Floquet engineering optimizes interactions between ultra-cold molecules and produces dual-axis torsional dynamics

Interactions between quantum spins are behind some of the most interesting phenomena in the universe, such as superconductors and magnets. However, physicists have struggled to design controllable systems in the laboratory that reproduce these interactions.

Now, in a recently published article Nature Jun Ye, a professor of physics at the University of Colorado Boulder and a member of JILA and NIST, and his team, along with collaborators from Mikhail Lukin’s group at Harvard University, used periodic microwave pulses in a process known as Floquet engineering to tune the interactions between ultracold potassium-rubidium molecules in a system suitable for studying fundamental magnetic systems. In addition, the researchers observed two-axis torsional dynamics within their system, which can generate entangled states for improved quantum sensing in the future.

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

“There’s a lot of interest in using these quantum systems, especially with polar molecules. They can be sensitive to many effects of the new physics because molecules have a rich energetic structure that depends on many different physical constants,” says Calder Miller, a JILA graduate student and first author of the study. “So if we can engineer their interactions, we can in principle create entangled states that are more sensitive to the new physics.”

Implementation of Floquet engineering

Floquet engineering has become a useful technique for controlling interactions within physical systems. The method acts like a “quantum strobe light,” which can create different visual effects, such as making objects appear to be moving in slow motion or even standing 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 the particles interact.

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

Before implementing Floquet’s engineering, the researchers first encoded quantum information in the molecules’ two lowest spin states (although molecules have many more states). Using an initial microwave pulse, the molecules were placed in 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 inherent quantum spins of particles 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 may be easier to visualize molecules changing their dance patterns based on how they interact with their neighbors, or dance partners. These molecular dancers can switch from pulling to pushing on their partners, which, at the quantum level, can be thought of as changes in spin orientation.

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

Do the twist (two-axis)

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

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

“It was really exciting to see the first two-axis torsion signatures,” Miller says. “We weren’t sure we could do it, but we tried and a day and a half later it was pretty clear we had a signal.”

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

Although 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 that we can actually verify the generation of entangled states,” Miller adds.