Team studies emergence of fluctuating hydrodynamics in chaotic quantum systems

Researchers from Ludwig-Maximilians-Universität, the Max-Planck-Institute for Quantum Optics, the Munich Center for Quantum Science and Technology (MCQST) and the University of Massachusetts have recently conducted a study on equilibrium fluctuations in large quantum systems. Their paper, published in Physics of naturepresents the results of large-scale quantum simulations performed using a quantum gas microscope, an experimental tool used to image and manipulate individual atoms in ultracold atomic gases.

“Imagine you have a large number of particles in a box and you want to predict how the system will evolve in the future,” study co-author Julian Wienand told Phys.org. “You know the physics of these particles and how they interact with each other. So in principle, you could set up a simulation that generates the motion of each particle. However, in practice, because there are so many particles to track, the simulation might fail due to a lack of computing resources. Fortunately, there is a way forward: hydrodynamics.”

Hydrodynamic theory offers quantum physicists an alternative way to simulate particle interactions in large systems. Indeed, if a system is chaotic, researchers can assume that particles will interact in a way that ensures a state of local thermal equilibrium.

“This allows us to come up with a macroscopic description and essentially describe the particles as a continuous density field that follows simple differential equations,” Wienand said. “In general, such a density field can fluctuate, because at the microscopic level it consists of fast-moving particles. Since these fluctuations are random, we can think of them as white noise, and integrating them into our differential equations gives us fluctuating hydrodynamics (FHD).”

FHD is an extension of classical hydrodynamic theory, which also predicts the effects of thermal fluctuations in a system. By also taking into account small-scale fluctuations, this extended theoretical framework allows physicists to efficiently describe and calculate complex systems.

Overall, FHD theory suggests that the entire evolution of complex systems depends on a few quantities, such as a diffusion constant. Although this theory has been used to study a wide range of classical systems, it is not clear whether it also applies to chaotic quantum systems.

“Quantum systems are fundamentally different from their classical counterparts because the particles that make them up can exhibit quantum phenomena like entanglement, which defy common intuition,” Wienand said. “They are also much harder to compute, so being able to describe them using FHD could help us better understand these systems and make predictions about them.”

Wienand and his colleagues performed various quantum simulations using a ¹³³Cs (cesium) quantum gas microscope. The team essentially trapped ultracold Cs atoms in an optical lattice (i.e. a lattice created by laser light). This produced a system of quantum particles interacting with each other, also known as a quantum many-body system.

“With our microscope, we can take snapshots of this system with single-site resolution, meaning we can detect which sites in the lattice are occupied by an atom and which are empty,” Wienand says. “This is crucial for counting the number of particles in certain areas of the system and measuring the statistics of this observable, including fluctuations in the number of atoms.”

The researchers prepared their system in an excited state by placing the cesium atoms in specific locations, producing a regular pattern. They then abruptly reduced the depth of the lattice, allowing the atoms to begin moving and interacting with each other.

“Therefore, the quantum many-body system undergoes a diffusion process and thermalizes,” Wienand explains. “During the thermalization process, we follow the evolution of the fluctuations over time and observe them growing. Comparing the growth rate of these fluctuations (and other observables) with the theory allows us to conclude that the system is well described by the FHD and, in addition, to measure the diffusion constant.”

The recent study by this team of researchers demonstrates for the first time that FHD theory can be used to describe chaotic quantum systems in a qualitative and quantitative way. This has been achieved so far in a simple experimental setting, which could eventually be applied to the study of various chaotic quantum systems.

“In our case, this means that the whole of microscopic quantum physics can be approximated macroscopically by a simple classical FHD scattering model, and that the entire macroscopic dynamics of the system is described by a single quantity: a diffusion constant,” Wienand said. “This provides us with new tools to study chaotic quantum systems and make predictions about their apparently complex behavior, at least at the macroscopic scale.”

The researchers’ results suggest that a well-established paradigm for classical systems also applies to quantum systems. This is the idea that even if the microscopic physics of a system is complex and chaotic, its macroscopic behavior can actually be very simple.

“Another surprising fact about the diffusion constant is that it is an equilibrium property of the system,” Wienand said. “However, when we measure, the quantum many-body system is out of equilibrium. FHD establishes a relationship between the equilibrium and out-of-equilibrium parameters. Our results take advantage of this relationship and use it as a new way to obtain the diffusion constant.”

Wienand and his colleagues are currently performing further quantum simulations using their Cs quantum gas microscope. These new studies could provide additional insights into the mechanisms underlying many-body quantum dynamics.

“Open questions for this next study will include: How do fluctuations behave in systems that do not thermalize? What about higher moments beyond fluctuations, such as asymmetry and kurtosis? And can FHD be adapted to include and properly describe more complex observables and/or in more exotic systems?” added Wienand.

“Our results provided a first indication of the great potential of FHD in describing quantum systems, but further experiments must follow in order to assess the scope and limitations of FHD in the quantum domain.”

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