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Stability and collapse dynamics of dipolar Bose-Einstein condensates in one-dimensional optical lattices

Stefan Müller

Published Jan 1, 2013• 1 citation
Publisher

Abstract

The subject of this thesis is the experimental investigation of a dipolar 52-Chromium Bose-Einstein condensate (BEC) in a one-dimensional optical lattice potential. At first, the influence of the periodic landscape on the stability of the quantum gas is investigated. Based on these measurements, the collapse dynamics of the system, i.e. its time evolution after passing the threshold to the unstable regime, is observed and analyzed. Both the investigations aim to contribute to the basic understanding of dipolar quantum gases. In addition, they may provide a basis for further experiments with dipolar BECs in optical lattices. Amongst others, the observation of self-organized density structures is one of the biggest goals in this field of research.

DOI
10.18419/opus-5097

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We report on the observation of the collapse of a dipolar Bose-Einstein condensate (BEC) upon release from a one-dimensional optical lattice. In strong contrast with the typical behavior of quantum gases under time of flight (TOF), we show here that a strongly dipolar BEC, stabilized in the lattice, may become unstable during the TOF dynamics due to the combined effect of the anisotropy of the dipolar interaction and intersite coherence. Such TOF-triggered collapse is a peculiar case of a collapse induced by the deconfinement of a dipolar many-body system at a fixed two-body interaction strength.

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The subject of this thesis is the experimental investigation of a dipolar 52-Chromium Bose-Einstein condensate (BEC) in a one-dimensional optical lattice potential. At first, the influence of the periodic landscape on the stability of the quantum gas is investigated. Based on these measurements, the collapse dynamics of the system, i.e. its time evolution after passing the threshold to the unstable regime, is observed and analyzed. Both the investigations aim to contribute to the basic understanding of dipolar quantum gases. In addition, they may provide a basis for further experiments with dipolar BECs in optical lattices. Amongst others, the observation of self-organized density structures is one of the biggest goals in this field of research.
We consider quantum droplets in dipolar Bose-Einstein condensates embedded in optical lattices within the framework of Gross-Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole-dipole interaction provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the dipole-dipole interaction increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of dipole-dipole interaction. In presence of optical lattices, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.
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.
Abstract We consider quantum droplets in dipolar Bose–Einstein condensates embedded in optical lattices (OLs) within the framework of Gross–Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole–dipole interaction (DDI) provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the DDI increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of DDI. In presence of OLs, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.
Motivated by recent experimental observations [Parker, Hua, and Chin, Nat. Phys. 9, 769 (2013)], we analyze the stability of a Bose-Einstein condensate (BEC) in a one-dimensional lattice subjected to periodic shaking. In such a system there is no thermodynamic ground state, but there may be a long-lived steady state, described as an eigenstate of a ``Floquet Hamiltonian.'' We calculate how scattering processes lead to a decay of the Floquet state. We map out the phase diagram of the system and find regions where the BEC is stable and regions where the BEC is unstable against atomic collisions. We show that Parker et al. performed their experiment in the stable region, which accounts for the long lifetime of the condensate $(\ensuremath{\sim}1\mathrm{s})$. We also estimate the scattering rate of the bosons in the region where the BEC is unstable.
In this thesis I report on experiments on the quantum dynamics of matter waves in a onedimensional lattice potential. A 87Rb Bose-Einstein condensates is prepared in a one-dimensional waveguide in the lowest band of a superimposed optical lattice potential. The action of a weak lattice potential allows to modify the linear wave dispersion. We realized dispersion management by switching from normal to anomalous dispersion during the evolution. In this way the initial expansion of a wave packet is reversed to a compression and thus the effective spreading can be suppressed. By preparing a BEC at the Brillouin zone edge, we observed bright atomic gap solitons – non-spreading wave packets. They form, if the atom number and the lattice potential depth is tuned such that the effect of the repulsive atomic interaction and the anomalous dispersion cancel. For deep lattice potentials our system is described by a discrete nonlinear Schrödinger equation, whose dynamics is determined by the tunneling between adjacent lattice sites and the nonlinear phase evolution. In the main part of this thesis I report on the first experimental observation of nonlinear self-trapping for matter waves. The transition from the diffusive regime, characterized by an continuous expansion of the condensate, to the self-trapping regime is accomplished by increasing the atomic density. Due to the corresponding increase of the repulsive atomic interaction the initial expansion stops and the width of the wave packet remains finite. The comparison with a numerical analysis reveals that the effect is due to an inhibition of the site-to-site tunneling induced by the nonlinear phase evolution.
We report on the observation of the collapse of a dipolar Bose-Einstein condensate (BEC) upon release from a one-dimensional optical lattice. In strong contrast with the typical behavior of quantum gases under time of flight (TOF), we show here that a strongly dipolar BEC, stabilized in the lattice, may become unstable during the TOF dynamics due to the combined effect of the anisotropy of the dipolar interaction and intersite coherence. Such TOF-triggered collapse is a peculiar case of a collapse induced by the deconfinement of a dipolar many-body system at a fixed two-body interaction strength.