We study the complex quantum dynamics of a system of many interacting atoms in an elongated anharmonic trap. The system is initially in a Bose–Einstein condensed state, well described by Thomas–Fermi profile in the elongated direction and the ground state in the transverse directions. After a sudden quench to a coherent superposition of the ground and lowest energy transverse modes, quantum dynamics starts. We describe this process employing a three-mode many-body model. The experimental realization of this system displays decaying oscillations of the atomic density distribution. While a mean-field description predicts perpetual oscillations of the atomic density distribution, our quantum many-body model exhibits a decay of the oscillations for sufficiently strong atomic interactions. We associate this decay with the fragmentation of the condensate during the evolution. The decay and fragmentation are also linked with the approach of the many-body model to the chaotic regime. The approach to chaos lifts degeneracies and increases the complexity of the eigenstates, enabling the relaxation to equilibrium and the onset of thermalization. We verify that the damping time and quantum signatures of chaos show similar dependences on the interaction strength and on the number of atoms.
We study the complex quantum dynamics of a system of many interacting atoms in an elongated anharmonic trap. The system is initially in a Bose–Einstein condensed state, well described by Thomas–Fermi profile in the elongated direction and the ground state in the transverse directions. After a sudden quench to a coherent superposition of the ground and lowest energy transverse modes, quantum dynamics starts. We describe this process employing a three-mode many-body model. The experimental realization of this system displays decaying oscillations of the atomic density distribution. While a mean-field description predicts perpetual oscillations of the atomic density distribution, our quantum many-body model exhibits a decay of the oscillations for sufficiently strong atomic interactions. We associate this decay with the fragmentation of the condensate during the evolution. The decay and fragmentation are also linked with the approach of the many-body model to the chaotic regime. The approach to chaos lifts degeneracies and increases the complexity of the eigenstates, enabling the relaxation to equilibrium and the onset of thermalization. We verify that the damping time and quantum signatures of chaos show similar dependences on the interaction strength and on the number of atoms.
Abstract We investigate the chaotic dynamics of a coupled three-level atom–molecular Bose–Einstein condensate system composed by one molecular mode and two atomic modes. With the increase of atom–molecular coupling strength, we reveal the emergence of chaotic oscillations of the relative population difference between two atomic modes, which can be proven by the broad windows with a huge number of frequencies in spectral density and the chaotic trajectories in phase space diagrams. The different effects of initial states on atomic population oscillations are revealed, where for more particles in the initial state of the molecular model, chaos appears in the larger parameter region of system dynamics. Furthermore, we find that strong intermolecular interaction strength can suppress chaos resulting from strong atom–molecule coupling. This is due to the difficult transformation between atomic and molecular modes, as well as the relatively independent dynamic evolution of atoms and molecules.
Within the past five years Albert Einstein's concept of a dilute atomic Bose Condensate has been realized in many experimental laboratories. Temperatures in the nano-Kelvin regime have been achieved using magnetic and optical trapping of laser and evaporatively cooled atoms. At such temperatures the relative de Broglie wavelengths of the gaseous trapped atoms can become long compared to their mean spacing, and through a process of bosonic amplification a "quantum phase transition" takes place involving 10 3 to 10 11 atoms, most of which end up in identical single particle quantum states, whose length scales are determined by the external trap. Rb, Na, Li and atomic H have been trapped at variable densities of the order of 10 13 /cm 3 , and in traps of varying geometries. Of these all but Li have an effective repulsive atomic pair interaction, but utilization of molecular Feshbach resonances allows the interactions of other species to be tuned over wide ranges of strengths, including control of the sign of the effective atomic pair interactions. Fully quantum and macroscopic systems at such low densities are a theorist's dream: simple Hartree type mean field theory provides a startlingly accurate description of density profiles, low energy excitation frequencies, and such a description, commonly called the Non-linear Schrödinger Equation (NLSE) or the Gross-Pitaevskii (GP) Equation, will be explored here. The NLSE appropriate for attractive atomic interactions is known to lead to chaotically unstable dynamics, and eventual implosion of the condensate should the local number density exceed a critical value. In this work we illustrate this type of chaotic collapse for attractive condensates, and then explore the types of chaotic dynamics of solitons and vortices, which are the signatures of dynamical non-linearity in the repulsive case. Finally the implications of the symmetry-breaking associated with phase rigidity are explored in model simulations of repulsive condensates: condensates with repulsive atomic interactions break into phase domains when subject to weak shocks and, perhaps surprisingly, break into chaotic "laser-speckle" type patterns as the shock level increases. The fully quantum mechanical NLSE thus displays a full range of chaotic types of motion: from particle-like chaotic collisions of solitons and vortices to fully developed time dependent wave chaos.
