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arXiv:2301.03276 · New Journal of Physics

Systematic study of tunable laser cooling for trapped-ion experiments

A. P. Kulosa, Прудников Олег Николаевич, Daniel Vadlejch, Henning A. Fürst, Anastasia Kirpichnikova, A. V. Taǐchenachev, Valeriy I. Yudin, T. E. Mehlstäubler

Published Apr 28, 2023• 7 citations
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Abstract

Abstract We report on a comparative analysis of quenched sideband cooling in trapped ions. We introduce a theoretical approach for time-efficient simulation of the temporal cooling characteristics and derive the optimal conditions providing fast laser cooling into the ion’s motional ground state. The simulations were experimentally benchmarked with a single 172Yb+ ion confined in a linear Paul trap. Sideband cooling was carried out on a narrow quadrupole transition, enhanced with an additional clear-out laser for controlling the effective linewidth of the cooling transition. Quench cooling was thus for the first time studied in the resolved sideband, intermediate and semi-classical regime. We discuss the non-thermal distribution of Fock states during laser cooling and reveal its impact on time dilation shifts in optical atomic clocks.

DOI
10.1088/1367-2630/acd13b

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Abstract We report on a comparative analysis of quenched sideband cooling in trapped ions. We introduce a theoretical approach for time-efficient simulation of the temporal cooling characteristics and derive the optimal conditions providing fast laser cooling into the ion’s motional ground state. The simulations were experimentally benchmarked with a single 172Yb+ ion confined in a linear Paul trap. Sideband cooling was carried out on a narrow quadrupole transition, enhanced with an additional clear-out laser for controlling the effective linewidth of the cooling transition. Quench cooling was thus for the first time studied in the resolved sideband, intermediate and semi-classical regime. We discuss the non-thermal distribution of Fock states during laser cooling and reveal its impact on time dilation shifts in optical atomic clocks.
Efficient cooling of trapped ions is a prerequisite for various applications of the ions in precision spectroscopy, quantum information, and coherence control. Raman sideband cooling is an effective method to cool the ions to their motional ground state. We investigate both numerically and experimentally the optimization of Raman sideband cooling strategies and propose an efficient one, which can simplify the experimental setup as well as reduce the number of cooling pulses. Several cooling schemes are tested and compared through numerical simulations. The simulation result shows that the fixed-width pulses and varied-width pulses have almost the same efficiency for both the first-order and the second-order Raman sideband cooling. The optimized strategy is verified experimentally. A single 25Mg+{^{25}\mathrm{Mg}}^{+}25Mg+ ion is trapped in a linear Paul trap and Raman sideband cooled, and the achieved average vibrational quantum numbers under different cooling strategies are evaluated. A good agreement between the experimental result and the simulation result is obtained.
An experimental study of sideband laser cooling of trapped ions in miniature radio-frequency traps is presented. In+{\mathrm{In}}^{+}In+ ions are laser cooled by exciting the narrow intercombination line ${5s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}5s5p{}^{3}{P}_{1}$, which shows resolved sidebands due to the vibrational motion of the ions in the trap. The influence of the micromotion at the frequency of the oscillating trapping field is investigated. Heating processes through coupling with the trapping field occur for certain regions of negative laser detuning. A method of bichromatic sideband cooling is introduced that combines efficient cooling from high temperatures with the possibility of reaching low mean vibrational quantum numbers 〈n〉<1〈n〉<1〈n〉<1 by using narrow optical transitions. This technique allows recording of high-resolution excitation spectra of the cooling transition in the Lamb-Dicke regime and thus determination of 〈n〉〈n〉〈n〉. Single ions as well as two-ion Coulomb crystals have been cooled to temperatures below $100 \ensuremath{\mu}\mathrm{K}$, and population of the ground state of motion to more than 50% over long time scales is demonstrated. These values are close to the lower limit for the detection of vibrational excitation with the present method.
Ground state cooling and coherent manipulation of ions in an rf-(Paul) trap is the prerequisite for quantum information experiments with trapped ions. With resolved sideband cooling on the optical S1/2−D5/2 quadrupole transition we have cooled one and two 40Ca+ ions to the ground state of vibration with up to 99.9% probability. With a novel cooling scheme utilizing electromagnetically induced transparency on the S1/2−P1/2 manifold we have achieved simultaneous ground state cooling of two motional sidebands 1.7 MHz apart. Starting from the motional ground state we have demonstrated coherent quantum state manipulation on the S1/2−D5/2 quadrupole transition at 729 nm. Up to 30 Rabi oscillations within 1.4 ms have been observed in the motional ground state and in the n=1 Fock state. In the linear quadrupole rf-trap with 700 kHz trap frequency along the symmetry axis (2 MHz in radial direction) the minimum ion spacing is more than 5 μm for up to 4 ions. We are able to cool two ions to the ground state in the trap and individually address the ions with laser pulses through a special optical addressing channel.
Resolved sideband cooling is a standard technique for cooling trapped ions below the Doppler limit to near their motional ground state. Yet, the most common methods for sideband cooling implicitly rely on low Doppler-cooled temperatures and tightly confined ions, and they cannot be optimized for different experimental conditions. Here, we introduce a framework which calculates the fastest possible sideband cooling sequence for any set of experimental parameters and verify its improvement compared to traditional methods using a trapped 171^{171}171Yb+^++ ion. After extensive cooling, we find that the ion motional distribution is distinctly non-thermal and thus not amenable to standard thermometry techniques. We therefore develop and experimentally validate an improved method to measure ion temperatures after sideband cooling. These techniques will enable more efficient cooling and thermometry within any trapped-ion system, especially those with high initial temperatures or spatially-extended ion wavepackets.
Abstract Efficient cooling of trapped ions is one of the key problems in the development of optical clocks and quantum sensors, in quantum computations, and many other fields. We numerically analyze the motion of linear Yb + crystals and optimized trapping potential to achieve a uniform spatial distribution of ions. Using a compact robust laser system we demonstrate Doppler cooling of a 174 Yb + isotope in a quadrupole Paul trap. This is an important step towards laser cooling of 171 Yb + ions, which will be used in single-ion optical clocks and for the realization of high-fidelity quantum gates.
Cooling down a trapped ion into its motional ground state is a central step for trapped-ion-based quantum information processing. State-of-the-art cooling schemes often work under a set of optimal cooling conditions derived analytically using a perturbative approach, in which the sideband coupling is assumed to be the weakest of all the relevant transitions. As a result, the cooling rate is severely limited. Here we propose to use a quantum control technique powered with automatic differentiation to speed up the classical cooling schemes. We demonstrate the efficacy of our approach by applying it to find the optimal cooling conditions for classical sideband cooling and electromagnetically induced transparency cooling schemes, which are in general beyond the weak-sideband-coupling regime. Based on those numerically found optimal cooling conditions, we show that faster cooling can be achieved while at the same time a low average phonon occupation can be retained.