46 research outputs found
Postquench prethermalization in a disordered quantum fluid of light
We study the coherence of a disordered and interacting quantum light field
after propagation along a nonlinear optical fiber. Disorder is generated by a
cross-phase modulation with a randomized auxiliary classical light field, while
interactions are induced by self-phase modulation. When penetrating the fiber
from free space, the incoming quantum light undergoes a disorder and
interaction quench. By calculating the coherence function of the transmitted
quantum light, we show that the decoherence induced by the quench spreads in a
light-cone fashion in the nonequilibrium many-body quantum system, leaving the
latter prethermalize with peculiar features originating from disorder.Comment: 18 pages, 5 figure
A new vibrational level of the H molecular ion
A new state of the H molecular ion with binding energy of
1.09 a.u. below the first dissociation limit is predicted, using
highly accurate numerical nonrelativistic quantum calculations. It is the first
L=0 excited state, antisymmetric with respect to the exchange of the two
protons. It manifests itself as a huge p-H scattering length of
Bohr radii.Comment: 6 pages + 3 figure
Analysis of dynamical tunnelling experiments with a Bose-Einstein condensate
Dynamical tunnelling is a quantum phenomenon where a classically forbidden
process occurs, that is prohibited not by energy but by another constant of
motion. The phenomenon of dynamical tunnelling has been recently observed in a
sodium Bose-Einstein condensate. We present a detailed analysis of these
experiments using numerical solutions of the three dimensional Gross-Pitaevskii
equation and the corresponding Floquet theory. We explore the parameter
dependency of the tunnelling oscillations and we move the quantum system
towards the classical limit in the experimentally accessible regime.Comment: accepted for publication in Physical Review
Symmetry Decomposition of Potentials with Channels
We discuss the symmetry decomposition of the average density of states for
the two dimensional potential and its three dimensional
generalisation . In both problems, the energetically
accessible phase space is non-compact due to the existence of infinite channels
along the axes. It is known that in two dimensions the phase space volume is
infinite in these channels thus yielding non-standard forms for the average
density of states. Here we show that the channels also result in the symmetry
decomposition having a much stronger effect than in potentials without
channels, leading to terms which are essentially leading order. We verify these
results numerically and also observe a peculiar numerical effect which we
associate with the channels. In three dimensions, the volume of phase space is
finite and the symmetry decomposition follows more closely that for generic
potentials --- however there are still non-generic effects related to some of
the group elements
Coherent Matter Wave Transport in Speckle Potentials
This article studies multiple scattering of matter waves by a disordered
optical potential in two and in three dimensions. We calculate fundamental
transport quantities such as the scattering mean free path , the
Boltzmann transport mean free path \elltrb, and the Boltzmann diffusion
constant , using a diagrammatic Green functions approach. Coherent
multiple scattering induces interference corrections known as weak localization
which entail a reduced diffusion constant. We derive the corresponding
expressions for matter wave transport in an correlated speckle potential and
provide the relevant parameter values for a possible experimental study of this
coherent transport regime, including the critical crossover to the regime of
strong or Anderson localization.Comment: 33 pages, minor corrections, published versio
Statistics of electromagnetic transitions as a signature of chaos in many-electron atoms
Using a configuration interaction approach we study statistics of the dipole
matrix elements (E1 amplitudes) between the 14 lower odd states with J=4 and
21st to 100th even states with J=4 in the Ce atom (1120 lines). We show that
the distribution of the matrix elements is close to Gaussian, although the
width of the Gaussian distribution, i.e. the root-mean-square matrix element,
changes with the excitation energy. The corresponding line strengths are
distributed according to the Porter-Thomas law which describes statistics of
transition strengths between chaotic states in compound nuclei. We also show
how to use a statistical theory to calculate mean squared values of the matrix
