arXiv subjects

A. Minguzzi

Publications and source records attributed to A. Minguzzi.

At least 37 records · Page 2Linked to original sources

arXiv2008

Number squeezing, quantum fluctuations and oscillations in mesoscopic Bose Josephson junctions

Starting from a quantum two-mode Bose-Hubbard Hamiltonian we determine the ground state properties, momentum distribution and dynamical evolution for a Bose Josephson junction realized by an ultracold Bose gas in a double-well trap. Varying the well asymmetry we identify Mott-like regions of parameters where number fluctuations are suppressed and the interference fringes in the momentum distribution are strongly reduced. We also show how Schroedinger cat states, realized from an initially phase coherent state by a sudden rise of the barrier among the two wells, will give rise to a destructive interference in the time-dependent momentum distribution.

cond-mat.mes-hall↗

arXiv2007

Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides

A generalized Fermi-Bose mapping method is used to determine the exact ground states of several models of mixtures of strongly interacting ultracold gases in tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas (1D Bose gas with point hard cores) and fermionic Tonks-Girardeau (FTG) gas (1D spin-aligned Fermi gas with infinitely strong zero-range attractions). We detail the case of a Bose-Fermi mixture with TG boson-boson (BB) and boson-fermion (BF) interactions. Exact results are given for density profiles in a harmonic trap, single-particle density matrices, momentum distributions, and density-density correlations. Since the ground state is highly degenerate, we analyze the splitting of the ground manifold for large but finite BB and BF repulsions.

cond-mat.other↗

arXiv2006

Pairing of a harmonically trapped fermionic Tonks-Girardeau gas

The fermionic Tonks-Girardeau (FTG) gas is a one-dimensional spin-polarized Fermi gas with infinitely strong attractive zero-range odd-wave interactions, arising from a confinement-induced resonance reachable via a three-dimensional p-wave Feshbach resonance. We investigate the off-diagonal long-range order (ODLRO) of the FTG gas subjected to a longitudinal harmonic confinement by analyzing the two-particle reduced density matrix for which we derive a closed-form expression. Using a variational approach and numerical diagonalization we find that the largest eigenvalue of the two-body density matrix is of order N/2, where N is the total particle number, and hence a partial ODLRO is present for a FTG gas in the trap.

cond-mat.supr-con↗

arXiv2006

Bosonization, Pairing, and Superconductivity of the Fermionic Tonks-Girardeau Gas

We determine some exact static and time-dependent properties of the fermionic Tonks-Girardeau (FTG) gas, a spin-aligned one-dimensional Fermi gas with infinitely strongly attractive zero-range odd-wave interactions. We show that the two-particle reduced density matrix exhibits maximal off-diagonal long-range order, and on a ring an FTG gas with an even number of atoms has a highly degenerate ground state with quantization of Coriolis rotational flux and high sensitivity to rotation and to external fields and accelerations. For a gas initially under harmonic confinement we show that during an expansion the momentum distribution undergoes a "dynamical bosonization", approaching that of an ideal Bose gas without violating the Pauli exclusion principle.

cond-mat.supr-con↗

arXiv2005

Exact coherent states of a harmonically confined Tonks-Girardeau gas

Using a scaling transformation we exactly determine the dynamics of an harmonically confined Tonks-Girardeau gas under arbitrary time variations of the trap frequency. We show how during a one-dimensional expansion a ``dynamical fermionization'' occurs as the momentum distribution rapidly approaches an ideal Fermi gas distribution, and that under a sudden change of the trap frequency the gas undergoes undamped breathing oscillations displaying alternating bosonic and fermionic character in momentum space. The absence of damping in the oscillations is a peculiarity of the truly Tonks regime.

