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arXiv:1707.03239 · Physical Review A

Adimensional theory of shielding in ultracold collisions of dipolar rotors

Maykel Leonardo González-Martínez, John L. Bohn, Goulven Quéméner

Published Sep 27, 2017• 58 citations
arXivHTMLPDF

Abstract

We investigate the electric field shielding of ultracold collisions of dipolar rotors, initially in their first rotational excited state, using an adimensional approach. We establish a map of good and bad candidates for efficient evaporative cooling based on this shielding mechanism, by presenting the ratio of elastic over quenching processes as a function of a rescaled rotational constant $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}=B/{s}_{{E}_{3}}$ and a rescaled electric field $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}=dF/B$. $B,d,F,\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}{s}_{{E}_{3}}$ are respectively the rotational constant, the full electric dipole moment of the molecules, the applied electric field, and a characteristic dipole-dipole energy. We identify two groups of bi-alkali-metal dipolar molecules. The first group, including RbCs, NaK, KCs, LiK, NaRb, LiRb, NaCs, and LiCs, is favorable with a ratio over 1000 at collision energies equal to (or even higher than) their characteristic dipolar energy. The second group, including LiNa and KRb, is not favorable. More generally, for molecules well described by Hund's case b, our adimensional study provides the conditions of efficient evaporative cooling. The range of appropriate rescaled rotational constant and rescaled field is approximately $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}\ensuremath{\ge}{10}^{8}$ and $3.25\ensuremath{\le}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}\ensuremath{\le}3.8$, with a maximum ratio reached for $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}\ensuremath{\simeq}3.4$ for a given $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}$. We also discuss the importance of the electronic van der Waals interaction on the adimensional character of our study.

