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arXiv:1112.4678 · Physical Review A

Controlled excitation and resonant acceleration of ultracold few-boson systems by driven interactions in a harmonic trap

Ioannis Brouzos, Peter Schmelcher

Published Mar 26, 2012• 13 citations
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Abstract

We investigate the excitation properties of finite ultracold bosonic systems in a one-dimensional harmonic trap with a time-dependent interaction strength. The driving of the interatomic coupling induces excitations of the relative motion exclusively with specific and controllable contributions of momentarily excited many-body states. Mechanisms for selective excitation to few-body analogs of collective modes and acceleration occur in the vicinity of resonances. Via the few-body spectrum and a Floquet analysis, we study the excitation mechanisms and the corresponding impact of the driving frequency and strength as well as the initial correlation of the bosonic state. The fundamental case of two atoms is analyzed in detail and forms a key ingredient for the bottom-up understanding of cases with higher atom numbers, thereby examining finite-size corrections to macroscopic collective modes of oscillation.

DOI
10.1103/physreva.85.033635

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We investigate the excitation properties of finite ultracold bosonic systems in a one-dimensional harmonic trap with a time-dependent interaction strength. The driving of the interatomic coupling induces excitations of the relative motion exclusively with specific and controllable contributions of momentarily excited many-body states. Mechanisms for selective excitation to few-body analogs of collective modes and acceleration occur in the vicinity of resonances. Via the few-body spectrum and a Floquet analysis, we study the excitation mechanisms and the corresponding impact of the driving frequency and strength as well as the initial correlation of the bosonic state. The fundamental case of two atoms is analyzed in detail and forms a key ingredient for the bottom-up understanding of cases with higher atom numbers, thereby examining finite-size corrections to macroscopic collective modes of oscillation.
Abstract The out-of-equilibrium dynamics of finite ultracold bosonic ensembles in periodically driven one-dimensional optical lattices is investigated. Our study reveals that the driving enforces the bosons in different wells to oscillate in-phase and to exhibit a dipole-like mode. A wide range from weak-to-strong driving frequencies is covered and a resonance-like behavior of the intra-well dynamics is discussed. In the proximity of the resonance a rich intraband excitation spectrum is observed. The single particle excitation mechanisms are studied in the framework of Floquet theory elucidating the role of the driving frequency. The impact of the interatomic repulsive interactions is examined in detail yielding a strong influence on the tunneling period and the excitation probabilities. Finally, the dependence of the resonance upon a variation of the tunable parameters of the optical lattice is examined. Our analysis is based on the ab initio multi-configuration time-dependent Hartree method for bosons.
We investigate the Floquet spectrum and excitation properties of a two-ultracold-atom system with periodically driven interaction in a three-dimensional harmonic trap. The interaction between the atoms is changed by varying the s-wave scattering length in two ways, the cosine and the square-wave modulations. It is found that as the driving frequency increases, the Floquet spectrum exhibits two main features for both modulations, the accumulating and the spreading of the quasienergy levels, which further lead to different dynamical behaviors. The accumulation is associated with collective excitations and the persistent growth of the energy, while the spread indicates that the energy is bounded at all times. The initial scattering length, the driving frequency and amplitude can all significantly change the Floquet spectrum as well as the dynamics. However, the corresponding relation between them is valid universally. Finally, we propose a mechanism for selectively exciting the system to one specific state by using the avoided crossing of two quasienergy levels, which could guide preparation of a desired state in experiments.
Following a ``bottom-up approach'' in understanding many-particle effects and dynamics we provide a systematic ab initio study of the dependence of the breathing dynamics of ultracold bosons in a one-dimensional (1D) harmonic trap on the number of bosons ranging from few to many. To this end, we employ the multilayer multiconfiguration time-dependent Hartree method for bosons (ML-MCTDHB) which has been developed very recently [Kr\"onke, Cao, Vendrell, and Schmelcher, New J. Phys. 15, 063018 (2013)]. The beating behavior for two bosons is found numerically and consequently explained by an analytical approach. Drawing on this, we show how to compute the complete breathing mode spectrum in this case. We examine how the two-mode breathing behavior of two bosons evolves to the single-frequency behavior of the many-particle limit when adding more particles. In the limit of many particles, we numerically study the dependence of the breathing mode frequency on both the interaction strength as well as on the particle number. We provide an estimate for the parameter region where the mean-field description provides a valid approximation.
Deterministic preparation of an ultracold harmonically trapped one-dimensional Fermi gas consisting of a few fermions has been realized by the Heidelberg group. Using Floquet formalism, we study the time dynamics of two- and three-fermion systems in a harmonic trap under an oscillating magnetic field. The oscillating magnetic field produces a time-dependent interaction strength through a Feshbach resonance. We explore the dependence of these dynamics on the frequency of the oscillating magnetic field for noninteracting, weakly interacting, and strongly interacting systems. We identify the regimes where the system can be described by an effective two-state model and an effective three-state model. We find an unbounded coupling to all excited states at the infinitely strong interaction limit and several simple relations that characterize the dynamics. Based on our findings, we propose a technique for driving transition from the ground state to the excited states using an oscillating magnetic field.
We unravel the periodically driven dynamics of two repulsively interacting bosonic impurities within a bosonic bath upon considering either the impact of a finite pulse or continuous shaking of the impurities harmonic trap. Following a pulse driving of initially miscible components, we reveal a variety of dynamical response regimes depending on the driving frequency. At resonant drivings, the impurities decouple from their host, while if exposed to a high-frequency driving, they remain trapped in the bosonic gas. For continuous shaking, we showcase that in the resonantly driven regime the impurities oscillate back and forth within and outside the bosonic medium. In all cases, the bosonic bath is perturbed performing a collective dipole motion. Referring to an immiscible initial state, we unveil that for moderate driving frequencies the impurities feature a dispersive behavior while for a high-frequency driving they oscillate around the edges of the Thomas-Fermi background. Energy transfer processes from the impurities to their environment are encountered, especially for large driving frequencies. Additionally, coherence losses develop in the course of the evolution with the impurities predominantly moving as a pair.
We deal with the effects of an anharmonic trap on an interacting two-boson system in one dimension. Our primary focus is on the role of the induced coupling between the center of mass and the relative motion as both anharmonicity and the (repulsive) interaction strength are varied. The ground state reveals a strong localization in the relative coordinate, counteracting the tendency to fragment for stronger repulsion. To explore the quantum dynamics, we study the system's response upon (i) exciting the harmonic ground state by continuously switching on an additional anharmonicity and (ii) displacing the center of mass, this way triggering collective oscillations. The interplay between collective and internal dynamics materializes in the collapse of oscillations, which are explained in terms of few-mode models.