cond-mat.stat-mech↗

arXiv2004

Collective modes and ballistic expansion of a Fermi gas in the BCS-BEC crossover

We evaluate the frequencies of collective modes and the anisotropic expansion rate of a harmonically trapped Fermi superfluid at varying coupling strengths across a Feshbach resonance driving a BCS-BEC crossover. The equations of motion for the superfluid are obtained from a microscopic mean-field expression for the compressibility and are solved within a scaling ansatz. Our results confirm non-monotonic behavior in the crossover region and are in quantitative agreement with current measurements of the transverse breathing mode by Kinast {\it et al.} [Phys. Rev. Lett. {\bf 92}, 150402 (2004)] and of the axial breathing mode by Bartenstein {\it et al.} [Phys. Rev. Lett. {\bf 92}, 203201 (2004)].

cond-mat.stat-mech↗

arXiv2004

Collisional oscillations of trapped boson-fermion mixtures approaching collapse

We study the collective modes of a confined gaseous cloud of bosons and fermions with mutual attractive interactions at zero temperature. The cloud consists of a Bose-Einstein condensate and a spin-polarized Fermi gas inside a spherical harmonic trap and the coupling between the two species is varied by increasing either the magnitude of the interspecies s-wave scattering length or the number of bosons. The mode frequencies are obtained in the collisional regime by solving the equations of generalized hydrodynamics and are compared with the spectra calculated in the collisionless regime within a random-phase approximation. We find that, as the mixture is driven towards the collapse instability, the frequencies of the modes of fermionic origin show a blue shift which can become very significant for large numbers of bosons. Instead the modes of bosonic origin show a softening, which becomes most pronounced in the very proximity of collapse. Explicit illustrations of these trends are given for the monopolar spectra, but similar trends are found for the dipolar and quadrupolar spectra except for the surface (n=0) modes which are essentially unaffected by the interactions.

cond-mat.soft↗

arXiv2003

Collective oscillations of a confined Bose gas at finite temperature in the random-phase approximation

We present a theory for the linear dynamics of a weakly interacting Bose gas confined inside a harmonic trap at finite temperature. The theory treats the motions of the condensate and of the non-condensate on an equal footing within a generalized random-phase approximation, which ({\it i}) extends the second-order Beliaev-Popov approach by allowing for the dynamical coupling between fluctuations in the thermal cloud, and ({\it ii}) reduces to an earlier random-phase scheme when the anomalous density fluctuations are omitted. Numerical calculations of the low-lying spectra in the case of isotropic confinement show that the present theory obeys with high accuracy the generalized Kohn theorem for the dipolar excitations and demonstrate that combined normal and anomalous density fluctuations play an important role in the monopolar excitations of the condensate. Mean-field theory is instead found to yield accurate results for the quadrupolar modes of the condensate. Although the restriction to spherical confinement prevents quantitative comparisons with measured spectra, it appears that the non-mean field effects that we examine may be relevant to explain the features exhibited by the breathing mode as a function of temperature in the experiments carried out at JILA on a gas of $^{87}$Rb atoms.

cond-mat.stat-mech↗

arXiv2003

Collective excitations in trapped boson-fermion mixtures: from demixing to collapse

We calculate the spectrum of low-lying collective excitations in a gaseous cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas over a range of the boson-fermion coupling strength extending from strongly repulsive to strongly attractive. Increasing boson-fermion repulsions drive the system towards spatial separation of its components (``demixing''), whereas boson-fermion attractions drive it towards implosion (``collapse''). The dynamics of the system is treated in the experimentally relevant collisionless regime by means of a Random-Phase approximation and the behavior of a mesoscopic cloud under isotropic harmonic confinement is contrasted with that of a macroscopic mixture at given average particle densities. In the latter case the locations of both the demixing and the collapse phase transitions are sharply defined by the same stability condition, which is determined by the softening of an eigenmode of either fermionic or bosonic origin. In contrast, the transitions to either demixing or collapse in a mesoscopic cloud at fixed confinement and particle numbers are spread out over a range of boson-fermion coupling strength, and some initial decrease of the frequencies of a set of collective modes is followed by hardening as evidenced by blue shifts of most eigenmodes. The spectral hardening can serve as a signal of the impending transition and is most evident when the number of bosons in the cloud is relatively large. We propose physical interpretations for these dynamical behaviors with the help of suitably defined partial compressibilities for the gaseous cloud under confinement.

