Designer Spatial Control of Interactions in Ultracold Gases

Designer optical control of interactions in ultracold atomic gases has wide applications, from creating new quantum phases to modeling the physics of black holes. We demonstrate wide tunability and spatial control of interactions in a two-component cloud of ${}^6\mathrm{Li}$ fermions, using electromagnetically induced transparency. With two control fields detuned $\simeq 1.5\mathrm{THz}$ from atomic resonance, megahertz changes in the frequency of one optical beam tune the measured scattering length over the full range achieved by magnetic control, with negligible (${10}^{-6}$) effect on the net optical confining potential. A 1D “sandwich” of resonantly and weakly interacting regions is imprinted on the trapped cloud and broadly manipulated with sub-MHz frequency changes. All of the data are in excellent agreement with our continuum-dressed state theoretical model of optical control, which includes both the spatial and momentum dependence of the scattering amplitude.

Figure 1

Basic level scheme to control interactions using electromagnetically induced transparency (EIT). (a) Optical fields ${\nu }_1$ (Rabi frequency ${\mathrm{\Omega }}_1$ and detuning ${\mathrm{\Delta }}_1$) and ${\nu }_2$ (Rabi frequency ${\mathrm{\Omega }}_2$ and detuning ${\mathrm{\Delta }}_2$) couple the ground molecular states $|g_1⟩$ and $|g_2⟩$ to the excited molecular state $|e⟩$ of the singlet potential, allowing precise tuning of the state $|g_1⟩$ from below ($\delta <0$) to above ($\delta >0$) its unshifted position, where $\delta ={\mathrm{\Delta }}_2-{\mathrm{\Delta }}_1$ is the two-photon detuning. Inset: Optical field arrangement for creating an interaction “sandwich.” The central region of the atomic cloud illuminated by both ${\nu }_1$ and ${\nu }_2$ beams is resonantly interacting. The outer regions of the atomic cloud illuminated only by the ${\nu }_1$ beam are weakly interacting. (b) Measuring mean-field interactions using rf spectroscopy. Fraction of atoms remaining in state $|3⟩$ by applying a rf $\pi$ pulse (1.2 ms) to transfer atoms from hyperfine state $|3⟩$ to $|2⟩$, obtained with (blue) and without (magenta) atoms present in state $|1⟩$. Solid curves are predictions (see text).

Figure 2

Optical control of the two-body scattering length near the energy-dependent narrow Feshbach resonance of ${}^6\mathrm{Li}$ at 543.27 G. (a) Measured frequency shifts in the rf spectra (red dots) and prediction (blue curve) as a function of two-photon detuning $\delta$, by changing ${\nu }_2$ and holding ${\nu }_1$ constant. $\delta \equiv 0$ denotes the two-photon resonance. (b) Momentum-averaged scattering length ${\overline{a}}_{12}$ (red dots) determined from the measured frequency shifts versus $\delta$ and prediction (green solid curve). Inset: Magnetically tuned $a_{12}$. Note that optical tuning achieves the same range as magnetic tuning. $a_{bg}=62a_0$.

Figure 3

Designer interaction patterns in an ultracold gas of ${}^6\mathrm{Li}$ atoms versus two-photon detuning $\delta$, with $\delta \equiv 0$ at the two-photon resonance. (a) Measured false-color 2D absorption images of atoms arriving into $|2⟩$ after transfer from state $|3⟩$ by a 1.2 ms rf $\pi$ pulse, in the presence of atoms in state $|1⟩$. (b) Predicted 2D images using measured parameters [24]. (c) Normalized 1D axial profiles $n_{1\mathrm{D}}/n_0$, where $n_0$ is the peak density with no atoms in state $|1⟩$. Measured (blue) and calculated (red). (d) Momentum-averaged two-body scattering length $a_{12}^{\mathrm{opt}}$ used to generate the predicted 2D and 1D spatial profiles.