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arXiv:2208.07394 · Physical Review Research

Continuous Raman sideband cooling beyond the Lamb-Dicke regime in a trapped ion chain

Qiming Wu, Yuejiang Shi, Jiehang Zhang

Published Apr 13, 2023• 11 citations
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Abstract

We report continuous Raman sideband cooling of a long ion chain close to the motional ground state beyond the Lamb-Dicke (LD) regime. By driving multiple sideband transitions simultaneously, we show that nearly all axial modes of a 24-ion chain are cooled to the ground state, with an LD parameter as large as $\ensuremath{\eta}=1.3$, spanning a frequency bandwidth of 4 MHz. Compared to traditional ground-state cooling methods such as pulsed sideband cooling or electromagnetically-induced-transparency cooling, our method offers two key advantages: disposal of pulse optimization, and a wide bandwidth covering the entire spectrum. This technique contributes as a crucial step for large-scale quantum information processing with linear ion chains and higher dimensions alike, and can be readily generalized to other atomic and molecular systems.

DOI
10.1103/physrevresearch.5.023022

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We report continuous Raman sideband cooling of a long ion chain close to the motional ground state beyond the Lamb-Dicke (LD) regime. By driving multiple sideband transitions simultaneously, we show that nearly all axial modes of a 24-ion chain are cooled to the ground state, with an LD parameter as large as \ensuremathη=1.3\ensuremath{\eta}=1.3\ensuremathη=1.3, spanning a frequency bandwidth of 4 MHz. Compared to traditional ground-state cooling methods such as pulsed sideband cooling or electromagnetically-induced-transparency cooling, our method offers two key advantages: disposal of pulse optimization, and a wide bandwidth covering the entire spectrum. This technique contributes as a crucial step for large-scale quantum information processing with linear ion chains and higher dimensions alike, and can be readily generalized to other atomic and molecular systems.
We present the results of simulations of optical sideband cooling of atomic ions in a trap with a shallow potential well. In such traps, an ion cannot be Doppler cooled near to the Lamb-Dicke regime $\mathrm{[}{\ensuremath{\eta}}^{2}(2\ensuremath{\langle}n\ensuremath{\rangle}+1)\ensuremath{\ll}1]$. Outside the Lamb-Dicke regime, the sideband cooling dynamics are altered by the existence of various Fock states with weak coupling where the cooling becomes very slow. A 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion trapped in our Penning trap realizes such a situation; hence single stage cooling is inefficient to prepare the ion in the motional ground state. For these systems, it is necessary to study the cooling dynamics in detail and we show that it is possible to implement an optimized cooling sequence to achieve efficient ground-state cooling. We also present the simulated cooling dynamics of two ions trapped in a Penning trap, where the presence of an additional motional mode requires a complicated cooling sequence in order to cool both axial modes to the ground state simultaneously. Additionally, we demonstrate the dissipative preparation of Fock states outside the Lamb-Dicke regime by sideband heating a single ion in a Penning trap.
Summary form only given. The preparation of quantum systems in pure states is a prerequisite for coherent control. In this context laser cooling of trapped particles to the ground state of the confining potential is a powerful tool for preparing e.g. ions for quantum logic. In particular sideband cooling has been demonstrated to be the most efficient technique, allowing to achieve more than 99% of occupation of the ground state of the trap. This cooling technique relies on two conditions: the Lamb-Dicke regime, and the strong confinement regime. This latter condition, which allows the spectral resolution of individual sidebands of the motion, is however a limitation on the cooling time. We propose a model for cooling single ions inside a trap as an alternative to sideband cooling. The scheme uses electromagnetically induced transparency (EIT) in a /spl Lambda/-level scheme, where one of the transitions is dressed by a strong laser field. For detuning of the dressing laser, the absorption spectrum for the transition shows EIT when the cooling (probe) laser has detuning. Then, by tuning the cooling laser on the dark resonance (or EIT), for a suitable set of parameters and in the Lamb-Dicke regime the atoms are cooled to the ground state by the sideband transitions which are resonantly excited. The scheme achieves efficient ground state cooling and fast cooling rates using a continuous driving, instead of a pulsed one as in Raman sideband cooling schemes. An example is illustrated, where the average vibrational number is plotted as a function of the cooling time, and the final probability of occupation is plotted as a function of the vibrational state. This method may also be applied to reduce phase errors in coherent manipulations of trapped ions for quantum logic.
We study laser cooling of two ions that are trapped in a harmonic potential and interact by Coulomb repulsion. Sideband cooling in the Lamb-Dicke regime is shown to work analogously to sideband cooling of a single ion. Outside the Lamb-Dicke regime, the incommensurable frequencies of the two vibrational modes result in a quasicontinuous energy spectrum that significantly alters the cooling dynamics. The cooling time decreases nonlinearly with the linewidth of the cooling transition, and the effect of dark states which may slow down the cooling is considerably reduced. We show that cooling to the ground state is also possible outside the Lamb-Dicke regime. We develop the model and use quantum Monte Carlo calculations for specific examples. We show that a rate equation treatment is a good approximation in all cases.
Abstract Trapped ion in the Lamb–Dicke (LD) regime with the LD parameter η ≪ 1 can be cooled down to its motional ground state using sideband cooling. Standard sideband cooling works in the weak sideband coupling (WSC) limit, where the sideband coupling strength is small compared to the natural linewidth γ of the internal excited state, with a cooling rate much less than γ. Here we consider cooling schemes in the strong sideband coupling (SSC) regime, where the sideband coupling strength is comparable or even greater than γ. We derive analytic expressions for the cooling rate and the average occupation of the motional steady state in this regime, based on which we show that one can reach a cooling rate which is proportional to γ, while at the same time the steady state occupation increases by a correction term proportional to η 2 compared to the WSC limit. We demonstrate with numerical simulations that our analytic expressions faithfully recover the exact dynamics in the SSC regime.
Sideband cooling enables preparation of trapped ion motion near the ground state and is essential for many scientific and technological applications of trapped ion devices. Here, we study the efficiency of continuous and pulsed sideband cooling using both first- and second-order sidebands applied to an ion where the motion starts outside the Lamb-Dicke regime. We find that after optimizing these distinct cooling methods, pulsed and continuous cooling achieve similar results based on simulations and experiments with a 40^{40}40Ca+^++ ion. We consider optimization of both average phonon number n‾\overline{n}n and population in the ground state. We also demonstrate the disparity between n‾\overline{n}n as measured by the sideband ratio method of trapped ion thermometry and the n‾\overline{n}n found by averaging over the ion's motional state distribution.
Sideband cooling enables preparation of trapped ion motion near the ground state and is essential for many scientific and technological applications of trapped ion devices. Here, we study the efficiency of continuous and pulsed sideband cooling using both first- and second-order sidebands applied to an ion where the motion starts outside the Lamb-Dicke regime. We find that after optimizing these distinct cooling methods, pulsed and continuous cooling achieve similar results based on simulations and experiments with a 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion. We consider optimization of both average phonon number n‾\overline{n}n and population in the ground state. We also demonstrate the disparity between n‾\overline{n}n as measured by the sideband ratio method of trapped ion thermometry and the n‾\overline{n}n found by averaging over the ion's motional state distribution.