cond-mat↗

arXiv2003

Free expansion of two-dimensional condensates with a vortex

We study the free expansion of a pancake-shaped Bose-condensed gas, which is initially trapped under harmonic confinement and containing a vortex at its centre. In the case of a radial expansion holding fixed the axial confinement we consider various models for the interactions, depending on the thickness of the condensate relative to the value of the scattering length. We are thus able to evaluate different scattering regimes ranging from quasi-three-dimensional (Q3D) to strictly two-dimensional (2D). We find that as the system goes from Q3D to 2D the expansion rate of the condensate increases whereas that of the vortex core decreases. In the Q3D scattering regime we also examine a fully free expansion in 3D and find oscillatory behaviour for the vortex core radius: an initial fast expansion of the vortex core is followed by a slowing down. Such a nonuniform expansion rate of the vortex core may be taken into account in designing new experiments.

cond-mat↗

arXiv2003

Collective excitations of a trapped boson-fermion mixture across demixing

We calculate the spectrum of low-lying collective excitations in a mesoscopic cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas as a function of the boson-fermion repulsions. The cloud is under isotropic harmonic confinement and its dynamics is treated in the collisional regime by using the equations of generalized hydrodynamics with inclusion of surface effects. For large numbers of bosons we find that, as the cloud moves towards spatial separation (demixing) with increasing boson-fermion coupling, the frequencies of a set of collective modes show a softening followed by a sharp upturn. This behavior permits a clear identification of the quantum phase transition. We propose a physical interpretation for the dynamical transition point in a confined mixture, leading to a simple analytical expression for its location.

cond-mat↗

arXiv2002

Temperature dependence of density profiles for a cloud of non-interacting fermions moving inside a harmonic trap in one dimension

We extend to finite temperature a Green's function method that was previously proposed to evaluate ground-state properties of mesoscopic clouds of non-interacting fermions moving under harmonic confinement in one dimension. By calculations of the particle and kinetic energy density profiles we illustrate the role of thermal excitations in smoothing out the quantum shell structure of the cloud and in spreading the particle spill-out from quantum tunnel at the edges. We also discuss the approach of the exact density profiles to the predictions of a semiclassical model often used in the theory of confined atomic gases at finite temperature.

cond-mat.stat-mech↗

arXiv2002

Bose-Einstein condensates at equilibrium inside a pancake-shaped trap: dimensional cross-over in the scattering properties

Two-dimensionality of the scattering events in a Bose-Einstein condensate introduces a logarithmic dependence on density in the coupling constant entering a mean-field theory of the equilibrium density profile, which becomes dominant as the s-wave scattering length gets larger than the condensate thickness. We analyze quantitatively the role of the form of the coupling constant in determining the transverse profile of a condensate confined in a harmonic pancake-shaped trap at zero temperature. We trace the regions of experimentally accessible system parameters for which the cross-over between different dimensionality behaviors may become observable through in situ imaging of the condensed cloud with varying trap anisotropy and scattering length.

cond-mat.stat-mech↗

arXiv2002

Single-particle density matrix and superfluidity in the two-dimensional Bose Coulomb fluid

A study by W. R. Magro and D. M. Ceperley [Phys. Rev. Lett. {\bf 73}, 826 (1994)] has shown that the ground state of the two-dimensional fluid of charged bosons with logarithmic interactions is not Bose-condensed, but exhibits algebraic off-diagonal order in the single-particle density matrix $ρ(r)$. We use a hydrodynamic Hamiltonian expressed in terms of density and phase operators, in combination with an $f$-sum rule on the superfluid fraction, to reproduce these results and to extend the evaluation of the density matrix to finite temperature $T$. This approach allows us to treat the liquid as a superfluid in the absence of a condensate. We find that (i) the off-diagonal order arises from the correlations between phase fluctuations; and (ii) the exponent in the power-law decay of $ρ(r)$ is determined by the superfluid density $n_s(T)$. We also find that the plasmon gap in the single-particle energy spectrum at long wavelengths decreases with increasing $T$ and closes at the critical temperature for the onset of superfluidity.

