Free expansion of Bose-Einstein condensates with quantized vortices

The expansion of Bose-Einstein condensates with quantized vortices is studied by solving numerically the time-dependent Gross-Pitaevskii equation at zero temperature. For a condensate initially trapped in a spherical harmonic potential, we confirm previous results obtained by means of variational methods showing that, after releasing the trap, the vortex core expands faster than the radius of the atomic cloud. This could make the detection of vortices feasible, by observing the depletion of the density along the axis of rotation. We find that this effect is significantly enhanced in the case of anisotropic disc-shaped traps. The results obtained as a function of the anisotropy of the initial configuration are compared with the analytic solution for a noninteracting gas in 3D as well as with the scaling law predicted for an interacting gas in 2D.Comment: 5 pages, 6 postscript figure

Feshbach Resonances and Medium Effects in ultracold atomic Gases

We develop an effective low energy theory for multi-channel scattering of cold atomic alkali atoms with particular focus on Feshbach resonances. The scattering matrix is expressed in terms of observables only and the theory allows for the inclusion of many-body effects both in the open and in the closed channels. We then consider the frequency and damping of collective modes for Fermi gases and demonstrate how medium effects significantly increase the scattering rate determining the nature of the modes. Our results obtained with no fitting parameters are shown to compare well with experimental data.Comment: Presented at the 5th workshop on Critical Stability, Erice, Italy 13-17 October 2008. 8 pages, 3 figures. Figure caption correcte

Resonance effects on the crossover of bosonic to fermionic superfluidity

Feshbach scattering resonances are being utilized in atomic gases to explore the entire crossover region from a Bose-Einstein Condensation (BEC) of composite bosons to a Bardeen-Cooper-Schrieffer (BCS) of Cooper pairs. Several theoretical descriptions of the crossover have been developed based on an assumption that the fermionic interactions are dependent only on the value of a single microscopic parameter, the scattering length for the interaction of fermion particles. Such a picture is not universal, however, and is only applicable to describe a system with an energetically broad Feshbach resonance. In the more general case in which narrow Feshbach resonances are included in the discussion, one must consider how the energy dependence of the scattering phase shift affects the physical properties of the system. We develop a theoretical framework which allows for a tuning of the scattering phase shift and its energy dependence, whose parameters can be fixed from realistic scattering solutions of the atomic physics. We show that BCS-like nonlocal solutions may build up in conditions of resonance scattering, depending on the effective range of the interactions.Comment: 8 pages,7 figure

Ideal Gases in Time-Dependent Traps

We investigate theoretically the properties of an ideal trapped gas in a time-dependent harmonic potential. Using a scaling formalism, we are able to present simple analytical results for two important classes of experiments: free expansion of the gas upon release of the trap; and the response of the gas to a harmonic modulation of the trapping potential is investigated. We present specific results relevant to current experiments on trapped Fermions.Comment: 5 pages, 3 eps figure

Magnetic ordering of Mn sublattice, dense Kondo lattice behavior of Ce in (RPd3)8Mn (R = La, Ce)

We have synthesized two new interstitial compounds (RPd3)8Mn (R = La and Ce). The Mn ions present in "dilute" concentration of just 3 molar percent form a sublattice with an unusually large Mn-Mn near neighbor distance of ~ 85 nm. While the existence of (RPd3)8M (where M is a p-block element) is already documented in the literature, the present work reports for the first time the formation of this phase with M being a 3d element. In (LaPd3)8Mn, the Mn sub-lattice orders antiferromagnetically as inferred from the peaks in low-field magnetization at 48 K and 23 K. The latter peak progressively shifts towards lower temperatures in increasing magnetic field and disappears below 1.8 K in a field of ~ 8 kOe. On the other hand in (CePd3)8Mn the Mn sublattice undergoes a ferromagnetic transition around 35 K. The Ce ions form a dense Kondo-lattice and are in a paramagnetic state at least down to 1.5 K. A strongly correlated electronic ground state arising from Kondo effect is inferred from the large extrapolated value of C/T = 275 mJ/Ce-mol K^2 at T = 0 K. In contrast, the interstitial alloys RPd3Mnx (x = 0.03 and 0.06), also synthesized for the first time, have a spin glass ground state due to the random distribution of the Mn ions over the available "1b" sites in the parent RPd3 crystal lattice.Comment: 18 figures and 20 pages of text documen

