26 research outputs found
Quantum stability of self-organized atomic insulator-like states in optical resonators
We investigate a paradigm example of cavity quantum electrodynamics with many
body systems: an ultracold atomic gas inside a pumped optical resonator. In
particular, we study the stability of atomic insulator-like states, confined by
the mechanical potential emerging from the cavity field spatial mode structure.
As in open space, when the optical potential is sufficiently deep, the atomic
gas is in the Mott-like state. Inside the cavity, however, the potential
depends on the atomic distribution, which determines the refractive index of
the medium, thus altering the intracavity field amplitude. We derive the
effective Bose-Hubbard model describing the physics of the system in one
dimension and study the crossover between the superfluid -- Mott insulator
quantum states. We determine the regions of parameters where the atomic
insulator states are stable, and predict the existence of overlapping stability
regions corresponding to competing insulator-like states. Bistable behavior,
controlled by the pump intensity, is encountered in the vicinity of the shifted
cavity resonance.Comment: 13 pages, 6 figures. Replaced with revised version. Accepted for
publication in New J. Phys., special issue "Quantum correlations in tailord
matter
Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics
The superposition principle is a very basic ingredient of quantum theory.
What may come as a surprise to many students, and even to many practitioners of
the quantum craft, is tha superposition has limitations imposed by certain
requirements of the theory. The discussion of such limitations arising from the
so-called superselection rules is the main purpose of this paper. Some of their
principal consequences are also discussed. The univalence, mass and particle
number superselection rules of non-relativistic quantum mechanics are also
derived using rather simple methods.Comment: 22 pages, no figure
Dilute gas of ultracold two-level atoms inside a cavity; generalized Dicke model
We consider a gas of ultracold two-level atoms confined in a cavity, taking
into account for atomic center-of-mass motion and cavity mode variations. We
use the generalized Dicke model, and analyze separately the cases of a
Gaussian, and a standing wave mode shape. Owing to the interplay between
external motional energies of the atoms and internal atomic and field energies,
the phase-diagrams exhibit novel features not encountered in the standard Dicke
model, such as the existence of first and second order phase transitions
between normal and superradiant phases. Due to the quantum description of
atomic motion, internal and external atomic degrees of freedom are highly
correlated leading to modified normal and superradiant phases.Comment: 10 pages, 7 figure
Statistical diagonalization of a random biased Hamiltonian:the case of the eigenvectors
We present a non perturbative calculation technique providing the mixed
moments of the overlaps between the eigenvectors of two large quantum
Hamiltonians: and , where is
deterministic and is random. We apply this method to recover the
second order moments or Local Density Of States in the case of an arbitrary
fixed and a Gaussian . Then we calculate the fourth order
moments of the overlaps in the same setting. Such quantities are crucial for
understanding the local dynamics of a large composite quantum system. In this
case, is the sum of the Hamiltonians of the system subparts and
is an interaction term. We test our predictions with numerical
simulations.Comment: 15 pages, 7 figure