cond-mat.stat-mech↗

arXiv2002

Demixing in mesoscopic boson-fermion clouds inside cylindrical harmonic traps: quantum phase diagram and role of temperature

We use a semiclassical three-fluid thermodynamic model to evaluate the phenomena of spatial demixing in mesoscopic clouds of fermionic and bosonic atoms at high dilution under harmonic confinement, assuming repulsive boson-boson and boson-fermion interactions and including account of a bosonic thermal cloud at finite temperature T. The finite system size allows three different regimes for the equilibrium density profiles at T=0: a fully mixed state, a partially mixed state in which the overlap between the boson and fermion clouds is decreasing, and a fully demixed state where the two clouds have zero overlap. We propose simple analytical rules for the two cross-overs between the three regimes as functions of the physical system parameters and support these rules by extensive numerical calculations. A universal ``phase diagram'' expressed in terms of simple scaling parameters is shown to be valid for the transition to the regime of full demixing, inside which we identify several exotic configurations for the two phase-separated clouds in addition to simple ones consisting of a core of bosons enveloped by fermions and "vice versa". With increasing temperature the main role of the growing thermal cloud of bosons is to transform some exotic configurations into more symmetric ones, until demixing is ultimately lost. For very high values of boson-fermion repulsive coupling we also report demixing between the fermions and the thermally excited bosons.

cond-mat.stat-mech↗

arXiv2002

High-momentum tail in the Tonks gas under harmonic confinement

We use boson-fermion mapping to show that the single-particle momentum distribution in a one-dimensional gas of hard point-like bosons (Tonks gas) inside a harmonic trap decays as $p^{-4}$ at large momentum $p$. The relevant integrals expressing the one-body density matrix are evaluated for small numbers of particles in a simple Monte Carlo approach to test the extent of the asymptotic law and to illustrate the slow decay of correlations between the matter-wave field at different points.

cond-mat.stat-mech↗

arXiv2002

Hartree-Fock-Bogoliubov theory of a charged Bose gas at finite temperature

We critically examine the Hartree-Fock-Bogoliubov (HFB) solution of the equations of motion for condensate fluctuations in a weakly coupled plasma of charged bosons at finite temperature. Analytic expressions are derived for the first two infrared-divergent terms in both the momentum distribution of the noncondensate and the anomalous Bose correlation function at low momenta. Incorporation into the theory of the appropriate form of the Hugenholtz-Pines relation for the chemical potential is needed to cancel an unphysical divergence. Exact cancellation of infrared-divergent terms is demonstrated in the HFB shift of the single-particle excitation energy away from the Bogoliubov value at long wavelengths, with the residual terms raising it towards the plasma frequency at low temperature. Numerical illustrations are presented for a number of properties of the boson plasma as functions of temperature and density in the weak-coupling regime: these are the chemical potential, the condensate fraction, the normal and anomalous momentum distribution functions and the corresponding one-body density matrices, and the dispersion relation of single-particle excitations.

cond-mat.stat-mech↗

arXiv2001

Phase separation in a boson-fermion mixture of Lithium atoms

We use a semiclassical three-fluid model to analyze the conditions for spatial phase separation in a mixture of fermionic Li-6 and a (stable) Bose-Einstein condensate of Li-7 atoms under cylindrical harmonic confinement, both at zero and finite temperature. We show that with the parameters of the Paris experiment [F. Schrek et al., Phys. Rev. Lett. 87 080403 (2001)] an increase of the boson-fermion scattering length by a factor five would be sufficient to enter the phase-separated regime. We give examples of configurations for the density profiles in phase separation and estimate that the transition should persist at temperatures typical of current experiments. For higher values of the boson-fermion coupling we also find a new phase separation between the fermions and the bosonic thermal cloud at finite temperature.

cond-mat.stat-mech↗