DOI
10.1103/physreva.96.032718

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We investigate the electric field shielding of ultracold collisions of dipolar rotors, initially in their first rotational excited state, using an adimensional approach. We establish a map of good and bad candidates for efficient evaporative cooling based on this shielding mechanism, by presenting the ratio of elastic over quenching processes as a function of a rescaled rotational constant B\ifmmode~\else˜\fi=B/sE3\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}=B/{s}_{{E}_{3}}B\ifmmode~\else˜\fi​=B/sE3​​ and a rescaled electric field F\ifmmode~\else˜\fi=dF/B\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}=dF/BF\ifmmode~\else˜\fi​=dF/B. B,d,F,andsE3B,d,F,\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}{s}_{{E}_{3}}B,d,F,andsE3​​ are respectively the rotational constant, the full electric dipole moment of the molecules, the applied electric field, and a characteristic dipole-dipole energy. We identify two groups of bi-alkali-metal dipolar molecules. The first group, including RbCs, NaK, KCs, LiK, NaRb, LiRb, NaCs, and LiCs, is favorable with a ratio over 1000 at collision energies equal to (or even higher than) their characteristic dipolar energy. The second group, including LiNa and KRb, is not favorable. More generally, for molecules well described by Hund's case b, our adimensional study provides the conditions of efficient evaporative cooling. The range of appropriate rescaled rotational constant and rescaled field is approximately B\ifmmode~\else˜\fi\ensuremath≥108\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}\ensuremath{\ge}{10}^{8}B\ifmmode~\else˜\fi​\ensuremath≥108 and 3.25\ensuremath≤F\ifmmode~\else˜\fi\ensuremath≤3.83.25\ensuremath{\le}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}\ensuremath{\le}3.83.25\ensuremath≤F\ifmmode~\else˜\fi​\ensuremath≤3.8, with a maximum ratio reached for F\ifmmode~\else˜\fi\ensuremath≃3.4\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}\ensuremath{\simeq}3.4F\ifmmode~\else˜\fi​\ensuremath≃3.4 for a given B\ifmmode~\else˜\fi\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}B\ifmmode~\else˜\fi​. We also discuss the importance of the electronic van der Waals interaction on the adimensional character of our study.
We investigate the ultracold collisions of rotationally excited dipolar molecules in free-space, taking the hetero-nuclear bi-alkali molecule of KRb as an example. We show that we can sharply tune the elastic, inelastic and reactive rate coefficients of lossy molecular collisions when a second rotationally excited colliding channel crosses the threshold of the initial colliding channel, with the help of an applied electric field, as found by Avdeenkov et al for non-lossy molecules ( Phys. Rev. A 73 022707 ). We can increase or decrease the inelastic and reactive processes whether the second channel is above or below the initial channel. This is seen for both bosonic and fermionic molecules. Additionally, we include the electric quadrupole and octopole moment to the dipole moment in the expression of the long-range multipole–multipole interaction. We found that for processes mediated by the incident channel, such as elastic and reactive collisions, the inclusion of quadrupole and octopole moments is not important at ultralow energies. The moments are important for processes mediated by state-to-state transitions like inelastic collisions.
By applying a circularly polarized and slightly blue-detuned microwave field with respect to the first excited rotational state of a dipolar molecule, one can engineer a long-range, shallow potential well in the entrance channel of the two colliding partners. As the applied microwave ac field is increased, the long-range well becomes deeper and can support a certain number of bound states, which in turn bring the value of the molecule-molecule scattering length from a large negative value to a large positive one. We adopt an adimensional approach where the molecules are described by a rescaled rotational constant B[over ˜]=B/s_{E_{3}} where s_{E_{3}} is a characteristic dipolar energy. We found that molecules with B[over ˜]>10^{8} are immune to any quenching losses when a sufficient ac field is applied, the ratio elastic to quenching processes can reach values above 10^{3}, and that the value and sign of the scattering length can be tuned. The ability to control the molecular scattering length opens the door for a rich, strongly correlated, many-body physics for ultracold molecules, similar to that for ultracold atoms.
Trapped samples of ultracold molecules are often short-lived because close collisions between them result in trap loss. We investigate the use of shielding with static electric fields to create repulsive barriers between polar molecules to prevent such loss. Shielding is very effective even for RbCs, with a relatively low dipole moment, and even more effective for molecules such as NaK, NaRb, and NaCs, with progressively larger dipoles. Varying the electric field allows substantial control over the scattering length, which will be crucial for the stability or collapse of molecular Bose-Einstein condensates. This arises because the dipole-dipole interaction creates a long-range attraction that is tunable with electric field. For RbCs, the scattering length is positive across the range where shielding is effective because the repulsion responsible for shielding dominates. For NaK, the scattering length can be tuned across zero to negative values. For NaRb and NaCs, the attraction is strong enough to support tetra-atomic bound states, and the scattering length passes through resonant poles where these states cross threshold. For KAg and CsAg, there are multiple bound states and multiple poles. For each molecule, we calculate the variation of the scattering length with field and comment on the possibilities for exploring new physics. Published by the American Physical Society 2024
The prospects for shielding ultracold, paramagnetic, dipolar molecules from inelastic and chemical collisions are investigated. Molecules placed in their first rotationally excited states are found to exhibit effective long-range repulsion for applied electric fields above a certain critical value, as previously shown for nonparamagnetic molecules. This repulsion can safely allow the molecules to scatter while reducing the risk of inelastic or chemically reactive collisions. Several molecular species of $^{2}\mathrm{\ensuremath{\Sigma}}$ molecules of experimental interest---RbSr, SrF, BaF, and YO---are considered, and all are shown to exhibit orders of magnitude suppression in quenching rates in a sufficiently strong laboratory electric field. It is further shown that, for these molecules described by Hund's coupling case (b), electronic and nuclear spins play the role of spectator with respect to the shielding.
Ultracold polar molecules possess long-range, anisotropic, and tunable dipolar interactions, providing unique opportunities to probe novel quantum phenomena. However, experimental progress has been hindered by excessive two-body loss, which also limits further cooling via evaporation. Recent work shows the loss can be mitigated by confining molecules in a two-dimensional geometry. However, a general approach for tuning molecular interactions in a full three-dimensional (3D) stable system has been lacking. Here, we demonstrate the use of an electric field-induced shielding resonance to suppress the reactive loss by a factor of 30 while preserving elastic, long-range dipolar interactions in a bulk gas of ultracold 40K87Rb molecules in 3D. The favorable ratio of elastic to inelastic collisions enables direct thermalization, the rate of which depends on the angle between the collisional axis and the dipole orientation controlled by an external electric field. This is a direct manifestation of the anisotropic dipolar interaction. We further achieve dipolar-interaction-mediated evaporative cooling in 3D. This work demonstrates control of a long-lived bulk quantum gas system with tunable long-range interactions, paving the way for the study of collective quantum many-body physics.
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 ≳106\gtrsim 10^{6}≳106 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.