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arXiv:2306.05877 · Physical Review A

Nonlinear multistate tunneling dynamics in a spinor Bose-Einstein condensate

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

Published Nov 8, 2023• 6 citations
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Abstract

We present an experimental realization of dynamic self-trapping and nonexponential tunneling in a multistate system consisting of ultracold sodium spinor gases confined in moving optical lattices. Taking advantage of the fact that the tunneling process between different momentum states in the sodium spinor system is resolvable over a broader dynamic energy scale than previously observed in rubidium scalar gases, we demonstrate that the tunneling dynamics in the multistate system strongly depends on an interaction induced nonlinearity and is influenced by the spin degree of freedom under certain conditions. We develop a rigorous multistate tunneling model to describe the observed dynamics. Combined with our recent observation of spatially manipulated spin dynamics, these results open up prospects for alternative multistate ramps and state transfer protocols.

DOI
10.1103/physreva.108.053307

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We present an experimental realization of dynamic self-trapping and nonexponential tunneling in a multistate system consisting of ultracold sodium spinor gases confined in moving optical lattices. Taking advantage of the fact that the tunneling process between different momentum states in the sodium spinor system is resolvable over a broader dynamic energy scale than previously observed in rubidium scalar gases, we demonstrate that the tunneling dynamics in the multistate system strongly depends on an interaction induced nonlinearity and is influenced by the spin degree of freedom under certain conditions. We develop a rigorous multistate tunneling model to describe the observed dynamics. Combined with our recent observation of spatially manipulated spin dynamics, these results open up prospects for alternative multistate ramps and state transfer protocols.
A Bose Einstein Condensate (BEC) is an extraordinarily versatile state of matterthat allows for the simulation of quantum phenomena on the macroscopic scale. This powerful platform features rich physics such as superfluidity, quantum phase coherence, long range order, and spontaneous symmetry breaking. A spinor BEC, or a BEC with a spin degree of freedom, in particular is highly controllable as a quantum simulator, especially under the application of customizable optical lattices. In this thesis I present a study of spinor BECs in moving optical lattices. The results of this thesis open the way for the exploitation of not only quantum based properties of a BEC, but also the classical spatial dynamics inherit to the system for simulating many-body quantum spin dynamics with highly tunable, time-dependent interactions.
We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.
Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.
Compared to single-component Bose-Einstein condensates, spinor Bose-Einstein condensates display much richer dynamics. In addition to density oscillations, spinor Bose-Einstein condensates exhibit intriguing spin dynamics that is associated with population transfer between different hyperfine components. This paper analyzes the validity of the widely employed single-mode approximation when describing the spin dynamics in response to a quench of the system Hamiltonian. The single-mode approximation assumes that the different hyperfine states all share the same time-independent spatial mode. This implies that the resulting spin Hamiltonian only depends on the spin interaction strength and not on the density interaction strength. Taking the spinor sodium Bose-Einstein condensate in the f=1f=1f=1 hyperfine manifold as an example and working within the mean-field theory framework, it is found numerically that the single-mode approximation misses, in some parameter regimes, intricate details of the spin and spatial dynamics. We develop a physical picture that explains the observed phenomenon. Moreover, using that the population oscillations described by the single-mode approximation enter into the effective potential felt by the mean-field spinor, we derive a semiquantitative condition for when dynamical mean-field induced corrections to the single-mode approximation are relevant. Our mean-field results have implications for a variety of published and planned experimental studies.
Self-trapping is a hallmark phenomenon of nonlinear dynamics. It has significant applications in modern physics, including band structure engineering, phase transition dynamics, quantum metrology, and more. Dilute-gas Bose-Einstein condensates (BECs), in which self-trapping can arise from interatomic interactions, are a prime testbed for probing nonlinear dynamics. In this Letter, we report the observation of self-trapping in a spin-orbit coupled BEC subjected to a stationary optical lattice. We employ Raman-induced spin-orbit coupling, complemented by a matching optical lattice that facilitates coupling between momentum eigenstates of the spin-orbit coupled system. By ramping the Raman detuning, we probe atomic current flow between these eigenstates and identify a clear distinction between a delocalized mixed state and a self-trapped regime. Following a quench of the Raman detuning, the time-averaged atomic current exhibits non-analytic behavior across the transition between these two regimes in certain parameter ranges, signaling a dynamical phase transition in the system.
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.