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arXiv:0911.4916 · Europhysics Letters (EPL)

A phonon laser in ultra-cold matter

José Tito Mendonça, Hugo Terças, Gert Brodin, M. Marklund

Published Aug 1, 2010• 27 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1209/0295-5075/91/33001

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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.
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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 study the spectrum of density fluctuations in the ultra-cold gas of neutral atoms, confined in a magneto-optical trap. We determine the corresponding amplitude and spectra of laser light scattered by this medium. We derive an expression for the dynamical structure function, by using a test particle method. We propose to use the collective laser scattering as a diagnostic method for the microscopic properties of the ultra-cold matter. This will also allow us to check on the atomic correlations which are mediated by the collective mean field inside the gas.
Here we discuss collective processes and plasma effects that can be found in ultra‐cold matter. First, we consider the ultra‐cold atomic gas that can be produced in a magneto‐optical trap. Due to the existence of long‐range repulsive forces, new collective oscillation can take place, resembling sound waves but with a cut‐off frequency. We also examine new phenomena in Rydberg plasmas, resulting from laser ionization of the ultra‐cold gas. In these very low temperature plasmas a large amount of excited Rydberg states can exist, leading to a new dispersion relation for the electromagnetic waves. Enhanced magnetic field generation will also be considered. Finally, we discuss the collective properties of Bose Einstein condensates, showing a strong analogy with collective plasma processes. Two related examples are given as an illustration: Bogoliubov oscillations in the condensate, and two‐stream instabilities of counter‐streaming BECs.