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arXiv:2610.41003

Tunable Three-Body Interactions in Microwave-Shielded Polar Molecules

Hanwei Yang, Tijs Karman

cond-mat.quant-gasphysics.atom-phphysics.chem-phquant-phSubmitted Oct 29, 2026• Announced Nov 2, 2026
arXivHTMLPDF

Abstract

We show that microwave shielding, which enables collisionally stable ultracold polar molecules, also leads to genuine nonadditive three-body interactions comparable to the shielding interaction itself. Their magnitude, sign, and geometrical dependence can be flexibly controlled through microwave parameters and orientation. Interaction strengths can reach the ten kilohertz-scale for ultrapolar molecules in typical optical lattices. The nonadditive three-body interactions can stabilize novel many-body phases, and should be accounted for in quantum simulation with microwave shielded molecules.

AI Summary

Microwave shielding suppresses losses in ultracold polar molecules, but effective descriptions commonly retain only pairwise interactions. This paper asks when shielding also generates appreciable nonadditive three-body forces and how these can be controlled. A second-order expansion of the dipole–dipole interaction identifies cross-pair processes in which one molecule is virtually excited by its interactions with two others. Microwave-induced parity mixing permits these processes, producing terms proportional to $R_{ij}^{-3}R_{jk}^{-3}$, rather than the $R^{-9}$ leading three-body interaction of undressed parity eigenstates. The effective potential separates into three microwave-dependent coefficients and angular factors. Numerical dressed-state calculations and accompanying Python code evaluate both pairwise and three-body potentials. At double-microwave dipolar compensation, three-body and residual pairwise interactions both scale as $R^{-6}$ and can be comparable. For KAg at lattice spacing $a=532\,\mathrm{nm}$ and total Rabi frequency $1\,\mathrm{MHz}$, predicted three-body strengths reach order $10\,\mathrm{kHz}$. Microwave settings and lattice orientation control magnitude and sign. Canceling the full nearest-neighbor pair potential allows the three-body contribution to exceed residual pair interactions for a selected three-site configuration. At compensation, the total second-order interaction remains repulsive despite potentially attractive three-body terms. The treatment assumes dipole couplings small relative to dressed-channel splittings. Calculations omit hyperfine structure and static electric and magnetic fields; the stated species-independent scaling has small nonuniversal corrections from additional rotational states. Proposed consequences for ordered many-body phases are not calculated.

Little sign of AI-generated textPossible error

Error found: The abstract's proposed stabilization of novel many-body phases is not demonstrated for the derived interactions by any many-body calculation in the paper. Equation (S11) omits the spherical-tensor factor (-1)^m required by Eq. (4), giving the wrong printed sign for w1, although the reported negative w1 is consistent with the corrected expression.

Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.

