Spin-correlation functions in ultracold paired atomic-fermion systems: sum rules, self-consistent approximations, and mean fields

The spin response functions measured in multi-component fermion gases by means of rf transitions between hyperfine states are strongly constrained by the symmetry of the interatomic interactions. Such constraints are reflected in the spin f-sum rule that the response functions must obey. In particular, only if the effective interactions are not fully invariant in SU(2) spin space, are the response functions sensitive to mean field and pairing effects. We demonstrate, via a self-consistent calculation of the spin-spin correlation function within the framework of Hartree-Fock-BCS theory, how one can derive a correlation function explicitly obeying the f-sum rule. By contrast, simple one-loop approximations to the spin response functions do not satisfy the sum rule. As we show, the emergence of a second peak at higher frequency in the rf spectrum, as observed in a recent experiment in trapped $^6\text{Li}$, can be understood as the contribution from the paired fermions, with a shift of the peak from the normal particle response proportional to the square of the BCS pairing gap.Comment: 7 pages, 1 figure, content adde

Unitary Fermi gas at finite temperature in the epsilon expansion

Thermodynamics of the unitary Fermi gas at finite temperature is investigated from the perspective of the expansion over epsilon=4-d with d being the dimensionality of space. We show that the thermodynamics is dominated by bosonic excitations in the low temperature region T<<Tc. Analytic formulas for the thermodynamic functions as functions of the temperature are derived to the lowest order in epsilon in this region. In the high temperature region where T Tc, bosonic and fermionic quasiparticles are excited. We determine the critical temperature Tc of the superfluid phase transition and the thermodynamic functions around Tc to the leading and next-to-leading orders in epsilon.Comment: 13 pages, 7 figures, revtex4; version to appear in Phys. Rev.

Conversion of LARSYS III.1 to an IBM 370 computer

A software system for processing multispectral aircraft or satellite data (LARSYS) was designed and written at the Laboratory for Applications of Remote Sensing at Purdue University. This system, being implemented on an IBM 360/67 computer utilizing the Cambridge Monitor System, is of an interactive nature. TAMU LARSYS maintains the essential capabilities of Purdue's LARSYS. The machine configuration for which it has been converted is an IBM-compatible Amdahl 470V/6 computer utilizing the time sharing option of the currently implemented OS/VS2 Operating System. Due to TSO limitations, the NASA-JSC deliverable TAMU LARSYS is comprised of two parts. Part one is a TSO Control Card Checker for LARSYS control cards, and part two is a batch version of LARSYS. Used together, they afford most of the capabilities of the original LARSYS III.1. Additionally, two programs have been written by TAMU to support LARSYS processing. The first is an ERTS-to-MIST conversion program used to convert ERTS data to the LARSYS input form, the MIST tape. The second is a system runtable code which maintains tape/file location information for the MIST data sets

Tuning Rashba and Dresselhaus spin-orbit couplings: Effects on singlet and triplet condensation with Fermi atoms

We investigate the pair condensation of a two-spin-component Fermi gas in the presence of both Rashba and Dresselhaus spin-orbit couplings. We calculate the condensate fraction in the BCS-BEC crossover both in two and in three dimensions by taking into account singlet and triplet pairings. These quantities are studied by varying the spin-orbit interaction from the case with the only Rashba to the equal-Rashba-Dresselhaus one. We find that, by mixing the two couplings, the singlet pairing decreases while the triplet pairing is suppressed in the BCS regime and increased in the BEC regime, both in two and three dimensions. At fixed spin-orbital strength, the greatest total condensate fraction is obtained when only one coupling (only Rashba or only Dresselhaus) is present.Comment: 9 pages, 6 figures, final versio

Short-distance and short-time structure of a unitary Fermi gas

We consider the operator product expansions for unitarity fermions. We compute the dynamic structure factor S(q,w) at large frequency and wavenumber away from the one-particle peak. The overall normalization of S(q,w) is determined by Tan's contact parameter, and the dependence on q and w is obtained in closed analytic form. We also find energy deposited into the system by small, rapid variations of the inverse scattering length.Comment: 11 pages, 8 figure

