Floquet engineering tunes ultracold molecule interactions and produces two-axis twisting dynamics

The interactions between quantum spins underlie some of the universe’s most interesting phenomena, such as superconductors and magnets. However, physicists have difficulty engineering controllable systems in the lab that replicate these interactions.

Now, in a recently published Nature paper, JILA and NIST Fellow and University of Colorado Boulder Physics Professor Jun Ye and his team, along with collaborators in Mikhail Lukin’s group at Harvard University, used periodic microwave pulses in a process known as Floquet engineering, to tune interactions between ultracold potassium-rubidium molecules in a system appropriate for studying fundamental magnetic systems. Moreover, the researchers observed two-axis twisting dynamics within their system, which can generate entangled states for enhanced quantum sensing in the future.

In this experiment, the researchers manipulated ultracold potassium-rubidium molecules, which are polar. As polar molecules are a promising platform for quantum simulations, the tunable molecular interactions using Floquet engineering could open new doors for understanding other quantum many-body systems.

“There is a lot of interest in using these quantum systems, especially [with] polar molecules— there can be sensitivity to many new physics effects because the molecules have a rich energy structure that depends on many different physical constants,” explains JILA graduate student, and the study’s first author, Calder Miller. “So, if we can engineer their interactions, in principle, we can create entangled states that give better sensitivity to new physics.”

Implementing Floquet engineering

Floquet engineering has emerged as a useful technique for driving interactions within physical systems. This method acts like a “quantum strobe light,” which can create different visual effects, like making objects appear to move in slow motion or even stand still, by adjusting the speed and intensity of the flashes.

Similarly, by using periodic microwave pulses to drive the system, scientists can create different quantum effects by controlling how particles interact.

“In our old setup, we were limited in the number of pulses we could drive,” says Annette Carroll, a JILA graduate student on Ye’s research team and a fellow author of this study. “So, we worked with the electronics shop to develop an FPGA-based arbitrary waveform generator, which allows us to apply thousands of pulses now. This means that not only can we engineer a pulse sequence that removes single particle noise, but we can also modify the interactions in the system.”

Before implementing the Floquet engineering, the researchers first encoded quantum information in the molecules’ two lowest rotational states (though molecules have many more states). Using an initial microwave pulse, the molecules were put into a quantum superposition of these two “spin” states.

After encoding the information, the researchers used the Floquet engineering technique to see if they could tune specific types of quantum interactions, known as XXZ and XYZ spin models. These models describe how the particles’ inherent quantum spins interact with each other, which is fundamental to understanding magnetic materials and other many-body phenomena.

While physicists use a mathematically constructed Bloch sphere to show how spins evolve in these models, it can be easier to visualize the molecules as changing their dance pattern based on how they interact with their neighbors, or dance partners. These molecular dancers may switch from pulling or pushing on their partners, which, on a quantum level, can be equated to changes in spin orientation.

In the study, the “quantum strobe light,” or Floquet engineering, nudged these changes in interactions between molecules, which the researchers verified had produced similar spin dynamics to those generated by fine-tuning of the interactions using an applied electric field. In addition, the researchers precisely controlled the pulse sequence to realize less symmetric interactions that cannot be generated using electric fields.

Doing the (two-axis) twist

The researchers also observed that their technique produced two-axis twisting dynamics.

Two-axis twisting involves pushing and pulling the quantum spins along two different axes, which can lead to highly entangled states. This process is valuable for advancing sensing and precision measurements, as it allows for the efficient creation of spin-squeezed states. These states reduce the quantum uncertainty in one component of a spin system while increasing it in another orthogonal component, leading to enhanced sensitivity in spectroscopy experiments.

“It was pretty exciting when we saw the initial signatures of two-axis twisting,” Miller says. We weren’t sure that we were going to be able to make it work, but we tried it, and a day and a half later, it was pretty clear that we had a signal.”

The concept of two-axis twisting was proposed in the early 1990s, but its realization in two JILA laboratories had to wait until 2024. In addition to this work by Ye and his team, JILA and NIST Fellow and University of Colorado Boulder Physics professor James Thompson and his team used a completely different approach to working on atoms—cavity quantum electrodynamics, or cavity QED—also demonstrating two-axis twisting this year.

While the researchers did not attempt to detect entanglement in their system, they plan to do so in the future.

“The most logical next step is to improve our detection so we can actually verify the generation of entangled states,” Miller adds.