19 research outputs found
Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement
We show that the quantum phase transition arising in a standard
radiation-matter model (Dicke model) belongs to the same universality class as
the infinitely-coordinated, transverse field XY model. The effective
qubit-qubit exchange interaction is shown to be proportional to the square of
the qubit-radiation coupling. A universal finite-size scaling is derived for
the corresponding two-qubit entanglement (concurrence) and a size-consistent
effective Hamiltonian is proposed for the qubit subsystem.Comment: 4 pages, 3 figures. Minor changes. Published versio
Dynamical instability in kicked Bose-Einstein condensates: Bogoliubov resonances
Bose-Einstein condensates subject to short pulses (`kicks') from standing
waves of light represent a nonlinear analogue of the well-known chaos paradigm,
the quantum kicked rotor. Previous studies of the onset of dynamical
instability (ie exponential proliferation of non-condensate particles)
suggested that the transition to instability might be associated with a
transition to chaos. Here we conclude instead that instability is due to
resonant driving of Bogoliubov modes. We investigate the excitation of
Bogoliubov modes for both the quantum kicked rotor (QKR) and a variant, the
double kicked rotor (QKR-2). We present an analytical model, valid in the limit
of weak impulses which correctly gives the scaling properties of the resonances
and yields good agreement with mean-field numerics.Comment: 8 page
Dynamical instability in kicked Bose-Einstein condensates
Bose-Einstein condensates subject to short pulses (kicks) from standing waves of light represent a nonlinear analog of the well-known chaos paradigm, the quantum kicked rotor. Previous studies of the onset of dynamical instability (i.e., exponential proliferation of noncondensate particles) suggested that the transition to instability might be associated with a transition to chaos. Here we conclude instead that instability is due to resonant driving of Bogoliubov modes. We investigate the Bogoliubov spectrum for both the quantum kicked rotor (QKR) and a variant, the double kicked rotor (QKR-2). We present an analytical model, valid in the limit of weak impulses which correctly gives the scaling properties of the resonances and yields good agreement with mean-field numerics
Time periodicity and dynamical stability in two-boson systems
We calculate the period of recurrence of dynamical systems comprising two
interacting bosons. A number of theoretical issues related to this problem are
discussed, in particular, the conditions for small periodicity. The knowledge
gathered in this way is then used to propose a notion of dynamical stability
based on the stability of the period. Dynamical simulations show good agreement
with the proposed scheme. We also apply the results to the phenomenon known as
coherent population trapping and find stability conditions in this specific
case.Comment: 7+ pages, 5 figure
Optical signatures of quantum phase transitions in a light-matter system
Information about quantum phase transitions in conventional condensed matter
systems, must be sought by probing the matter system itself. By contrast, we
show that mixed matter-light systems offer a distinct advantage in that the
photon field carries clear signatures of the associated quantum critical
phenomena. Having derived an accurate, size-consistent Hamiltonian for the
photonic field in the well-known Dicke model, we predict striking behavior of
the optical squeezing and photon statistics near the phase transition. The
corresponding dynamics resemble those of a degenerate parametric amplifier. Our
findings boost the motivation for exploring exotic quantum phase transition
phenomena in atom-cavity, nanostructure-cavity, and
nanostructure-photonic-band-gap systems.Comment: 4 pages, 4 figure
Coherent State Description of the Ground State in the Tavis-Cummings Model and its Quantum Phase Transitions
Quantum phase transitions and observables of interest of the ground state in
the Tavis-Cummings model are analyzed, for any number of atoms, by using a
tensorial product of coherent states. It is found that this "trial" state
constitutes a very good approximation to the exact quantum solution, in that it
globally reproduces the expectation values of the matter and field observables.
These include the population and dipole moments of the two-level atoms and the
squeezing parameter. Agreement in the field-matter entanglement and in the
fidelity measures, of interest in quantum information theory, is also found.The
analysis is carried out in all three regions defined by the separatrix which
gives rise to the quantum phase transitions. It is argued that this agreement
is due to the gaussian structure of the probability distributions of the
constant of motion and the number of photons. The expectation values of the
ground state observables are given in analytic form, and the change of the
ground state structure of the system when the separatrix is crossed is also
studied.Comment: 38 pages, 16 figure
Entanglement entropy in collective models
We discuss the behavior of the entanglement entropy of the ground state in
various collective systems. Results for general quadratic two-mode boson models
are given, yielding the relation between quantum phase transitions of the
system (signaled by a divergence of the entanglement entropy) and the
excitation energies. Such systems naturally arise when expanding collective
spin Hamiltonians at leading order via the Holstein-Primakoff mapping. In a
second step, we analyze several such models (the Dicke model, the two-level BCS
model, the Lieb-Mattis model and the Lipkin-Meshkov-Glick model) and
investigate the properties of the entanglement entropy in the whole parameter
range. We show that when the system contains gapless excitations the
entanglement entropy of the ground state diverges with increasing system size.
We derive and classify the scaling behaviors that can be met.Comment: 11 pages, 7 figure
Spin-glasses in optical cavity
Recent advances in nanofabrication and optical control have garnered
tremendous interest in multi-qubit-cavity systems. Here we analyze a spin-glass
version of such a nanostructure, solving analytically for the phase diagrams in
both the matter and radiation subsystems in the replica symmetric regime.
Interestingly, the resulting phase transitions turn out to be tunable simply by
varying the matter-radiation coupling strength