Composite fermions,trios, and quartets in the Fermi-Bose mixture of neutral particles

We consider the model of a Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, in addition to the standard anomalous averages of the type 〈b〉, 〈bb〉, and 〈cc〉, pairing between fermions and bosons of the type 〈bc〉 is possible. This pairing corresponds to creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons, composite fermions are further paired into quartets. At higher temperatures, trios consisting of composite fermions and elementary bosons are also present in the system. Our investigations are important in connection with the recent observation of weakly bound dimers in magnetic and optical dipole traps at ultralow temperatures and with the observation of collapse of a Fermi gas in an attractive Fermi-Bose mixture of neutral particles.     

Bound states of three and four resonantly interacting particles

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonance bound state of two fermions in a spin-singlet state, with corresponding scattering length a _F . Applying this approach to the calculation of the dimmer-dimer scattering length a _B , we recover exactly the already known result a _B = 0.6 a _F . We use the developed approach to obtain new results in 2D for fermions and bosons. Namely, we calculate bound state energies for three bbb and four bbbb resonantly interacting bosons in 2D. For the case of resonance interaction between fermions and bosons, we exactly calculate bound state energies of the following complexes: two bosons plus one fermion bbf, two bosons plus two fermions bf↑bf↓, and three bosons plus one fermion bbbf.     

Bosonic and fermionic dipoles on a ring

We show that dipolar bosons and fermions confined in a quasi-one-dimensional ring trap exhibit a rich variety of states because their interaction is inhomogeneous. For purely repulsive interactions, with increasing strength of the dipolar coupling there is a crossover from a gaslike state to an inhomogeneous crystal-like one. For small enough angles between the dipoles and the plane of the ring, there are regions with attractive interactions, and clustered states can form.     

Momentum-Space Decoherence of Distinguishable and Identical Particles in the Caldeira–Leggett Formalism

In this work, momentum-space decoherence using minimum and nonminimum-uncertainty-product (stretched) Gaussian wave packets in the framework of Caldeira–Leggett formalism and under the presence of a linear potential is studied. As a dimensionless measure of decoherence, purity, a quantity appearing in the definition of the linear entropy, is studied taking into account the role of the stretching parameter. Special emphasis is on the open dynamics of the well-known cat states and bosons and fermions compared to distinguishable particles. For the cat state, while the stretching parameter speeds up the decoherence, the external linear potential strength does not affect the decoherence time; only the interference pattern is shifted. Furthermore, the interference pattern is not observed for minimum-uncertainty-product-Gaussian wave packets in the momentum space. Concerning bosons and fermions, the question we have addressed is how the symmetry of the wave functions of indistinguishable particles is manifested in the decoherence process, which is understood here as the loss of being indistinguishable due to the gradual emergence of classical statistics with time. We have observed that the initial bunching and anti-bunching character of bosons and fermions, respectively, in the momentum space are not preserved as a function of the environmental parameters, temperature, and damping constant. However, fermionic distributions are slightly broader than the distinguishable ones and these similar to the bosonic distributions. This general behavior could be interpreted as a residual reminder of the symmetry of the wave functions in the momentum space for this open dynamics.     

Supersolid bose-fermi mixtures in optical lattices

We study a mixture of strongly interacting bosons and spinless fermions with on-site repulsion in a three-dimensional optical lattice. For this purpose we develop and apply a generalized dynamical mean-field theory, which is exact in infinite dimensions and reliably describes the full range from weak to strong coupling. We restrict ourselves to half filling. For weak Bose-Fermi repulsion a supersolid forms, in which bosonic superfluidity coexists with charge-density wave order. For stronger interspecies repulsion the bosons become localized while the charge-density wave order persists. The system is unstable against phase separation for weak repulsion among the bosons.     

Exact solution of strongly interacting quasi-one-dimensional spinor Bose gases

We present an exact analytical solution of the fundamental system of quasi-one-dimensional spin-1 bosons with infinite delta repulsion. The eigenfunctions are constructed from the wave functions of noninteracting spinless fermions, based on Girardeau's Fermi-Bose mapping. We show that the spinor bosons behave like a compound of noninteracting spinless fermions and noninteracting distinguishable spins. This duality is especially reflected in the spin densities and the energy spectrum. We find that the momentum distribution of the eigenstates depends on the symmetry of the spin function. Furthermore, we discuss the splitting of the ground state multiplet in the regime of large but finite repulsion.     

Exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions

The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with δ-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the SU(2|2) supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin and isospin rapidities at the ground state are real if the interactions between the particles are repulsive; while the fermions form two-particle bounded states and the bosons form one large bound state, which means the bosons condensed at the zero momentum point, if the interactions are attractive. The charge, spin and isospin excitations are discussed in detail. The thermodynamic Bethe ansatz equations are also derived and their solutions at some special cases are obtained analytically.     

Quantum fluid-solid transition in a simple variational approach

A determinant (permanent) of plane waves for N fermions (bosons) in their lowest-energy state, and a determinant (permanent) of spatially-localized, nonoverlapping, single-particle functions are used to determine conditions on the short-ranged, square-well repulsive plus Yukawa attractive, two-body potential for which the spatially homogeneous or periodic particle-density states are energetically preferred. A considerable region in the coupling parameter-density plane is found where “crystalline” solutions are preferred. In particular, for purely repulsive forces, the low-density region for which the “fluid” solution is lowest shrinks to zero in the limit of infinitely repulsive cores, but faster for bosons than fermions. Inclusion of attractive forces is seen not to alter qualitatively the main results.     

Out of equilibrium dynamics of supersymmetry at high energy density

We investigate the out of equilibrium dynamics of global chiral supersymmetry at finite energy density. We concentrate on two specific models. The first is the massive Wess–Zumino model which we study in a self-consistent one-loop approximation. We find that for energy densities above a certain threshold, the fields are driven dynamically to a point in field space at which the fermionic component of the superfield is massless. The state, however, is found to be unstable, indicating a breakdown of the one-loop approximation. To investigate further, we consider an O(N) massive chiral model which is solved exactly in the large N limit. For sufficiently high energy densities, we find that for late times the fields reach a nonperturbative minimum of the effective potential degenerate with the perturbative minimum. This minimum is a true attractor for O(N) invariant states at high energy densities, and this provides a mechanism for determining which of the otherwise degenerate vacua is chosen by the dynamics. The final state for large energy density is a cloud of massless particles (both bosons and fermions) around this new nonperturbative supersymmetric minimum. By introducing boson masses which softly break the supersymmetry, we demonstrate a see-saw mechanism for generating small fermion masses. We discuss some of the cosmological implications of our results.     

Applications of exact solution for strongly interacting one-dimensional Bose-Fermi mixture: Low-temperature correlation functions, density profiles, and collective modes

We consider one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in current experiments with ultracold Bose-Fermi mixtures. We apply the Bethe ansatz technique to find the exact ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We use it to prove the absence of the demixing, contrary to prediction of a mean-field approximation. Combining exact solution with local density approximation in a harmonic trap, we calculate the density profiles and frequencies of collective modes in various limits. In the strongly interacting regime, we predict the appearance of low-lying collective oscillations which correspond to the counterflow of the two species. In the strongly interacting regime, we use exact wavefunction to calculate the single particle correlation functions for bosons and fermions at low temperatures under periodic boundary conditions. Fourier transform of the correlation function is a momentum distribution, which can be measured in time-of-flight experiments or using Bragg scattering. We derive an analytical formula, which allows to calculate correlation functions at all distances numerically for a polynomial time in the system size. We investigate numerically two strong singularities of the momentum distribution for fermions at k_f and k_f + 2k_b. We show, that in strongly interacting regime correlation functions change dramatically as temperature changes from 0 to a small temperature ∼E_f/γ ? E_f, where E_f = (π?n)²/(2m), n is the total density and γ = mg/(?²n) ? 1 is the Lieb-Liniger parameter. A strong change of the momentum distribution in a small range of temperatures can be used to perform a thermometry at very small temperatures.     

Permutation symmetry and condensation of identical particles consisting of fermions

For identical particles, consisting of fermions, the upper bound for the number of particles that can occupy a single state is determined. In the macroscopic case, it is proportional to the square root of the number of possible ways of formation of particles of a given composition of all fermions present in the mixture (the normalization constant of the respective density matrix). Particles capable of accumulating in macroscopic quantities in one state can consist only of an even number of fermions of different kinds. In the case of atoms in a trap, this bound can approach arbitrarily close to the total number of atoms. Since the state of the centers of mass of the atoms is described by a symmetric wave function, they, like elementary bosons, can form a condensate, the coherence properties of the components of which are characterized by an antisymmetric wave function of a single atom in relative coordinates.     

