Molecular Assembly of Ground-State Cooled Single Atoms

We demonstrate full quantum state control of two species of single atoms using optical tweezers and assemble the atoms into a molecule. Our demonstration includes 3D ground-state cooling of a single atom (Cs) in an optical tweezer, transport by several microns with minimal heating, and merging with a single Na atom. Subsequently, both atoms occupy the simultaneous motional ground state with 61(4)% probability. This realizes a sample of exactly two cotrapped atoms near the phase-space-density limit of one, and allows for efficient stimulated-Raman transfer of a pair of atoms into a molecular bound state of the triplet electronic ground potential $a^3{\mathrm{\Sigma }}^{+}$. The results are key steps toward coherent creation of single ultracold molecules for future exploration of quantum simulation and quantum information processing.

Popular Summary

Building complex quantum systems one molecule at a time is a promising approach to applications such as exploring quantum chemistry or building quantum computers. This technique hinges on the ability to generate and precisely control ultracold molecules. Here, we experimentally demonstrate key steps of such a molecular assembler, allowing us to trap, transport, and merge two different atoms.

Building on our earlier work, we trap one sodium and one cesium atom in separate optical tweezers, bring them together, then trigger the formation of an NaCs molecule with a laser pulse. To further push this reaction to its quantum mechanical limit, we add steps to purify the quantized motion of the atoms into their lowest energy state in the tweezer. As a result, we are able to turn 70% of sodium-cesium atom pairs into electronic ground-state molecules.

In the future, we envision that “designer” molecules for quantum computing and simulation would be assembled using this method, where full quantum control of the initial atoms and resulting molecule can be achieved.

Figure 1

Single-atom trapping and transport for molecular assembly. (a) Schematic of apparatus. Two neighboring optical tweezers at 976 and 700 nm trap a single Cs (blue) and Na (orange) atom in the vacuum chamber. Both tweezer beams are combined on a dichroic mirror and focused by an objective. The 976-nm tweezer can be moved in the focal plane by changing the drive frequency of an upstream acousto-optic deflector (AOD). Once atoms are cooled and merged into the same tweezer, a laser propagating along ${\mathbf{k}}_{\mathbf{R}}$ transfers them into a bound molecular state in the presence of a quantization $B$ field. (b) Experimental assembly steps of ultracold molecules demonstrated in this paper. A single Na and Cs atom are cooled, merged into the same trap, and transferred to a weakly bound molecule. (c) Single-shot fluorescence image of single Na and Cs atoms in adjacent tweezers separated by $3\mu \mathrm{m}$.

Figure 2

3D motional control of a single Cs atom. (a) Level scheme for Cs RSC. $F3$ and $F4$ Raman beams coherently couple adjacent motional states to reduce motional energy, while optical pumping provides the dissipation needed for cooling. Inset: Directions of laser beams. Switching Raman $F4$ beam directions allows addressing motion in all three dimensions. (b) 3D sideband thermometry for Cs after RSC. Black, blue, and red spectral peaks in the unshaded (shaded) region correspond to $\mathrm{\Delta }n=+1$ ($-1$) sidebands for the axial and two radial directions, respectively. Top: Spectra after suboptimal RSC reveals the $\mathrm{\Delta }n=-1$ sidebands, and hence the motional frequencies. The 3D ground-state population is $P_0^{3\mathrm{D}}=44(5)\%$. Bottom: Spectra after cooling with optimized motional frequencies, yielding $P_0^{3\mathrm{D}}\ge 96(3)\%$.

