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arXiv:2508.00607 · Physical Review A

Two-photon-assisted collisions in ultracold gases of polar molecules

Charbel Karam, Gohar Hovhannesyan, Romain Véxiau, Maxence Lepers, Nadia Bouloufa-Maafa, Olivier Dulieu

Published Sep 22, 2025• 1 citation
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Abstract

We present a theoretical formalism to treat the ultracold dynamics of a pair of colliding polar molecules submitted to two laser fields. We express the dressed Hamiltonian including the dipole-dipole interaction of the colliding molecular pair, both in their ground and electronic excited states, as well as their interaction with the two laser fields. We apply adiabatic elimination of the electronic excited state to reduce the size of the dressed-state basis in which the dressed Hamiltonian is expressed. In an application, we investigate the feasibility of two-photon collisional shielding between two $^{23}\mathrm{Na}^{39}\mathrm{K}$ molecules, which could be favored by the Raman resonance condition suppressing unwanted spontaneous emission and photon scattering. We demonstrate the influence of laser Rabi frequencies on the dynamics through the computation of elastic, inelastic, and reactive collision rates, which is still insufficient to ensure noticeable shielding.

DOI
10.1103/9q1s-pjrs

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We present a theoretical formalism to treat the ultracold dynamics of a pair of colliding polar molecules submitted to two laser fields. We express the dressed Hamiltonian including the dipole-dipole interaction of the colliding molecular pair, both in their ground and electronic excited states, as well as their interaction with the two laser fields. We apply adiabatic elimination of the electronic excited state to reduce the size of the dressed-state basis in which the dressed Hamiltonian is expressed. In an application, we investigate the feasibility of two-photon collisional shielding between two 23Na39K^{23}\mathrm{Na}^{39}\mathrm{K}23Na39K molecules, which could be favored by the Raman resonance condition suppressing unwanted spontaneous emission and photon scattering. We demonstrate the influence of laser Rabi frequencies on the dynamics through the computation of elastic, inelastic, and reactive collision rates, which is still insufficient to ensure noticeable shielding.
We theoretically investigate the collisions between ultracold polar molecules in the presence of two lasers ensuring a Raman resonant transition on individual molecules to suppress photon scattering, taking the example of bosonic Na 23 K 39 molecules. By varying laser detunings and intensities, we enable a repulsive long-range interaction potential between molecules. After solving a set of coupled Schrödinger equations with the Hamiltonian written in the basis of laser-dressed states of the molecule pair at infinite distance, we identify quasiresonant conditions under which elastic collisions are favored over inelastic and reactive ones, by a factor of about 2, thus demonstrating a promising pathway for efficient two-photon optical shielding of ultracold molecular collisions. The results are analyzed in terms of scattering length of the colliding laser-dressed molecules, which exhibit prominent resonances assigned to the interaction of the entrance channel with other specific channels, consistent with the existence of a quasibound level of the long-range molecular pair induced by the lasers.
Abstract Ultracold temperatures in dilute quantum gases opened the way to an exquisite control of matter at the quantum level. Here we focus on the control of ultracold atomic collisions using a laser to engineer their interactions at large interatomic distances. We show that the entrance channel of two colliding ultracold atoms can be coupled to a repulsive collisional channel by the laser light so that the overall interaction between the two atoms becomes repulsive: this prevents them to come close together and to undergo inelastic processes, thus protecting the atomic gases from unwanted losses. We illustrate such an optical shielding (OS) mechanism with 39 K and 133 Cs atoms colliding at ultracold temperature (<1 μK). The process is described in the framework of the dressed-state picture and we then solve the resulting stationary coupled Schrödinger equations. The role of spontaneous emission and photoinduced inelastic scattering is also investigated as possible limitations of the shielding efficiency. We predict an almost complete suppression of inelastic collisions over a broad range of Rabi frequencies and detunings from the 39 K D2 line of the OS laser, both within the [0, 200 MHz] interval. We found that the polarization of the shielding laser has a minor influence on this efficiency. This proposal could easily be formulated for other bialkali-metal pairs as their long-range interaction are all very similar to each other.
Research focusing on the formation of ultracold atomic and molecular quantum gases is a continuously expanding field due to its envisioned applications such as quantum-controlled chemistry or quantum simulation. The aim of our theoretical work is to find ways to suppress inelastic or reactive processes between colliding particles in ultracold quantum gases. Using a laser field detuned to the blue of a relevant transition, we propose to couple the initial colliding particle state to a repulsive excited one, thus preventing the particles to come close to each other. This "blueshielding" technique is applied for ultracold quantum gases, close to quantum degeneracy. We investigate the optical shielding in ultracold39K-Cs collision by using close-coupling channel method. As the (3)3Σ+and (2)3Π+molecular states are repulsive in long range[1], one verified effective optical shielding can be realized via driving the transition from the ground α3Σ+state to these excited states in the presence of linear-polarized light. We demonstrate that a strong field with a small blue detuning to the atomic transition is to the benefit of shielding since the Condon point is farther away from the inner region of ground triplet state. The spontaneous emission effect is taken into account by considering excited optical potentials with the modified formula of shielding rate [2]. We expect the shielding efficiency could be improved by using circular-polarized light [3].
Polar quantum gases represent promising platforms for studying many-body physics and strongly correlated systems with possible applications e.g. in quantum simulation or quantum computation. Due to their large permanent electric dipole moment polar molecules in electric field exhibit strong long-range anisotropic dipole-dipole interactions (DDIs). The creation and trapping of ultracold dipolar diatomic molecules of various species are feasible in many experimental groups nowadays. However long time trapping is still a challenge even in the case of the so called nonreactive molecules which are supposed to be immune against inelastic collisions in their absolute ground state [1] . Various hypothesis have been invoked to explain the possible mechanisms behind the trapping loss, however the check of their pertinence is not trivial since the final products can not be easily detected [2] . To overcome the loss processes we propose the suppression of inelastic collisions between molecules using optical shielding (OS). OS relies on the modification of long-range interactions between ground-state and excited molecules by laser light. The first experimental proof of OS process was demonstrated in case of the collision between identical ultracold alkali-metal atoms [3] .
We analyze the temporal evolution of the population of ultracold polar molecules in a microwave (mw) field with a circular polarization. The molecules are in their ground state and treated as rigid rotors with a permanent dipole moment which interact with each other via the dipole–dipole (DD) interaction V dd . The mw field mixes states with different quantum and photon numbers and the collisional dynamics in the mw field is mostly controlled by the ratios of the mw field frequency versus the rotational constant, and mw field Rabi frequency versus the rotational constant. There exists a special scattering process which is elastic by nature and due to a rotational energy exchange between the ground and the first excited rotational states. To analyze dynamics of polar molecules system in the mw field the equation of motion for the bare and dressed states is solved under different mw field parameters and molecular gas characteristics. Depending on the ratio of the Rabi frequency of a mw field and the magnitude of the DD interaction, beatings and oscillations occur in the bare and dressed states time-development. At a certain relation between the magnitudes of the mw detuning δ and the DD interaction , peak structures appear in the population of the excited bare state. Each peak is associated with an avoided crossing between the dressed states adiabatic curves at the same position of mw detuning.
We discuss the influence of collisions on the dynamics of an ultracold gas whose constituents interact via dipolar forces. This dynamics is governed by the elastic scattering cross section of the molecules, which is to some extent under the experimentalist's control. We compare side-by-side several different situations, highlighting their similarities and differences. These situations are collisions between: 1) point dipoles; 2) electric-field-shielded polar molecules; and 3) microwave-shielded polar molecules, including the effect of microwave ellipticity.