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arXiv:2211.12336 · Physical Review A

Interacting Stark localization dynamics in a three-dimensional lattice Bose gas

Laura Wadleigh, Nicholas Kowalski, Brian DeMarco

Published Apr 28, 2023• 2 citations
arXivHTMLPDF

Abstract

We measure the thermalization dynamics of a lattice Bose gas that is Stark localized by a parabolic potential. A nonequilibrium thermal density distribution is created by quickly removing an optical barrier. The resulting spatiotemporal dynamics are resolved using Mardia's $B$ statistic, which is a measure sensitive to the shape of the entire density distribution. We conclude that equilibrium is achieved for all lattice potential depths that we sample, including the strongly interacting and localized regime. However, thermalization is slow and nonexponential, requiring up to 500 tunneling times. We show that the Hubbard $U$ term is not responsible for thermalization via comparison to an exact diagonalization calculation, and we rule out equilibration driven by lattice-light heating by varying the laser wavelength. The thermalization timescale is comparable to the next-nearest-neighbor tunneling time, which suggests that a continuum, strongly interacting theory may be needed to understand equilibration in this system.

DOI
10.1103/physreva.107.043325

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We measure the thermalization dynamics of a lattice Bose gas that is Stark localized by a parabolic potential. A nonequilibrium thermal density distribution is created by quickly removing an optical barrier. The resulting spatiotemporal dynamics are resolved using Mardia's BBB statistic, which is a measure sensitive to the shape of the entire density distribution. We conclude that equilibrium is achieved for all lattice potential depths that we sample, including the strongly interacting and localized regime. However, thermalization is slow and nonexponential, requiring up to 500 tunneling times. We show that the Hubbard UUU term is not responsible for thermalization via comparison to an exact diagonalization calculation, and we rule out equilibration driven by lattice-light heating by varying the laser wavelength. The thermalization timescale is comparable to the next-nearest-neighbor tunneling time, which suggests that a continuum, strongly interacting theory may be needed to understand equilibration in this system.
Using a 3D spin-dependent optical lattice, we study thermalization and energy exchange between two ultracold Bose gases, one of which is strongly correlated and bound to the lattice and another that is free from the lattice potential. Disruption of interspecies thermalization is revealed through measurements of condensate fraction after the lattice is superimposed on the parabolic confining potential. By selectively heating the lattice-bound species and measuring the rate of heat transfer to the free state, suppression of energy exchange is observed. Comparison with a Fermi's golden rule prediction confirms that this effect is caused by a dispersion mismatch that reduces the phase space available for elastic collisions. This result has critical implications for methods proposed to cool strongly correlated lattice gases.
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"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 investigate the loss of spatial coherence of one-dimensional bosonic gases in optical lattices illuminated by a near-resonant excitation laser. Because the atoms recoil in a random direction after each spontaneous emission, the atomic momentum distribution progressively broadens. Equivalently, the spatial correlation function (the Fourier-conjugate quantity of the momentum distribution) progressively narrows down as more photons are scattered. Here we measure the correlation function of the matter field for fixed distances corresponding to nearest-neighbor (n-n) and next-nearest-neighbor (n-n-n) sites of the optical lattice as a function of time, hereafter called n-n and n-n-n correlators. For strongly interacting lattice gases, we find that the n-n correlator C 1 decays as a power-law at long times, C 1 ∝ 1 / t α , in stark contrast with the exponential decay expected for independent particles. The power-law decay reflects a non-trivial dissipative many-body dynamics, where interactions change drastically the interplay between fluorescence destroying spatial coherence, and coherent tunnelling between neighboring sites restoring spatial coherence at short distances. The observed decay exponent α ≈ 0 . 54 ( 6 ) is in good agreement with the prediction α = 1 / 2 from a dissipative Bose–Hubbard model accounting for the fluorescence-induced decoherence. Furthermore, we find that the n-n correlator C 1 controls the n-n-n correlator C 2 through the relation C 2 ≈ C 1 2 , also in accordance with the dissipative Bose–Hubbard model.
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We study the temporal expansion of an ultracold Bose gas in two-dimensional, square optical lattices. The gas is described by the Bose-Hubbard model deep in the superfluid regime, with initially all bosons condensed in the central site of the lattice. We use the previously developed nonequilibrium propagator method for capturing the time evolution of an interacting bosonic system, where the many-body Hamiltonian is represented in an appropriate local basis and the corresponding field operators are separated into the classical (BEC) part and quantum mechanical fluctuations. After a quench, i.e. after a sudden switch of the lattice nearest-neighbor hopping, the expanding, bosonic cloud separates spatially into a fast, ballistic forerunner and a slowly expanding central part controlled by selftrapping. We show that the forerunner expansion is driven by the coherent dynamics of the BEC and that its velocity is consistent with the Lieb-Robinson bound. For smaller lattices we analyze how quasiparticle collisions lead to enhanced condensate depletion and oscillation damping.