**Harnessing Quantum Control with Floquet Engineering**  



Researchers at JILA and Harvard have employed Floquet engineering to fine-tune interactions between ultracold potassium-rubidium molecules. This breakthrough allowed them to observe *two-axis twisting dynamics*, a process that can create highly entangled states, opening new possibilities for advanced quantum sensing technologies.


**Unlocking the Secrets of Quantum Spins**  

Quantum spin interactions are at the heart of fascinating phenomena like superconductivity and magnetism. However, recreating and controlling these interactions in laboratory conditions remains a major challenge for physicists. Developing systems with precise control over these quantum behaviors is essential for pushing the frontiers of quantum research and technology.


In a recent *Nature* paper, JILA and NIST Fellow Jun Ye, a physics professor at the University of Colorado Boulder, and his team—working with collaborators from Mikhail Lukin’s group at Harvard—leveraged periodic microwave pulses through a technique called Floquet engineering. This approach allowed them to precisely control interactions between ultracold potassium-rubidium molecules, creating a system ideal for exploring fundamental magnetic behaviors. Notably, the team observed two-axis twisting dynamics, a key mechanism for generating entangled states, paving the way for future advancements in quantum sensing.


### **Leveraging Polar Molecules for Quantum Simulations**  

In this experiment, the researchers focused on ultracold potassium-rubidium molecules, which are polar—a promising platform for quantum simulations. By using Floquet engineering to fine-tune molecular interactions, they opened new pathways for exploring complex quantum many-body systems.


“There is significant interest in these quantum systems, especially with polar molecules, because their rich energy structure depends on multiple physical constants,” explains Calder Miller, a JILA graduate student and the study’s lead author. “This makes them highly sensitive to new physics effects. If we can engineer their interactions, we can potentially create entangled states with enhanced sensitivity to uncover new physics.”



### **Enhancing Quantum Sensing**  

Floquet engineering has proven to be a powerful tool for manipulating interactions in physical systems. This technique functions like a “quantum strobe light,” where adjusting the frequency and intensity of pulses can create unique effects—similar to how objects can appear to slow down or freeze under flashing lights. 


In a similar way, scientists use periodic microwave pulses to drive quantum systems, precisely controlling how particles interact. This ability to tune interactions allows them to generate novel quantum effects, opening new possibilities for advanced sensing applications and quantum technologies.



### **Achieving Precise Control Over Quantum States**  

“In our old setup, we were limited by how many pulses we could apply,” explains Annette Carroll, a JILA graduate student and co-author of the study. “To overcome this, we collaborated with the electronics shop to design an FPGA-based arbitrary waveform generator. Now, we can apply thousands of pulses, enabling us not only to engineer sequences that eliminate single-particle noise but also to modify the system’s interactions.”


Before employing Floquet engineering, the team encoded quantum information in the two lowest rotational states of the molecules—though many other states are available. An initial microwave pulse placed the molecules into a quantum superposition of these two “spin” states, laying the foundation for precise manipulation of their interactions.



### **Tuning Quantum Interactions with Floquet Engineering**  

After encoding quantum information, the researchers used Floquet engineering to adjust specific types of quantum interactions, specifically the XXZ and XYZ spin models. These models describe how particles’ quantum spins interact, playing a crucial role in understanding magnetic materials and many-body phenomena. 


Physicists often represent spin dynamics using a Bloch sphere, but a more intuitive analogy is to think of the molecules as dancers changing their steps based on interactions with their partners. Depending on the interaction, these "dancers" may push or pull on one another—representing shifts in spin orientation at the quantum level. By controlling these interactions, the researchers demonstrated a new way to choreograph the complex dynamics essential for future quantum research.



### **Tuning Interactions with Floquet Engineering**  

In the experiment, the researchers used Floquet engineering—acting like a “quantum strobe light”—to subtly alter the interactions between ultracold molecules. They verified that this approach produced spin dynamics comparable to those achieved through precise tuning with an applied electric field. However, the use of controlled pulse sequences allowed them to create less symmetric interactions that electric fields alone cannot generate, showcasing the unique versatility of Floquet engineering.


### **Observing Two-Axis Twisting Dynamics**  

A key breakthrough in the study was the observation of two-axis twisting dynamics. This phenomenon is essential for generating entangled quantum states, which are critical for advanced quantum sensing applications, offering new ways to enhance precision and sensitivity in future quantum technologies.



### **The Role of Two-Axis Twisting in Quantum Sensing**  

Two-axis twisting involves simultaneously pushing and pulling quantum spins along two different axes, generating highly entangled states. This process is crucial for advancing quantum sensing and precision measurements, as it efficiently creates *spin-squeezed states*. These states minimize quantum uncertainty in one direction of the spin system while increasing it in the orthogonal direction, enhancing sensitivity in experiments like high-precision spectroscopy. 


“It was pretty exciting when we saw the initial signatures of two-axis twisting,” recalls Calder Miller, the study’s first author. “We weren’t sure if it would work, but we gave it a try—and within a day and a half, it became clear that we had a signal.”



### **Realizing Two-Axis Twisting After Decades**  

The idea of two-axis twisting was first proposed in the early 1990s, but its experimental realization at JILA took until 2024. Alongside the work by Jun Ye and his team on ultracold molecules, another milestone was achieved by JILA and NIST Fellow James Thompson and his group. Using an entirely different method—cavity quantum electrodynamics (cavity QED)—they also demonstrated two-axis twisting, showing the versatility of this concept across different quantum platforms.


### **Planning Future Research Endeavors**  

While Ye’s team did not attempt to directly detect entanglement in their current system, they are already planning to explore it in future experiments. Successfully detecting entanglement would be a crucial next step toward realizing the full potential of their system for advanced quantum sensing and many-body physics research.



“The most logical next step is to improve our detection capabilities so we can effectively verify the generation of entangled states,” Miller adds. This enhancement will be essential for confirming their results and advancing the applications of their research in quantum sensing and beyond.