417 research outputs found
Zero-point energy of ultracold atoms
We analyze the divergent zero-point energy of a dilute and ultracold gas of
atoms in D spatial dimensions. For bosonic atoms we explicitly show how to
regularize this divergent contribution, which appears in the Gaussian
fluctuations of the functional integration, by using three different
regularization approaches: dimensional regularization, momentum-cutoff
regularization and convergence-factor regularization. In the case of the ideal
Bose gas the divergent zero-point fluctuations are completely removed, while in
the case of the interacting Bose gas these zero-point fluctuations give rise to
a finite correction to the equation of state. The final convergent equation of
state is independent of the regularization procedure but depends on the
dimensionality of the system and the two-dimensional case is highly nontrivial.
We also discuss very recent theoretical results on the divergent zero-point
energy of the D-dimensional superfluid Fermi gas in the BCS-BEC crossover. In
this case the zero-point energy is due to both fermionic single-particle
excitations and bosonic collective excitations, and its regularization gives
remarkable analytical results in the BEC regime of composite bosons. We compare
the beyond-mean-field equations of state of both bosons and fermions with
relevant experimental data on dilute and ultracold atoms quantitatively
confirming the contribution of zero-point-energy quantum fluctuations to the
thermodynamics of ultracold atoms at very low temperatures.Comment: 56 pages, 5 figures, 1 table, accepted for publication in Physics
Report
Collisionless Dynamics in Two-Dimensional Bosonic Gases
We study the dynamics of dilute and ultracold bosonic gases in a quasi
two-dimensional (2D) configuration and in the collisionless regime. We adopt
the 2D Landau-Vlasov equation to describe a three-dimensional gas under very
strong harmonic confinement along one direction. We use this effective equation
to investigate the speed of sound in quasi 2D bosonic gases, i.e. the sound
propagation around a Bose-Einstein distribution in collisionless 2D gases. We
derive coupled algebraic equations for the real and imaginary parts of the
sound velocity, which are then solved taking also into account the equation of
state of the 2D bosonic system. Above the Berezinskii-Kosterlitz-Thouless
critical temperature we find that there is rapid growth of the imaginary
component of the sound velocity which implies a strong Landau damping. Quite
remarkably, our theoretical results are in good agreement with very recent
experimental data obtained with a uniform 2D Bose gas of Rb atoms.Comment: 5 pages, 2 figures, improved introduction and conclusions, accepted
for publication in Physical Review
Superfluidity, Sound Velocity and Quasi Condensation in the 2D BCS-BEC Crossover
We study finite-temperature properties of a two-dimensional superfluid made
of ultracold alkali-metal atoms in the BCS-BEC crossover. We investigate the
region below the critical temperature of the
Berezinskii-Kosterlitz-Thouless phase transition, where there is
quasi-condensation, by analyzing the effects of phase and amplitude
fluctuations of the order parameter. In particular, we calculate the superfluid
fraction, the sound velocity and the quasi-condensate fraction as a function of
the temperature and of the binding energy of fermionic pairs.Comment: 7 pages, 4 figures, improved version to be published in Phys. Rev.
Quantum-tunneling dynamics of a spin-polarized Fermi gas in a double-well potential
We study the exact dynamics of a one-dimensional spin-polarized gas of
fermions in a double-well potential at zero and finite temperature. Despite the
system is made of non-interacting fermions, its dynamics can be quite complex,
showing strongly aperiodic spatio-temporal patterns during the tunneling. The
extension of these results to the case of mixtures of spin-polarized fermions
in interaction with self-trapped Bose-Einstein condensates (BECs) at zero
temperature is considered as well. In this case we show that the fermionic
dynamics remains qualitatively similar to the one observed in absence of BEC
but with the Rabi frequencies of fermionic excited states explicitly depending
on the number of bosons and on the boson-fermion interaction strength. From
this, the possibility to control quantum fermionic dynamics by means of
Feshbach resonances is suggested.Comment: Accepted for publication in Phys. Rev.
Beliaev damping of the Goldstone mode in atomic Fermi superfluids
Beliaev damping in a superfluid is the decay of a collective excitation into
two lower frequency collective excitations; it represents the only decay mode
for a bosonic collective excitation in a superfluid at T = 0. The standard
treatment for this decay assumes a linear spectrum, which in turn implies that
the final state momenta must be collinear to the initial state. We extend this
treatment, showing that the inclusion of a gradient term in the Hamiltonian
yields a realistic spectrum for the bosonic excitations; we then derive a
formula for the decay rate of such excitations, and show that even moderate
nonlinearities in the spectrum can yield substantial deviations from the
standard result. We apply our result to an attractive Fermi gas in the BCS-BEC
crossover: here the low-energy bosonic collective excitations are density
oscillations driven by the phase of the pairing order field. These collective
excitations, which are gapless modes as a consequence of the Goldstone
mechanism, have a spectrum which is well established both theoretically and
experimentally, and whose linewidth, we show, is determined at low temperatures
by the Beliaev decay mechanism.Comment: 8 pages, 3 figure
Composite bosons in the 2D BCS-BEC crossover from Gaussian fluctuations
We study Gaussian fluctuations of the zero-temperature attractive Fermi gas
in the 2D BCS-BEC crossover showing that they are crucial to get a reliable
equation of state in the BEC regime of composite bosons, bound states of
fermionic pairs. A low-momentum expansion up to the fourth order of the
quadratic action of the fluctuating pairing field gives an ultraviolent
divergent contribution of the Gaussian fluctuations to the grand potential.
Performing dimensional regularization we evaluate the effective coupling
constant in the beyond-mean-field grand potential. Remarkably, in the BEC
regime our grand potential gives exactly the Popov's equation of state of 2D
interacting bosons, and allows us to identify the scattering length of
the interaction between composite bosons as , with is the scattering length of fermions. Remarkably, the value
from our analytical relationship between the two scattering lengths is in full
agreement with that obtained by recent Monte Carlo calculations.Comment: 5 pages, no figures, submitted for publication; typos corrected; to
be published in Phys. Rev. A as a Rapid Communicatio
Competition between symmetry breaking and onset of collapse in weakly coupled atomic condensates
We analyze the symmetry breaking of matter-wave solitons in a pair of
cigar-shaped traps coupled by tunneling of atoms. The model is based on a
system of linearly coupled nonpolynomial Schr\"odinger equations (NPSEs).
Unlike the well-known spontaneous-symmetry-breaking (SSB) bifurcation in
coupled cubic equations, in the present model the SSB competes with the onset
of collapse in this system. Stability regions of symmetric and asymmetric
solitons, as well as the collapse region, are identified in the parameter space
of the system.Comment: Physical Review A, in pres
Variational Monte Carlo for spin-orbit interacting systems
Recently, a diffusion Monte Carlo algorithm was applied to the study of spin
dependent interactions in condensed matter. Following some of the ideas
presented therein, and applied to a Hamiltonian containing a Rashba-like
interaction, a general variational Monte Carlo approach is here introduced that
treats in an efficient and very accurate way the spin degrees of freedom in
atoms when spin orbit effects are included in the Hamiltonian describing the
electronic structure. We illustrate the algorithm on the evaluation of the
spin-orbit splittings of isolated carbon and lead atoms. In the case of the
carbon atom, we investigate the differences between the inclusion of spin-orbit
in its realistic and effective spherically symmetrized forms. The method
exhibits a very good accuracy in describing the small energy splittings,
opening the way for a systematic quantum Monte Carlo studies of spin-orbit
effects in atomic systems.Comment: 7 pages, 0 figure
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