arXiv subjects

L. D. Carr

Publications and source records attributed to L. D. Carr.

53 records · Page 3Linked to original sources

arXiv2005

Quantum phase transitions in the Fermi-Bose Hubbard model

We propose a multi-band Fermi-Bose Hubbard model with on-site fermion-boson conversion and general filling factor in three dimensions. Such a Hamiltonian models an atomic Fermi gas trapped in a lattice potential and subject to a Feshbach resonance. We solve this model in the two state approximation for paired fermions at zero temperature. The problem then maps onto a coupled Heisenberg spin model. In the limit of large positive and negative detuning, the quantum phase transitions in the Bose Hubbard and Paired-Fermi Hubbard models are correctly reproduced. Near resonance, the Mott states are given by a superposition of the paired-fermion and boson fields and the Mott-superfluid borders go through an avoided crossing in the phase diagram.

cond-mat.other↗

arXiv2004

Nonlinear Band Structure in Bose Einstein Condensates: The Nonlinear Schrödinger Equation with a Kronig-Penney Potential

All Bloch states of the mean field of a Bose-Einstein condensate in the presence of a one dimensional lattice of impurities are presented in closed analytic form. The band structure is investigated by analyzing the stationary states of the nonlinear Schrödinger, or Gross-Pitaevskii, equation for both repulsive and attractive condensates. The appearance of swallowtails in the bands is examined and interpreted in terms of the condensates superfluid properties. The nonlinear stability properties of the Bloch states are described and the stable regions of the bands and swallowtails are mapped out. We find that the Kronig-Penney potential has the same properties as a sinusoidal potential; Bose-Einstein condensates are trapped in sinusoidal optical lattices. The Kronig-Penney potential has the advantage of being analytically tractable, unlike the sinusoidal potential, and, therefore, serves as a good model for experimental phenomena.

cond-mat.other↗

arXiv2004

Effect of a potential step or impurity on the Bose-Einstein condensate mean field

The full set of stationary states of the mean field of a Bose-Einstein condensate in the presence of a potential step or point-like impurity are presented in closed analytic form. The nonlinear Schrödinger equation in one dimension is taken as a model. The nonlinear analogs of the continuum of stationary scattering states, as well as evanescent waves, are discussed. The solutions include asymmetric soliton trains and other wavefunctions of novel form, such as a pair of dark solitons bound by an impurity.

cond-mat.other↗

arXiv2004

Limits of sympathetic cooling of fermions: The role of the heat capacity of the coolant

The sympathetic cooling of an initially degenerate Fermi gas by either an ideal Bose gas below $T_c$ or an ideal Boltzmann gas is investigated. It is shown that the efficiency of cooling by a Bose gas below $T_c$ is by no means reduced when its heat capacity becomes much less than that of the Fermi gas, where efficiency is measured by the decrease in the temperature of the Fermi gas per number of particles evaporated from the coolant. This contradicts the intuitive idea that an efficient coolant must have a large heat capacity. In contrast, for a Boltzmann gas a minimal value of the ratio of the heat capacities is indeed necessary to achieve T=0 and all of the particles must be evaporated.

cond-mat.stat-mech↗

arXiv2004

Endpoint thermodynamics of an atomic Fermi gas subject to a Feshbach resonance

The entropy and kinetic, potential, and interaction energies of an atomic Fermi gas in a trap are studied under the assumption of thermal equilibrium for finite temperature. A Feshbach resonance can cause the fermions to pair into diatomic molecules. The entropy and energies of mixtures of such molecules with unpaired atoms are calculated, in relation to recent experiments on molecular Bose-Einstein condensates produced in this manner. It is shown that, starting with a Fermi gas of temperature $T= 0.1 T_F^0$, where $T_F^0$ is the non-interacting Fermi temperature, an extremely cold degenerate Fermi gas of temperature $T \lesssim 0.01 T_F^0$ may be produced without further evaporative cooling. This requires adiabatic passage of the resonance, subsequent sudden removal of unpaired atoms, and adiabatic return. We also calculate the ratio of the interaction energy to the kinetic energy, a straightforward experimental signal which may be used to determine the temperature of the atoms and indicate condensation of the molecules.

