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arXiv:2309.00592 · Physical Review A

Engineering dynamical phase diagrams with driven lattices in spinor gases

Jared Austin, Zachary Shaw, Qingze Guan, C. Binegar, D. Blume, Robert J. Lewis-Swan, Yingmei Liu

Published Apr 10, 2024• 9 citations
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Abstract

We experimentally demonstrate that well-designed driven lattices are versatile tools to simultaneously tune multiple key parameters (spin-dependent interactions, spinor phase, and quadratic Zeeman energy) for manipulating phase diagrams of spinor gases with negligible heating and atom losses. This opens avenues for studying engineered Hamiltonians and dynamical phase transitions. Modulation-induced harmonics generate progressively narrower separatrices at driving-frequency-determined higher magnetic-field strengths. This technique enables exploration of multiple, previously inaccessible parameter regimes of spinor dynamics (notably high magnetic-field strengths, tunable spinor phase, and individually tunable spin-preserving and spin-changing collisions) and widens the range of cold-atom applications, e.g., in quantum sensing and studies of nonequilibrium dynamics.

DOI
10.1103/physreva.109.043309

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We experimentally demonstrate that well-designed driven lattices are versatile tools to simultaneously tune multiple key parameters (spin-dependent interactions, spinor phase, and quadratic Zeeman energy) for manipulating phase diagrams of spinor gases with negligible heating and atom losses. This opens avenues for studying engineered Hamiltonians and dynamical phase transitions. Modulation-induced harmonics generate progressively narrower separatrices at driving-frequency-determined higher magnetic-field strengths. This technique enables exploration of multiple, previously inaccessible parameter regimes of spinor dynamics (notably high magnetic-field strengths, tunable spinor phase, and individually tunable spin-preserving and spin-changing collisions) and widens the range of cold-atom applications, e.g., in quantum sensing and studies of nonequilibrium dynamics.
We demonstrate the real-time detection of dynamical phase transitions (DPTs) in lattice-confined spinor gases subject to a priori unknown time-variant interactions, via the temporal behaviors of both the system energy and spinor phases extracted from the observed spin dynamics. Using this technique, we describe the observed nonequilibrium spin dynamics, governed by intricate spin-spatial couplings, across a range of conditions. This work also introduces an observable that can quickly identify DPTs at holding times when commonly-used order parameters still exhibit transient, nonuniversal behavior. Our approach can naturally extend to other complex systems subject to time-dependent parameters, such as Floquet systems under driven magnetic fields, driven interactions, or spin-flopping fields, with potential applications in the study of DPTs in nonintegrable models.
Utilizing ultracold spinor gases as large-scale, many-body quantum simulation platforms, we establish a toolbox for the precise control, characterization, and detection of nonequilibrium dynamics via internal spinor phases. We develop a method to extract the phase evolution from the observed spin population dynamics, allowing us to define an order parameter that sharply identifies dynamical phase transitions over a wide range of conditions. This work also demonstrates a technique for inferring spin-dependent interactions from a single experimental time trace, in contrast to the standard approach that requires mapping a cross section of the phase diagram, with immediate applications to systems experiencing complex time-dependent interactions. Additionally, we demonstrate experimental access to and control over non-ergodic relaxation dynamics, where states of similar energy in the (nominally) thermal region of the energy spectrum retain a dependence on the initial state, via the manipulation of spinor phases, enabling the study of non-ergodic thermalization dynamics connected to quantum scarring.
We propose the realization of a spin-2 Floquet spinor Bose-Einstein condensate via Floquet engineering of the quadratic Zeeman energy. In the Floquet system, the coupling strengths of all angular-momentum-conserving spin-flip processes are renormalized by driving-parameter-dependent Bessel functions. Such Floquet-engineered interactions significantly enriches possible ground states in homogeneous gases. The resulting phase diagrams, which map the distributions of these possible ground states, are presented in the space of the driving parameters.
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.
The isolation and control of disparate degrees of freedom underpins quantum simulators. We advance the programmability of cold atom quantum simulators with a realization of the dynamic coupling of spatial and spin degrees of freedom. We experimentally demonstrate that violent spatial evolutions tune long-lived coherent spin dynamics and develop a model of quantum spin mixing incorporating the spatial evolution via time-dependent spin-spin interactions. Our results may open new paths towards the simulation of quantum spin models with tunable interactions via tailored spatial dynamics.
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.