Quantum Dynamics of Near-One-Dimensional Systems

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Understanding the behavior of many interacting particles whose dynamics is dictated by quantum rather than classical physics is a current frontier in science. In addition to its fundamental appeal, it is, for example, of relevance to understanding what happens when many qubits are coupled together to create and scale up quantum computers, as well as for the development of effective hydrodynamics descriptions equivalent to those used to describe classical fluids. The latter descriptions are used in a wide range of applications, e.g., in aeronautics, hydrology, and geophysics, and their quantum counterparts are expected to play a similarly important role in quantum technologies. Central roles in the outcomes of the quantum dynamics are played by the geometry of the quantum system and by the type of interactions between the particles. Of special interest in recent years has been the case in which the particles are cooled to ultra-low temperatures (nano Kelvins) and trapped in such a way that their motion is restricted to a line (one dimension). The goal of this project is two-fold, on the one hand the PI will develop and use theoretical tools to understand and quantitatively describe experiments in the ultra-low temperature regime, and on the other hand will theoretically study quantum states that can be created in those systems in the presence of different types of interactions and symmetries. This award will support the training of graduate students in quantum physics and computational physics. Some of the most important theory-experiment findings will be included in a graduate quantum mechanics book that the PI is co-writing. The PI will continue his recruiting efforts to attract graduate students from underrepresented groups to the physics graduate program at Penn State, and will continue his efforts to encourage members of those groups to pursue careers in Physics. In the context of theory-experiment collaborations, the PI plans to study the dynamics of near-one-dimensional ultracold gases following Bragg scattering pulses. The main goal of these studies will be to explore universal processes that occur at very short times, such as hydrodynamization (which also occurs in heavy-ion collisions in particle accelerators), and local equilibration processes that depend strongly on the nature and interactions in the system. At longer times, the PI plans to develop and use generalized hydrodynamics approaches to study the effect of dipolar interactions in the dynamics following sudden changes of a confining potential. For the latter studies, the PI and his group will consider thermodynamically stable states with repulsive contact interactions and metastable states with attractive contact interactions. Central to all the previous studies will be the characterization of the far-from-equilibrium states using rapidity and momentum distributions. Beyond near-integrable one dimensional systems, the PI and his group will use typical fidelity susceptibilities and spectral functions to study the onset of quantum chaos in 2D lattice systems. They will also study the properties of eigenstates of integrable and nonintegrable models with SU(2) symmetry, as well as far from equilibrium dynamics in those models. The latter studies will characterize the entanglement entropy and eigenstate thermalization (lack thereof) in the quantum-chaotic regime (at integrability). For the quantum dynamics, the goal is to understand prethermalization when the SU(2) symmetry is weakly broken, and the far-from-equilibrium dynamics of specially engineered initial states with support in exponentially small Hilbert space sectors.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.