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We show that microwave shielding, which enables collisionally stable ultracold polar molecules, also leads to genuine nonadditive three-body interactions comparable to the shielding interaction itself. Their magnitude, sign, and geometrical dependence can be flexibly controlled through microwave parameters and orientation. Interaction strengths can reach the ten kilohertz-scale for ultrapolar molecules in typical optical lattices. The nonadditive three-body interactions can stabilize novel many-body phases, and should be accounted for in quantum simulation with microwave shielded molecules.
Microwave shielding suppresses losses in ultracold polar molecules, but effective descriptions commonly retain only pairwise interactions. This paper asks when shielding also generates appreciable nonadditive three-body forces and how these can be controlled.
A second-order expansion of the dipole–dipole interaction identifies cross-pair processes in which one molecule is virtually excited by its interactions with two others. Microwave-induced parity mixing permits these processes, producing terms proportional to Rij−3Rjk−3R_{ij}^{-3}R_{jk}^{-3}Rij−3​Rjk−3​, rather than the R−9R^{-9}R−9 leading three-body interaction of undressed parity eigenstates. The effective potential separates into three microwave-dependent coefficients and angular factors. Numerical dressed-state calculations and accompanying Python code evaluate both pairwise and three-body potentials.
At double-microwave dipolar compensation, three-body and residual pairwise interactions both scale as R−6R^{-6}R−6 and can be comparable. For KAg at lattice spacing a=532 nma=532\,\mathrm{nm}a=532nm and total Rabi frequency 1 MHz1\,\mathrm{MHz}1MHz, predicted three-body strengths reach order 10 kHz10\,\mathrm{kHz}10kHz. Microwave settings and lattice orientation control magnitude and sign. Canceling the full nearest-neighbor pair potential allows the three-body contribution to exceed residual pair interactions for a selected three-site configuration. At compensation, the total second-order interaction remains repulsive despite potentially attractive three-body terms.
The treatment assumes dipole couplings small relative to dressed-channel splittings. Calculations omit hyperfine structure and static electric and magnetic fields; the stated species-independent scaling has small nonuniversal corrections from additional rotational states. Proposed consequences for ordered many-body phases are not calculated.
The ability to tune interparticle interactions is one of the main advantages of using ultracold quantum gases for quantum simulation of many-body physics. Current experiments with ultracold polar molecules employ shielding with microwave or static electric fields to prevent destructive collisional losses. The interaction potential of microwave-shielded molecules can be tuned by using microwaves of two different polarisations, while for static-field-shielded molecules the tunability of interactions is more limited and depends on the particular species. In this work, we propose a general method to tune the interactions between static-field-shielded molecules by applying a microwave field. We carry out coupled-channel scattering calculations in a field-dressed basis set to determine loss rate coefficients and scattering lengths. We find that both the s-wave scattering length and the dipole length can be widely tuned by changing the parameters of the microwave field, while maintaining strong suppression of lossy collisions.
We propose encoding a pseudo-spin-1/21/21/2 system in the ground (v=0v=0v=0) and first excited (v=1v=1v=1) vibrational states of polar molecules. Double microwave shielding simultaneously shields molecules in both states, suppressing two-body losses by orders of magnitude while strictly avoiding three-body recombination. The microwave dressing is state-dependent and results in highly tunable, long-range dipolar Ising exchange (JzJ_zJz​), density-density (VVV), and spin-density (WWW) interactions. These interaction length scales readily exceed the typical interparticle spacing, pushing the molecules deep into the strongly interacting regime. In bulk gases, this enables the exploration of itinerant quantum magnetism and quantum droplets with novel anisotropic spin textures; in optical lattices, it naturally realizes extended Hubbard and ttt-JzJ_zJz​ models, opening new directions in quantum simulation.
We develop double microwave shielding, which has recently enabled evaporative cooling to the first Bose-Einstein condensate of polar molecules [Bigagli , Nature , 289 (2024)]. Two microwave fields of different frequency and polarization are employed to effectively shield polar molecules from inelastic collisions and three-body recombination. Here, we describe in detail the theory of double microwave shielding. We demonstrate that double microwave shielding effectively suppresses two- and three-body losses. Simultaneously, dipolar interactions and the scattering length can be flexibly tuned, enabling comprehensive control over interactions in ultracold gases of polar molecules. We show that this approach works universally for a wide range of molecules. This opens the door to studying many-body physics with strongly interacting dipolar quantum matter.
We show that, in appropriate regimes, ultracold collisionally shielded molecules in an optical lattice realize a controlled extended Hubbard model, despite their large-radius hard-core repulsion. We compute the Hubbard parameters and show lattice depth and microwave-induced dipolar interactions provide flexible, independent control of on- and off-site interactions. This makes shielded molecules a powerful platform for extended Hubbard models and enables an interaction microscope that can distinguish inter-hole interactions in doped Mott insulators - crucial to superconductivity and strange metallicity - that are indistinguishable with quantum gas microscopy alone.
We propose a method to realize stable, tunable two-component quantum mixtures of ultracold polar molecules. First, we show that a pair of polar molecules in two distinct rovibrational states exhibits a repulsive interaction, thereby leading to collisional shielding without requiring any external field. We refer to this as "vibrational shielding". This intercomponent interaction is tunable by an external static electric or a microwave field, with the latter stabilizing both inter- and intracomponent interactions in a two-component bulk mixture. Additionally, we show that two microwave fields can independently tune the interactions of the individual components. Our findings thus open the door to the experimental realization of tunable quantum mixtures using polar molecules, analogous to tunable magnetic Feshbach resonances in two-component atomic quantum gases.
We describe the ro-vibrational van der Waals interaction between ultracold polar molecules. This interaction is strong, leading to fast elastic collisions and orders of magnitude suppression of collisional loss. This enables evaporative cooling of Fermi mixtures of molecules in different ro-vibrational states, without active shielding by applying external fields. The scheme is compatible with microwave shielding, where it enables controlled state dependent interactions, opening up new opportunities for quantum simulation and impurity physics. The interaction can also be used to stabilize fermionic molecules in optical lattices, to control interactions in synthetic dimensions, for enhanced tweezer loading, and direct infrared shielding.