Â鶹ÒùÔº

As the number of particles in a physical system increases, its properties can change and different phase transitions (i.e., shifts into different phases of matter) can take place. Microscopic systems (i.e., containing only a few particles) and macroscopic ones (i.e., containing many particles) are thus typically very different, even if the types of particles they are made up of are the same.

Mesoscopic systems lie somewhere between microscopic and macroscopic systems, as they are small enough for individual particle fluctuations to impact their dynamics and yet large enough to support collective particle dynamics. Studying these middle-sized physical systems can yield interesting insight into how the fluctuations of individual particles can give rise to the collective particle behavior observed as a system grows.

Researchers at the University of California Berkeley and Columbia University recently introduced a new approach to precisely realize physical systems that are ideal for studying mesoscopic physics and the underpinnings of phase transitions. Their approach, outlined in a paper in Nature Â鶹ÒùÔºics, relies on the use of atom tweezer arrays to control the number of atoms in a system and how they interact with light.

"My research group has been involved for many years in experiments where ultracold gases of atoms are placed within optical resonators, allowing us to explore a wide range of quantum mechanical phenomena that come about from the strong interaction between atoms and light," Dan M. Stamper-Kurn, senior author of the paper, told Â鶹ÒùÔº.

"That work has advanced technically over several generations of experiment: a first setup where we could place a large gas containing hundreds of thousands of atoms in an optical cavity, but with little control over where the atoms are located; a second setup where we could place smaller ensembles of thousands of atoms, but could control precisely where the atoms were located; and now a third generation experiment where we adapt the new and rapidly advancing method of atom tweezer arrays to place mesoscopic samples (between 1 and 20 atoms for now) at precise locations within the cavity."

These optical cavity systems, consisting of two highly reflective mirrors facing each other, can be used to study a wide range of physical processes. These include atom-light interactions, collective light scattering, the collecting of mid-circuit measurements in quantum computers, and the exploration of the quantum limits in sensing applications and more.

"The area where perhaps my group has had the most creative contributions is in creating cavity optomechanical systems using ultracold atoms and high-finesse optical cavities," said Stamper-Kurn. "The topic of cavity optomechanics brings us in contact with people using LIGO to do gravity wave astronomy, people using acoustics for quantum information processing, people developing all sorts of sensors, including those searching for quantum effects of gravity, and so on. So, the topic of cavity optomechanics was fresh on my mind when our latest cavity/tweezer system came online."

The team's experiment had two key objectives, the first of which was to answer a scientific question and the second to open new possibilities for research. The scientific question they addressed is: How do phase transitions and symmetry breaking change when passing from a macroscopic system, which typically presents sharp phase transitions, to a mesoscopic system, in which phase transitions smear out more gradually?

"Our experiment highlights that, really for any system, large or small, the question of 'Does a phase transition occur' should really be asked in the context of a timescale," explained Stamper-Kurn. "The question is 'Over a period of time, does a system undergo a phase transition to a permanent symmetry breaking phase?'

"For macroscopic systems, the answer is 'yes' out to exceedingly large timescales, but even for a macroscopic system, there is still a very long timescale over which the system will not persist in its symmetry breaking phase. For mesoscopic systems, the timescale that divides a 'yes' and a 'no' answer to the question above is much shorter, experimentally accessible, and an interesting quantity to measure."

The researchers tried to address this timescale-related question by collecting time-resolved measurements showing the dynamics of a system that would undergo symmetry breaking on a macroscopic scale. The second objective of their study was to pave the way for the realization of a more programmable quantum simulator of symmetry-breaking dynamics in open quantum systems.

"The current study highlights some programmability: we can vary the number of atoms in the system, the strength of their coupling to the cavity, and the extent to which the initial state breaks symmetry by construction," said Stamper-Kurn.

"However, we are now considering a richer set of control parameters where we change the strength and phase of the atom-cavity coupling or impose several different patterns of coupling simultaneously or in succession. We understand theoretically that this kind of control can produce systems with much richer dynamics and phase diagrams, including systems that effectively perform a numerical optimization."

In their experiments, Stamper-Kurn and his colleagues employed a new and rapidly advancing technique. They first trapped atoms in several individually controlled optical tweezer traps and then illuminated them with near-resonant light.

"This light does three things: it cools the atoms so that they become deeply trapped in the tweezers; it ejects atoms from the tweezers in pairs, leaving either zero or one atom in the tweezer; and it generates fluorescence that we image to determine which tweezers have an atom and which don't," explained Stamper-Kurn. "Once we have that information, we turn off some tweezers so that we have a fixed number of atoms left, and we displace the remaining tweezer traps so that atoms are placed at precise locations in an optical cavity."

Once they positioned the atoms where they wanted them to be, the researchers directly illuminated the atom array with light that enters perpendicular to the optical cavity. To study interactions between the atoms and light, they collected light emitted from the cavity and measured its electric field, using a device known as an optical heterodyne detector.

