752 research outputs found
Decoherence and dephasing in strongly driven colliding Bose-Einstein condensates
We report on a series of measurements of decoherence and wavepacket dephasing
between two colliding, strongly coupled, identical Bose-Einstein condensates.
We measure, in the strong excitation regime, a suppression of the mean-field
shift, compared to the shift which is observed for a weak excitation. This
suppression is explained by applying the Gross-Pitaevskii energy functional. By
selectively counting only the non-decohered fraction in a time of flight image
we observe oscillations for which both inhomogeneous and Doppler broadening are
suppressed, in quantitative agreement with a full Gross-Pitaevskii equation
simulation. If no post selection is used, the decoherence rate due to
collisions can be extracted, and is in agreement with the local density average
calculated rate.Comment: 4 pages, 5 figure
Bose-Einstein condensate in a rapidly rotating non-symmetric trap
A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional
harmonic trap can be described with the lowest Landau-level set of
single-particle states. The condensate wave function psi(x,y) is a Gaussian
exp(-r^2/2), multiplied by an analytic function f(z) of the complex variable z=
x+ i y. The criterion for a quantum phase transition to a non-superfluid
correlated many-body state is usually expressed in terms of the ratio of the
number of particles to the number of vortices. Here, a similar description
applies to a rapidly rotating non-symmetric two-dimensional trap with arbitrary
quadratic anisotropy (omega_x^2 < omega_y^2). The corresponding condensate wave
function psi(x,y) is a complex anisotropic Gaussian with a phase proportional
to xy, multiplied by an analytic function f(z), where z = x + i \beta_- y is a
stretched complex variable and 0< \beta_- <1 is a real parameter that depends
on the trap anisotropy and the rotation frequency. Both in the mean-field
Thomas-Fermi approximation and in the mean-field lowest Landau level
approximation with many visible vortices, an anisotropic parabolic density
profile minimizes the energy. An elongated condensate grows along the soft trap
direction yet ultimately shrinks along the tight trap direction. The criterion
for the quantum phase transition to a correlated state is generalized (1) in
terms of N/L_z, which suggests that a non-symmetric trap should make it easier
to observe this transition or (2) in terms of a "fragmented" correlated state,
which suggests that a non-symmetric trap should make it harder to observe this
transition. An alternative scenario involves a crossover to a quasi
one-dimensional condensate without visible vortices, as suggested by Aftalion
et al., Phys. Rev. A 79, 011603(R) (2009).Comment: 20 page
ac Stark shift and multiphoton-like resonances in low-frequency driven optical lattices
We suggest that Bose-Einstein condensates in optical lattices subjected to ac
forcing with a smooth envelope may provide detailed experimental access to
multiphoton-like transitions between ac-Stark-shifted Bloch bands. Such
transitions correspond to resonances described theoretically by avoided
quasienergy crossings. We show that the width of such anticrossings can be
inferred from measurements involving asymmetric pulses. We also introduce a
pulse tracking strategy for locating the particular driving amplitudes for
which resonances occur. Our numerical calculations refer to a currently
existing experimental set-up [Haller et al., PRL 104, 200403 (2010)].Comment: 5 pages, 6 figure
Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems: II. Dipole-dipole versus current-current correlations
Based on Takayama-Lin-Liu-Maki model, analytical expressions for the
third-harmonic generation, DC Kerr effect, DC-induced second harmonic optical
Kerr effect, optical Kerr effect or intensity-dependent index of refraction and
DC-electric-field-induced optical rectification are derived under the static
current-current() correlation for one-dimensional infinite chains. The
results of hyperpolarizabilities under correlation are then compared
with those obtained using the dipole-dipole () correlation. The comparison
shows that the conventional correlation, albeit quite successful for
the linear case, is incorrect for studying the nonlinear optical properties of
periodic systems.Comment: 11 pages, 5 figure
Unitary expansion of the time evolution operator
We propose an expansion of the unitary evolution operator, associated to a
given Schr\"odinger equation, in terms of a finite product of explicit unitary
operators. In this manner, this unitary expansion can be truncated at the
desired level of approximation, as shown in the given examples.Comment: 6 pages, 7 figures. Updated version, minor final change
Harmonic oscillators coupled by springs: discrete solutions as a Wigner Quantum System