Nonclassical correlations of photon number and field components in the vacuum state

It is shown that the quantum jumps in the photon number n from zero to one or more photons induced by backaction evasion quantum nondemolition measurements of a quadrature component x of the vacuum light field state are strongly correlated with the quadrature component measurement results. This correlation corresponds to the operator expectation value which is equal to one fourth for the vacuum even though the photon number eigenvalue is zero. Quantum nondemolition measurements of a quadrature component can thus provide experimental evidence of the nonclassical operator ordering dependence of the correlations between photon number and field components in the vacuum state.Comment: 13 pages, 3 figures, corrections of omissions in equations (6) and (25). To be published in Phys. Rev.

Exact first-order density matrix for a d-dimensional harmonically confined Fermi gas at finite temperature

We present an exact closed form expression for the {\em finite temperature} first-order density matrix of a harmonically trapped ideal Fermi gas in any dimension. This constitutes a much sought after generalization of the recent results in the literature, where exact expressions have been limited to quantities derived from the {\em diagonal} first-order density matrix. We compare our exact results with the Thomas-Fermi approximation (TFA) and demonstrate numerically that the TFA provides an excellent description of the first-order density matrix in the large-N limit. As an interesting application, we derive a closed form expression for the finite temperature Hartree-Fock exchange energy of a two-dimensional parabolically confined quantum dot. We numerically test this exact result against the 2D TF exchange functional, and comment on the applicability of the local-density approximation (LDA) to the exchange energy of an inhomogeneous 2D Fermi gas.Comment: 12 pages, 3 figures included in the text, RevTeX4. Text before Eq.(25) corrected. Additional equation following Eq.(25) has been adde

Laser cooling of a trapped two-component Fermi gas

The collective Raman cooling of a trapped two-component Fermi gas is analyzed. We develop the quantum master equation that describes the collisions and the laser cooling, in the festina lente regime, where the heating due to photon reabsorption can be neglected. The numerical results based on Monte Carlo simulations show, that three-dimensional temperatures of the order of 0.008 T_F can be achieved. We analyze the heating related to the background losses, and conclude that our laser-cooling scheme can maintain the temperature of the gas without significant additional losses. Finally we derive an analytic expression for the temperature of a trapped Fermi gas heated by background collisions, that agrees very well with the data obtained from the numerical simulation.Comment: 5 pages, 3 figure

Quantum correlated twin atomic beams via photo-dissociation of a molecular Bose-Einstein condensate

We study the process of photo-dissociation of a molecular Bose-Einstein condensate as a potential source of strongly correlated twin atomic beams. We show that the two beams can possess nearly perfect quantum squeezing in their relative numbers.Comment: Corrected LaTeX file layou

Nonclassical correlations of phase noise and photon number in quantum nondemolition measurements

The continuous transition from a low resolution quantum nondemolition measurement of light field intensity to a precise measurement of photon number is described using a generalized measurement postulate. In the intermediate regime, quantization appears as a weak modulation of measurement probability. In this regime, the measurement result is strongly correlated with the amount of phase decoherence introduced by the measurement interaction. In particular, the accidental observation of half integer photon numbers preserves phase coherence in the light field, while the accidental observation of quantized values increases decoherence. The quantum mechanical nature of this correlation is discussed and the implications for the general interpretation of quantization are considered.Comment: 16 pages, 5 figures, final version to be published in Phys. Rev. A, Clarifications of the nature of the measurement result and the noise added in section I