Tunable state-dependent interactions in collisionally stable mixtures of polar molecules

The gist: The authors propose encoding a pseudo-spin-1/2 system in the vibrational states of polar molecules using double microwave shielding to create collisionally stable mixtures with tunable, longrange dipolar interactions.

Encoding and Shielding Mechanism

The proposed method involves encoding a pseudo-spin-1/2 system in the ground (v = 0) and first excited (v = 1) vibrational states of polar molecules The double microwave shielding simultaneously shields molecules in both states, suppressing two-body losses by orders of magnitude while strictly avoiding threebody recombination This results in highly tunable, longrange dipolar Ising exchange (Jz), density-density (V), and spin-density (W) interactions. The microwave dressing is state-dependent and results in highly tunable, longrange dipolar Ising exchange (Jz), density-density (V), and spin-density (W) interactions.

Tunable Interaction Hamiltonian

The resulting effective dipolar interactions are parameterized by the dipolar lengths a v,v′ dd which in general depend on the vibrational state of both molecules v, v′ This pseudo-spin-dependence can equivalently be written as Vdd = ħ 2/2M1 − 3 cos squared θ12 / R312 h JzSˆz1Sˆz2 + V + W Sˆz1 + Sˆz2 i, with the Ising Jz = a00 dd + a11 dd − 2a01 dd, density-density V = (a00 dd + a11 dd + 2a01 dd)/4, and density-spin coupling W = (a00 dd − a11 dd)/2. These interaction length scales readily exceed the typical interparticle spacing, pushing the molecules deep into the strongly interacting regime.

Collision Stability and Loss Suppression

The central result of this work is that this dressing can simultaneously induce appreciably state-dependent interactions and suppress collisional loss in all relevant vibrational states. The molecules experience no transverse “flip-flop” interactions [J⊥(Sˆx1 Sˆx2 +Sˆy1Sˆy2)], which in principle result from first-order dipole-dipole interactions between molecules in different vibrational states. The molecular mixture must first be collisionally stable with respect to both two-body and three-body loss. The overall stability of the gas is dictated by the highest of these three loss rates, max(kvv′). A viable overlap window at ∆π/omegaπ > 2.5 is found where losses across all three collisional pairs are simultaneously suppressed.

Tuning Interaction Parameters

The authors demonstrate that scanning through these stable windows provides independent control over the interaction parameters. Two compelling tuning paths are highlighted, starting from configurations where the spin-dependence vanishes (W ≈ 0, Jz ≈ 0), but the spin-independent density-density interaction (V) is strong. The first path occurs for balanced fields (omegaσ/omegaπ = 1) and is shown in Fig. 3(b). The second path occurs for (omegaσ/omegaπ = 2) as shown in Fig. 3(c). These paths allow tuning interaction length scales exceeding the interparticle distance, placing the spin system in the strongly-interacting regime.

Applications and Extensions

In bulk gases, this setup enables the exploration of itinerant quantum magnetism and quantum droplets with novel anisotropic spin textures. In optical lattices, it naturally realizes extended Hubbard and t-Jz models. The scheme can be extended to higher vibrational manifolds, which is particularly promising for heavier molecules with significantly smaller rotation-vibration coupling constants. Furthermore, the framework applies equally to fermionic molecules, and the induced dipolar interactions are independent of quantum statistics. The interaction length scales can exceed typical interparticle spacing in both optical lattices and bulk gases.

Conclusion

In conclusion, the authors have proposed encoding pseudo-spin into the vibrational degree of freedom of ultracold polar molecules, where double microwave shielding eliminates collisional loss. This realizes long-range anisotropic dipolar interactions of the Ising exchange, density-density, and spin-density type that are all tunable by the microwave fields. The detunings and Rabi frequencies of the two microwave fields provide flexible independent control over interactions in multiple states.

How it works

1. Pseudo-spin encoding is achieved in the ground (v = 0) and first excited (v = 1) vibrational states.

2. Double microwave shielding suppresses two-body losses by orders of magnitude while avoiding threebody recombination.

3. Microwave fields are near-resonant with the rotational j = 0 → 1 transition, characterized by Rabi frequencies (omegaσ, omegaπ) and detunings (∆σ, ∆π).

4. The effective dipolar interactions are given by Vdd = ħ 2/2M1 − 3 cos squared θ12 / R312 h JzSˆz1Sˆz2 + V + W Sˆz1 + Sˆz2 i, where Jz, V, and W are dipolar length scales.

5. The strength of the dipolar interactions scales as (1+ ∆(v)/omega 2) −1, enabling state-dependent interactions.

Summary of Key Findings

- The system provides broad tunability and access to the strongly interacting regime using bosonic NaCs as a relevant example. 1

- The loss rates are continuously suppressed below 10−13 cm3/s across all three distinct types of collisions along the two trajectories shown in Fig. 5. 2

- Both proposed tuning paths continuously suppress all three loss rates below 10−13 cm3/s, enabling experiments to operate at high density. 3

- The interaction length scales can exceed typical interparticle spacing in both optical lattices and bulk gases. 4

**- The scheme can be extended to higher vibrational manifolds, suggesting applicability across v = 0 − 4.

1. Bold headers for tunable interaction parameters: The system can realize long-range anisotropic dipolar interactions that are tunably spin-dependent, allowing for independent control over interaction strengths parameterized by Ising (Jz), density-density (V), and density-spin (W) dipolar length scales.

2. Quantum simulation of strongly correlated electron models: The improved system can realize extended Hubbard and t-J models in optical lattices, enabling the exploration of physics underlying hightemperature superconductivity and magnetic ordering by realizing systems where interaction length scales readily exceed the typical interparticle spacing.

3. High-density, collisionally stable quantum gases: The system enables operation in the strongly interacting regime at densities such as 1014 cm−3, where the two-body lifetime exceeds 100 ms, allowing for observation of many-body dynamics.

4. Anisotropic spin texture generation: The setup can generate anisotropic spin textures in inhomogeneous gases and droplets through the induced dipolar spin-density interaction, a phenomenon that cannot arise from exchange interactions alone.

5. Extended SU(N) magnetism: By combining vibrational pseudo-spin with nuclear hyperfine states, the model can be extended to exhibit U(1) × SU(N) × SU(N−1) interactions, allowing for the realization of full SU(2N) symmetry.

We propose encoding a pseudo-spin- 1/2 system in the ground (v=0) and first excited (v=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 (J z), density-density (V), and spin-density (W) 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 t - J z models, opening new directions in quantum simulation.