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The stability of an unpolarized two-component dipolar Fermi gas is studied within mean-field theory. Besides the known instability towards spontaneous magnetization with Fermi sphere deformation, another instability towards spontaneous formation of a spin-orbit coupled phase with a Rashba-like spin texture is found. A phase diagram is presented and consequences are briefly discussed.

We apply the light bending model of X-ray variability to Suzaku data of the Seyfert 1 galaxy MCG-6-30-15. We analyze the energy dependence of the root mean square (rms) variability, and discuss conditions necessary for the model to explain the characteristic decrease of the source variability around 5-8 keV. A model, where the X-ray source moves radially rather than vertically close to the disk surface, can indeed reproduce the reduced variability near the energy of the Fe Kalpha line, although the formal fit quality is poor. The model then predicts the energy spectra, which can be compared to observational data. The spectra are strongly reflection dominated, and do not provide a good fit to Suzaku spectral data of the source. The inconsistency of this result with some previous claims can be traced to our using data in a broader energy band, where effects of warm absorber in the spectrum cannot be neglected., Comment: 6 pages, PASJ, accepted

We study in detail the GR models of the X-ray spectral variability for various geometries of the X-ray source and with various relativistic effects being the dominant cause of spectral variability. The predicted properties are compared with the Suzaku observational data of the Seyfert 1 galaxy MCG--6-30-15. The data disfavor models with the X-ray source (1) moving vertically on the symmetry axis or (2) corotating with the disc and changing height not far above the disc surface. The most likely explanation for the observed variability is given by the model involving the X-ray source located at a very small, varying distance from a rapidly rotating black hole. This model predicts some enhanced variations in the red wing of the Fe line, which are not seen in the Suzaku observations. However, the enhanced variability of the red wing, while ruled out by the Suzaku data, is consistent with an excess RMS variability, between 5 and 6 keV, reported for some previous ASCA and XMM observations. We speculate that the presence or lack of such a feature is related to the change of the ionization state of the innermost part of the disc, however, investigation of such effects is currently not possible in our model (where a neutral disc is assumed). If the model, completed by description of ionization effects, proves to be fully consistent with the observational data, it will provide a strong indication that the central black hole in MCG--6-30-15 rotates rapidly, supporting similar conclusions derived from the Fe line profile., Comment: 15 pages, accepted for publication in A&A

We investigate dynamical properties of a one-component Fermi gas with dipole-dipole interaction between particles. Using a variational function based on the Thomas-Fermi density distribution in phase space representation, the total energy is described by a function of deformation parameters in both real and momentum space. Various thermodynamic quantities of a uniform dipolar Fermi gas are derived, and then instability of this system is discussed. For a trapped dipolar Fermi gas, the collective oscillation frequencies are derived with the energy-weighted sum rule method. The frequencies for the monopole and quadrupole modes are calculated, and softening against collapse is shown as the dipolar strength approaches the critical value. Finally, we investigate the effects of the dipolar interaction on the expansion dynamics of the Fermi gas and show how the dipolar effects manifest in an expanded cloud., Comment: 14 pages, 8 figures, submitted to New J. Phys

Quantum optics has been a major driving force behind the rapid experimental developments that have led from the first laser cooling schemes to the Bose-Einstein condensation (BEC) of dilute atomic and molecular gases. Not only has it provided experimentalists with the necessary tools to create ultra-cold atomic systems, but it has also provided theorists with a formalism and framework to describe them: many effects now being studied in quantum-degenerate atomic and molecular systems find a very natural explanation in a quantum optics picture. This article briefly reviews three such examples that find their direct inspiration in the trailblazing work carried out over the years by Herbert Walther, one of the true giants of that field. Specifically, we use an analogy with the micromaser to analyze ultra-cold molecules in a double-well potential; study the formation and dissociation dynamics of molecules using the passage time statistics familiar from superradiance and superfluorescence studies; and show how molecules can be used to probe higher-order correlations in ultra-cold atomic gases, in particular bunching and antibunching., Comment: This is a contribution to a Festschrift in honor of H. Walther's 70th birthday

We investigate the temporal fluctuations characteristic of the formation of molecular dimers from ultracold fermionic atoms via Raman photoassociation. The quantum fluctuations inherent to the initial atomic state result in large fluctuations in the passage time from atoms to molecules. Assuming degeneracy of kinetic energies of atoms in the strong coupling limit we find that a heuristic classical stochastic model yields qualitative agreement with the full quantum treatment in the initial stages of the dynamics. We also show that in contrast to the association of atoms into dimers, the reverse process of dissociation from a condensate of bosonic dimers exhibits little passage time fluctuations. Finally we explore effects due to the non-degeneracy of atomic kinetic energies., Comment: 7 pages, 6 figures

