Flow and critical velocity of an imbalanced Fermi gas through an optical potential

Optical lattices offer the possibility to investigate the superfluid properties of both Bose condensates and Fermionic superfluid gases. When a population imbalance is present in a Fermi mixture, this leads to frustration of the pairing, and the superfluid properties will be affected. In this contribution, the influence of imbalance on the flow of a Fermi superfluid through an optical lattice is investigated. The flow through the lattice is analysed by taking into account coupling between neighbouring layers of the optical lattice up to second order in the interlayer tunneling amplitude for single atoms. The critical velocity of flow through the lattice is shown to decrease monotonically to zero as the imbalance is increased to 100%. Closed-form analytical expressions are given for the tunneling contribution to the action and for the critical velocity as a function of the binding energy of pairs in the (quasi) two-dimensional Fermi superfluid and as a function of the imbalance.Comment: 8 pages, 1 figure, contribution for the QFS 2007 conferenc

Rapidly Rotating Fermions in an Anisotropic Trap

We consider a cold gas of non-interacting fermions in a two dimensional harmonic trap with two different trapping frequencies $\omega_x \leq \omega_y$, and discuss the effect of rotation on the density profile. Depending on the rotation frequency $\Omega$ and the trap anisotropy $\omega_y/\omega_x$, the density profile assumes two qualitatively different shapes. For small anisotropy ($\omega_y/\omega_x \ll \sqrt{1+4 \Omega^2/\omega_x^2}$), the density consists of elliptical plateaus of constant density, corresponding to Landau levels and is well described by a two dimensional local density approximation. For large anisotropy ($\omega_y/\omega_x \gg \sqrt{1+4 \Omega^2/\omega_x^2}$), the density profile is Gaussian in the strong confining direction and semicircular with prominent Friedel oscillations in the weak direction. In this regime, a one dimensional local density approximation is well suited to describe the system. The crossover between the two regimes is smooth where the step structure between the Landau level edges turn into Friedel oscillations. Increasing the temperature causes the step structure or the Friedel oscillations to wash out leaving a Boltzmann gas density profile.Comment: 14 pages, 7 figure

Dynamics of quantum quenching for BCS-BEC systems in the shallow BEC regime

The problem of coupled Fermi-Bose mixtures of an ultracold gas near a narrow Feshbach resonance is approached through the time-dependent and complex Ginzburg-Landau (TDGL) theory. The dynamical system is constructed using Ginzburg-Landau-Abrikosov-Gor'kov (GLAG) path integral methods with the single mode approximation for the composite Bosons, and the equilibrium states are obtained in the BEC regime for adiabatic variations of the Feshbach detuning along the stationary solutions of the dynamical system. Investigations into the rich superfluid dynamics of this system in the shallow BEC regime yields the onset of multiple interference patterns in the dynamics as the system is quenched from the deep-BEC regime. This results in a partial collapse and revival of the coherent matter wave field of the BEC, whose temporal profile is reported.Comment: 24 pages, 7 figures. Submitted to European Journal of Physics Plu

Time-dependent Gross-Pitaevskii equation for composite bosons as the strong-coupling limit of the fermionic BCS-RPA approximation

The linear response to a space- and time-dependent external disturbance of a system of dilute condensed composite bosons at zero temperature, as obtained from the linearized version of the time-dependent Gross-Pitaevskii equation, is shown to result also from the strong-coupling limit of the time-dependent BCS (or broken-symmetry RPA) approximation for the constituent fermions subject to the same external disturbance. In this way, it is possible to connect excited-state properties of the bosonic and fermionic systems by placing the Gross-Pitaevskii equation in perspective with the corresponding fermionic approximationsComment: 4 pages, 1 figur

Backpropagation training in adaptive quantum networks

We introduce a robust, error-tolerant adaptive training algorithm for generalized learning paradigms in high-dimensional superposed quantum networks, or \emph{adaptive quantum networks}. The formalized procedure applies standard backpropagation training across a coherent ensemble of discrete topological configurations of individual neural networks, each of which is formally merged into appropriate linear superposition within a predefined, decoherence-free subspace. Quantum parallelism facilitates simultaneous training and revision of the system within this coherent state space, resulting in accelerated convergence to a stable network attractor under consequent iteration of the implemented backpropagation algorithm. Parallel evolution of linear superposed networks incorporating backpropagation training provides quantitative, numerical indications for optimization of both single-neuron activation functions and optimal reconfiguration of whole-network quantum structure.Comment: Talk presented at "Quantum Structures - 2008", Gdansk, Polan

