Floquet-Engineering of Feshbach Resonances in Ultracold Gases

Abstract

Scattering resonances are fundamental in science, spanning energy scales from stellar nuclear fusion to ultracold collisions. In ultracold quantum gases, magnetic Feshbach resonances have transformed quantum many-body research by enabling precise interaction control between atoms. Here, we demonstrate unprecedented control to engineer new Feshbach resonances at tunable positions via Floquet driving in a $^{6}$Li atom gas, achieved through strong magnetic field modulation at MHz frequencies. This periodic modulation creates new resonances whenever dressed molecular levels cross the atomic threshold. By adding a second modulation at twice the base frequency, we tune the asymmetry of resonance loss profiles and suppress two-body losses from Floquet heating. This technique enhances control over atomic interactions, expanding possibilities for quantum simulations of complex systems and studies of exotic quantum phases.

Figures (6)

• Figure 1: Occurance of Floquet-Feshbach resonances. (A) Simplified sketch of the two-channel model for Feshbach resonances. An atom pair collides on potential B, coupled to potential A with a bound state $\ket{e}$. A Feshbach resonance occurs when the colliding pair is resonant with $\ket{e}$. If the potentials correspond to molecular configurations with different magnetic moments, their energy shift $\Delta_E$ can be tuned via the magnetic bias field. (B) Magnetic field dependence of the two highest molecular levels and the atomic threshold of two 6Li atoms in the lowest hyperfine states $\ket{a}$ and $\ket{b}$. The two accessible $s$-wave Feshbach resonances correspond to molecular levels with total nuclear spin $I=2$ (narrow resonance at $\qty{543.28}{G}$) PhysRevLett.108.045304 and $I=0$ (broad resonance at $\qty{832.18}{G}$) PhysRevLett.110.135301. At low collision energies, a Feshbach resonance occurs when a molecular state crosses the atomic threshold. Inset highlights the $I=2$ resonance. (C) and (D) Modulating the magnetic field dresses the molecular levels, and a Floquet-Feshbach scattering resonance occurs when a dressed molecular state crosses the atomic threshold. Arrows indicate resonance positions, with dashed lines indicating the continuation of the $I=2$ scattering pole into the continuum. (E) Floquet-Feshbach resonances at $\qty{18.15}{MHz}$ modulation with $B_\text{rf}^{(\text{a})} \approx \qty{3}{G}$. The upper panel shows experimental loss spectroscopy data, fitted with Gaussians to extract resonance positions. The lower panel displays the calculated real (blue) and imaginary (ochre) parts of the $s$-wave scattering length $a_s$, both showing resonant features corresponding to atom loss. Error bars represent standard deviation over at least five measurements per data point.
• Figure 2: Tuning of Floquet-Feshbach resonances. (A) Floquet-Feshbach resonance positions as a function of modulation frequency. Solid lines show resonance position obtained from numerical coupled-channel calculations. Data points show measured resonance positions using loss spectroscopy. The error bars indicate $1 \sigma$ statistical error arising due to bias coil current fluctuations, with frequency uncertainty being negligible. (B) Magnetic field shift of the $(I=0, \Delta_N= + 1)$ Floquet-Feshbach resonance for five modulation frequencies. The upper panel shows experimental data fitted with Gaussians, while the lower panel shows theoretical scattering length calculations. This resonance shows the largest shift of $\qty{40.3}{G}$ between $\qty{7.3}{MHz}$ and $\qty{39.0}{MHz}$. (C) Loss spectrum and scattering length recorded at a modulation frequency of $\qty{9}{MHz}$ and a modulation strength of $B_\text{rf}^{(\text{a})} \approx \qty{5}{G}$ showing Floquet-Feshbach resonances of the $I=2$ level up to order $\pm3$. Error bars indicate $1 \sigma$ of observed variation in atom number $N_\text{rel}$. (D) Dependence of the $(I=0,\Delta_N=+1)$ resonance's position on the modulation strength for a driving frequency of $\qty{12.95}{MHz}$. The left panel shows calculated (solid line) and measured resonance positions. The right panel shows atomic loss spectroscopy data taken without artificial broadening of the resonance, exhibiting a strong asymmetry. The atomic loss is fitted with a Fano profile.
• Figure 3: Two-color engineering of Floquet-Feshbach resonances. Effect of the additional two-color drive on the losses at the $(I=0,\Delta_N=+1)$ Floquet-Feshbach resonance. The strength of the first harmonic $B_\text{rf}^{(\text{a})}$ and the frequency $\nu$ are fixed at $\qty{8.9}{G}$ and $\qty{13.1}{MHz}$ respectively, while the strengths of the second harmonic $B_\text{rf}^{(\text{b})}$ is varied. (A) Atomic loss data and theoretical scattering length for six different strengths of $B_\text{rf}^{(\text{b})}$. The imaginary part of the scattering length is dramatically affected by the two-color drive, while the real part is affected only very slightly. The effect of this can be seen in the reduced atomic loss. (B) Loss data for 36 different values of $B_\text{rf}^{(\text{b})}$. The upper part shows the loss spectra for increasing $B_\text{rf}^{(\text{b})}$ with $\phi=0$. The lower part shows respectively the loss spectra for $\phi=\pi$, corresponding to negative $B_\text{rf}^{(\text{b})}$. (C) Thermally averaged inelastic scattering cross section $\sigma_\text{inel}^\text{avg}$ calculated using coupled-channel calculations, for the same range as in (B).
• Figure 4: Induced elastic interactions along a Floquet-Feshbach resonance. (A) Evolution of the atomic cloud's width after a sudden quench of the trap depth for various magnetic fields across the static $I=0$ resonance, respectively in (D) across the $(I=0, \Delta_N=+1)$ Floquet-Feshbach resonance. The magnetic field values correspond to elastic scattering lengths as indicated in (B) and (E). By fitting the cloud's oscillatory response we can extract oscillation amplitude $A$ and decay rate $\gamma_A$. Plotting the ratio $A/\gamma_A$ over the magnetic field value shows typical resonance behavior, seen in (C) and (F). Errors bars give fit uncertainties.
• Figure 5: Schematic of the rf circuit. The circuit features two coupled, resonantly driven LC circuits, with variable capacitors for tuning the resonance frequency. Impedance matching to the $\qty{50}{\Omega}$ amplifiers is achieved using quarter-wavelength transformers, constructed by connecting several coaxial cables in parallel.