Lowest Landau-level description of a Bose-Einstein condensate in a rapidly rotating anisotropic trap

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional trap can be described with the lowest Landau-level set of states. In this case, the condensate wave function psi(x,y) is a Gaussian function of r^2 = x^2 + y^2, multiplied by an analytic function P(z) of the single complex variable z= x+ i y; the zeros of P(z) denote the positions of the vortices. Here, a similar description is used for a rapidly rotating anisotropic two-dimensional trap with arbitrary anisotropy (omega_x/omega_y le 1). The corresponding condensate wave function psi(x,y) has the form of a complex anisotropic Gaussian with a phase proportional to xy, multiplied by an analytic function P(zeta), where zeta is proportional to x + i beta_- y and 0 le beta_- le 1 is a real parameter that depends on the trap anisotropy and the rotation frequency. The zeros of P(zeta) again fix the locations of the vortices. Within the set of lowest Landau-level states at zero temperature, an anisotropic parabolic density profile provides an absolute minimum for the energy, with the vortex density decreasing slowly and anisotropically away from the trap center.Comment: 13 pages, 1 figur

Density and spin response functions in ultracold fermionic atom gases

We propose a new method of detecting the onset of superfluidity in a two-component ultracold fermionic gas of atoms governed by an attractive short-range interaction. By studying the two-body correlation functions we find that a measurement of the momentum distribution of the density and spin response functions allows one to access separately the normal and anomalous densities. The change in sign at low momentum transfer of the density response function signals the transition between a BEC and a BCS regimes, characterized by small and large pairs, respectively. This change in sign of the density response function represents an unambiguous signature of the BEC to BCS crossover. Also, we predict spin rotational symmetry-breaking in this system

Inequivalent representations of commutator or anticommutator rings of field operators and their applications

Hamiltonian of a system in quantum field theory can give rise to infinitely many partition functions which correspond to infinitely many inequivalent representations of the canonical commutator or anticommutator rings of field operators. This implies that the system can theoretically exist in infinitely many Gibbs states. The system resides in the Gibbs state which corresponds to its minimal Helmholtz free energy at a given range of the thermodynamic variables. Individual inequivalent representations are associated with different thermodynamic phases of the system. The BCS Hamiltonian of superconductivity is chosen to be an explicit example for the demonstration of the important role of inequivalent representations in practical applications. Its analysis from the inequivalent representations' point of view has led to a recognition of a novel type of the superconducting phase transition.Comment: 25 pages, 6 figure

Bogoliubov Quasiparticle Excitations in the Two-Dimensional t-J Model

Using a proposed numerical technique for calculating anomalous Green's functions characteristic of superconductivity, we show that the low-lying excitations in a wide parameter and doping region of the two-dimensional $t$$-$$J$ model are well described by the picture of dressed Bogoliubov quasiparticles in the BCS pairing theory. The pairing occurs predominantly in $d_{x^2-y^2}$-wave channel and the energy gap has a size $\Delta_d$$\simeq$$0.15J$$-0.27J$ between quarter and half fillings. Opening of the superconducting gap in the photoemission and inverse-photoemission spectrum is demonstrated.Comment: 6 pages, RevTe

The Coherence Field in the Field Perturbation Theory of Superconductivity

We re-examine the Nambu-Gorkov perturbation theory of superconductivity on the basis of the Bogoliubov-Valatin quasi-particles. We show that two different fields (and two additional analogous fields) may be constructed, and that the Nambu field is only one of them. For the other field- the coherence field- the interaction is given by means of two interaction vertices that are based on the Pauli matrices tau1 and tau3. Consequently, the Hartree integral for the off-diagonal pairing self-energy may be finite, and in some cases large. We interpret the results in terms of conventional superconductivity, and also discuss briefly possible implications to HTSC

Quantum Field Theory of Meson Mixing

We have developed a quantum field theoretic framework for scalar and pseudoscalar meson mixing and oscillations in time. The unitary inequivalence of the Fock space of base (unmixed) eigenstates and the physical mixed eigenstates is proven and shown to lead to a rich condensate structure. This is exploited to develop formulas for two flavor boson oscillations in systems of arbitrary boson occupation number. The mixing and oscillation can be understood in terms of vacuum condensate which interacts with the bare particles to induce non-trivial effects. We apply these formulas to analyze the mixing of $\eta$ with $\eta'$ and comment on the $K_L K_S$ system. In addition, we consider the mixing of boson coherent states, which may have future applications in the construction of meson lasers.Comment: 12 pages, 3 figures; Eqs.(10-12) corrected, leading to new physical insights; added paragraph under Eq.(24) explaining physical interpretation of mixing in terms of vacuum condensation; references added and minor typo correcte

Resonance superfluidity in a quantum degenerate Fermi gas

We consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. We apply our theory to consider a specific resonance in potassium-40, and find that for achievable experimental conditions, the transition to a superfluid phase is possible at the high critical temperature of about 0.5 T_F. Observation of superfluidity in this regime would provide the opportunity to experimentally study the crossover from the superfluid phase of weakly-coupled fermions to the Bose-Einstein condensation of strongly-bound composite bosons.Comment: 4 pages, 3 figure

Dynamical moment of inertia and quadrupole vibrations in rotating nuclei

The contribution of quantum shape fluctuations to inertial properties of rotating nuclei has been analysed within the self-consistent one-dimensional cranking oscillator model. It is shown that in even-even nuclei the dynamical moment of inertia calculated in the mean field approximation is equivalent to the Thouless-Valatin moment of inertia calculated in the random phase approximation if and only if the self-consistent conditions for the mean field are fulfilled.Comment: 4 pages, 2 figure

A New Interpretation of Flux Quantization

We study the effect of Aharonov-Bohm flux on the superconducting state in metallic cylinders. Although Byers and Yang attributed flux quantization to the flux-dependent minimum of kinetic energies of the Cooper pairs, it is shown that kinetic energies do not produce any discernible oscillations in the free energy of the superconducting state (relative to that of normal state) as a function of the flux. This result is indeed anticipated by the observation of persistent current in normal metal rings at low temperature. Instead, we have found that pairing interaction depends on the flux, leading to flux quantization. When the flux $(\Phi$) is given by $\Phi=n\times hc/2e$ (with integer n), the pairing interaction and the free energy become unchanged (even n) or almost unchanged (odd n), due to degenerate-state pairing resulting from the energy level crossing. As a result, flux quantization and Little-Parks oscillations follow.Comment: Revtex, 10 pages, 6 figures, For more information, send me an e-mail at [email protected]

Four-particle condensate in strongly coupled fermion systems

Four-particle correlations in fermion systems at finite temperatures are investigated with special attention to the formation of a condensate. Instead of the instability of the normal state with respect to the onset of pairing described by the Gorkov equation, a new equation is obtained which describes the onset of quartetting. Within a model calculation for symmetric nuclear matter, we find that below a critical density, the four-particle condensation (alpha-like quartetting) is favored over deuteron condensation (triplet pairing). This pairing-quartetting competition is expected to be a general feature of interacting fermion systems, such as the excition-biexciton system in excited semiconductors. Possible experimental consequences are pointed out.Comment: LaTeX, 11 pages, 2 figures, uses psfig.sty (included), to be published in Phys. Rev. Lett., tentatively scheduled for 13 April 1998 (Volume 80, Number 15