Dynamical tunnelling with ultracold atoms in magnetic microtraps

Abstract

The study of dynamical tunnelling in a periodically driven anharmonic potential probes the quantum-classical transition via the experimental control of the effective Planck's constant for the system. In this paper we consider the prospects for observing dynamical tunnelling with ultracold atoms in magnetic microtraps on atom chips. We outline the driven anharmonic potentials that are possible using standard magnetic traps, and find the Floquet spectrum for one of these as a function of the potential strength, modulation, and effective Planck's constant. We develop an integrable approximation to the non-integrable Hamiltonian and find that it can explain the behaviour of the tunnelling rate as a function of the effective Planck's constant in the regular region of parameter space. In the chaotic region we compare our results with the predictions of models that describe chaos-assisted tunnelling. Finally we examine the practicality of performing these experiments in the laboratory with Bose-Einstein condensates.

V1: 12 pages, 10 figures. V2: 14 pages, 12 figures, significantly updated in response to referee report. Some figures are lower quality to reduce file sizes, please contact submitter for high quality versions. V3: Introduction rewritten, but mostly unchanged; updated to published version

References in corpus (5)

• Squeezing and entanglement in a Bose-Einstein condensate
• Regular-to-chaotic tunneling rates using a fictitious integrable system
• Influence of classical resonances on chaotic tunnelling
• Macroscopic Quantum Self-Trapping in Dynamical Tunnelling
• Two-dimensional boson-fermion mixtures

Cited by in corpus (8)

• Physical interpretation of the Planck's constant based on the Maxwell theory
• Routes towards the experimental observation of the large fluctuations due to chaos assisted tunneling effects with cold atoms
• Observing quantum chaos with noisy measurements and highly mixed states
• Chaos-assisted tunneling in the presence of Anderson localization
• Quasiparticle tunneling in a periodically driven bosonic Josephson junction
• Dynamical tunnelling of a Nano-mechanical Oscillator
• Chaos assisted many-body tunnelling
• Epistemic uncertainty from an averaged Hamilton-Jacobi formalism