Pairing in spin polarized two-species fermionic mixtures with mass asymmetry

We discuss on the pairing mechanism of fermions with mismatch in their fermi momenta due to a mass asymmetry. Using a variational ansatz for the ground state we also discuss the BCS -BEC crossover of this system. It is shown that the breached pairing solution with a single fermi surface is stable in the BEC regime. We also include the temperatures effect on the fermion pairing within an approximation that is valid for temperatures much below the critical temperature.Comment: 8 pages and 6 figures, few typos corrected, version to appear in EPJ

Unitary Fermi gas, epsilon expansion, and nonrelativistic conformal field theories

We review theoretical aspects of unitary Fermi gas (UFG), which has been realized in ultracold atom experiments. We first introduce the epsilon expansion technique based on a systematic expansion in terms of the dimensionality of space. We apply this technique to compute the thermodynamic quantities, the quasiparticle spectrum, and the critical temperature of UFG. We then discuss consequences of the scale and conformal invariance of UFG. We prove a correspondence between primary operators in nonrelativistic conformal field theories and energy eigenstates in a harmonic potential. We use this correspondence to compute energies of fermions at unitarity in a harmonic potential. The scale and conformal invariance together with the general coordinate invariance constrains the properties of UFG. We show the vanishing bulk viscosities of UFG and derive the low-energy effective Lagrangian for the superfluid UFG. Finally we propose other systems exhibiting the nonrelativistic scaling and conformal symmetries that can be in principle realized in ultracold atom experiments.Comment: 44 pages, 15 figures, contribution to Lecture Notes in Physics "BCS-BEC crossover and the Unitary Fermi Gas" edited by W. Zwerge

Thermodynamic Measurements in a Strongly Interacting Fermi Gas

We conduct a series of measurements on the thermodynamic properties of an optically-trapped strongly interacting Fermi gas, including the energy $E$, entropy $S$, and sound velocity $c$. Our model-independent measurements of $E$ and $S$ enable a precision study of the finite temperature thermodynamics. The $E(S)$ data are directly compared to several recent predictions. The temperature in both the superfluid and normal fluid regime is obtained from the fundamental thermodynamic relation $T=\partial E/\partial S$ by parameterizing the $E(S)$ data. Our $E(S)$ data are also used to experimentally calibrate the endpoint temperatures obtained for adiabatic sweeps of the magnetic field between the ideal and strongly interacting regimes. This enables the first experimental calibration of the temperature scale used in experiments on fermionic pair condensation. Our calibration shows that the ideal gas temperature measured for the onset of pair condensation corresponds closely to the critical temperature estimated in the strongly interacting regime from the fits to our $E(S)$ data. The results are in very good agreement with recent predictions. Finally, using universal thermodynamic relations, we estimate the chemical potential and heat capacity of the trapped gas from the $E(S)$ data.Comment: 29 pages, 12 figures. To appear in JLTP online, and in the January, 2009 volum

Homogeneous Fermion Superfluid with Unequal Spin Populations

For decades, the conventional view is that an s-wave BCS superfluid can not support uniform spin polarization due to a gap $\Delta$ in the quasiparticle excitation spectrum. We show that this is an artifact of the dismissal of quasiparticle interactions $V_{qp}^{}$ in the conventional approach at the outset. Such interactions can cause triplet fluctuations in the ground state and hence non-zero spin polarization at "magnetic field" $h<\Delta$. The resulting ground state is a pairing state of quasiparticles on the ``BCS vacuum". For sufficiently large $V_{qp}$, the spin polarization of at unitarity has the simple form $m\propto \mu^{1/2}$. Our study is motivated by the recent experiments at Rice which found evidence of a homogenous superfluid state with uniform spin polarization.Comment: 4 pages, 3 figure

An ansatz for the nonlinear Demkov-Kunike problem for cold molecule formation

We study nonlinear mean-field dynamics of ultracold molecule formation in the case when the external field configuration is defined by the level-crossing Demkov-Kunike model, characterized by a bell-shaped coupling and finite variation of the detuning. Analyzing the fast sweep rate regime of the strong interaction limit, which models a situation when the peak value of the coupling is large enough and the resonance crossing is sufficiently fast, we construct a highly accurate ansatz to describe the temporal dynamics of the molecule formation in the mentioned interaction regime. The absolute error of the constructed approximation is less than 3*10^-6 for the final transition probability while at certain time points it might increase up to 10^-3. Examining the role of the different terms in the constructed approximation, we prove that in the fast sweep rate regime of the strong interaction limit the temporal dynamics of the atom-molecule conversion effectively consists of the process of resonance crossing, which is governed by a nonlinear equation, followed by atom-molecular coherent oscillations which are basically described by a solution of the linear problem, associated with the considered nonlinear one.Comment: Accepted for publication in J. Contemp. Phys. (Armenian National Academy of Sciences) 8 pages, 4 figure