Figure 3

Merging atoms in two tweezers while maintaining quantum motional states. (a) Radial cuts of optical potential experienced by Na and Cs during the merge time sequence. Blue and orange lines show paths of the 976- and 700-nm tweezers, respectively. The 976-nm tweezer containing Cs is translated by $2.95\mu \mathrm{m}$ in 7.6 ms until it overlaps with the 700-nm tweezer. Then, the 700-nm tweezer power is linearly ramped from 48 to 0 mW in 1.5 ms, followed by a $50\text{−}\mu \mathrm{s}$ wait. Dashed potential in the left 5.7-ms panel (marked by red square) shows the conditions for nonideal tweezer powers, leading to spilling of Na. Dashed potential in the 8.55-ms panel (marked by red circle) shows the conditions for a different set of nonideal tweezer powers giving rise to antitrapping for Cs. (b) Raman sideband spectroscopy to characterize heating associated with atom transport. Top: A control experiment holding the atoms stationary for 18 ms. Bottom: After the round-trip merge sequence [the sequence shown in (a) followed by its time reverse]. Dashed blue lines indicate expected position of $\mathrm{\Delta }n=-1$ sidebands. The round-trip sequence causes minimal heating. Inset: Coordinates of the transport direction versus a thermometry axis. Blue and orange circles represent 976- and 700-nm tweezers, respectively. (c) $\mathrm{Na}+\mathrm{Cs}$ joint axial ground-state fraction after round-trip merge sequence as a function of 700- and 976-nm tweezer powers. The lower triangle in red corresponds to spilling of Na. Red square is an exemplary point in this regime, whose radial potential is plotted with a dashed line in the correspondingly marked panel in (a). Upper triangle in purple indicates antitrapping of Cs. Red circle is an exemplary point, whose potential is plotted with a dashed line in the correspondingly marked panel in (a). Dark purple stripe shows parametric heating resonance (due to technical imperfection) during transport of Cs. Our usual operating point is indicated by the star.

Figure 4

(a) Level diagram for two-photon Raman transfer from an atom pair to a weakly bound molecule. Two lasers $L_1$ and $L_2$ with a frequency difference $\delta$ derived from an acousto-optic modulator (AOM) are phase coherent and drive the atoms from the tweezer motional ground state ($v^{\prime \prime }=25$) to the weakly bound molecular state $a^3{\mathrm{\Sigma }}^{+}$ ($v^{\prime \prime }=24$ or $v^{\prime \prime }=-1$). A large detuning $\mathrm{\Delta }$ from the excited state $c^3\mathrm{\Sigma }(v^{\prime }=0)$, which decays at a rate ${\mathrm{\Gamma }}_e$, reduces spontaneous emission during molecular transfer, which occurs when the two-photon frequency difference $\delta$ is resonant with the binding energy. (b) Photoassociation spectroscopy of the intermediate excited state. With the laser $L_2$ off, the $L_1$ laser drives the atoms to the excited molecular vibrational states when resonant. The $\mathrm{Na}+\mathrm{Cs}$ two-body loss probability is measured as a function of the PA frequency for a 75-ms pulse duration. The $c^3{\mathrm{\Sigma }}_1^{+}(v^{\prime }=0,J^{\prime }=2,F^{\prime }=7)$ state is observed at 288 698.64(6) GHz. (c) Two-photon Raman resonance for transferring single atoms to a molecule. With a detuning $\mathrm{\Delta }=2\pi \times 3.2\mathrm{GHz}$, the frequency difference $\delta$ of the $L_1$ and $L_2$ beams is scanned around the binding energy of the $a^3{\mathrm{\Sigma }}^{+}(v^{\prime \prime }=24)$ state. The Raman resonance is observed at 298.0795(6) MHz with a FWHM of 8(2) kHz, indicating transfer of the atom pair to the weakly bound molecular state.

Figure 5

Minimum merge time. We numerically simulate the motional excitation as a function of merge time with fixed trap depth.

Figure 6

Simulated 2D tweezer power scan. Numerical simulation of the axial ground-state population for Na and Cs following the merge sequence described in Sec. 3. All the fundamental heating mechanisms (delineated by purple lines) are qualitatively reproduced.

Figure 7

Scattering rate due to the 15-mW 976-nm (307-THz) tweezer from $a^3\mathrm{\Sigma }(v^{\prime \prime }=24)$. The calculation is performed using the $c^3\mathrm{\Sigma }$ potential from Ref. [39] and $a^3\mathrm{\Sigma }$ potential from Ref. [47]. The peaks correspond to different vibrational states of the $c^3\mathrm{\Sigma }$ potential.