Dissipationless tune-out trapping for a lanthanide-alkali quantum gas mixture

Abstract

Quantum gas mixtures offer a wide field of research, ranging from few-body physics of impurities to many-body physics with emergent long-range interactions and ultracold molecular gases. Achieving precision control of mixtures is much harder than for single-component gases and, consequently, the respective techniques are less developed. Here we report on a decisive step forward in this direction by realizing dissipationless and fully differential optical control of the motional degrees of freedom of one of the species without affecting the other. This is achieved in a novel Bose-Fermi mixture with extreme mass imbalance, erbium-166 and lithium-6. Our experiments pave the way to a new generation of precision many-body experiments with quantum gas mixtures with unprecedented long lifetimes and low temperatures.

Figures (4)

• Figure 1: System comparison and tune-out spectroscopy. (a) We compare three mixtures, for which tune-out trapping has been realized regarding their normalized photon scattering $\gamma/\tilde{U}$ (top) and their polarizabilities $\alpha$ in atomic units (a.u.) (bottom). The normalization by $\widetilde{U}=U/k_\text{B}$, with $k_\text{B}$ being Boltzmann's constant, is done with regard to the potential $U$ seen by the trapped species. The arrows in the top panel indicate the relevant value dominated by the most dissipative partner, and the dashed line is a reference value for the often realized single species configuration: Rb trapped in $\unit[1064]{nm}$ light. In both panels, the red lines indicate the tuned-out element (Er, Rb, Cs), the blue lines the trapped partners (Li, Yb, Li). The horizontal axis displays the normalized and scaled detuning $10^n \Delta/\Gamma$, where $\Delta$ is the frequency difference to the tune-out point (for Er: $\unit[841]{nm}$, Rb: $\unit[423]{nm}$, Cs: $\unit[880]{nm}$), $\Gamma$ is the line width of the nearest transition line of the tuned-out element and $n$ accounts for the different distance of this line to the tune-out point. We use the polarizability of Li and Cs from UDportal. (b) Trap-loss spectrum of Er in the $\unit[1064]{mm}$ optical trap beam, which is superimposed with a $\unit[841]{nm}$ dimple beam. The intensity of the dimple beam is amplitude-modulated at different frequencies $\nu_\text{mod}$. The red data is representative for a non-fine-tuned dimple wavelength away from the tune-out, the black data is on the tune-out. We attribute the slight modulation of the black data to experimental instabilities during the measurement. (c) Remaining normalized Er atom number (red dots) for resonant modulation at the frequency of the first minimum in (b) for different dimple beam detunings from the $\unit[841]{nm}$ line. The tune-out shown here at $\unit[237]{GHz}$ is close to the maximum detuning of $\unit[245]{GHz}$ for $\theta=90^\circ$. Error bars of one standard deviation are smaller than the marker size. A Gaussian fit (dashed line) is used to extract the tune-out wavelength $\delta_\theta$ and its uncertainty.
• Figure 2: Dissipative effects of the tune-out beam on Er and Li. Lifetime measurements of Er in the $\unit[1064]{nm}$ optical dipole trap are shown for the $\unit[841]{nm}$ dimple beam set to the tune-out wavelength at full (dark red) and zero power (light red). The right vertical axis gives the trapped Erbium atom number $N^\text{(Er)}$ versus holding time $dt_{\text{hold}}$. Each data point is averaged over five experimental repetitions. Lifetimes are extracted by an exponential fit (dashed lines) to the data. In blue, we show lifetime measurements of Li in the same dimple beam for three powers: $\unit[(0.1, 0.3, 0.5)]{W}$ (light to dark blue). In-trap atom numbers for Li $N^\text{(Li)}$ are given on the left vertical axis, and each point is the average of ten experimental runs. The extracted lifetimes are found to be power-independent within the experimental uncertainties. For all measurements, the error bars represent the standard error of the mean. The two different measurement settings are sketched in the upper right corner inset.
• Figure 3: Polarization dependence of the tune-out wavelength. Measured tune-out frequencies (red dots) are given as detuning from the $\unit[841]{nm}$-line for different angles between the linear polarization $\theta$ and the magnetic field. The tune-out frequencies $\delta_\theta$ change sinusoidally in dependence of $\theta$ in an interval of $\unit[165]{GHz}$. The contributing lines up to $\unit[400]{nm}$ are visualized in the energy level diagram (inset, top left), where the lines connecting to the dark red states cause the $\theta$-dependence. The inset on the bottom right displays the calculated polarizability for parallel and perpendicular polarized linear light, visualizing the shift of the zero-crossing/tune-out point for the two extreme configurations. While the theory (black line) matches the measurements for small angles, a significant deviation becomes apparent closer to perpendicular alignment of polarization and magnetic field. We use a fit (dashed red line) to quantify the origin of this deviation, as detailed in the main text.
• Figure 4: (a) Polarizabilities of Er and Li, with the relevant tune-out highlighted (star). The total polarizability of Er (gray) consists of contributions from many lines, but it is dominated by strong lines in the blue and UV. Those lines together with the $\unit[841]{nm}$ line (red) govern the position of the tune-out wavelength, which is blue detuned from this $2\pi \times \unit[8]{kHz}$ narrow line. The polarizability of Li (blue) is dominated by the $\unit[671]{nm}$$\mathrm{D_1}$ and $\mathrm{D_2}$ lines. The tune-out point near $\unit[841]{nm}$ of Er is far red-detuned to them, which allows creating attractive optical dipole traps for Li at that wavelength. (b) Energy levels for Er and Li. Arrows indicate commonly used cooling transitions. Strong and weak Er lines are colored the same way as in (a).