elements or transition amplitudes between chaotic many-body states. We draw
some support for our conclusions from the analysis of the 228 experimental line
strengths in Ce [J. Opt. Soc. Am. v. 8, p. 1545 (1991)], although direct
comparison with the calculations is impeded by incompleteness of the
experimental data. Nevertheless, the statistics observed evidence that highly
excited many-electron states in atoms are indeed chaotic.Comment: 16 pages, REVTEX, 4 PostScript figures (submitted to Phys Rev A
Sensitivity of the eigenfunctions and the level curvature distribution in quantum billiards
In searching for the manifestations of sensitivity of the eigenfunctions in
quantum billiards (with Dirichlet boundary conditions) with respect to the
boundary data (the normal derivative) we have performed instead various
numerical tests for the Robnik billiard (quadratic conformal map of the unit
disk) for 600 shape parameter values, where we look at the sensitivity of the
energy levels with respect to the shape parameter. We show the energy level
flow diagrams for three stretches of fifty consecutive (odd) eigenstates each
with index 1,000 to 2,000. In particular, we have calculated the (unfolded and
normalized) level curvature distribution and found that it continuously changes
from a delta distribution for the integrable case (circle) to a broad
distribution in the classically ergodic regime. For some shape parameters the
agreement with the GOE von Oppen formula is very good, whereas we have also
cases where the deviation from GOE is significant and of physical origin. In
the intermediate case of mixed classical dynamics we have a semiclassical
formula in the spirit of the Berry-Robnik (1984) surmise. Here the agreement
with theory is not good, partially due to the localization phenomena which are
expected to disappear in the semiclassical limit. We stress that even for
classically ergodic systems there is no global universality for the curvature
distribution, not even in the semiclassical limit.Comment: 19 pages, file in plain LaTeX, 15 figures available upon request
Submitted to J. Phys. A: Math. Ge
Classical Evolution of Quantum Elliptic States
The hydrogen atom in weak external fields is a very accurate model for the
multiphoton excitation of ultrastable high angular momentum Rydberg states, a
process which classical mechanics describes with astonishing precision. In this
paper we show that the simplest treatment of the intramanifold dynamics of a
hydrogenic electron in external fields is based on the elliptic states of the
hydrogen atom, i.e., the coherent states of SO(4), which is the dynamical
symmetry group of the Kepler problem. Moreover, we also show that classical
perturbation theory yields the {\it exact} evolution in time of these quantum
states, and so we explain the surprising match between purely classical
perturbative calculations and experiments. Finally, as a first application, we
propose a fast method for the excitation of circular states; these are
ultrastable hydrogenic eigenstates which have maximum total angular momentum
and also maximum projection of the angular momentum along a fixed direction. %Comment: 8 Pages, 2 Figures. Accepted for publication in Phys. Rev.
The Hydrogen Atom in Combined Electric and Magnetic Fields with Arbitrary Mutual Orientations
For the hydrogen atom in combined magnetic and electric fields we investigate
the dependence of the quantum spectra, classical dynamics, and statistical
distributions of energy levels on the mutual orientation of the two external
fields. Resonance energies and oscillator strengths are obtained by exact
diagonalization of the Hamiltonian in a complete basis set, even far above the
ionization threshold. At high excitation energies around the Stark saddle point
the eigenenergies exhibit strong level repulsions when the angle between the
fields is varied. The large avoided crossings occur between states with the
same approximately conserved principal quantum number, n, and this
intramanifold mixing of states cannot be explained, not even qualitatively, by
conventional perturbation theory. However, it is well reproduced by an extended
perturbation theory which takes into account all couplings between the angular
momentum and Runge-Lenz vector. The large avoided crossings are interpreted as
a quantum manifestation of classical intramanifold chaos. This interpretation
is supported by both classical Poincar\'e surfaces of section, which reveal a
mixed regular-chaotic intramanifold dynamics, and the statistical analysis of
nearest-neighbor-spacingComment: two-column version, 10 pages, REVTeX, 10 figures, uuencoded,
submitted to Rhys. Rev.