Dynamics of condensed particles in a few site system (2011)

The physics of N bosons in an M site system is described by the Bose-Hubbard Hamiltonian. The M=2 problem is integrable and equivalent to j=N/2 spin problem, while the M=3 problem has both non-trivial topology and mixed phase space. Our studies concerns the analysis of fluctuations, occupation statistics and quantum stirring in such systems.
 
The time dependent dynamics in a Bosonic Josephson junction with no driving can be regarded as a quantum version of a pendulum. Adding driving to this system, we have studied the many-body Landau-Zener dynamics; the Kapitza pendulum dynamics; and the Quantum Zeno dynamics due to erratic driving. In particular we have studied the stabilization and the suppression of collision-induced dephasing by periodic, erratic, or noisy driving.
 
We had initiated a study of quantum stirring in a trimer (3site) system, analyzing how the interaction modifies the nature of the dynamical process. This has motivated a detailed study of the manybody Landau-Zener transition. Specifically we have analyzed the adiabatic-diabatic-sudden crossover, and showed that the occupation statistics obeys sub-Binomial scaling due to phase space squeezing.
 
     wigner function prep      wigner function
 
Fig1: The Wigner function of a prepared Fock state (left), and after finite time evolution (right).

Bloch; BlochE
Fig2: The time evolution of the Bloch vector for various coherent preparations (left) and the quantum Zeno effect for Pi preparation due to the presence of noise (right).

csf scars

Fig3: Phase space tomography for a kicked top:  the participation number for all coherent preparations is imaged for an integrable phase-space (left), for a mixed phase-space (middle) and for a chaotic phase-space (right).  In the latter case one observes the effect of scarring.


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