It is well known that one can map certain properties of random matrices, fermionic gases, and zeros of the Riemann zeta function to a unique point process on the real line. Here we analytically provide exact generalizations of such a point process in d-dimensional Euclidean space for any d, which are special cases of determinantal processes. In particular, we obtain the n-particle correlation functions for any n, which completely specify the point processes. We also demonstrate that spin-polarized fermionic systems have these same n-particle correlation functions in each dimension. The point processes for any d are shown to be hyperuniform. The latter result implies that the pair correlation function tends to unity for large pair distances with a decay rate that is controlled by the power law r^[-(d+1)]. We graphically display one- and two-dimensional realizations of the point processes in order to vividly reveal their "repulsive" nature. Indeed, we show that the point processes can be characterized by an effective "hard-core" diameter that grows like the square root of d. The nearest-neighbor distribution functions for these point processes are also evaluated and rigorously bounded. Among other results, this analysis reveals that the probability of finding a large spherical cavity of radius r in dimension d behaves like a Poisson point process but in dimension d+1 for large r and finite d. We also show that as d increases, the point process behaves effectively like a sphere packing with a coverage fraction of space that is no denser than 1/2^d.
The partition function for a canonical ensemble of 2D Coulomb charges in a background potential (the Dyson gas) is realized as a vacuum expectation value of a group-like element constructed in terms of free fermionic operators. This representation provides an explicit identification of the partition function with a tau-function of the 2D Toda lattice hierarchy. Its dispersionless (quasiclassical) limit yields the tau-function for analytic curves encoding the integrable structure of the inverse potential problem and parametric conformal maps. A similar fermionic realization of partition functio…
By rotating two-component fermionic atom gases in uniform magnetic field, a similar physical situation with de Haas-van Alphen effect is constructed. We calculate magnetic moment of the system and find that owing to an existence of effective magnetic field coming from the rotation, the magnetic moment also shows the oscillatory behavior about magnetic field, but it is completely different from the famous oscillation of de Haas-van Alphen effect. This distinction is due to that in the atomic gases the orbital motion of atom only couples to rotation and does not contribute to magnetic moment in …
We report on the observation of sympathetic cooling of a cloud of fermionic 6-Li atoms which are thermally coupled to evaporatively cooled bosonic 87-Rb. Using this technique we obtain a mixture of quantum-degenerate gases, where the Rb cloud is colder than the critical temperature for Bose-Einstein condensation and the Li cloud colder than the Fermi temperature. From measurements of the thermalization velocity we estimate the interspecies s-wave triplet scattering length |a_s|=20_{-6}^{+9} a_B. We found that the presence of residual rubidium atoms in the |2,1> and the |1,-1> Zeeman substates …
We present a unified overview, from the mean-field to the unitarity regime, of the stability of a trapped Fermi gas with short range attractive interactions. Unlike in a system of bosons, a Fermi gas is always stable in these regimes, no matter how large the particle number. However, when the interparticle spacing becomes comparable to the range of the interatomic interactions, instability is not precluded.
We study the structure of Fermionic networks, i.e., a model of networks based on the behavior of fermionic gases, and we analyze dynamical processes over them. In this model, particle dynamics have been mapped to the domain of networks, hence a parameter representing the temperature controls the evolution of the system. In doing so, it is possible to generate adaptive networks, i.e., networks whose structure varies over time. As shown in previous works, networks generated by quantum statistics can undergo critical phenomena as phase transitions and, moreover, they can be considered as thermody…
We present an exact many-body theory of ultracold fermionic gases for the Bose-Einstein condensation (BEC) regime of the BEC-BCS crossover. This is a purely fermionic approach which treats explicitely and systematically the dimers formed in the BEC regime as made of two fermions. We consider specifically the zero temperature case and calculate the first terms of the expansion of the chemical potential in powers of the density $n$. We derive first the mean-field contribution, which has the expected standard expression when it is written in terms of the dimer-dimer scattering length $a_M$. We go…
he BCS-like pairing in ultracold fermionic atomic ($UCFAG$) gases is studied in the model of "isotopic-spin" pairing proposed in 1991 \cite% {Ku-Hof-SSC}. This model assumes a mismatch ($δ$) in chemical potentials of pairing fermionic atoms. It is shown that a $π$-Josephson junction can be realized in $UCFAG$ systems, where the left and right banks $% S$ are the $UCFAG$ superfluids. The weak link $M$ consists from the normal $% UCFAG$ with the finite mismatch $δ$. If the $π$-junction is a part of a closed ring the superfluid mass-current flows spontaneously in the ring, i.e., the time-reversal…
We address the effects of dissipative defects giving rise to a localized particle loss, in one-dimensional non-interacting lattice fermionic gases confined within a region of size $\ell$. We consider homogeneous systems within hard walls and inhomogeneous systems where the particles are trapped by space-dependent external potentials, such as harmonic traps. We model the dissipative particle-decay mechanism by Lindblad master equations governing the time evolution of the density matrix. The resulting quantum dynamics is analyzed in protocols starting from the ground state of the Hamiltonian for…
The virial expansion of ideal quantum gases reveals some interesting and amusing properties when considered as a function of dimensionality $d$. In particular, the convergence radius $ρ_c(d)$ of the expansion is particulary large at {\em exactly\/} $d=3$ dimensions, $ρ_c(3) = 7.1068\ldots \times \lim_{d\to3} ρ_c(d)$. The same phenomenon occurs in a few other special (non-integer) dimensions. We explain the origin of these facts, and discuss more generally the structure of singularities governing the asymptotic behavior of the ideal gas virial expansion.