"Light inside of our cavity forms a standing wave, and thus the cavity field has a sinusoidal profile with the antinodes alternating between positive and negative sign. Atoms placed exactly at the nodes of the cavity field should not scatter any light into the cavity," said Jacquelyn Ho, lead author on the paper.

"However, quantum and thermal fluctuations cause displacements in the atom positions and lead to light being scattered into the cavity. Once the strength of the illumination light surpasses a critical threshold, the light that builds up inside the cavity exerts enough force to overcome the pull of the optical tweezer traps.

"This causes the atoms to move away from the cavity nodes and towards the antinodes, where they then scatter even more light into the cavity. That scattered light acts back on all the atoms and pulls them further towards the antinodes, leading to an avalanche effect in which the atoms collectively self-organize."

The team observed that the self-organization of their atom-light system breaks symmetry, as atoms spontaneously move either to the positively or negatively signed antinodes of the cavity field. The position of the atoms determines the sign and magnitude of the cavity field, which ultimately allows the team's detector to pick up what is happening inside the cavity.

"With this system we measured a few neat things," said Stamper-Kurn. "We could detect when the cavity output bifurcates into a strong either positive- or negative-signed field. From this information, we could identify precisely when the conditions favoring a phase transition are reached. By controlling the atom number stepwise, we were able to measure precisely how the critical coupling strength to the cavity varies with atom number. Another exciting measurement involved analyzing the time dynamics of symmetry breaking."

The researchers found that longer-lived symmetry breaking could only take place if a system was driven further into the symmetry-breaking phase. This observed "tendency" suggests that mesoscopic systems are characteristically "indecisive" about breaking symmetry.

"A third important measurement was that of the mechanical susceptibility of the system," said Stamper-Kurn. "Phase transitions in macroscopic systems are accompanied by divergences in the susceptibility, as it takes only a little nudge to push the system into a symmetry-breaking phase. But for mesoscopic systems, the divergence remains finite at the point where symmetry breaking is first observed."

The recent work by Stamper-Kurn and his colleagues demonstrates the potential of atom tweezer arrays for constructing precise physical systems, which can then be used to study mesoscopic physics and phase transitions. The researchers plan to continue studying mesoscopic systems using the same method employed in their recent experiment, and hope that other labs will be inspired to do the same.

"Our experiments highlighted this capability particularly for the study of open quantum mechanical systems," said Stamper-Kurn. "We also observed clear mesoscopic signatures in a quantum system undergoing a symmetry-breaking transition. This topic is interesting both for the long-standing study of mesoscopic systems (nanomechanics, biological molecules, mesoscopic electronics, etc.) and for the study of quantum phase transitions."

By allowing physicists to time resolve the dynamics of symmetry breaking in mesoscopic systems, the methods employed by this research group could help to answer open physics questions. For instance, it could help to determine how long a mesoscopic system remains in a symmetry-broken state and the statistics of this persistence time or of the time it takes for the system to switch between states. In addition, it could help to find out if systems ever fluctuate entirely from one symmetry broken state to another and to answer various other fascinating research questions.

"We are excited to study how fluctuations and dissipation relate in this driven/dissipative mesoscopic system," explained Ho. "In equilibrium systems, this is quantified through the fluctuation-dissipation theorem, which relates fluctuations in time to the system's susceptibility, or response to external forces. We expect that due to the various timescales at play in our system, we may find violations of the canonical fluctuation-dissipation relationship."

In their next studies, Stamper-Kurn and his colleagues plan to further improve their methods to further enhance the extent to which a system can be programmed. For instance, they would like to engineer the mesoscopic system realized in their recent study so that it has a larger selection of broken symmetry states and so that it hosts non-reciprocal forces, which seemingly violate Newton's third law.

"This idea will be described in a forthcoming theoretical paper," added Stamper-Kurn. "Finally, a third exciting direction for our future work will be to move from the mechanical to the spin degree of freedom and using our tweezer-cavity system to realize closer analogs of the Dicke phase transition," added Stamper-Kurn.

Asked what inspired her to pursue this topic for her doctoral research, Ho responded, "I am constantly in awe that the laws of physics unify so many seemingly disparate physical systems. Self-organization is an example of a phenomenon that transcends differences in physical platforms. The more I learn about this subject, the more I've realized how our quantum system connects to topics in non-equilibrium physics, biophysics, and active matter, to name a few. I find that pretty fascinating."

This study came to fruition through a team effort between experimentalists and theorists. "Many aspects of this experiment worked in part due to the hard work of Zhenjie Yan, Yue-Hui Lu, and Tai Xiang," added Ho. "In addition to giving us many insights and perspectives, our collaborators at Columbia University (Ana Asenjo-Garcia and her postdocs Cosimo Rusconi and Stuart Masson) did amazing work to provide a rigorous mathematical framework for explaining our results."

© 2025 Science X Network