Condensed matter physics with trapped atomic Fermi gases

We present an overview of the various phase transitions that we anticipate to occur in trapped fermionic alkali gases. We also discuss the prospects of observing these transitions in (doubly) spin-polarized Li-6 and K-40 gases, which are now actively being studied by various experimental groups around the world.Comment: 18 pages of LaTeX and 2 postscript figures. Contribution to the international summer school `Enrico Fermi' on Bose-Einstein condensation in atomic gases, Varenna 199

Theory of Interacting Quantum Gases

We present a unified picture of the interaction effects in dilute atomic quantum gases. We consider fermionic as well as bosonic gases and, in particular, discuss for both forms of statistics the fundamental differences between a gas with effectively repulsive and a gas with effectively attractive interatomic interactions, i.e.\ between a gas with either a positive or a negative scattering length.Comment: Invited paper for the NIST Journal of Researc

Critical Temperature of a Trapped Bose Gas: Mean-Field Theory and Fluctuations

We investigate the possibilities of distinguishing the mean-field and fluctuation effects on the critical temperature of a trapped Bose gas with repulsive interatomic interactions. Since in a direct measurement of the critical temperature as a function of the number of trapped atoms these effects are small compared to the ideal gas results, we propose to observe Bose-Einstein condensation by adiabatically ramping down the trapping frequency. Moreover, analyzing this adiabatic cooling scheme, we show that fluctuation effects can lead to the formation of a Bose condensate at frequencies which are much larger than those predicted by the mean-field theory.Comment: 4 pages of ReVTeX and 3 figures. Submitted to Physical Review

Influence of infection on the distribution patterns of NIH-Chronic Prostatitis Symptom Index scores in patients with chronic prostatitis/chronic pelvic pain syndrome (CP/CPPS)

Chronic prostatitis/chronic pelvic pain syndrome (CP/CPPS) is a complex condition for which the etiological determinants are still poorly defined. To better characterize the diagnostic and therapeutic profile of patients, an algorithm known as UPOINT was created, addressing six major phenotypic domains of CP/CPPS, specifically the urinary (U), psycho-social (P), organ-specific (O), infection (I), neurological/systemic (N) and muscular tenderness (T) domains. An additional sexual dysfunction domain may be included in the UPOINT(S) system. The impact of the infection domain on the severity of CP/CPPS symptoms is a controversial issue, due to the contradictory results of different trials. The aim of the present retrospective study was to further analyze the extent to which a positive infection domain of UPOINTS may modify the pattern of CP/CPPS symptom scores, assessed with the National Institutes of Health-Chronic Prostatitis Symptom Index (NIH-CPSI). In a cohort of 935 patients that was divided on the basis of the presence or absence of prostatic infection, more severe clinical symptoms were shown by the patients with infection (median NIH total score: 24 versus 20 points in uninfected patients; P<0.001). Moreover, NIH-CPSI score distribution curves were shifted towards more severe symptoms in patients with a positive infection domain. Division of the patients into the six most prominent phenotypic clusters of UPOINTS revealed that the 'prostate infection-related sexual dysfunction' cluster, including the highest proportion of patients with evidence of infection (80%), scored the highest number of NIH-CPSI points among all the clusters. To assess the influence of the infection domain on the severity of patients' symptoms, all subjects with evidence of infection were withdrawn from the 'prostate infection-related sexual dysfunction' cluster. This modified cluster showed symptom scores significantly less severe than the original cluster, and the CPSI values became comparable to the scores of the five other clusters, which were virtually devoid of patients with evidence of infection. These results suggest that the presence of pathogens in the prostate gland may significantly affect the clinical presentation of patients affected by CP/CPPS, and that the infection domain may be a determinant of the severity of CP/CPPS symptoms in clusters of patients phenotyped with the UPOINTS system. This evidence may convey considerable therapeutic implications

Cooper pair formation in trapped atomic Fermi gases

We apply the closed time-path formalism to evaluate the dynamics of the BCS transition to the superfluid state in trapped atomic $^6$Li. We find that the Fokker-Planck equation for the probability distribution of the order parameter is, sufficiently close to the critical temperature, identical to the equation that describes the switching on of a single-mode laser.Comment: 4 pages revtex including 1 figur

The Superfluid State of Atomic Li6 in a Magnetic Trap

We report on a study of the superfluid state of spin-polarized atomic Li6 confined in a magnetic trap. Density profiles of this degenerate Fermi gas, and the spatial distribution of the BCS order parameter are calculated in the local density approximation. The critical temperature is determined as a function of the number of particles in the trap. Furthermore we consider the mechanical stability of an interacting two-component Fermi gas, both in the case of attractive and repulsive interatomic interactions. For spin-polarized Li6 we also calculate the decay rate of the gas, and show that within the mechanically stable regime of phase space, the lifetime is long enough to perform experiments on the gas below and above the critical temperature if a bias magnetic field of about 5 T is applied. Moreover, we propose that a measurement of the decay rate of the system might signal the presence of the superfluid state.Comment: 16 pages Revtex including 10 figures, submitted to Phys. Rev.

Magnetic field control of elastic scattering in a cold gas of fermionic lithium atoms

We study elastic collisions in an optically trapped spin mixture of fermionic lithium atoms in the presence of magnetic fields up to 1.5kG by measuring evaporative loss. Our experiments confirm the expected magnetic tunability of the scattering length by showing the main features of elastic scattering according to recent calculations. We measure the zero crossing of the scattering length that is associated with a predicted Feshbach resonance at 530(3)G. Beyond the resonance we observe the expected large cross section in the triplet scattering regime

Equivalent Linear Two-Body Equations for Many-Body Systems

A method has been developed for obtaining equivalent linear two-body equations (ELTBE) for the system of many ($N$) bosons using the variational principle. The method has been applied to the one-dimensional N-body problem with pair-wise contact interactions (McGurie-Yang N-body problem) and to the dilute Bose-Einstein condensation (BEC) of atoms in anisotropic harmonic traps at zero temperature. For both cases, it is shown that the method gives excellent results for large N.Comment: 12 pages, Late

Critical temperature and Ginzburg-Landau equation for a trapped Fermi gas

We discuss a superfluid phase transition in a trapped neutral-atom Fermi gas. We consider the case where the critical temperature greatly exceeds the spacing between the trap levels and derive the corresponding Ginzburg-Landau equation. The latter turns out to be analogous to the equation for the condensate wave function in a trapped Bose gas. The analysis of its solution provides us with the value of the critical temperature $T_{c}$ and with the spatial and temperature dependence of the order parameter in the vicinity of the phase transition point.Comment: 6 pages, 1 figure, REVTeX. The figure improved. Misprints corrected. More discussion adde