9 research outputs found
Atom-molecule coexistence and collective dynamics near a Feshbach resonance of cold fermions
Degenerate Fermi gas interacting with molecules near Feshbach resonance is
unstable with respect to formation of a mixed state in which atoms and
molecules coexist as a coherent superposition. Theory of this state is
developed using a mapping to the Dicke model, treating molecular field in the
single mode approximation. The results are accurate in the strong coupling
regime relevant for current experimental efforts. The exact solution of the
Dicke model is exploited to study stability, phase diagram, and nonadiabatic
dynamics of molecular field in the mixed state.Comment: 5 pages, 2 figure
Synchronization in the BCS Pairing Dynamics as a Critical Phenomenon
Fermi gas with time-dependent pairing interaction hosts several different
dynamical states. Coupling between the collective BCS pairing mode and
individual Cooper pair states can make the latter either synchronize or
dephase. We describe transition from phase-locked undamped oscillations to
Landau-damped dephased oscillations in the collisionless, dissipationless
regime as a function of coupling strength. In the dephased regime, we find a
second transition at which the long-time asymptotic pairing amplitude vanishes.
Using a combination of numerical and analytical methods we establish a
continuous (type II) character of both transitions
Time evolution of Matrix Product States
In this work we develop several new simulation algorithms for 1D many-body
quantum mechanical systems combining the Matrix Product State variational
ansatz with Taylor, Pade and Arnoldi approximations to the evolution operator.
By comparing all methods with previous techniques based on Trotter
decompositions we demonstrate that the Arnoldi method is the best one, reaching
extremely good accuracy with moderate resources. Finally we apply this
algorithm to studying the formation of molecules in an optical lattices when
crossing a Feschbach resonance with a cloud of two-species hard-core bosons.Comment: More extensive comparison with all nearest-neighbor spin s=1/2
models. The results in this manuscript have been superseded by a more
complete work in cond-mat/061021
Variational ansatz for the nonlinear Landau-Zener problem for cold atom association
We present a rigorous analysis of the Landau-Zener linear-in-time term
crossing problem for quadratic-nonlinear systems relevant to the coherent
association of ultracold atoms in degenerate quantum gases. Our treatment is
based on an exact third-order nonlinear differential equation for the molecular
state probability. Applying a variational two-term ansatz, we construct a
simple approximation that accurately describes the whole-time dynamics of
coupled atom-molecular system for any set of involved parameters. Ensuring an
absolute error less than for the final transition probability, the resultant
solution improves by several orders of magnitude the accuracy of the previous
approximations by A. Ishkhanyan et al. developed separately for the weak
coupling [J. Phys. A 38, 3505 (2005)] and strong interaction [J. Phys. A 39,
14887 (2006)] limits. In addition, the constructed approximation covers the
whole moderate-coupling regime, providing for this intermediate regime the same
accuracy as for the two mentioned limits. The obtained results reveal the
remarkable observation that for the strong-coupling limit the resonance
crossing is mostly governed by the nonlinearity, while the coherent
atom-molecular oscillations arising soon after the resonance has been crossed
are basically of linear nature. This observation is supposed to be of a general
character due to the basic attributes of the resonance crossing processes in
the nonlinear quantum systems of the discussed type of involved quadratic
nonlinearity
Quantum quenches from integrability: the fermionic pairing model
Understanding the non-equilibrium dynamics of extended quantum systems after
the trigger of a sudden, global perturbation (quench) represents a daunting
challenge, especially in the presence of interactions. The main difficulties
stem from both the vanishing time scale of the quench event, which can thus
create arbitrarily high energy modes, and its non-local nature, which curtails
the utility of local excitation bases. We here show that nonperturbative
methods based on integrability can prove sufficiently powerful to completely
characterize quantum quenches: we illustrate this using a model of fermions
with pairing interactions (Richardson's model). The effects of simple (and
multiple) quenches on the dynamics of various important observables are
discussed. Many of the features we find are expected to be universal to all
kinds of quench situations in atomic physics and condensed matter.Comment: 10 pages, 7 figure
Quantum Quenches in Extended Systems
We study in general the time-evolution of correlation functions in a extended
quantum system after the quench of a parameter in the hamiltonian. We show that
correlation functions in d dimensions can be extracted using methods of
boundary critical phenomena in d+1 dimensions. For d=1 this allows to use the
powerful tools of conformal field theory in the case of critical evolution.
Several results are obtained in generic dimension in the gaussian (mean-field)
approximation. These predictions are checked against the real-time evolution of
some solvable models that allows also to understand which features are valid
beyond the critical evolution.
All our findings may be explained in terms of a picture generally valid,
whereby quasiparticles, entangled over regions of the order of the correlation
length in the initial state, then propagate with a finite speed through the
system. Furthermore we show that the long-time results can be interpreted in
terms of a generalized Gibbs ensemble. We discuss some open questions and
possible future developments.Comment: 24 Pages, 4 figure