State Selective Production of Molecules in Optical Lattices

We demonstrate quantum control over both internal and external quantum degrees of freedom in a high number of identical “chemical reactions,” carried out in an array of microtraps in a 3D optical lattice. Starting from a Mott insulating phase of an ultracold atomic quantum gas, we use two-photon Raman transitions to create molecules on lattice sites occupied by two atoms. In the atom-molecule conversion process, we can control both the internal rovibronic and external center of mass quantum state of the molecules. The lattice isolates the microscopic chemical reactions from each other, thereby allowing photoassociation spectra without collisional broadening even at high densities of up to $2\times {10}^{15}{\mathrm{c}\mathrm{m}}^{-3}$.

Figure 1

Two-color photoassociation process of two atoms being placed in the external ground state at a single site of an optical lattice potential. Both the rovibrational quantum state in the relative motion of the two atoms forming the molecule (a) and the c.m. motional quantum state of the molecule (b) can be controlled.

Figure 2

Time-resolved one-color photoassociation; in 1D (empty circles) and 3D lattice (filled circles) configurations. The photoassociation laser is tuned to resonance with an intensity of $I=5\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$ and illuminates the sample for a varying time, after which the total atom number is measured. The inset shows the 1D lattice loss data in a log-lin plot.

Figure 3

Two-photon photoassociation of the uppermost vibrational level in the electronic ground state ${}^3\Sigma _u^{+}$ at $\delta /2\pi \approx 24\mathrm{M}\mathrm{H}\mathrm{z}$ and at $\delta /2\pi \approx 636\mathrm{M}\mathrm{H}\mathrm{z}$, with the quantized c.m. motion resolved. The remaining atom number after a photoassociation time of about 120 ms is measured for varying difference frequencies $\delta$ at a constant detuning of (a) $\Delta =2\pi \times 700\mathrm{M}\mathrm{H}\mathrm{z}$ and laser intensities of $I_a=12\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$ and $I_b=6\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$ and (b) a detuning of $\Delta =-2\pi \times 990\mathrm{M}\mathrm{H}\mathrm{z}$ and $I_a=16\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$ and $I_b=12\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$. The solid curve is a fit assuming four independent Lorentzian profiles and a constant background. The difference in the vibrational level spacings between (a) and (b) are mainly due to different lattice depths of (a) $18E_r$ and (b) $27E_r$ along the optical lattice axis of the photoassociation lasers.

Figure 4

High resolution two-photon photoassociation of the transition to the most weakly bound internal vibrational state in the ${}^3\Sigma _u^{+}$ potential and the ground state of the c.m. motion. The scan was taken at an intermediate detuning of $\Delta =-2\pi \times 900\mathrm{M}\mathrm{H}\mathrm{z}$. The solid line is a Lorentzian fit to the data with a width of $\gamma =1.1(2)\mathrm{k}\mathrm{H}\mathrm{z}$.