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.
Fig1: The Wigner function of a prepared Fock state (left), and after finite time evolution (right).
;
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).
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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