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arXiv:2304.07423

Instability and Momentum Bifurcation of molecular BEC in Exotic Dispersion with Shaken Lattice

Kaiyue Wang, Feng Xiong, Long Yun, Ma, Yun, Colin Parker

Published Apr 14, 2023• 0 citations
arXivHTMLPDF

Abstract

We place a molecular Bose-Einstein condensate in a 1D shaken lattice with a Floquet-engineered dispersion, and observe the dynamics in both position and momentum space. At the initial condition of zero momentum, our engineered dispersion is inverted, and therefore unstable. We observe that the condensate is destabilized by the lattice shaking as expected, but rather than decaying incoherently or producing jets, as in other unstable condensates, under our conditions the condensate bifurcates into two portions in momentum space, with each portion subsequently following semi-classical trajectories that suffer minimal spreading in momentum space as they evolve. We can model the evolution with a Gross-Pitaevskii equation, which suggests the initial bifurcation is facilitate by a nearly linear "inverted V"-shaped dispersion at the zone center, while the lack of spreading in momentum space is facilitated by interactions, as in a soliton. We propose that this relatively clean bifurcation in momentum space has applications for counter-diabatic preparation of exotic ground states in many-body quantum simulation schemes.

DOI
10.48550/arxiv.2304.07423

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We place a molecular Bose-Einstein condensate in a 1D shaken lattice with a Floquet-engineered dispersion, and observe the dynamics in both position and momentum space. At the initial condition of zero momentum, our engineered dispersion is inverted, and therefore unstable. We observe that the condensate is destabilized by the lattice shaking as expected, but rather than decaying incoherently or producing jets, as in other unstable condensates, under our conditions the condensate bifurcates into two portions in momentum space, with each portion subsequently following semi-classical trajectories that suffer minimal spreading in momentum space as they evolve. We can model the evolution with a Gross-Pitaevskii equation, which suggests the initial bifurcation is facilitate by a nearly linear "inverted V"-shaped dispersion at the zone center, while the lack of spreading in momentum space is facilitated by interactions, as in a soliton. We propose that this relatively clean bifurcation in momentum space has applications for counter-diabatic preparation of exotic ground states in many-body quantum simulation schemes.
Cold atoms trapped in optical lattices (crystals of light) provide a pristine platform for exploring quantum many body physics. Motivated by several recent experiments, this thesis examines the equilibrium and non-equilibrium dynamics of a Bose-Einstein condensate (BEC) loaded in a low dimensional optical lattice in order to realize novel quantum phases. There are two main research directions in this thesis. The first one involves the possibility that exotic order spontaneously forms when two-component bosons are trapped in a honeycomb lattice. My studies on this theme is motivated by the observation of a “twisted superfluid” state in Prof. Klaus Sengstock’s group at Hamburg (Soltan-Panahi et al., Nat. Phys. 8, 71 (2012)). A twisted superfluid involves Bose-Einstein condensation into a state whose order parameter has a spatially varying phase. In chapter 3, I study the stability of a Bose-Einstein condensate towards forming a twisted superfluid within the framework of mean field theory. Despite a exhaustive numerical search I do not find a parameter regime with a twisted superfluid. This search involved all experimentally relevant parameter regimes and therefore mean field theory predicted that the experimentalists should not observe a twisted superfluid. I conclude that the experimental observations were either a manifestation of counter superfluidity or due to interactions during time-of-flight. Subsequent experiments showed that the observations were an artifact of the measurement process. The second research direction in this thesis is an exploration of the stability of periodically driven quantum systems (also known as Floquet systems). Floquet systems can be used to realize exotic non-equilibrium quantum phases which do not have a counterpart in static systems. However, the driving can cause these systems to heat up which presents a major obstacle to creating exotic states. To explore this issue in a concrete example, I model an experiment (Parker, Ha, and Chin, Nat. Phys. 9, 769 (2013)) where a Bose-Einstein condensate loaded in an optical lattice is subjected to periodic shaking. I investigate the stability of this Floquet BEC to interactions. This research direction consists of 3 studies. In chapter 4, I first do this analysis for a purely one-dimensional system and identify a large parameter regime where the BEC is stable. In the next two chapters, I go beyond 1D and consider the role of transverse degrees of freedom. This is because the shaken lattice experiments that I model involves a 1D array of pancakes. I find that this geometry leads to much more dissipation than a purely 1D system. This extra dissipation arises because interactions can transfer energy between different directions. In chapter 5, I consider the extreme case where there is no transverse confinement. I find that in the absence of transverse confinement, a one-dimensional Floquet BEC is generically unstable. Finally, in chapter 6, I consider harmonic transverse confinement modeling the crossover between chapters 4 and 5. I find that as the transverse confinement is made stronger, the atom loss rate initially increases, but beyond a critical transverse confinement, the atom loss disappears due to unavailability of phase space for scattering. I also predict that if the transverse confinement is tuned to the vicinity of certain magic values, the heating rate exhibits a sharp drop. I perform similar analyses for a shaken square lattice and find that generically a low-dimensional Floquet BEC can be stabilized by suitably designing the transverse confinement.