We study numerically the evolution of Bose-Einstein condensate in the Sinai-oscillator trap described by the Gross-Pitaevskii equation in two dimensions. In the absence of interactions, this trap mimics the properties of Sinai billiards where the classical dynamics is chaotic and the quantum evolution is described by generic properties of quantum chaos and random matrix theory. We show that, above a certain border, the nonlinear interactions between atoms lead to the emergence of dynamical thermalization which generates the statistical Bose-Einstein distribution over eigenmodes of the system without interactions. Below the thermalization border, the evolution remains quasi-integrable. Such a Sinai-oscillator trap, formed by the oscillator potential and a repulsive disk located in the vicinity of the center, had been already realized in first experiments with the Bose-Einstein condensate formation by Ketterle group in 1995 and we argue that it can form a convenient test bed for experimental investigations of dynamical of thermalization. Possible links and implications for Kolmogorov turbulence in absence of noise are also discussed.
In a quantum many-body system, such as atoms, molecules, and atomic nuclei, interparticle interactions generate a complex quantum level scheme that can be analyzed progressively: from the simplest picture of independent quasiparticles moving in a self-consistent mean field to more complete descriptions that include residual interactions and the opening of decay channels above some excitation thresholds. Residual interactions lead to two seemingly contrasting phenomena: the emergence of collective modes (such as rotational and vibrational excitations) associated with specific symmetries, and internal thermalization, which gives rise to features of quantum chaos and causes these collective modes to damp. The picture becomes more intricate once decay channels become energetically accessible, allowing the system to decay irreversibly by means such as particle emission and thus transition to an open quantum regime. In this work, we investigate the competition between internal many-body dynamics and explicit, irreversible decay. These processes can occur on comparable timescales, leading to an initial stage of rapid dynamics followed by equilibration. We show that the decay of the faster components drives the system into an exponentially decaying regime, characterized by a noisy decay current. For this study, we adopt a general, albeit simplified, model of a collective mode embedded in a chaotic background and coupled to open decay channels. The interplay of timescales revealed in this framework appears to reflect universal features of open quantum systems.
Abstract We report the first experimental observation of dissipation-driven coherent quantum many-body oscillation, and this oscillation is manifested as the coherent exchange of atoms between the thermal and condensate components in a three-dimensional partially condensed Bose gas. Firstly, we observe that the dissipation leads to two different atom loss rates between the thermal and the condensate components, such that the thermal fraction increases as dissipation time increases. Therefore, this dissipation process serves as a tool to uniformly ramp up the system’s temperature without introducing extra density excitation. Subsequently, a coherent pair exchange of atoms between the thermal and the condensate components occurs, resulting in coherent oscillation of atom numbers in both components. This oscillation, permanently embedded in the atom loss process, is revealed clearly when we inset a duration of dissipation-free evolution into the entire dynamics, manifested as an oscillation of total atom number at the end. Finally, we also present a theoretical calculation to support this physical mechanism, which simultaneously includes dissipation, interaction, finite temperature, and harmonic trap effects. Our work introduces a highly controllable dissipation as a new tool to control quantum many-body dynamics.
By quenching the strength of interactions in a partially condensed Bose gas, we create a "supersaturated" vapor which has more thermal atoms than it can contain in equilibrium. Subsequently, the number of condensed atoms (N(0)) grows even though the temperature (T) rises and the total atom number decays. We show that the nonequilibrium evolution of the system is isoenergetic and, for small initial N(0), observe a clear separation between T and N(0) dynamics, thus explicitly demonstrating the theoretically expected "two-step" picture of condensate growth. For increasing initial N(0) values, we observe a crossover to classical relaxation dynamics. The size of the observed quench-induced effects can be explained using a simple equation of state for an interacting harmonically trapped atomic gas.