At the location of a magnetic-field Feshbach resonance, a mixture gas of fermionic atoms and dimers of fermionic atom pairs is investigated in the unitarity limit where the absolute value of the scattering length is much larger than the mean distance between atoms. The dynamic equilibrium of the mixture gases is characterized by the minimum of the Gibbs free energy. For the fermionic atoms and dimers with divergent scattering length, it is found that the fraction of the dimers based on a very simple theory agrees with the high fraction of zero-momentum molecules observed in a recent experiment…
A functional renormalisation group study for the BEC-BCS crossover for ultracold gases of fermionic atoms is presented. We discuss the fixed point which is at the origin of universality for broad Feshbach resonances. All macroscopic quantities depend only on one relevant parameter, the concentration a k_F, besides their dependence on the temperature in units of the Fermi energy. In particular, we compute the universal ratio between molecular and atomic scattering length in vacuum. We also present an estimate to which level of accuracy universality holds for gases of Li and K atoms.
We calculate numerically and analytically the fluctuations of the fermionic condensate and of the number of particles above the condensate for systems of constant density of states. We compare the canonical fluctuations, obtained from the equivalent Bose condensate fluctuation, with the grandcanonical fermionic calculation. The fluctuations of the condensate are almost the same in the two ensembles, with a small correction comming from the total particle number fluctuation in the grandcanonical ensemble. On the other hand the number of particles above the condensate and its fluctuation is inse…
The use of Feshbach resonances for tuning the interparticle interaction in ultracold Fermi gases has led to remarkable developments, in particular to the creation and Bose-Einstein condensation of weakly bound diatomic molecules of fermionic atoms. These are the largest diatomic molecules obtained so far, with a size of the order of thousands of angstroms. They represent novel composite bosons, which exhibit features of Fermi statistics at short intermolecular distances. Being highly excited, these molecules are remarkably stable with respect to collisional relaxation, which is a consequence o…
We use a T-matrix approximation to calculate the single particle spectrum of the normal state of a gas of Fermionic atoms at low temperature. In the strongly interacting regime of the polarized gas, we find that the spectrum is separated in two branches, leading to a double-peaked radiofrequency spectral feature.
We apply the S-matrix based finite temperature formalism to non-relativistic Bose and Fermi gases in 1+1 and 2+1 dimensions. In the 2+1 dimensional case, the free energy is given in terms of Roger's dilogarithm in a way analagous to the relativistic 1+1 dimensional case. The 1d fermionic case with a quasi-periodic 2-body potential provides a physical framework for understanding the Riemann hypothesis.
We consider a weakly-interacting fermionic gas of alkali-metal atoms characterized by two hyper- fine states which are Rabi coupled. By using a Hartree approximation for the repulsive interaction we determine the zero-temperature equation of state of this Fermi gas in D spatial dimensions (D = 1, 2, 3). Then, adopting the Landau-Vlasov equation and hydrodynamic equations, we investi- gate the speed of first sound and zero sound. We show that the two sounds, which occur respectively in collisional and collisionless regimes, crucially depend on the interplay between interaction strength and Rabi…
We explain why the experimental efficiency observed in the conversion of ultracold Fermi gases of $^{40}$K and $^{6}$Li atoms into diatomic Bose gases is limited to 0.5 when the Feshbach resonance sweep rate is sufficiently slow to pass adiabatically through the Landau Zener transition but faster than ``the collision rate'' in the gas, and increases beyond 0.5 when it is slower. The 0.5 efficiency limit is due to the preparation of a statistical mixture of two spin-states, required to enable s-wave scattering. By constructing the many-body state of the system we show that this preparation yiel…
Bose-condensed gases are considered with an effective interaction strength varying in the whole range of the values between zero and infinity. The consideration is based on the usage of a representative statistical ensemble for Bose systems with broken global gauge symmetry. Practical calculations are illustrated for a uniform Bose gas at zero temperature, employing a self-consistent mean-field theory, which is both conserving and gapless.
The quantum-kinetic energy of a finite number of trapped fermionic atoms provides a restoring force for shear motion due to a distortion of the momentum distribution. In analogy to the twist mode of nuclear physics it is proposed that counter-rotating the upper and lower hemisphere of a spherical atomic cloud yields a finite-frequency mode closely related to transverse zero-sound waves in bulk Fermi liquids.
We have produced a quantum degenerate Li-6 Fermi gas with up to 7 x 10^7 atoms, an improvement by a factor of fifty over all previous experiments with degenerate Fermi gases. This was achieved by sympathetic cooling with bosonic Na-23 in the F=2, upper hyperfine ground state. We have also achieved Bose-Einstein condensation of F=2 sodium atoms by direct evaporation.
We study the entanglement entropy of connected bipartitions in free fermion gases of N particles in arbitrary dimension d. We show that the von Neumann and Renyi entanglement entropies grow asymptotically as N^(1-1/d) ln N, with a prefactor that is analytically computed using the Widom conjecture both for periodic and open boundary conditions. The logarithmic correction to the power-law behavior is related to the area-law violation in lattice free fermions. These asymptotic large-N behaviors are checked against exact numerical calculations for N-particle systems.
We study density profiles in trapped fermionic gases, near Feshbach resonances, at all $T \leq T_c$ and in the near-BEC and unitary regimes. For the latter, we quantify and characterize the generally neglected contribution from noncondensed Cooper pairs. As a consequence of these pairs, our profiles are rather well fit to a Thomas-Fermi (TF) functional form, and equally well fit to experimental data. Our work lends support to the notion that TF fits can be used in an experimental context to obtain information about the temperature.
