Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Avalanches in Bose-Einstein Condensates

Since Bose-Einstein condensates (BECs) became an experimental reality, much effort is made to characterize its properties. A very attractive field is the study of the dynamics of ultra cold atoms in optical lattices with its potential application in quantum computation and the emerging atomtronics technologies. We investigate the atom current emitted from a BEC, where the BEC is loaded into a leaky optical lattice. In ref. [1] the open Bose-Hubbard model with two sites was analyzed. Here, we present results on the nonlinear mean field dynamics in larger 1D lattices with a coupling to the outside at both ends, which can be realized experimentally, e.g., by gravitation or by applying additional microwave fields.

We find [2] that for some critical values of the interatomic interaction strength, the current decays in avalanches that follow a power-law distribution (see Fig. 1) and indicate the existence of a novel phase transition. This behavior is due to the creation of discrete breathers. We show that the power law distribution of avalanches of BECs leaving the optical trap reflects the complexity and the hierarchical structure of the underlying classical mixed phase space.

Avalanches of BECs

Figure 1: Distribution (over initial conditions) of avalanches P(δP) for an open optical lattice with a rescaled interatomic interaction U/M=2, where M=128 is the sample size, and U is the interatomic interactions (in units of the intra-tunneling rate). A scale free power law distribution is evident. The best linear fit is indicated with the red dashed line. Inset: A representative realization of the decaying BEC population P(t) showing avalanches.



[1] M. Hiller, T. Kottos, and A. Ossipov, Phys. Rev. A 73, 063625 (2006)

Contact:  Holger Hennig 

Members working within this Project:

 Theo Geisel 
 Ragnar Fleischmann 

Former Members:

 Holger Hennig 
 Tsampikos Kottos 
 Moritz Hiller 

Selected Publications:

T. Pudlik, H. Hennig, D. Witthaut, and D.K. Campbell (2013).
Dynamics of entanglement in a dissipative Bose-Hubbard dimer
Phys. Rev. A 88:063606. download file

D. Witthaut, F. Trimborn, H. Hennig, G. Kordas, T. Geisel, and S. Wimberger (2011).
Beyond mean-field dynamics in open Bose-Hubbard chains
Phys. Rev. A 83:063608. download file

F. Trimborn, D. Witthaut, H. Hennig, G. Kordas, T. Geisel, and S. Wimberger (2011).
Decay of a Bose-Einstein condensate in a dissipative lattice - the mean-field approximation and beyond
Eur. Phys. J. D. 63(1):63-71. download file

H. Hennig, J. Dorignac, and D.K. Campbell (2010).
Transfer of Bose-Einstein condensates through discrete breathers in an optical lattice
Phys. Rev. A 82:053604. download file

G.S. Ng, H. Hennig, R. Fleischmann, T. Kottos, and T. Geisel (2009).
Avalanches of Bose-Einstein Condensates in Leaking Optical Lattices
New J. Phys. 11:073045. download file

K. Smith-Mannschott, M. Chuchem, M. Hiller, T. Kottos, and D. Cohen (2009).
Occupation Statistics of a Bose-Einstein Condensate for a Driven Landau-Zener Crossing
Phys. Rev. Lett. 102:230401.

M. Hiller, T. Kottos, and A. Ossipov (2006).
Bifurcations in resonance widths of an open Bose-Hubbard dimer
Physical Review A 73:063625.