Researchers have discovered a non-uniform temperature distribution in micromechanical resonators that affects their design and performance in quantum science and precision measurements. To measure small changes in quantities such as forces, magnetic fields, masses of small particles, and even gravitational waves, physicists use micromechanical resonators that act like tuning forks and resonate at specific frequencies. Traditionally it was believed that the temperature in these devices was uniform.

Temperature change in resonators

However, JILA Fellow and University of Colorado Boulder physics professor Cindy Regal and her team, Dr. New research by Ravid Shaniv and graduate student Chris Ritz found that temperature can change in certain scenarios, such as advanced studies of interactions between light and mechanical objects. differs in different parts of the resonator, leading to unexpected behavior. His observations were published Physical Examination ResearchIt could potentially revolutionize the design of micromechanical resonators for quantum technologies and precision sensing.

“In quantum science experiments, understanding the consequences of this temperature difference will allow you to create your mechanical quantum state more precisely and keep it unchanged for longer periods of time, which are important starting points for quantum applications,” said JILA research associate and first author Ravid. Shaniv.

Minute meter modes

Because of their flexible design, micromechanical resonators are a standard tool in many different areas of physics. These devices are often made of silicone or similar materials and can take many forms: beams, cantilevers, membranes, or disks. Their small size allows them to oscillate at high frequencies, usually in the megahertz (MHz) to gigahertz (GHz) range.
The versatility of micromechanical resonator design also allows physicists to fine-tune its oscillations. Just as a guitar string can vibrate in a variety of ways (either the entire string moving back and forth, or just part of it vibrating while the rest remains stationary), micromechanical resonators can vibrate in different patterns, or “modes.” The most famous mode is the basic mode, in which the entire structure moves in harmony. But there are also higher order modes in which other parts of the resonator act in more complex patterns.

To measure the movement of the resonator, physicists use laser beams. The cavity acts as a “moving mirror” and the reflected laser light carries information about its position. When compared to light reflected from a single fixed mirror, an interference pattern emerges that shows the movement of the resonator with ultra-high precision.

By observing these modes optically and discussing them with other physicists over the years, Shaniv and Regal noticed something interesting. “People noticed that some of these modes showed more thermal motion than others,” Shaniv said. “Often people want to eliminate this movement as much as possible because it can overshadow any subtle effects they want to experience.”

Physicists have suggested that this extreme thermal motion may be due to the resonator absorbing the laser light as heat. Different resonator modes can have different motion patterns that lead to different stress or strain zones, which can lead to different amounts of thermal motion.

In many observations, the more complex the mode of the resonator, the more its thermal energy deviates from previous theories that assumed the temperature of each mode was the same. “We wanted to investigate why this is and how we could achieve an optimal design for these modes,” Shaniv continued.

Creation of temperature profiles

To delve deeper into this temperature mystery, Shaniv and Regal created custom temperature profiles for each mode. For this, the researchers used a “phonon crystal” made of silicon nitride. The crystal served as a playground where the researchers could design resonator modes and create different temperature profiles, allowing them to observe the induced thermal motion of each resonator mode.

To create the temperature profile, the team heated a spot on the crystal to very high temperatures while keeping the edge of the gap at room temperature. After developing the profile and measuring the thermal motion, the researchers found some very interesting results. Depending on the geometry of the mode, some modes showed increased thermal motion, although some parts of the cavity became extremely hot, others showed only moderate heating, and some showed no heating at all. “You could see this dramatic difference when you turned the knob all the way through the trial,” Regal explained.

“By looking at really large temperature differences between modes, we were able to reconstruct the temperature profile of the resonator directly from the measured thermal motion and even find some material parameters that are not usually easy to predict, such as the emission coefficient, which indicates how much radiation our device emits,” Shaniv continued.
By seeing which modes are associated with different thermal motions, the team can begin to predict how the performance of the resonators might vary depending on the modes. As Rigal explains, “The natural next step is to ask whether these concepts can be used not only to understand how to keep resonators cold for quantum research, but also for thermal dating.”

Designing better resonators

With the knowledge gained, the scientific and engineering communities can make significant advances in the development and application of these small but extremely important devices. “We have actually given a real merit figure in our document where groups can work towards this,” Shaniv explained. “For example, we now have a certain parameter that we can put as a constraint on the computer and try to make the best resonator possible.”