Zero Temperature Thermodynamics of Asymmetric Fermi Gases at Unitarity

The equation of state of a dilute two-component asymmetric Fermi gas at unitarity is subject to strong constraints, which affect the spatial density profiles in atomic traps. These constraints require the existence of at least one non-trivial partially polarized (asymmetric) phase. We determine the relation between the structure of the spatial density profiles and the T=0 equation of state, based on the most accurate theoretical predictions available. We also show how the equation of state can be determined from experimental observations.Comment: 10 pages and 7 figures. (Minor changes to correspond with published version.

Even-Odd Correlation Functions on an Optical Lattice

We study how different many body states appear in a quantum gas microscope, such as the one developed at Harvard [Bakr et al. Nature 462, 74 (2009)], where the site-resolved parity of the atom number is imaged. We calculate the spatial correlations of the microscope images, corresponding to the correlation function of the parity of the number of atoms at each site. We produce analytic results for a number of well-known models: noninteracting bosons, the large U Bose-Hubbard model, and noninteracting fermions. We find that these parity correlations tend to be less strong than density-density correlations, but they carry similar information.Comment: 8 pages, 4 figures. Published versio

Superfluidity in Three-species Mixture of Fermi Gases across Feshbach Resonances

In this letter a generalization of the BEC-BCS crossover theory to a multicomponent superfluid is presented by studying a three-species mixture of Fermi gas across two Feshbach resonances. At the BEC side of resonances, two kinds of molecules are stable which gives rise to a two-component Bose condensate. This two-component superfluid state can be experimentally identified from the radio-frequency spectroscopy, density profile and short noise measurements. As approaching the BCS side of resonances, the superfluidity will break down at some point and yield a first-order quantum phase transition to normal state, due to the mismatch of three Fermi surfaces. Phase separation instability will occur around the critical regime.Comment: 4 pages, 3 figures, revised versio

Reply to "Comment on 'Topological stability of the half-vortices in spinor exciton-polariton condensates'"

In a recent work [H. Flayac, I.A. Shelykh, D.D. Solnyshkov and G. Malpuech, Phys. Rev. B 81, 045318 (2010)], we have analyzed the effect of the TE-TM splitting on the stability of the exciton-polariton vortex states. We considered classical vortex solutions having cylindrical symmetry and we found that the so-called half-vortex states [Yu. G. Rubo, Phys. Rev. Lett. 99, 106401 (2007)] are not solutions of the stationary Gross-Pitaevskii equation. In their Comment [M. Toledo Solano, Yu.G. Rubo, Phys. Rev. B 82, 127301 (2010)], M. Toledo Solano and Yuri G. Rubo claim that this conclusion is misleading and pretend to demonstrate the existence of static half-vortices in an exciton-polariton condensate in the presence of TE-TM splitting. In this reply we explain why this assertion is not demonstrated satisfactorily.Comment: 3 Pages, no figur

Condensate density and superfluid mass density of a dilute Bose gas near the condensation transition

We derive, through analysis of the structure of diagrammatic perturbation theory, the scaling behavior of the condensate and superfluid mass density of a dilute Bose gas just below the condensation transition. Sufficiently below the critical temperature, $T_c$, the system is governed by the mean field (Bogoliubov) description of the particle excitations. Close to $T_c$, however, mean field breaks down and the system undergoes a second order phase transition, rather than the first order transition predicted in Bogoliubov theory. Both condensation and superfluidity occur at the same critical temperature, $T_c$ and have similar scaling functions below $T_c$, but different finite size scaling at $T_c$ to leading order in the system size. Through a simple self-consistent two loop calculation we derive the critical exponent for the condensate fraction, $2\beta\simeq 0.66$.Comment: 4 page