Two-photon-assisted collisions in ultracold gases of polar molecules II : Optical shielding of ultracold polar molecular collisions

TL;DR

This work develops and analyzes a two-photon optical shielding (2-OS) scheme for ultracold polar molecules by coupling ground-state channels to excited channels via two lasers in a Raman-resonant Λ configuration, thereby engineering a laser-dressed, repulsive long-range interaction between colliding molecules. The authors formulate a dynamical five-level framework, construct a comprehensive Hamiltonian for two interacting molecules under two coherent fields, and compute laser-dressed potential energy curves that reveal long-range wells and dense avoided crossings in the entrance channel. Through full quantum scattering calculations at ultracold temperatures, they identify quasi-resonant conditions where elastic collisions are favoured over inelastic and reactive routes by up to a factor of a few, demonstrating a controllable, MHz-scale detuning sensitivity and narrow resonance features. While the shielding efficiency is moderate compared with microwave-based methods, the results establish 2-OS as a tunable, laser-based route to suppress losses and stabilize ultracold molecular samples, with potential synergy when combined with static electric fields or other shielding strategies.

Abstract

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 $^{23}$Na$^{39}$K 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 quasi-resonant 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 quasi-bound level of the long-range molecular pair induced by the lasers.

Figures (10)

• Figure 1: Schematic view of the five-level system relevant for 2-OS in the case of blue-detuned lasers. Energies are not to scale. The two photons with energies $\hbar \omega_1$ and $\hbar \omega_2$ (upper arrows) are detuned by a small detuning $\Delta$ with respect to the molecular transitions $\ket{j_i=0} \rightarrow \ket{j'_i=1}$ and $\ket{j_i=2} \rightarrow \ket{j'_i=1}$. ($i=A,B$) The sketched long-range potential energy curves (PECs) describe the interaction between two polar molecules colliding with the energy $E_{\mathrm{col}}$ in the space-fixed frame, characterized by their rotational quantum numbers $j_A$ and $j_B$ (see text for more details about the chosen system). This defines the five relevant coupled states $\ket{g_1}$, $\ket{g_2}$, $\ket{g_3}$, $\ket{e_1}$, $\ket{e_2}$, labeled at infinite distances by the rotational quantum numbers of the molecules. At all distances, the attractive entrance channel $\ket{g_1}$ is coupled to the repulsive channel $\ket{g_2}$ via the excited channel $\ket{e_1}$ by the two photons. The same coupling scheme occurs between $\ket{g_2}$ and $\ket{g_3}$ via $\ket{e_2}$.
• Figure 2: Adiabatic dressed PECs of two interacting NaK molecules prepared in the $\ket{j_X=0}$ level of the rovibronic ground state exposed to two lasers with $\Omega_1=2\pi \times 300$ MHz and $\Omega_2=2\pi \times 0.5$ MHz, and a blue detuning $\Delta=-2\pi \times 100$ MHz pictured by a downward blue arrow. (a) The laser $L_2$ is detuned by a large amount $\delta= 2\pi \times 60$ GHz from the Raman resonance. (b) The two lasers are tuned to the chosen Raman resonance ($\delta=0$, see text). The curves are labeled with the basis vector $\ket{n}$ that has the largest component in the expansion of Eq.\ref{['eq:dressed']} for $R \rightarrow \infty$.
• Figure 3: (a) Adiabatic dressed PECs of two interacting NaK molecules prepared in the $\ket{j_X=0}$ level of the rovibronic ground state exposed to two lasers with $\Omega_1=2\pi \times 456$ MHz and $\Omega_2=2\pi \times 831$ MHz, and a blue detuning $\Delta=-2\pi \times 4$ MHz (pictured by a downward blue arrow). (b) Enlarged view of the zone inside the red box in panel (a). The curves are labeled as in Fig. \ref{['fig:Dressed_pecs_non_eff']}. The red arrow shows the entrance channel for the collision. The choice of these specific values for the laser parameters is explained in Section \ref{['sec:dynamics']}.
• Figure 4: Collision rate coefficients $\beta_i^{\text{el}}$ (magenta), $\beta_i^{\text{inel}}$ (blue), and $\beta_i^{\text{rea}}$ (orange) at $E_{\mathrm{col}} = k_B \times 300$ nK as functions of $\Delta$ for $\Omega_2=2 \pi \times 200$ MHz and (a) $\Omega_1=2 \pi \times 50$ MHz, (b) $2 \pi \times 100$ MHz, (c) $2 \pi \times 150$ MHz, (d) $2 \pi \times 200$ MHz.
• Figure 5: (a) Variation of the 2-OS efficiency parameter $\gamma_i$ as a function of $\Delta$ at an energy $E_{\mathrm{col}} = k_B \times 300$ nK, for the Rabi frequencies $\Omega_1/(2\pi)=420$ MHz and $\Omega_1/(2\pi)=880$ MHz which generates two peaks at two values of $\Delta$ where elastic collisions dominate. (b) Variation of the corresponding rate coefficients $\beta_i^{\text{el}}$ (magenta line), $\beta_i^{\text{inel}}$ (blue line), $\beta_i^{\text{rea}}$ (orange line) (all labeled as $\beta$ on the vertical axis, for simplicity). (c) Variation of $\gamma_i$ with $\Omega_2$ for $\Omega_1/(2\pi)=420$ MHz and $\Delta/(2\pi)=-5$ MHz.