cond-mat.stat-mech↗

arXiv2004

A pulsed atomic soliton laser

It is shown that simultaneously changing the scattering length of an elongated, harmonically trapped Bose-Einstein condensate from positive to negative and inverting the axial portion of the trap, so that it becomes expulsive, results in a train of self-coherent solitonic pulses. Each pulse is itself a non-dispersive attractive Bose-Einstein condensate that rapidly self-cools. The axial trap functions as a waveguide. The solitons can be made robustly stable with the right choice of trap geometry, number of atoms, and interaction strength. Theoretical and numerical evidence suggests that such a pulsed atomic soliton laser can be made in present experiments.

cond-mat.soft↗

arXiv2004

Transition from Resonances to Bound States in Nonlinear Systems: Application to Bose-Einstein condensates

It is shown using the Gross-Pitaevskii equation that resonance states of Bose-Einstein condensates with attractive interactions can be stabilized into true bound states. A semiclassical variational approximation and an independent quantum variational numerical method are used to calculate the energies (chemical potentials) and linewidths of resonances of the time-independent Gross-Pitaevskii equation; both methods produce similar results. Borders between the regimes of resonances, bound states, and, in two and three dimensions, collapse, are identified.

cond-mat.soft↗

arXiv2004

Achieving a BCS transition in an atomic Fermi gas

We consider a gas of cold fermionic atoms having two spin components with interactions characterized by their s-wave scattering length $a$. At positive scattering length the atoms form weakly bound bosonic molecules which can be evaporatively cooled to undergo Bose-Einstein condensation, whereas at negative scattering length BCS pairing can take place. It is shown that, by adiabatically tuning the scattering length $a$ from positive to negative values, one may transform the molecular Bose-Einstein condensate into a highly degenerate atomic Fermi gas, with the ratio of temperature to Fermi temperature $T/T_F \sim 10^{-2}$. The corresponding critical final value of $k_{F}|a|$ which leads to the BCS transition is found to be about one half, where $k_F$ is the Fermi momentum.

cond-mat.supr-con↗

arXiv2004

Limits of sympathetic cooling of fermions by zero temperature bosons due to particle losses

It has been suggested by Timmermans [Phys. Rev. Lett. {\bf 87}, 240403 (2001)] that loss of fermions in a degenerate system causes strong heating. We address the fundamental limit imposed by this loss on the temperature that may be obtained by sympathetic cooling of fermions by bosons. Both a quantum Boltzmann equation and a quantum Boltzmann \emph{master} equation are used to study the evolution of the occupation number distribution. It is shown that, in the thermodynamic limit, the Fermi gas cools to a minimal temperature $k_{\rm B}T/μ\propto(γ_{\rm loss}/γ_{\rm coll})^{0.44}$, where $γ_{\rm loss}$ is a constant loss rate, $γ_{\rm coll}$ is the bare fermion--boson collision rate not including the reduction due to Fermi statistics, and $μ\sim k_{\rm B}T_{\rm F}$ is the chemical potential. It is demonstrated that, beyond the thermodynamic limit, the discrete nature of the momentum spectrum of the system can block cooling. The unusual non-thermal nature of the number distribution is illustrated from several points of view: the Fermi surface is distorted, and in the region of zero momentum the number distribution can descend to values significantly less than unity. Our model explicitly depends on a constant evaporation rate, the value of which can strongly affect the minimum temperature.

cond-mat.soft↗

arXiv2003

Spontaneous soliton formation and modulational instability in Bose-Einstein condensates

The dynamics of an elongated attractive Bose-Einstein condensate in an axisymmetric harmonic trap is studied. It is shown that density fringes caused by self-interference of the condensate order parameter seed modulational instability. The latter has novel features in contradistinction to the usual homogeneous case known from nonlinear fiber optics. Several open questions in the interpretation of the recent creation of the first matter-wave bright soliton train [Strecker {\it et al.} Nature {\bf 417} 150 (2002)] are addressed. It is shown that primary transverse collapse, followed by secondary collapse induced by soliton--soliton interactions, produce bursts of hot atoms at different time scales.

