Tunneling and the onset of chaos in a driven bistable system

Abstract

We study the interplay between coherent transport by tunneling and diffusive transport through classically chaotic phase-space regions, as it is reflected in the Floquet spectrum of the periodically driven quartic double well. The tunnel splittings in the semiclassical regime are determined with high numerical accuracy, and the association of the corresponding doublet states to either chaotic or regular regions of the classical phase space is quantified in terms of the overlap of the Husimi distribution with the chaotic layer along the separatrix. We find a strong correlation between both quantities. They show an increase by orders of magnitude as chaotic diffusion between the wells starts to dominate the classical dynamics. We discuss semiclassical explanations for this correlation. 05.45.+b, 03.65.Sq, 73.40.Gk

Beyond-mean-field behavior of large Bose-Einstein condensates in double-well potentials

“…For a BEC in a double well, the Husimi distribution (10) can be used to average over mean-field solutions (Refs. [24,26] and references therein). Without tilt (μ 0 = 0) and driving (μ 1 = 0), the mean-field dynamics is known analytically (see, e.g., Ref.…”

“…In general, situations with important quantum correlations, where a mean-field approach is no longer adequate, are in the focus of current research, e.g., many-particle entanglement [15], the experimental realization * b.gertjerenken@uni-oldenburg.de of entangled squeezed states [16], mesoscopic quantum superpositions [17][18][19][20][21], and mean-field chaos [22,23]. In order to estimate time scales on which the mean-field dynamics still agrees with N -particle quantum dynamics, classical-field methods can be used to approximate the quantum dynamics by averaging over mean-field solutions [24][25][26][27][28][29][30][31][32], thus mimicking quantum uncertainties that disappear in the mean-field limit (2) but will always be present for finite particle numbers.…”

Driven tunneling: New possibilities for coherent and incoherent quantum transport

“…In Fig. 4, we compare the S dependencies of the tunnel splittings and the overlaps for the seven quasienergy doublets from lea ), 1¢2) to [ ¢13), 1¢14) [17,18]. Qualitatively, they are strikingly similar: There is only a weak S dependence, reflecting the influence of the growing first resonance, for S ~ l0 -3.…”

“…The present work forms a synopsis of results partially published elsewhere [11][12][13][14][15][16][17][18].…”

“…The breakup of the tunnel doublets in the chaotic layer is not a direct consequence of the Lyapunov exponent of the classical dynamics being positive there, but rests on the global condition that diffusive spreading connects all parts of the chaotic layer, bridging the symmetry plane. In order to allow for a numerical check, we quantify the distinction between "regular" and "chaotic" eigenstates on the basis of the overlap of the Husimi representation [36] of an eigenstate with the chaotic layer in phase space [17,18]. To illustrate these concepts, the Husimi distribution for the quasienergy state 1¢7) is superposed, in Fig.…”