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arXiv:1003.1577 · Physical Review A

Single-ion nonlinear mechanical oscillator

N. Akerman, Shlomi Kotler, Yinnon Glickman, Yehonatan Dallal, Anna Keselman, Roee Ozeri

Published Dec 16, 2010• 44 citations
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Abstract

We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.

DOI
10.1103/physreva.82.061402

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We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.
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We discuss laser cooling of a string of two-level atoms confined in a linear ion trap. The equations for the dynamics are first analysed in the Lamb–Dicke regime (i.e. when the size of the mechanical wavefunction is much smaller than the laser wavelength), and then in general, for Doppler cooling. In the latter case, using several consecutive steps of averaging we derive from the full quantum mechanical master equation an equation for the total mechanical energy of the one-dimensional crystal, defined on a coarse-grained energy scale whose grid size is smaller than the linewidth of the electronic transition. This equation describes the cooling dynamics for an arbitrary number of ions in the quantum regime. We discuss the analogy and the scalability of the string's laser-cooling dynamics with that of a single trapped ion.
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.
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