cond-mat.soft↗

arXiv2002

Dynamics of a matter-wave bright soliton in an expulsive potential

The stability regimes and nonlinear dynamics of bright solitons created in a harmonic potential which is transversely attractive and longitudinally expulsive are presented. This choice of potential is motivated by the recent creation of a matter-wave bright soliton from an attractive Bose-Einstein condensate (L. Khaykovich {\it et al.}, Science 296, 1290 (2002)). The critical branches for collapse due to the three-dimensional character of the gas and explosion caused by the expulsive potential are derived based on variational studies. Particle loss from the soliton due to sudden changes in the trapping potential and scattering length are quantified. It is shown that higher order solitons can also be created in present experiments by an abrupt change of a factor of four in the scattering length. It is demonstrated that quantum evaporation occurs by nonlinear tunneling of particles out of the soliton, leading eventually to its explosion.

cond-mat↗

arXiv2002

Formation of a Matter-Wave Bright Soliton

We report the production of matter-wave solitons in an ultracold lithium 7 gas. The effective interaction between atoms in a Bose-Einstein condensate is tuned with a Feshbach resonance from repulsive to attractive before release in a one-dimensional optical waveguide. Propagation of the soliton without dispersion over a macroscopic distance of 1.1 mm is observed. A simple theoretical model explains the stability region of the soliton. These matter-wave solitons open fascinating possibilities for future applications in coherent atom optics, atom interferometry and atom transport.

cond-mat↗

arXiv2002

Generation and interaction of solitons in Bose-Einstein condensates

Generation, interaction and detection of dark solitons in Bose-Einstein condensates is considered. In particular, we focus on the dynamics resulting from phase imprinting and density engineering. The generation of soliton pairs as well as their interaction is also considered. Finally, motivated by the recent experimental results of Cornish et al. (Phys. Rev Lett. 85, 1795, 2000), we analyze the stability of dark solitons under changes of the scattering length and thereby demonstrate a new way to detect them. Our theoretical and numerical results compare well with the existing experimental ones and provide guidance for future experiments.

cond-mat.soft↗

arXiv2001

Tunable tunneling: An application of stationary states of Bose-Einstein condensates in traps of finite depth

The fundamental question of how Bose-Einstein condensates tunnel into a barrier is addressed. The cubic nonlinear Schrodinger equation with a finite square well potential, which models a Bose-Einstein condensate in a quasi-one-dimensional trap of finite depth, is solved for the complete set of localized and partially localized stationary states, which the former evolve into when the nonlinearity is increased. An immediate application of these different solution types is tunable tunneling. Magnetically tunable Feshbach resonances can change the scattering length of certain Bose-condensed atoms, such as $^{85}$Rb, by several orders of magnitude, including the sign, and thereby also change the mean field nonlinearity term of the equation and the tunneling of the wavefunction. We find both linear-type localized solutions and uniquely nonlinear partially localized solutions where the tails of the wavefunction become nonzero at infinity when the nonlinearity increases. The tunneling of the wavefunction into the non-classical regime and thus its localization therefore becomes an external experimentally controllable parameter.

cond-mat↗

arXiv2000

Stability of Attractive Bose-Einstein Condensates in a Periodic Potential

Using a standing light wave trap, a stable quasi-one-dimensional attractive dilute-gas Bose-Einstein condensate can be realized. In a mean-field approximation, this phenomenon is modeled by the cubic nonlinear Schrödinger equation with attractive nonlinearity and an elliptic function potential of which a standing light wave is a special case. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schrödinger equation nor in the integrable nonlinear Schrödinger equation. Their stability is examined using analytic and numerical methods. Trivial-phase solutions are experimentally stable provided they have nodes and their density is localized in the troughs of the potential. Stable time-periodic solutions are also examined.

cond-mat↗

arXiv2000

Dark soliton creation in Bose-Einstein condensates

It is demonstrated that stable, standing dark solitons can be created in current dilute-gas Bose-Einstein condensate experiments by the proper combination of phase and density engineering. Other combinations result in a widely controllable range of grey solitons. The phonon contribution is small and is calculated precisely. The ensuing dynamics should be observable in situ, i.e. without ballistic expansion of the condensate.

cond-mat↗

arXiv2000

Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential

The cubic nonlinear Schrödinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schrödinger equation nor in the integrable nonlinear Schrödinger equation. Their stability is examined using analytic and numerical methods. All trivial-phase stable solutions are deformations of the ground state of the linear Schrödinger equation. Our results show that a large number of condensed atoms is sufficient to form a stable, periodic condensate. Physically, this implies stability of states near the Thomas-Fermi limit.

cond-mat↗