Motional ground-state cooling of single atoms in state-dependent optical tweezers

Laser cooling of single atoms in optical tweezers is a prerequisite for neutral atom quantum computing and simulation. Resolved sideband cooling comprises a well-established method for efficient motional ground-state preparation, but typically requires careful cancellation of light shifts in so-called magic traps. Here, we study a novel laser cooling scheme which overcomes such constraints, and applies when the ground state of a narrow cooling transition is trapped stronger than the excited state. We demonstrate our scheme, which exploits sequential addressing of red sideband transitions via frequency chirping of the cooling light, at the example of ${}^{88}\mathrm{Sr}$ atoms and report ground-state populations compatible with recent experiments in magic tweezers. The scheme also induces light-assisted collisions, which are key to the assembly of large atom arrays. Our work enriches the toolbox for tweezer-based quantum technology, also enabling applications for tweezer-trapped molecules and ions that are incompatible with resolved sideband cooling conditions.

Figure 1

Chirp-cooling in state-dependent optical tweezers. (a) Radial tweezer potential for the ${|g\rangle =|}^1{S}_0\rangle$ and ${|e\rangle =|}^3{P}_1\rangle$ states of the cooling transition. The state-dependent trap depth enables transfer of excited motional states into the trap ground-state via strong red sideband transitions, reducing ${\nu }_g$ by $\mathrm{\Delta }\nu >1$ vibrational quanta (arrows denote excitation and subsequent spontaneous decay). The potential curves are offset vertically so that $U_{\mathrm{diff}}$ indicates the (positive) light shift of the electronic transition between the motional ground states from the free-space resonance. (b) Numerical simulations of the cooling dynamics, demonstrating ground-state transfer when the laser detuning $\delta$ (measured from the trap shifted resonance at $U_{\mathrm{diff}}$) is ramped from a large red detuning towards $\delta \approx -{\omega }_g$. The thickness of the yellow areas is proportional to the population in $|{\nu }_g\rangle$. Arrows indicate population transfer when the resonance condition for the sideband transitions drawn in (a) is matched. (c) Experimental realization: Single ${}^{88}\mathrm{Sr}$ atoms are trapped in an optical tweezer (green), using a high-NA objective. The polarization of the tweezer light is indicated by the arrow in the NA cone. Chirp-cooling is realized with three pairs of counter-propagating, circularly polarized $689\mathrm{nm}$ MOT beams (cooling). Additional laser beams (probe and shelving) are used for sideband thermometry. (d) Ratio of the AC polarizability (and hence of the trap depths) between ${|}^1{S}_0\rangle$ and the light-shifted substates $|e_0\rangle$ and $|e_{\pm }\rangle$ of ${|}^3{P}_1\rangle$ as a function of trapping wavelength. The dotted line indicates the wavelength used in the experiment.

Figure 2

Thermometry after chirp-cooling via release-and-recapture. (a) Atom-survival probability as a function of the release time $t_r$ is shown for three different values of ${\delta }_f$ as indicated (triangles, squares, diamonds) after cooling on the transition to $|e_{\pm }\rangle$, and compared to a measurement with no cooling applied (circles). Solid lines are fits of a classical particle trajectory simulation to the data to extract the temperature. The blue-dashed line shows the prediction of a quantum mechanical simulation for an atom in the motional ground state (see Appendix pp4). (b) Temperature $T_{\mathrm{cl}}$ extracted from classical trajectory simulations of data as shown in (a) as a function of the detuning ${\delta }_f$ at the end of the frequency chirp. Triangles (squares) are results for cooling on the transition to $|e_{\pm }\rangle$ ($|e_0\rangle$). The circle denotes the temperature without cooling applied. The vertical line indicates the resonance condition (${\delta }_f=-{\omega }_g$) for the lowest red sideband $|g,{\nu }_g=1\rangle \to |e,{\nu }_e=0\rangle$. At this point, the minimal temperature is achieved. The dashed line depicts the temperature-equivalent $T_{\mathrm{gs}}$ of the radial zero-point motion energy in the trap. Error bars in all figures show one standard deviation and are mostly smaller than the data points.

Figure 3

(a) Scheme for sideband thermometry via shelving into metastable states. The atom in the ground state ${}^1{S}_0$ is excited to the ${}^3{P}_1$ ($|e_0\rangle$) state by a short probe laser pulse. The population transferred to ${}^3{P}_1$ is hidden from the imaging cycle (${}^1{S}_0-{}^1{P}_1$) by optically pumping into the metastable ${}^3{P}_0$ and ${}^3{P}_2$ states via ${}^3{S}_1$. (b) Measured loss fraction from ${}^1{S}_0$ due to shelving as a function of probe detuning ${\delta }_p$ after cooling on the transition to $|e_{\pm }\rangle$ to ${\delta }_f=-1.2{\omega }_g$ (diamonds) and ${\delta }_f=-5.5{\omega }_g$ (circles). Solid lines are numerical simulations fitted to the data to extract the ground-state fraction (see text).

Figure 4

Light-induced losses and parity projection during cooling. (a) Histograms of photon counts before (yellow) and after (blue) cooling on $|e_{\pm }\rangle$ to ${\delta }_f=-1.2{\omega }_g$. The vertical dashed (dotted) line indicates the lower threshold set for identifying $N=1$ ($N\ge 2$) atom(s). Dash-dotted lines are Gaussian fits to the data to guide the eye. The inset shows the fluorescence of a single atom imaged onto at 3x3 pixel array of the sCMOS camera. (b) Probability to detect $N=1$ (circles) and $N\ge 2$ (triangles) atom(s) in the tweezer after chirp-cooling to a final detuning ${\delta }_f$. The dashed line indicates unity filling with $50\%$ probability. Note the change in scaling of the axis of abscissas for ${\delta }_f/{\omega }_g>-2$ (shaded area).

Figure 5

Chirp-cooling in a one-dimensional tweezer array. (a) Averaged fluorescence image of a line of ten tweezers (10 $\mu \mathrm{m}$ spacing) after cooling chirp (including parity projection). [(b)–(d)] Release-and-recapture thermometry data (cf. Fig. 2) for the three tweezers indicated with boxes after a cooling chirp to ${\delta }_f=-1.2{\omega }_g$ on the transition to $|e_{\pm }\rangle$. Solid lines are fits of a classical particle trajectory simulation to extract the temperature $T_{\mathrm{cl}}$. The blue dash-dotted line shows the prediction of a quantum mechanical simulation for an atom in the motional ground state. The red dashed line (gray dotted line) shows the classical fit to the single-tweezer data of Fig. 2 for the same cooling parameters (with no cooling applied). (e) Temperatures $T_{\mathrm{cl}}$ as a function of the tweezer index shown in (a). Again, the red dashed line depicts the single-tweezer result after cooling with the same cooling parameters, and the gray dotted line is the temperature measured in a single tweezer without cooling. The blue dash dotted line depicts the temperature-equivalent $T_{\mathrm{gs}}$ of the radial zero-point motion energy in the trap. Error bars show one standard deviation and are mostly smaller than the data points.

Figure 6

Measurement of the probe Rabi frequency $\mathrm{\Omega }$ used for sideband spectroscopy. Measured loss fraction from ${}^1{S}_0$ due to shelving as a function of probe time for different detunings from the carrier transition, i.e., ${\nu }_e={\nu }_g$, to $|e_0\rangle$. Solid lines show numerical simulations fit to the data, which yield $\mathrm{\Omega }=2\pi \times 44.9\left(5\right)\text{kHz}$.