Two Cold Atoms in a Time-Dependent Harmonic Trap in One Dimension

Abstract

We analyze the dynamics of two atoms with a short-ranged pair interaction in a one-dimensional harmonic trap with time-dependent frequency. Our analysis is focused on two representative cases: (i) a sudden change of the trapping frequency from one value to another, and (ii) a periodic trapping frequency. In case (i), the dynamics of the interacting and the corresponding non-interacting systems turn out to be similar. In the second case, however, the interacting system can behave quite differently, especially close to parametric resonance. For instance, in the regions where such resonance occurs we find that the interaction can significantly reduce the rate of energy increase. The implications for applications of our findings to cool or heat the system are also dicussed.

arXiv commentVersion accepted for publication in Annalen der Physik

References in corpus (15)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Deterministic Preparation of a Tunable Few-Fermion System
• Evolution of a Bose-condensed gas under variations of the confining potential
• Fermionization of two distinguishable fermions
• Breakdown of time-dependent mean-field theory for a one-dimensional condensate of impenetrable bosons
• Shortcuts to adiabaticity for trapped ultracold gases
• The quantum Arnold transformation
• Ideal Gases in Time-Dependent Traps
• Exploring the few- to many-body crossover using cold atoms in one dimension
• Cooling atoms in an optical trap by selective parametric excitation
• On a scale-invariant Fermi gas in a time-dependent harmonic potential
• Simulation of Time-dependent Heisenberg Models in 1D
• Controlled excitation and resonant acceleration of ultracold few-boson systems by driven interactions in a harmonic trap
• Parametric Excitation of a 1D Gas in Integrable and Nonintegrable Cases
• Non-perturbative theoretical description of two atoms in an optical lattice with time-dependent perturbations

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• One-dimensional mixtures of several ultracold atoms: a review
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• Static and dynamic properties of a few spin $1/2$ interacting fermions trapped in an harmonic potential
• Quench Dynamics of Two One-Dimensional Harmonically Trapped Bosons Bridging Attraction and Repulsion
• Broken scale-invariance in time-dependent trapping potentials
• Method for finding the exact effective Hamiltonian of time driven quantum systems
• Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well
• Dynamics and Redistribution of Entanglement and Coherence in Three Time-Dependent Coupled Harmonic Oscillators
• Dynamics of small trapped one-dimensional Fermi gas under oscillating magnetic fields
• A Solvable Model for Decoupling of Interacting Clusters
• Dynamical resistivity of a few interacting fermions to the time-dependent potential barrier
• Comment on: "Quantum dynamics of a general time-dependent coupled oscillator"
• Impenetrability in Floquet scattering in one dimension
• Dynamics of entanglement entropy of interacting fermions in a 1D driven harmonic trap
• Few strongly interacting fermions of different mass driven in the vicinity of a critical point