Master’s Thesis on Floquet-Feshbach resonances

In April 2023, I completed my master’s thesis with the title Towards probing and understanding radio-frequency induced Floquet-Feshbach resonances in ultracold lithium-6 gases at RPTU Kaiserslautern-Landau (former TU Kaiserslautern) in the group of Artur Widera. The work centers on theoretical studies how the interaction between two colliding lithium-6 atoms can be modified using strong oscillatory magnetic fields and the production of such fields in an experiment.

Small spoiler 2025: during my PhD, I was able to experimentally verify and investigate these resonances. The preprint of the corresponding paper can be found here. Once it is peer-reviewed and published, I’ll share a more detailed article about it. But for now, back to the Master’s thesis.

Background: Tunable Interactions in Ultracold Gases

Tuning interactions between ultracold atoms is not new. The established method uses Feshbach resonances, which occur when a bound molecular state becomes degenerate with a scattering channel. By adjusting an external static magnetic field, the scattering length $a_s$, and thus the effective interaction strength, can be precisely controlled.

Lithium-6 is particularly special because it features an exceptionally broad Feshbach resonance, enabling fine control over the scattering properties.

Previous work suggested that not only static, but also oscillatory magnetic fields can induce new resonances. However, specific calculations for lithium-6 were lacking.

Theoretical Work

A central part of my thesis was to explore the effect of oscillatory magnetic fields on lithium-6 using numerical coupled-channel calculations. For this, I implemented a published algorithm that solves coupled Lippmann–Schwinger equations via a Chebyshev polynomial expansion.

The results showed that oscillatory magnetic fields in the MHz regime can induce an entire series of new resonances. For example, around the narrow I = 2 resonance at 543 G, applying an oscillatory field of ν = 4 MHz and BRF = 10 G generates many additional, equally spaced resonances. Moreover, new Floquet-Feshbach resonances appear, linked to the I = 0 channel.

Experimental Constraints

The theoretical results predicted that observing these resonances would require modulation amplitudes of about 8 G. To achieve this in the planned experimental setup, a glass chamber with ~35 mm size, I calculated the magnetic field produced by two spiral Helmholtz coils spaced 37 mm apart. The simulations showed that reaching 8 G would require RF currents of ~7 A.

Driving such large currents at RF frequencies is far from trivial. Thus, the second part of my thesis focused on designing and building the necessary RF coils and circuitry.

RF Circuit Engineering

The basic concept was to resonantly drive two coupled high-Q LC circuits with high-power RF amplifiers. This presented a challenge: the resistance at resonance was only about 2 Ω, which mismatches the 50 Ω impedance that amplifiers are designed for.

The solution was to use quarter-wavelength transformers, constructed by cutting standard coaxial cables to the right length and soldering them in parallel. This allowed efficient power transfer into the LC circuits.

Still, one major issue remained: heating. At high RF power, most of the energy was dissipated in the coils. To mitigate this, the coils were made from hollow copper tubing and cooled with water.

However, heating caused the resonance frequency of the LC circuits to drift, which destabilized the fields. To solve this, I developed an automatic tuning circuit: reflected RF power was continuously monitored and used to adjust variable capacitors via stepper motors, keeping the resonance frequency locked even as the system heated up