We analyze the dynamics of the molecular field incoherently pumped by the photoassociation of fermionic atoms and coupled by quantum tunnelling in a double-well potential. The relative phase distribution of the molecular modes in each well and their phase coherence are shown to build up owing to quantum mechanical fluctuations starting from the vacuum state. We identify three qualitatively different steady-state phase distributions, depending on the ratio of the molecule-molecule interaction strength to interwell tunnelling, and examine the crossover from a phase-coherent regime to a phase-incoherent regime as this ratio increases., Comment: 5 pages, 2 figures

We analyze the full nonlinear dynamics of the four-wave mixing between an incident beam of fermions and a fermionic density grating. We find that when the number of atoms in the beam is comparable to the number of atoms forming the grating, the dephasing of that grating, which normally leads to a decay of its amplitude, is suppressed. Instead, the density grating and the beam density exhibit large nonlinear coupled amplitude oscillations. In this case four-wave mixing can persist for much longer times compared to the case of negligible back-action. We also evaluate the efficiency of the four-wave mixing and show that it can be enhanced by producing an initial density grating with an amplitude that is less than the maximum value. These results indicate that efficient four-wave mixing in fermionic alkali gases should be experimentally observable., Comment: 9 pages, 8 figures

We perform Random Phase Approximation (RPA) study of collective excitations in the bose-fermi mixed degenerate gas of Alkali-metal atoms at T=0. The calculation is done by diagonalization in a model space composed of particle-hole type excitations from the ground state, the latter being obtained from the coupled Gross-Pitaevskii and Thomas-Fermi equations. We investigate strength distributions for different combinations of bose and fermi multipole ($L$) operators with $L=0,1,2,3$. Transition densities and dynamical structure factors are calculated for collective excitations. Comparison with the sum rule prediction for the collective frequency is given. Time dependent behavior of the system after an external impulse is studied., Comment: 28 pages, 13 figures, submitted to Phys. Rev. A

The behavior of collective oscillations of a trapped boson-fermion mixed condensate is studied in the sum rule approach. Mixing angle of bosonic and fermionic multipole operators is introduced so that the mixing characters of the low-lying collective modes are studied as functions of the boson-fermion interaction strength. For an attractive boson-fermion interaction, the low-lying monopole mode becomes a coherent oscillation of bosons and fermions and shows a rapid decrease in the excitation energy towards the instability point of the ground state. In contrast, the low-lying quadrupole mode keeps a bosonic character over a wide range of the interaction strengths. For the dipole mode the boson-fermion in-phase oscillation remains to be the eigenmode under the external oscillator potential. For weak repulsive values of the boson-fermion interaction strengths we found that an average energy of the out-of-phase dipole mode stays lower than the in-phase oscillation. Physical origin of the behavior of the multipole modes against boson-fermion interaction strength is discussed in some detail., Comment: 6 pages, 3 figures, to be appeared in Phys.Rev.A

Instabilities for boson-fermion mixed condensates of trapped Alkali atoms due to the boson-fermion attractive interaction are studied using a variational method. Three regions are shown for their instabilities according to the boson-fermion interaction strength: stable, meta-stable and unstable ones. The stability condition is obtained analytically from the asymptotic expansion of the variational total energy. The life-time of metastable states is discussed for tunneling decay, and is estimated to be very long. It suggests that, except near the unstable border, meta-stable mixed condensate should be almost-stable against clusterizations. The critical border between meta-stable and unstable phases is calculated numerically and is shown to be consistent with the M{\o}lmer scaling condition., Comment: 7 pages, 3figures

The s-wave scattering length for the Positronium-Positronium interaction is estimated semi-phenomenologically with the long-range van der Waals force and the short-range repulsive potential that represents the hard core between two positronium. The obtained value of the scattering length is $a \sim 0.44{\rm nm}$, and its stability is also checked for different parametrizations. Using this value, the Gross-Pitaevskii equation can be fixed for the Positronium Bose-Einstein condensates (Ps BEC). The static properties of Ps BEC are studied from the solutions of that equation. The phase-transition temperature shift of the Ps BEC due to the Ps-Ps interaction is also evaluated with the mean-field approximation., Comment: 7 pages, 6 figures, submitted to Phys. Rev. A

Static properties of a bose-fermi mixture of trapped potassium atoms are studied in terms of coupled Gross-Pitaevskii and Thomas-Fermi equations for both repulsive and attractive bose-fermi interatomic potentials. Qualitative estimates are given for solutions of the coupled equations, and the parameter regions are obtained analytically for the boson-density profile change and for the boson/fermion phase separation. Especially, the parameter ratio $R_{int}$ is found that discriminates the region of the large boson-profile change. These estimates are applied for numerical results for the potassium atoms and checked their consistency. It is suggested that a small fraction of fermions could be trapped without an external potential for the system with an attractive boson-fermion interaction., Comment: 8 pages,5 figures