We derive exact relations between the Renyi entanglement entropies and the particle number fluctuations of spatial connected regions in systems of N noninteracting fermions in arbitrary dimension. We prove that the asymptotic large-N behavior of the entanglement entropies is proportional to the variance of the particle number. We also consider 1D Fermi gases with a localized impurity, where all particle cumulants contribute to the asymptotic large-N behavior of the entanglement entropies. The particle cumulant expansion turns out to be convergent for all integer-order Renyi entropies (except for the von Neumann entropy) and the first few cumulants provide already a good approximation. Since the particle cumulants are accessible to experiments, these relations may provide a measure of entanglement in these systems.
We exploit and clarify the use of random matrix theory for the calculation of the entanglement entropy of free Fermi gases. We apply this method to obtain analytic predictions for Renyi entanglement entropies of a one-dimensional gas trapped by a harmonic potential in all the relevant scaling regimes. We confirm our findings with accurate numerical calculations obtained by means of an ingenious discretisation of the reduced correlation matrix.
We introduce a systematic framework to calculate the bipartite entanglement entropy of a spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. To show the wide range of applicability of the proposed formalism, we use it for the calculation of the entanglement in the eigenstates of periodic systems, in a gas confined by boundaries or external potentials, in junctions of quantum wires and in a time-dependent parabolic potential.
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 the ground-state entanglement entropy of a subsystem of size $L$ of non-interacting fermions scattered by a potential of finite range $a$. We derive a general relation between the scattering matrix and the overlap matrix and use it to prove, that for a one-dimensional symmetric potential the von Neumann entropy, the Rényi entropies and the full counting statistics are robust against potential scattering, provided that $L/a\gg 1$. The results of numerical calculations support the validity of this conclusion for a generic potential.
We investigate quantum correlations in the ground state of noninteracting Fermi gases of N particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose, we compute one-particle correlations, particle fluctuations and bipartite entanglement entropies of extended space regions, and study their large-N scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining S_HS = c_l N^(d-1)/d ln N, analogously to homogenous systems, with c_l=1/6, 1/(6\sqrt{2}), 1/(6\sqrt{6}) in one, two and three dimensions respective…
We investigate the entanglement properties of the equilibrium and nonequilibrium quantum dynamics of 2D and 3D Fermi gases, by computing entanglement entropies of extended space regions, which generally show multiplicative logarithmic corrections to the leading power-law behaviors, corresponding to the logarithmic corrections to the area law. We consider 2D and 3D Fermi gases of N particles constrained within a limited space region, for example by a hard-wall trap, at equilibrium at T=0, i.e. in their ground state, and compute the first few terms of the asymptotic large-N behaviors of entangle…
We study the properties of a spin-polarized Fermi gas in a harmonic trap, using the semiclassical (Thomas-Fermi) approximation. Universal forms for the spatial and momentum distributions are calculated, and the results compared with the corresponding properties of a dilute Bose gas.
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.
In this paper, we calculate the explicit expression for the fugacity for two- and three-dimensional weakly interacting Bose and Fermi gases from their equations of state in isochoric and isobaric processes, respectively, based on the mathematical result of the boundary problem of analytic functions --- the homogeneous Riemann-Hilbert problem. We also discuss the Bose-Einstein condensation phase transition of three-dimensional hard-sphere Bose gases.
Second-order phase transitions have no latent heat and are characterized by a change in symmetry. In addition to the conventional symmetric and anti-symmetric states under permutations of bosons and fermions, mathematical group-representation theory allows for non-Abelian permutation symmetry. Such symmetry can be hidden in states with defined total spins of spinor gases, which can be formed in optical cavities. The present work shows that the symmetry reveals itself in spin-independent or coordinate-independent properties of these gases, namely as non-Abelian entropy in thermodynamic properti…
A significant feature of the one-dimensional super Tonks-Girardeau gas is its metastable gas-like state with a stronger Fermi-like pressure than for free fermions which prevents a collapse of atoms. This naturally suggests a way to search for such strongly correlated behaviour in systems of interacting fermions in one dimension. We thus show that the strongly attractive Fermi gas without polarization can be effectively described by a super Tonks-Girardeau gas composed of bosonic Fermi pairs with attractive pair-pair interaction. A natural description of such super Tonks-Girardeau gases is prov…
We present an analytical approximation for nonlinear dynamics of trapped Bose-co ndensed gases. The new approximation is a substantial improvement over the Thomas-Fermi approximation and is shown to be applicable for systems with a rather small number of atoms $N$. The calculated aspect ratios after ballistic expansion are found to be in good agreement with those observed in recent experiments.
