Dynamical tunnelling of ultracold atoms

Abstract

The divergence of quantum and classical descriptions of particle motion is clearly apparent in quantum tunnelling between two regions of classically stable motion. An archetype of such non-classical motion is tunnelling through an energy barrier. In the 1980s, a new process, 'dynamical' tunnelling, was predicted, involving no potential energy barrier; however, a constant of the motion (other than energy) still forbids classically the quantum-allowed motion. This process should occur, for example, in periodically driven, nonlinear hamiltonian systems with one degree of freedom. Such systems may be chaotic, consisting of regions in phase space of stable, regular motion embedded in a sea of chaos. Previous studies predicted dynamical tunnelling between these stable regions. Here we observe dynamical tunnelling of ultracold atoms from a Bose-Einstein condensate in an amplitude-modulated optical standing wave. Atoms coherently tunnel back and forth between their initial state of oscillatory motion (corresponding to an island of regular motion) and the state oscillating 180 degrees out of phase with the initial state.

Simulation of chaos-assisted tunneling in a semiclassical regime on existing quantum computers

“…This situation is qualitatively different comparing to SQUIDs [3] where even for a macroscopic number of particles (analogous to n q ) the evolution is described by a Hamiltonian with two levels and effectivē h ∼ 1 [16]. It also differs from the experiments [12,13] where effectivelyh ∼ 1 independently of number of cold atoms.…”

“…This unusual tunneling is strongly influenced by complex instanton orbits and scarring effects [10,11] and a chaos enhancement of tunneling rate by orders of magnitude may be reached by a small variation of parameters. The first direct experimental observations of the chaos-assisted tunneling have been realized recently with cold [12] and ultracold atoms from a Bose-Einstein condensate [13] thus opening new possibilities for investigation of this interesting process. However, quantum tunneling is a very sensitive phenomenon and experimental studies are complicated by the decoherence produced by the environment.…”

Switching via quantum activation: A parametrically modulated oscillator

“…Such experiment requires preparing the system in one of the wells. Tunneling between period two states of a strongly modulated strongly nonlinear system has been demonstrated in atomic optics [45,46,47]. For a weakly nonlinear oscillator, tunneling splitting between the lowest states of the Hamiltonianĝ for µ = 0 was found in Ref.…”

Kicked-rotor quantum resonances in position space

“…The experimental realization of the QKR has triggered in the last decade an impressive number of studies involving dynamical localization [5,6,7,8,9,10,11], quantum transport [12,13,14,15], ratchets [16,17,18], chaosassisted tunneling [19,20], classical and quantum resonances [21,22,23,24]. Quantum resonances have been used in studies of fundamental aspects of quantum chaos such as quantum stabilization [25] or measurements of the gravitation [26].…”