We consider a quantum system consisting of a one-dimensional chain of M
identical harmonic oscillators with natural frequency , coupled by
means of springs. Such systems have been studied before, and appear in various
models. In this paper, we approach the system as a Wigner Quantum System, not
imposing the canonical commutation relations, but using instead weaker
relations following from the compatibility of Hamilton's equations and the
Heisenberg equations. In such a setting, the quantum system allows solutions in
a finite-dimensional Hilbert space, with a discrete spectrum for all physical
operators. We show that a class of solutions can be obtained using generators
of the Lie superalgebra gl(1|M). Then we study the properties and spectra of
the physical operators in a class of unitary representations of gl(1|M). These
properties are both interesting and intriguing. In particular, we can give a
complete analysis of the eigenvalues of the Hamiltonian and of the position and
momentum operators (including multiplicities). We also study probability
distributions of position operators when the quantum system is in a stationary
state, and the effect of the position of one oscillator on the positions of the
remaining oscillators in the chain
Splitting in the Excitation Spectrum of A Bose-Einstein Condensate Undergoing Strong Rabi Oscillations
We report on a measurement of splitting in the excitation spectrum of a
condensate driven by an optical travelling wave. Experimental results are
compared to a numerical solution of the Gross Pitaevskii equation, and analyzed
by a simple two level model and by the more complete band theory, treating the
driving beams as an optical lattice. In this picture, the splitting is a
manifestation of the energy gap between neighboring bands that opens on the
boundary of the Brillouin zone.Comment: 5 pages, 5 figure
An Exact Approach to the Oscillator Radiation Process in an Arbitrarily Large Cavity
Starting from a solution of the problem of a mechanical oscillator coupled to
a scalar field inside a reflecting sphere of radius , we study the behaviour
of the system in free space as the limit of an arbitrarily large radius in the
confined solution. From a mathematical point of view we show that this way of
facing the problem is not equivalent to consider the system {\it a} {\it
priori} embedded in infinite space. In particular, the matrix elements of the
transformation turning the system to principal axis, do not tend to
distributions in the limit of an arbitrarily large sphere as it should be the
case if the two procedures were mathematically equivalent. Also, we introduce
"dressed" coordinates which allow an exact description of the oscillator
radiation process for any value of the coupling, strong or weak. In the case of
weak coupling, we recover from our exact expressions the well known decay
formulas from perturbation theory.Comment: 27 page
Theory of Umklapp-assisted recombination of bound excitons in Si:P
We present the calculations for the oscillator strength of the recombination
of excitons bound to phosphorous donors in silicon. We show that the direct
recombination of the bound exciton cannot account for the experimentally
measured oscillator strength of the no-phonon line. Instead, the recombination
process is assisted by an umklapp process of the donor electron state. We make
use of the empirical pseudopotential method to evaluate the Umklapp-assisted
recombination matrix element in second-order perturbation theory. Our result is
in excellent agreement with the experiment. We also present two methods to
improve the optical resolution of the optical detection of the spin state of a
single nucleus in silicon.Comment: 9 pages, 6 EPS figures, Revtex
Repulsive Fermions in Optical Lattices: Phase separation versus Coexistence of Antiferromagnetism and d-Superfluidity
We investigate a system of fermions on a two-dimensional optical square
lattice in the strongly repulsive coupling regime. In this case, the
interactions can be controlled by laser intensity as well as by Feshbach
resonance. We compare the energetics of states with resonating valence bond
d-wave superfluidity, antiferromagnetic long range order and a homogeneous
state with coexistence of superfluidity and antiferromagnetism. We show that
the energy density of a hole has a minimum at doping that
signals phase separation between the antiferromagnetic and d-wave paired
superfluid phases. The energy of the phase-separated ground state is however
found to be very close to that of a homogeneous state with coexisting
antiferromagnetic and superfluid orders. We explore the dependence of the
energy on the interaction strength and on the three-site hopping terms and
compare with the nearest neighbor hopping {\it t-J} model
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