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Dynamics of periodically driven matter waves with negative effective mass

Matthew Mitchell, Andrea Di Carli, G. Sinuco-León, Arthur La Rooij, Stefan Kuhr, Elmar Haller

Published Jun 1, 2021• 0 citations
OpenAlex

Abstract

We experimentally study the dynamics of a weakly interacting Bose-Einstein condensate of cesium atoms in a 1D optical lattice with a periodic driving force. The time evolution is analysed after a quench of the driving strength which leads to an inversion of the dispersion relation in the lattice band and to a redistribution of atoms in the 1st Brillouin zone (BZ). We use the concept of a negative effective mass and the resulting changes to the effective trapping potential and interaction strength to explain the time evolution of wave packets with weak repulsive interaction. In addition, the formation of stable wave packets with a negative effective mass is observed at the center of the BZ, and we interpret these as gap solitons in a periodically driven system.

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It is known that solitons of Bose-Einstein condensates with positive scattering lengths can be produced in optical lattices. The key of this process is the negative sign of the effective mass of the wavepacket as it comes closer to the edge of the first Brillouin zone. However, the underlying assumption of the effective mass approach is the slow variation of the wavefunction envelope between consecutive lattice cells. Previous experiments and computations on this type of solitons show that this is not the usual case. In this contribution we will go beyond the slowly varying assumption to demonstrate that the equations governing the dynamics of gap solitons contain a third derivative in the dispersion. As a result, the dynamics of the stabilized wavepackets is found different that the soliton's. In particular, a radiative component is present, and the stability under collisions is only partially achieved.

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We experimentally study the dynamics of a weakly interacting Bose-Einstein condensate of cesium atoms in a 1D optical lattice with a periodic driving force. The time evolution is analysed after a quench of the driving strength which leads to an inversion of the dispersion relation in the lattice band and to a redistribution of atoms in the 1st Brillouin zone (BZ). We use the concept of a negative effective mass and the resulting changes to the effective trapping potential and interaction strength to explain the time evolution of wave packets with weak repulsive interaction. In addition, the formation of stable wave packets with a negative effective mass is observed at the center of the BZ, and we interpret these as gap solitons in a periodically driven system.
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.
We demonstrate the control of the dispersion of matter wave packets utilizing periodic potentials. This is analogous to the technique of dispersion management known in photon optics. Matter wave packets are realized by Bose-Einstein condensates of 87Rb in an optical dipole potential acting as a one-dimensional waveguide. A weak optical lattice is used to control the dispersion relation of the matter waves during the propagation of the wave packets. The dynamics are observed in position space and interpreted using the concept of effective mass. By switching from positive to negative effective mass, the dynamics can be reversed. The breakdown of the approximation of constant, as well as experimental signatures of an infinite effective mass are studied.
We study the dynamics of one-dimensional solitons in attractive and repulsive Bose–Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. First, we demonstrate analytically that, in the repulsive BEC, where the soliton is of the gap type, its effective mass is negative . This gives rise to a prediction for the experiment: such a soliton cannot be held by the usual parabolic trap, but it can be captured (performing slow harmonic oscillations, with a period that is estimated to be ∼0.01 s in realistic experimental conditions) by an anti-trapping inverted parabolic potential. We also study the motion of the soliton in a long system, concluding that, in the cases of both the positive and negative mass, it moves freely, provided that its amplitude is below a certain critical value; above it, the soliton's velocity decreases due to interaction with the OL. At a later stage, the damped motion becomes chaotic. We also investigate the evolution of a two-soliton pulse in the attractive model. The pulse generates a persistent breather, if its amplitude is not too large; otherwise, fusion into a single fundamental soliton takes place. Collisions between two solitons captured in the parabolic trap or anti-trap are considered too. Depending on their amplitudes and phase difference, the solitons either perform stable oscillations, colliding indefinitely many times, or merge into a single soliton. Effects reported in this work for BECs can also be formulated for optical solitons in nonlinear photonic crystals. In particular, the capture of the negative-mass soliton in the anti-trap implies that a bright optical soliton in a self-defocusing medium with a periodic structure of the refractive index may be stable in an anti-waveguide .
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.
It is known that solitons of Bose-Einstein condensates with positive scattering lengths can be produced in optical lattices. The key of this process is the negative sign of the effective mass of the wavepacket as it comes closer to the edge of the first Brillouin zone. However, the underlying assumption of the effective mass approach is the slow variation of the wavefunction envelope between consecutive lattice cells. Previous experiments and computations on this type of solitons show that this is not the usual case. In this contribution we will go beyond the slowly varying assumption to demonstrate that the equations governing the dynamics of gap solitons contain a third derivative in the dispersion. As a result, the dynamics of the stabilized wavepackets is found different that the soliton's. In particular, a radiative component is present, and the stability under collisions is only partially achieved.