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Nonequilibrium dynamics and indirect microscopy in a three-dimensional spinor Bose-Hubbard model quantum simulator

Austin-Harris, Jared O.

Published Dec 1, 2023• 0 citations
OpenAlex

Abstract

Quantum simulators are easily controllable quantum systems that allow us to physically model the behavior of more complex systems, that are intractable with even the most advanced supercomputers, to gain insight into their behavior. Using lattice confined spinor Bose-Einstein condensates (BEC) as quantum simulators, we explore the quantum critical dynamics of the superfluid to Mott insulator phase transition in a three-dimensional cubic optical lattice. Our observations reveal that, in a quantum version of the Kibble-Zurek mechanism, the dynamics can be frozen by a sufficiently quick ramp across the transition. Additionally, we utilize discrete energy signatures in nonequilibrium spin mixing dynamics generated by atoms that are tightly confined to single lattice sites after a quench across this transition to understand the spatial dynamics of a BEC during this transition. This "indirect microscopy" method is required to determine the spatial distribution because achieving single lattice site resolved imaging of three dimensional lattice confined quantum gases remains experimentally challenging even with advanced quantum gas microscopy methods. The observed number distributions additionally demonstrate that it may be possible to design lattice ramp sequences to manipulate the distribution of atoms to enhance desired effects.