Crystallization of the charged Bose gas at 0 K

From variational upper bounds of the ground state energies of the fluid and solid phases, we estimate that charged bosons melt at r_s ≈ 135, while charged fermions melt around r_s ≈ 70.     

Large N expansion for strongly-coupled boson–fermion mixtures

We study a many-body mixture of an equal number of bosons and two-component fermions with a strong contact attraction. In this system bosons and fermions can be paired into composite fermions. We construct a large N extension where both bosons and fermions have the extra large N degrees of freedom and the boson–fermion interaction is extended to a four-point contact interaction which is invariant under the O(N) group transformation, so that the composite fermions become singlet in terms of the O(N) group. It is shown that such O(N) singlet fields have controllable quantum fluctuations suppressed by 1/N factors and yield a systematic 1/N-expansion in terms of composite fermions. We derive an effective action described by composite fermions up to the next-to-leading-order terms in the large N expansion, and show that there can be the BCS superfluidity of composite fermions at sufficiently low temperatures.     

Unitary quantum three-body problem in a harmonic trap

We consider either 3 spinless bosons or 3 equal mass spin-1/2 fermions, interacting via a short-range potential of infinite scattering length and trapped in an isotropic harmonic potential. For a zero-range model, we obtain analytically the exact spectrum and eigenfunctions: for fermions all the states are universal; for bosons there is a coexistence of decoupled universal and efimovian states. All the universal states, even the bosonic ones, have a tiny 3-body loss rate. For a finite range model, we numerically find for bosons a coupling between zero angular momentum universal and efimovian states; the coupling is so weak that, for realistic values of the interaction range, these bosonic universal states remain long-lived and observable.     

On the excited quarks and leptons

Using a duality-like finite energy sum rule, we discuss the assumption of having excited fermions at the W scale in a supersymmetric(SUSY) and non-supersymmetric hypercolour theory where quarks and leptons are bound states of fermion and scalar preon constituents. We conclude that a SUSY-like composite model cannot have excited fermions having a mass smaller than 0.5 TeV. A non-SUSY composite model having composite fermions but elementary W bosons can produce an excited fermion mass of the order of M_W provided that the scalar vacuum condensate is of the order of the (TeV)² scale of compositeness.     

On the critical temperature in a Boson-Fermion mixture with attraction between the components

The dependence of the critical temperature shift in the Bose component of a degenerate Bose-Fermi gas mixture in a harmonic trap on the number of bosons and fermions has been obtained on the basis of the effective Hamiltonian of the Bose subsystem. The presence of the Fermi component leads to a qualitatively new behavior of the shift, as compared to the case of a single interacting Bose gas in the trap. Namely, the T _c(N) dependence has a different curvature in the presence of the Fermi component.     

Universally coupled extraZ bosons from extended technicolor models

We show that in extended technicolor models there are several neutralZ bosons whose couplings to fermions are independent of family. TheseZ bosons are therefore additional to that of the standard model and induce corrections to the low energy effective Hamiltonian. These corrections are calculated in the most general model which includes technileptons (introduced to give mass to leptons).     

Inhomogeneous atomic Bose-Fermi mixtures in cubic lattices

We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices and parabolic confining potentials. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimension within mean-field and perturbation theory. The results are compared with a new numerical method that is based on a Gutzwiller variational approach for the bosons and an exact treatment for the fermions. The findings can be applied as a guideline for future experiments with trapped atomic Bose-Fermi mixtures in optical lattices.     

Coherence properties of two trapped particles

We analyse the coherence properties of two particles trapped in a one-dimensional harmonic potential. This simple model allows us to derive analytic expressions for the first and second order coherence functions. We investigate their properties depending on the particle nature and the temperature of the quantum gas. We find that at zero temperature non-interacting bosons and fermions show very different correlations, while they coincide for higher temperatures. We observe atom bunching for bosons and atom anti-bunching for fermions. When the effect of s-wave scattering between bosons is taken into account, we find that the range of coherence is enhanced or reduced for repulsive or attractive potentials, respectively. Strongly repelling bosons become in some way more “fermion-like" and show anti-bunching. Their first order coherence function, however, differs from that for fermions. Received 19 September 2002 Published online 4 February 2003