We experimentally study the dynamics of weakly interacting Bose-Einstein condensates of cesium atoms in a 1D optical lattice with a periodic driving force. After a sudden start of the driving we observe the formation of stable wave packets at the center of the first Brillouin zone (BZ) in momentum space, and we interpret these as Floquet solitons in periodically driven systems. The wave packets become unstable when we add a trapping potential along the lattice direction leading to a redistribution of atoms within the BZ. The concept of a negative effective mass and the resulting changes to the interaction strength and effective trapping potential are used to explain the stability and the time evolution of the wave packets. We expect that similar states of matter waves exist for discrete breathers and other types of lattice solitons in periodically driven systems.
We experimentally study the dynamics of weakly interacting Bose-Einstein condensates of cesium atoms in a 1D optical lattice with a periodic driving force. After a sudden start of the driving, we observe the formation of stable wave packets at the center of the first Brillouin zone (BZ) in momentum space, and we interpret these as Floquet solitons in periodically driven systems. The wave packets become unstable when we add a trapping potential along the lattice direction, leading to a redistribution of atoms within the BZ. The concept of a negative effective mass and the resulting changes to the interaction strength and effective trapping potential are used to explain the stability and the time evolution of the wave packets. We expect that similar states of matter waves exist for discrete breathers and other types of lattice solitons in periodically driven systems.
Bose-Einstein condensates (BECs) in an optical lattice driven out of equilibrium and the subsequent dynamics are investigated in the limit of weak atom-atom interactions both within the classical mean-field approximation and by incorporating an approximate model for quantum fluctuations. A prediction of pulsating dynamical instability in which atoms periodically collect together and subsequently disperse back into the initial homogeneous state is made. This instability is a unique feature of this Hamiltonian system characterized by a single unstable mode and can be considered as a remnant of the integrability of the non-integrable system. A phase-space model has been employed to incorporate the quantum fluctuations within the truncated Wigner approximation. It is observed that the quasiperiodic behavior of the pulsating dynamics persists in the individual stochastic realizations that represent the typical experimental outcomes, but the effect of quantum fluctuations is manifested in the ensemble averages of various properties of the system. Quantum effects are increasingly prominent and the revivals of the ensemble averages of the wave function become progressively weaker when the effective interaction strength is increased. Motivated by these predictions, we apply similar methods to two-component BECs. Within the mean-field model we demonstrate a spontaneous emergence of a vector soliton like structure, a bound pair of a soliton and an anti-soliton, from the homogeneous imbalanced mixture of two BEC species. This is a feature that uniquely combines phase separation, pulsating instability, and formation of a dark-bright soliton pair when the parameters involved are tuned properly. ^
A superfluid flow beyond a critical momentum in an optical lattice decays drastically by the interplay between nonlinearity due to the interparticle interactions in Bose-Einstein condensate and periodicity of the lattice; this instability is called dynamical instability. The complex density modulational profiles after the condensate becomes unstable observed experimentally is not completely understood, while the dynamical instability has been studied theoretically and experimentally. In this paper, we analyze the density modulation of condensates as a precursor of the dynamical instability in the two-dimensional Bose-Hubbard model. Our analysis has clarified the unexplored properties of the density modulations associated with the dynamical instability at low filling and in a wide range of interactions, while the previous works have analyzed the density modulation on the basis of Gross-Pitaevskii equation under the specific condition that one-dimensional optical lattice is very shallow and the filling is very large. The numerical simulations based on the dynamical Gutzwiller approximation elucidate that the principal mode of density modulation highly depends on interaction strength U and the momentum acceleration rate. We briefly discuss these features with the stability phase diagram calculated on the basis of the Bogoliubov theory.