Bound-state-free Förster resonant shielding of strongly dipolar ultracold molecules

Abstract

We propose a method to suppress collisional loss in strongly dipolar, rotationally excited ultracold molecules using a combination of static (dc) and microwave (ac) electric fields. By tuning two excited pair molecular rotational states into a Förster resonance with a dc field, simultaneously driving excited rotational transitions with an ac field removes all long-range bound states, allowing near complete suppression of all two- and three-body collisional loss channels. While permitting tunable dipolar and anti-dipolar interactions, this bound-state-free ac/dc scheme is not subject to photon-changing collisions that are the primary source of two-body loss in shielding with two microwave fields, used to achieve the first molecular Bose-Einstein condensate [Bigagli et al., Nature 631, 289 (2024)]. Using NaCs as a representative example for strongly dipolar molecules, close-coupling calculations are performed to show that bound-state-free shielding can achieve ratios of elastic-to-loss rates $\gtrsim 10^{6}$ at 100 nK, with currently accessible ac and dc field generation technologies. This work opens new opportunities for realizing large, long-lived samples of strongly interacting degenerate molecular gases with tunable long-range interactions.

Figures (5)

• Figure 1: (a) Illustration of the ac/dc dressing scheme for bound-state-free shielding. (b) The squared effective dipole moment as a function of ac detuning and Rabi frequency. White on the colorbar indicates a zero effective dipole moment, while the solid black vertical line indicates the Förster defect along the ac detuning axis.
• Figure 2: Adiabatic potential energy curves for two NaCs molecules approaching along (a) $\theta = 0$ and (b) $\theta = \pi/2$ respectively. Parameters are set at compensation with $d{\rm E}_{\rm dc} = 3.25 B_0$, $\Omega/\Delta = 0.733$ and $\Delta = 1.5 \Delta_F$. The shielded adiabatic curve is colored black, while the other inelastic channels are colored gray. Labels for the asymptotic thresholds are ordered from top to bottom by descending energy. The insets are zoomed in versions of their parent plots, comparing the shielded adiabatic curve from full-basis diagonalization (solid black curve) to the effective potential (dashed red curve).
• Figure 3: Calculated two-body elastic (solid black), inelastic (dotted-dashed blue), short-rang (dotted green) and total loss (dashed red) rate coefficients between NaCs molecules at collision energy $E_c/k_B = 100$ nK, as a function of Rabi frequency at compensation with $\Omega = \Omega^*$. The ratio of elastic-to-loss rates are provided at $\Omega/\Delta_F = 1, 3, 5$ in the figure. The gray shaded area indicates the region where shielding is no longer Förster resonant dominated with $\Delta < 0.893 \Delta_F$.
• Figure 4: The effective potential between ac/dc shielded NaCs molecules in the $x,z$-plane, assuming the dipoles are oriented along $\hat{\boldsymbol{z}}$. The subplots are tuned to have (a) dipolar interactions with $\Omega/\Delta = 0.1$; (b) compensated interactions with $\Omega/\Delta = 0.733$; and (c) anti-dipolar interactions with $\Omega/\Delta = 0.3$. The microwaves are detuned by $\Delta = \Delta_F$ in all three plots. The colormaps saturate at 500 kHz except for subplot (a) which saturates at 100 kHz for clarity of the potential wells.
• Figure 5: Upper panel: Effective dipole length (solid red curve), and real part of the $s$-wave scattering length from multichannel calculations (dashed-dotted black curve) and from the effective potential (dotted green curve) as a function of Rabi frequency for NaCs. Lower panel: Calculated two-body elastic (solid black) and total loss (dashed red) rate coefficients at collision energy $E_c/k_B = 100$ nK, as a function of Rabi frequency. The vertical gray line indicates the compensation Rabi frequency $\Omega^*$, at fixed detuning $\Delta = 1.5 \Delta_F$.