Tailored Single-Atom Collisions at Ultralow Energies

We employ collisions of individual atomic cesium (Cs) impurities with an ultracold rubidium (Rb) gas to probe atomic interaction with hyperfine- and Zeeman-state sensitivity. Controlling the Rb bath’s internal state yields access to novel phenomena observed in interatomic spin exchange. These can be tailored at ultralow energies, owing to the excellent experimental control over all relevant energy scales. First, detecting spin-exchange dynamics in the Cs hyperfine-state manifold, we resolve a series of previously unreported Feshbach resonances at magnetic fields below 300 mG, separated by energies as low as $h\times 15\mathrm{kHz}$. The series originates from a coupling to molecular states with binding energies below $h\times 1\mathrm{kHz}$ and wave function extensions in the micrometer range. Second, at magnetic fields below $\approx 100\mathrm{mG}$, we observe the emergence of a new reaction path for alkali atoms, where in a single, direct collision between two atoms two quanta of angular momentum can be transferred. This path originates from the hyperfine analog of dipolar spin-spin relaxation. Our work yields control of subtle ultralow-energy features of atomic collision dynamics, opening new routes for advanced state-to-state chemistry, for controlling spin exchange in quantum many-body systems for solid-state simulations, or for determination of high-precision molecular potentials.

Figure 1

System overview. (a) In the experiment, individual Cs atoms collide with atoms of an ultracold, thermal Rb bath [temperature typically $450(80)\mathrm{nK}$, atom number $3.0(6)\times {10}^3$]. Elastic collisions between Cs and Rb lead to thermalization of Cs in Rb. Additionally, in a spin-exchange (SE) collision, Cs (bottom left) and Rb (bottom right) can exchange angular momentum by $\mathrm{\Delta }{m}_F=1$ (blue, solid) or $\mathrm{\Delta }{m}_F=2$ (green, dashed). Interaction parameters, i.e., collision energy, magnetic field, and internal states, are experimentally controlled, which allows tailoring the dynamics. In a SE collision with $\mathrm{\Delta }{m}_F=1$, the energy $Q=|V_{\mathrm{Rb}}^Z-V_{\mathrm{Cs}}^Z|=h\times 350\mathrm{kHz}/\mathrm{G}\times B$ is released. (b) Collision cross sections for Rb in $m_{F,\mathrm{Rb}}=0$, where only $\mathrm{\Delta }{m}_F=1$ is allowed, showing Feshbach resonances ($I$) and quasi-constant SE cross sections ($II$). (c) For Rb in $m_{F,\mathrm{Rb}}=-1$, at low $B$ fields $\mathrm{\Delta }{m}_F=+2$ processes become accessible as well ($I$, dashed lines).

Figure 2

Spin control in the Feshbach resonance regime. SE dynamics of Cs atoms (initially in $m_{F,\mathrm{Cs}}=3$), immersed in a Rb bath of $m_{F,\mathrm{Rb}}=0$. The color code indicates the total measured Cs population $N$ for respective $m_{F,\mathrm{Cs}}$ states. (a) Measurement at $B=440\mathrm{mG}$, showing uniform $m_{F,\mathrm{Cs}}$ evolution. SE occurs at rate $\approx {\mathrm{\Gamma }}_{+1}=26\mathrm{Hz}$ for our density overlap of $⟨n⟩=2\times {10}^{12}{\mathrm{cm}}^{-3}$. (b) Measurement at $B=220\mathrm{mG}$ shows a metastable $m_{F,\mathrm{Cs}}=0$ state, where the population freezes in the vicinity of the zero value of the SE scattering section of the $|-1,0⟩$ Feshbach resonance [compare Fig. 1]. (c) Time evolution of the $m_{F,\mathrm{Cs}}=0$ population [dashed arrow in (a),(b)] for $B$ fields of (a) (triangle) and (b) (circles) compared to results of our coupled-channel model (dashed lines, no free parameters), demonstrating the emergence of a metastable state $m_{F,\mathrm{Cs}}=0$ in the resonance regime (b). (d) $m_{F,\mathrm{Cs}}$ population for a given interaction time $t_i=120\mathrm{ms}$ [solid arrow in (a),(b)], showing enhanced population in $m_{F,\mathrm{Cs}}=0$ and suppressed population in $m_{F,\mathrm{Cs}}=-2$. Open symbols show the same model as in (c), with solid lines guiding the eye. Atom counts in (a)–(c) result from the repetition of the experiment under the same conditions and error bars give statistical count uncertainties.

Figure 3

Low-energy Feshbach spectroscopy. Spin population of Cs (initially in $m_{F,\mathrm{Cs}}=3$) immersed in a Rb $m_{F,\mathrm{Rb}}=0$ bath for $t_i=100\mathrm{ms}$ and various magnetic fields. (a) Metastable states, where the evolution towards the global energy minimum with $m_{F,\mathrm{Cs}}=-3$ is interrupted in multiple $|m_{F,\mathrm{Cs}},m_{F,\mathrm{Rb}}=0⟩$ channels, indicating zero values of respective Feshbach resonances [marked in (b)]. High $m_F=-3$ population at low magnetic fields results from enhanced SE cross sections in all channels at low $B$ fields and thermal broadening [see Fig. 1]. (b) Coupled-channel scattering model corresponding to measurement in (a), including thermally distributed relative collision energies (no free parameters), which shifts the Feshbach zero value (white square) towards higher $B$ fields (white circles). (c) Comparison of measurement (a) (data points) and our model (b) (solid lines) for two Cs states $m_{F,\mathrm{Cs}}=-3$ (red) and $m_{F,\mathrm{Cs}}=-1$ (blue), showing excellent agreement. (d) Direct measurement of the scattering cross section for $\mathrm{\Delta }{m}_F=1$ in the $|-2,0⟩$ channel, by measuring $m_{F,\mathrm{Cs}}$ populations for two interaction times $t_i$ (see [23]). Lines show the coupled-channel results for a fixed collision energy (gray), and temperature-broadened model for $T=450\mathrm{nK}$ (red, solid) and $T=1.5\mu \mathrm{K}$ (red, dashed).

Figure 4

SE measurement with $\mathrm{\Delta }{m}_F=2$. Spin evolution of Cs $m_{F,\mathrm{Cs}}=3$ in Rb $m_{F,\mathrm{Rb}}=-1$ bath, measured for (a) $B=50\mathrm{mG}$ and (b) $B=250\mathrm{mG}$. (c) Modeled evolution (no free parameters) for settings in (a). (d) Difference of low and high $B$-field evolution in $m_{F,\mathrm{Cs}}=-3$ state. Positive values mean faster evolution at low $B$-field values (data points). Solid lines give the expectation from our model, including $2\hslash \mathrm{SE}$ (blue, solid), and a model, where $2\hslash$ processes are excluded (red dashed), for comparison. Counts and errors, see Fig. 2.