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Quantum simulators are easily controllable quantum systems that allow us to physically model the behavior of more complex systems, that are intractable with even the most advanced supercomputers, to gain insight into their behavior. Using lattice confined spinor Bose-Einstein condensates (BEC) as quantum simulators, we explore the quantum critical dynamics of the superfluid to Mott insulator phase transition in a three-dimensional cubic optical lattice. Our observations reveal that, in a quantum version of the Kibble-Zurek mechanism, the dynamics can be frozen by a sufficiently quick ramp across the transition. Additionally, we utilize discrete energy signatures in nonequilibrium spin mixing dynamics generated by atoms that are tightly confined to single lattice sites after a quench across this transition to understand the spatial dynamics of a BEC during this transition. This "indirect microscopy" method is required to determine the spatial distribution because achieving single lattice site resolved imaging of three dimensional lattice confined quantum gases remains experimentally challenging even with advanced quantum gas microscopy methods. The observed number distributions additionally demonstrate that it may be possible to design lattice ramp sequences to manipulate the distribution of atoms to enhance desired effects.
We present an experimental study demonstrating the manipulation of atom-number distributions of spinor gases after nonequilibrium quantum quenches across superfluid to Mott-insulator phase transitions in cubic optical lattices. Our data indicate that atom distributions in individual Mott lobes can be tuned by properly designing quantum quench sequences, which suggests methods of maximizing the fraction of atoms in Mott lobes of even occupation numbers and has applications in attaining different quantum magnetic phases including massively entangled states. Spatial distributions of gases in three-dimensional lattices are derived from the observed number distributions, which reveal complex spatial dynamics during the quantum quenches. Qualitative agreements are also found between our experimental data and numerical simulations based on time-dependent Gutzwiller approximations in two-dimensional systems.
We present an experimental study on nonequilibrium dynamics of a spinor condensate after it is quenched across a superfluid to Mott insulator (MI) phase transition in cubic lattices. Intricate dynamics consisting of spin-mixing oscillations at multiple frequencies are observed in time evolutions of the spinor condensate localized in deep lattices after the quantum quench. Similar spin dynamics also appear after spinor gases in the MI phase are suddenly moved away from their ground states via quenching magnetic fields. We confirm these observed spectra of spin-mixing dynamics can be utilized to reveal atom number distributions of an inhomogeneous system, and to study transitions from two-body to many-body dynamics. Our data also imply the nonequilibrium dynamics depend weakly on the quench speed but strongly on the lattice potential. This enables precise measurements of the spin-dependent interaction, a key parameter determining the spinor physics.
Abstract Three-dimensional (3D) strongly correlated many-body systems, especially their dynamics across quantum phase transitions, are prohibitively difficult to be numerically simulated. We experimentally demonstrate that such complex many-body dynamics can be efficiently studied in a 3D spinor Bose–Hubbard model quantum simulator, consisting of antiferromagnetic spinor Bose–Einstein condensates confined in cubic optical lattices. We find dynamics and scaling effects beyond the scope of existing theories at superfluid–insulator quantum phase transitions, and highlight spin populations as a good observable to probe the quantum critical dynamics. Our data indicate that the scaling exponents are independent of the nature of the quantum phase transitions. We also conduct numerical simulations in lower dimensions using time-dependent Gutzwiller approximations, which qualitatively describe our observations.
We study quenches across the Bose-Hubbard Mott-insulator-to-superfluid quantum phase transition by using an ultracold atomic gas trapped in an optical lattice. Quenching from the Mott insulator to the superfluid phase is accomplished by continuously tuning the ratio of Hubbard tunneling to interaction energy. Excitations of the condensate formed after the quench are measured by using time-of-flight imaging. We observe that the degree of excitation is proportional to the fraction of atoms that cross the phase boundary and that the quantity of excitations and energy produced during the quench have a power-law dependence on the quench rate. These phenomena suggest an excitation process analogous to the Kibble-Zurek mechanism for defect generation in nonequilibrium classical phase transitions.
"This thesis presents research on a variety of dynamical phenomena in strongly correlated systems. We use 87Rb atoms trapped in a disordered optical lattice to realize the 3D Bose Hubbard model, with independently, dynamically tunable lattice depth and disorder strength. The equilibrium behavior of the Bose Hubbard and disordered Bose Hubbard models are understood, but there are many outstanding questions about dynamics. One area of interest is in dynamical behavior near quantum phase boundaries, such as the generation of quench-induced excitations in the presence of disorder. Another area concerns heat flow, relaxation, and thermalization. The primary focus of this thesis is driving a gas across a disorder-induced quantum phase transition from the Bose glass to the superfluid phase via quenching the disorder. We measured excitations generated during the quench and related them to crossing the equilibrium phase transition determined by quantum Monte Carlo simulations of the trapped system. The behavior we observe is reminiscent of the quantum Kibble Zurek mechanism, where the relaxation timescale diverges and local fluctuations are ""frozen"" into the system near the phase boundary. Understanding how disorder impacts the Kibble Zurek paradigm about behavior near a phase boundary provides insight into the dynamics of strongly interacting, disordered systems. The three other works discussed in this thesis concern relaxation and energy transfer in clean optical lattices. Understanding these dynamical properties of lattice gases is key to developing tools such as cooling in a lattice. In the first result, a gas comprised of two spin states was loaded into a spin-dependent optical lattice, such that one spin state experienced the lattice, and the other did not. We found that when the lattice gas was heated, energy transfer to the non-lattice gas did not occur at higher lattice depths due to the mismatch in the dispersion relations. In the second result, lattice atoms were excited to a higher band and found to decay to the ground state via two mechanisms. One decay channel involved generating excitations in the non-lattice atoms, while the other channel involved collisions between lattice atoms, where one atom decayed to the ground state and the other was excited to a higher band. The final result measured relaxation timescales by removing atoms with low quasimomentum and measuring rethermalization. The observed timescales are faster than the tunneling time and interaction time of the lattice. Proof-of-principle cooling was also demonstrated by removing atoms with higher quasimomentum and allowing the remaining atoms rethermalize to a cooler temperature."
We present an experimental study demonstrating the manipulation of atom number distributions of spinor gases after nonequilibrium quantum quenches across superfluid to Mott insulator phase transitions in cubic optical lattices. Our data indicate that atom distributions in individual Mott lobes can be tuned by properly designing quantum quench sequences, which suggest methods of maximizing the fraction of atoms in Mott lobes of even occupation numbers and have applications in attaining different quantum magnetic phases including massively entangled states. In addition, we find qualitative agreements between our experimental data and numerical simulations based on time-dependent Gutzwiller approximations in two-dimensional systems.