometimes described as an instance of a phonon laser, has recently received attention as interesting in its own right and for its application to non-destructive readout of internal states of non-fluorescing ions. Previous theoretical work has been limited to cases of two-level ions. Here, we perform simulations to study the dynamics of a phonon laser involving the $\Lambda$-type $^{138}\mbox{Ba}^{+}$ ion, in which coherent population trapping effects lead to different behavior than in the previously studied cases. We also explore optimization of the laser parameters to maximize amplification gain and signal-to-noise ratio for internal state readout.

Aug 14, 20162 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

An ion-trap phonon laser

K.J. Vahala, M. G. Herrmann, S. Knünz +4 more

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.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.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)Jun 1, 20090 citations

Phonon Lasing from Optical Frequency Comb Illumination of Trapped Ions

Michael Ip, Anthony Ransford, Andrew M. Jayich +3 more

We demonstrate the use of a frequency-doubled optical frequency comb to load, cool, and crystallize trapped atomic ions as an alternative to ultraviolet (UV) or even deep UV continuous-wave lasers. We find that the Doppler shift from the atom's oscillation in the trap, driven by the blue-detuned comb teeth, introduces additional cooling and amplification which gives rise to steady-state phonon lasing of the ion's harmonic motion in the trap. The phonon laser's gain saturation keeps the optical frequency comb from continually adding energy without bound. This protection allows us to demonstrate loading and crystallization of hot ions directly with the comb, eliminating the need for a continuous-wave cooling laser, a technique that is extendable to the deep UV.We demonstrate the use of a frequency-doubled optical frequency comb to load, cool, and crystallize trapped atomic ions as an alternative to ultraviolet (UV) or even deep UV continuous-wave lasers. We find that the Doppler shift from the atom's oscillation in the trap, driven by the blue-detuned comb teeth, introduces additional cooling and amplification which gives rise to steady-state phonon lasing of the ion's harmonic motion in the trap. The phonon laser's gain saturation keeps the optical frequency comb from continually adding energy without bound. This protection allows us to demonstrate loading and crystallization of hot ions directly with the comb, eliminating the need for a continuous-wave cooling laser, a technique that is extendable to the deep UV.

arXiv:1711.11156Physical Review LettersJul 25, 201826 citations

Transient fluorescence with a single trapped ion

Nicolás A. Nuñez Barreto, Lucas Giardino, Carla Crucianelli +3 more

In this paper, we present a method to measure transient fluorescent dynamics with single trapped ions in a Paul trap. We use 40 Ca + ions that exhibit a Λ-type three-level system and measure the characteristic optical pumping times between the ground S 1/2 and the meta-stable D 3/2 levels. We prepare one of these states and then pump it to the opposite via the excited P 1/2 state. By measuring the scattered photons of the ion, we retrieve transient curves of the atomic fluorescence. These curves provide fundamental information about the atomic system, such as branching fractions and excited-state lifetimes, as well as experimental parameters like the efficiency of the detection system and the saturation parameter of one of the transitions. Finally, we study the time-dependent fluorescence as a function of optical power and detuning of the lasers and find a very good agreement with simulating the dynamics via a three-level open quantum system through a set of optical Bloch equations. Being able to record time-dependent fluorescence is of particular interest as it contains information about the temperature, cooling, and heating dynamics of the ion.In this paper, we present a method to measure transient fluorescent dynamics with single trapped ions in a Paul trap. We use 40 Ca + ions that exhibit a Λ-type three-level system and measure the characteristic optical pumping times between the ground S 1/2 and the meta-stable D 3/2 levels. We prepare one of these states and then pump it to the opposite via the excited P 1/2 state. By measuring the scattered photons of the ion, we retrieve transient curves of the atomic fluorescence. These curves provide fundamental information about the atomic system, such as branching fractions and excited-state lifetimes, as well as experimental parameters like the efficiency of the detection system and the saturation parameter of one of the transitions. Finally, we study the time-dependent fluorescence as a function of optical power and detuning of the lasers and find a very good agreement with simulating the dynamics via a three-level open quantum system through a set of optical Bloch equations. Being able to record time-dependent fluorescence is of particular interest as it contains information about the temperature, cooling, and heating dynamics of the ion.

arXiv:2303.00650Journal of the Optical Society of America BFeb 8, 20231 citation

Prototype of a phonon laser with trapped ions

Chen-Yu Lee, Kuan-Ting Lin, Guin-Dar Lin

We propose a tunable phonon laser prototype with a large trapped ion array, where some of the ions are effectively pinned by optical tweezers, thus isolating a subset of ions that mimics an acoustic cavity used as a phonon lasing resonator. The cavity loss can then be controlled by the tweezer strength and the ``wall thickness'', the number of pinned ions for isolation. We pump the resonator by applying blue-sideband lasers, and investigate the lasing dynamics of the ``cavity'' motional modes such as threshold behavior, population distribution, the second-order coherence, and linewidth narrowing. This scheme can be generalized to multimode resonators, for which we report the mode competition phenomenon and lasing mode multistability. Our work provides an excellent platform for acoustic quantum state manipulation, paving the way towards phonon-mediated quantum computing, communications, and metrology.We propose a tunable phonon laser prototype with a large trapped ion array, where some of the ions are effectively pinned by optical tweezers, thus isolating a subset of ions that mimics an acoustic cavity used as a phonon lasing resonator. The cavity loss can then be controlled by the tweezer strength and the ``wall thickness'', the number of pinned ions for isolation. We pump the resonator by applying blue-sideband lasers, and investigate the lasing dynamics of the ``cavity'' motional modes such as threshold behavior, population distribution, the second-order coherence, and linewidth narrowing. This scheme can be generalized to multimode resonators, for which we report the mode competition phenomenon and lasing mode multistability. Our work provides an excellent platform for acoustic quantum state manipulation, paving the way towards phonon-mediated quantum computing, communications, and metrology.

arXiv:2011.08051Physical Review ResearchMay 8, 20238 citations

\Lambda

-type $^{138}\mbox{Ba}^{+}$ ion, in which coherent population trapping effects lead to different behavior than in the previously studied cases. We also explore optimization of the laser parameters to maximize amplification gain and signal-to-noise ratio for internal state readout.