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$Λ$-Enhanced Gray Molasses Cooling of $^{85}$Rb Atoms in Tweezers Using the D$_2$ Line

Deon Janse van Rensburg, Rogier Venderbosch, Yuri van der Werf, Jesus del Pozo Mellado, Marijn Venderbosch, Rianne Lous, Edgar Vredenbregt, Servaas Kokkelmans

TL;DR

The paper demonstrates Λ-enhanced gray molasses cooling on the D2 line of $^{85}$Rb in an optical tweezer array, achieving $T\approx 4.0(2)\ \mu$K and extending the hyperfine clock qubit coherence time $T_2^*$ by up to a factor of 1.5. It combines an alignment-free GMC implementation using MOT beams with a four-level density-matrix model that captures the strong dependence on carrier detuning and Raman resonance, and shows good agreement between experiment and theory. The work identifies the crucial role of the intermediate excited state $|4\rangle$ and the hyperfine structure in enabling efficient cooling on the D2 line, and demonstrates tangible improvements in motional and coherence properties relevant for scalable quantum information processing with neutral atoms. These results pave the way for robust, multi-qubit tweezer arrays and potential dual-species implementations using the ubiquitous D2 transition.

Abstract

We demonstrate the implementation of $Λ$-enhanced gray molasses cooling on the D$_2$ line of $^{85}$Rb atoms in an optical tweezer array. This technique yields lower atomic temperatures of 4.0(2) $μ$K compared to red-detuned polarization gradient cooling, and consequently extends the $T_2^*$ coherence time of the hyperfine clock qubit by a factor of 1.5. The method is alignment-free and can be readily implemented on laser beams used for magneto-optical trapping, as it only requires frequency and phase modulation control. Our experimental observations are corroborated by a numerical model based on a semi-classical force approach extended to a four-level system, including two hyperfine states of the upper manifold that are 120 MHz apart.

$Λ$-Enhanced Gray Molasses Cooling of $^{85}$Rb Atoms in Tweezers Using the D$_2$ Line

TL;DR

The paper demonstrates Λ-enhanced gray molasses cooling on the D2 line of Rb in an optical tweezer array, achieving K and extending the hyperfine clock qubit coherence time by up to a factor of 1.5. It combines an alignment-free GMC implementation using MOT beams with a four-level density-matrix model that captures the strong dependence on carrier detuning and Raman resonance, and shows good agreement between experiment and theory. The work identifies the crucial role of the intermediate excited state and the hyperfine structure in enabling efficient cooling on the D2 line, and demonstrates tangible improvements in motional and coherence properties relevant for scalable quantum information processing with neutral atoms. These results pave the way for robust, multi-qubit tweezer arrays and potential dual-species implementations using the ubiquitous D2 transition.

Abstract

We demonstrate the implementation of -enhanced gray molasses cooling on the D line of Rb atoms in an optical tweezer array. This technique yields lower atomic temperatures of 4.0(2) K compared to red-detuned polarization gradient cooling, and consequently extends the coherence time of the hyperfine clock qubit by a factor of 1.5. The method is alignment-free and can be readily implemented on laser beams used for magneto-optical trapping, as it only requires frequency and phase modulation control. Our experimental observations are corroborated by a numerical model based on a semi-classical force approach extended to a four-level system, including two hyperfine states of the upper manifold that are 120 MHz apart.

Paper Structure

This paper contains 12 sections, 12 equations, 6 figures.

Table of Contents

  1. Introduction
  2. $\Lambda$-GMC Demonstration
  3. Method
  4. Experimental Results
  5. Four-level Cooling model
  6. Theory
  7. Numerical Results
  8. Comparison Simulation and Experiment
  9. Extended $T_2^*$ of Hyperfine Qubits
  10. Discussion and Outlook
  11. Release-Recapture Temperature Measurement
  12. Simulation model

Figures (6)

  • Figure 1: D$_2$ line of $^{85}$Rb, focusing on the four levels {$| 1 \rangle , | 2 \rangle , | 3 \rangle , | 4 \rangle$} involved in $\Lambda$-GMC. The parameters $\{\delta_1,\Omega_1\}$ represent the repumper detuning and Rabi frequency (blue, $F=2 \rightarrow F'=3)$, the repumper light is an EOM sideband on the cooling laser. The parameters $\{\delta_2,\Omega_2\}$ are the cooling laser carrier detuning and Rabi frequency (green, $F=3\rightarrow F'=3$), $\delta = \delta_1-\delta_2$ is the Raman detuning, and $\delta_4$ the hyperfine splitting.
  • Figure 2: $\Lambda$-GMC and heating features in $^{85}$Rb. (a) Recapture probability after the traps are turned off for 40µs as a function of the Raman detuning $\delta$ for carrier detuning $\delta_2=6\,\Gamma$. Approximate 5$^2$S$_{1/2}$$| F = 2 \rangle$$\leftrightarrow$ 5$^{2}$P$_{3/2}$$| F' = X \rangle$ resonances are indicated by the vertical lines for $X\in\{1,2,3\}$. The probability of recapture without $\Lambda$-GMC is indicated by the horizontal dashed black line. The inset depicts the narrow cooling/heating feature around the Raman resonance. Error bars (not visible) represent one standard error of the array mean. (b) Release-recapture probability for a fixed $40µs$ trap off time as a function of Raman detuning $\delta$ for varying $\delta_2$. (c) Temperature as a function of $\delta_2$ after an optimal $\Lambda$-GMC pulse with Raman detuning $\delta=-0.016\,\Gamma$. Temperatures are extracted from Monte Carlo simulations to release-recapture curves, and error bars are derived from the $\chi^2$ value of the Monte Carlo simulations.
  • Figure 3: Simulation of cooling mechanisms around the Raman resonance. (a) Normalized phase-averaged force $\langle F(v)\rangle_{\phi}$ defined in Eq. \ref{['eq:force-phase-avg']} at the Raman resonance ($\delta$ = 0) as a function of normalized velocity for $\Omega_1 = 0.58\,\Gamma$, $\Omega_2 = 1.63\,\Gamma$, $\delta_4=19.9\,\Gamma$, and varying carrier detuning $\delta_2$. The cooling is most efficient at $\delta_2=\delta_1=5\,\Gamma$, and the phase-averaged force is presented for different $\delta$ around the Raman resonance in the App \ref{['app:model']}. (b) Friction coefficient $\alpha$ as function of repumper detuning $\delta_1$ for varying carrier detuning $\delta_2$ using the parameters $\Omega_1 = 0.58\,\Gamma$, $\Omega_2 = 1.63\,\Gamma$, $\delta_4=19.9\,\Gamma$, and phase $\phi =0$. (c) Population $\rho_{33}$ and $\rho_{44}$ averaged over relative phases $\phi$ as a function of detuning $\delta_1$. Using standard parameters from (a,b) and $kv/\Gamma = 0.01$.
  • Figure 4: Damped Ramsey oscillation including fit for a single array site. The circular data points (dark blue) represent the Ramsey signal after $\Lambda$-GMC, and triangular data points (green) represent the Ramsey signal without $\Lambda$-GMC. Error bars are statistical and represent one standard error of the mean.
  • Figure A1: Release and recapture measurements. Curves after $\Lambda$-GMC with and without state preparation (SP) after cooling, including the best fit Monte Carlo simulation curves as faint lines. The yellow-green line shows the fit of the quantum model to the coldest dataset after optimal $\Lambda$-GMC, and the yellow dashed line depicts the radial expansion due to the zero-point motion energy in the trap. Error bars are statistical and represent one standard error of the array mean.
  • ...and 1 more figures