We show that atomic Fermi gases in quasi2D geometries are promising for achieving superfluidity. In the regime of BCS pairing for weak attraction, we calculate the critical temperature T_c and analyze possibilities of increasing the ratio of T_c to the Fermi energy. In the opposite limit, where a strong coupling leads to the formation of weakly bound quasi2D dimers, we find that their Bose-Einstein condensate will be stable on a long time scale.
We discuss 3-body processes in ultracold two-component Fermi gases with short-range intercomponent interaction characterized by a large and positive scattering length $a$. It is found that in most cases the probability of 3-body recombination is a universal function of the mass ratio and $a$, and is independent of short-range physics. We also calculate the scattering length corresponding to the atom-dimer interaction.
We study theoretically the ultracold two-component Fermi gases when a gradient magnetic field is used to tune the scattering length between atoms. For Li6 at the narrow resonance B0=543.25G, it is shown that the gases would be in a coexistence of the regimes of BCS, BEC and unitarity limit with the present experimental technique. In the case of thermal and chemical equilibrium, we investigate the density distribution of the gases and show that a double peak of the density distribution can give us a clear evidence for the coexistence of BCS, BEC and unitarity limit.
Fermi inhibition is a quantum statistical analogue for the inhibition of spontaneous emission by an excited atom in a cavity. This is achieved when the relevant motional states are already occupied by a cloud of cold atoms in the internal ground state. We exhibit non-trivial effects at finite temperature and in anisotropic traps, and briefly consider a possible experimental realization.
We have produced a macroscopic quantum system in which a Li-6 Fermi sea coexists with a large and stable Na-23 Bose-Einstein condensate. This was accomplished using inter-species sympathetic cooling of fermionic Li-6 in a thermal bath of bosonic Na-23.
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.
The charged Fermi gas with a small Lande-factor $g$ is expected to be diamagnetic, while that with a larger $g$ could be paramagnetic. We calculate the critical value of the $g$-factor which separates the dia- and para-magnetic regions. In the weak-field limit, $g_{c}$ has the same value both at high and low temperatures, $g_{c}=1/\sqrt{12}$. Nevertheless, $g_{c}$ increases with the temperature reducing in finite magnetic fields. We also compare the $g_{c}$ value of Fermi gases with those of Boltzmann and Bose gases, supposing the particle has three Zeeman levels $σ=\pm1, 0$, and find that $g_…
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 investigate the elementary excitations of charge and spin degrees for the 1D interacting two-component Bose and Fermi gases by means of the discrete Bethe ansatz equations. Analytic results in the limiting cases of strong and weak interactions are derived, where the Bosons are treated in the repulsive and the fermions in the strongly attractive regime. We confirm and complement results obtained previously from the Bethe ansatz equations in the thermodynamic limit.
One-dimensional Bose and Fermi gases with contact interactions are known to exhibit the weak-strong duality, where the equilibrium thermodynamic properties of one system at weak coupling are identical to those of the other system at strong coupling. Here, we show that such duality extends beyond the thermodynamics to the frequency-dependent complex bulk viscosity, which is provided by the contact-contact response function. In particular, we confirm that the bulk viscosities of the Bose and Fermi gases agree in the high-temperature limit, where the systematic expansion in terms of fugacity is a…
We propose a coherent framework allowing to deal with many-body effects in dense ultracold Fermi gases in the presence of a Feshbach resonance. We show that the simple effect of Pauli exclusion induces a strong modification of the basic scattering properties, leading in particular to an energy dependence of the effective scattering length on the scale of the chemical potential. This results in a smearing of the Feshbach resonance and provides a natural explanation for recent experimental findings.
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.
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 examine the collisional behavior of two-component Fermi gases released at zero temperature from a harmonic trap. Using a phase-space formalism to calculate the collision rate during expansion, we find that Pauli blocking plays only a minor role for momentum changing collisions. As a result, for a large scattering cross-section, Pauli blocking will not prevent the gas from entering the collisionally hydrodynamic regime. In contrast to the bosonic case, hydrodynamic expansion at very low temperatures is therefore not evidence for fermionic superfluidity.
The zero-temperature and finite-temperature thermodynamics of two-component Fermi gases with finite-range attractive interaction suffer from fermion sign problem, which seems like an insurmountable problem in exact numerical simulations. In a recent work, we find a reliable method to simulate the thermodynamic properties of single-component Fermi gases for both noninteracting and repulsively interacting cases based on the method of parametrized partition function and the $ξ_E$ curve of constant energy. In the present work, this method is generalized to two-component Fermi gases with finite-ran…
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.
