Atomic Rydberg Reservoirs for Polar Molecules

We discuss laser-dressed dipolar and van der Waals interactions between atoms and polar molecules, so that a cold atomic gas with laser admixed Rydberg levels acts as a designed reservoir for both elastic and inelastic collisional processes. The elastic scattering channel is characterized by large elastic scattering cross sections and repulsive shields to protect from close encounter collisions. In addition, we discuss a dissipative (inelastic) collision where a spontaneously emitted photon carries away (kinetic) energy of the collision partners, thus providing a significant energy loss in a single collision. This leads to the scenario of rapid thermalization and cooling of a molecule in the mK down to the $\mu \mathrm{K}$ regime by cold atoms.

Figure 1

(a) Energy levels of a laser excited atom and a rotational spectrum of a polar molecule. The Rydberg state $|r⟩$ interacts with the molecule via a dipole-dipole interaction $V_{\mathrm{dd}}$ (see text). (b) Born-Oppenheimer (BO) potentials for the laser-dressed atom $+$ molecule complex. We consider a dissipative collision, where (1) the particles collide on the potential curve $V_1(r)$ with the atom in $|g_1⟩$, climb the “blue shield” step at $r_c$, and (2) are quenched to the potential $V_2(r)$ with atom in $g_2$. The dominant atomic state is indicated with the molecule in its ground state. (c) Decay rate ${\gamma }_1(r)$ of the BO potential (see text).

Figure 2

Dissipative collisions: (a) Energy loss $E_{\mathrm{loss}}$ per collision vs impact parameter $b$ and initial relative kinetic energy $E_{\mathrm{kin}}$. (b) Distribution $f$ of final relative kinetic energies $E_{\mathrm{kin}}^{\prime }$ after a single collision for different $b$, for an initial Boltzmann distribution with $k_{B}T/\delta \approx 0.5$. (c) Average final kinetic energy $⟨E_{\mathrm{kin}}^{\prime }⟩$ of the corresponding distribution after a single collision. (d) $E_{\mathrm{kin}}$ (solid lines, left axis) and the average relative kinetic energy $⟨E_{\mathrm{kin}}⟩$ (dotted line, right axis) vs time with $\Gamma =\rho \sigma v_{\mu }\approx 2\pi \times 2.3\mathrm{kHz}$ the collision rate. Parameters: $d_m=7\mathrm{Debye}$, $d_r=4400\mathrm{Debye}$, $E_0=2\pi \times 2.5\mathrm{GHz}$, ${\Delta }_r=2\pi \times 60\mathrm{MHz}$, ${\Omega }_r/{\Delta }_r=0.42$, $\delta /{\Delta }_r=0.33$, ${\Omega }_e/{\Delta }_r=0.25$, $r_c\approx 218\mathrm{nm}$, $r_c^{\prime }/r_c\approx 0.95$, and $r_c^{\prime \prime }/r_c\approx 0.81$ [21], ${\rho }_{\max }^{-1/3}\simeq 1.7\mu \mathrm{m}$, $\rho =(2\mu \mathrm{m}{)}^{-3}$, $v_{\mu }=\sqrt{3k_{B}T/\mu }\approx 0.78\mathrm{m}/\mathrm{s}$.

Figure 3

Energy loss vs mass ratio $m_A/m_M$. The dashed red and solid black lines are analytic results for a model of sympathetic cooling only ($\delta =0$) and finite $\delta$, respectively, see Eqs. (2) and text. Blue dots and squares are averages over 200 runs of molecular dynamics simulations for finite $\delta$, for laser parameters as in Fig. 2.