We present a hierarchical equations of motion approach, which allows a numerically exact simulation of nonequilibrium transport in general open quantum systems involving multiple macroscopic bosonic and fermionic environments. The performance of the method is demonstrated for a model of a nanosystem, which involves interacting electronic and vibrational degrees of freedom and is coupled to fermionic and bosonic baths. The results show the intricate interplay of electronic and vibrational degrees of freedom in this nonequilibrium transport scenario for both voltage and thermally driven transport processes. Furthermore, the use of importance criteria to improve the efficiency of the method is discussed.
Mixtures of bosonic and fermionic atoms in optical lattices provide a promising arena to study strongly correlated systems. In experiments realizing such mixtures in the quantum degenerate regime the temperature is a key parameter. In this work, we investigate the intrinsic heating and cooling effects due to an entropy-preserving raising of the optical lattice potential. We analyze this process, identify the generic behavior valid for a wide range of parameters, and discuss it quantitatively for the recent experiments with 87Rb and 40K atoms. In the absence of a lattice, we treat the bosons in…
We relate the reduced density matrices of quadratic bosonic and fermionic models to their Green's function matrices in a unified way and calculate the scaling of bipartite entanglement of finite systems in an infinite universe exactly. For critical fermionic 2D systems at T=0, two regimes of scaling are identified: generically, we find a logarithmic correction to the area law with a prefactor dependence on the chemical potential that confirms earlier predictions based on the Widom conjecture. If, however, the Fermi surface of the critical system is zero-dimensional, we find an area law with a …
We construct bosonic and fermionic eigenstates for the generalized Sutherland models associated with arbitrary reduced root systems respectively, through W-symmetrization and W-anti-symmetrization of Heckman-Opdam's nonsymmetric Jacobi polynomials. Square norms of the nonsymmetric Heckman-Opdam polynomials are evaluated from their Rodrigues formulae. The W-symmetrization and W-anti-symmetrization of the nonsymmetric polynomials enable us to evaluate square norms of bosonic and fermionic eigenstates for the generalized Sutherland models.
The topology of two-dimensional movement allows for existing of anyons -- particles obeying statistics intermediate between that of bosons and fermions. In this article, the functional form of the occupation numbers of free anyons is suggested as a modification of the Gibbs factor in the Bose and Fermi statistics. The proposed expressions are studied in the bosonic and fermionic limits. The obtained virial coefficients coincide with those of free anyons up to the fourth and fifth virial coefficients (the proposed approach can be extended for higher ones as well) and up to the second order in t…
Recently, there has been a surge of interest in using Rényi entropies as quantifiers of correlations in many-body quantum systems. However, it is well known that in general these entropies do not satisfy the strong subadditivity inequality, which is a central property ensuring the positivity of correlation measures. In fact, in many cases they do not even satisfy the weaker condition of subadditivity. In the present paper we shed light on this subject by providing a detailed survey of Rényi entropies for bosonic and fermionic Gaussian states. We show that for bosons the Rényi entropies always …
We observe a localized phase of ultracold bosonic quantum gases in a 3-dimensional optical lattice induced by a small contribution of fermionic atoms acting as impurities in a Fermi-Bose quantum gas mixture. In particular we study the dependence of this transition on the fermionic 40K impurity concentration by a comparison to the corresponding superfluid to Mott insulator transition in a pure bosonic 87Rb gas and find a significant shift in the transition parameter. The observed shift is larger than expected based on a mean-field argument, which is a strong indication that disorder-related eff…
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 derive a general relation between the bosonic and fermionic entanglement in the ground states of supersymmetric quadratic Hamiltonians. For this, we construct canonical identifications between bosonic and fermionic subsystems. Our derivation relies on a unified framework to describe both, bosonic and fermionic Gaussian states in terms of so-called linear complex structures $J$. The resulting dualities apply to the full entanglement spectrum between the bosonic and the fermionic systems, such that the von Neumann entropy and arbitrary Renyi entropies can be related. We illustrate our finding…
Quantum walk represents one of the most promising resources for the simulation of physical quantum systems, and has also emerged as an alternative to the standard circuit model for quantum computing. Up to now the experimental implementations have been restricted to single particle quantum walk, while very recently the quantum walks of two identical photons have been reported. Here, for the first time, we investigate how the particle statistics, either bosonic or fermionic, influences a two-particle discrete quantum walk. Such experiment has been realized by adopting two-photon entangled state…
We investigate the properties of trapped Bose-Fermi mixtures for experimentally relevant parameters in one dimension. The effect of the attractive Bose-Fermi interaction onto the bosons is to deepen the parabolic trapping potential, and to reduce the bosonic repulsion in higher order, leading to an increase in bosonic coherence. The opposite effect was observed in ${}^{87}$Rb - ${}^{40}$K experiments, most likely due to a sharp rise in temperature. We also discuss low-temperature features, such as a bosonic Mott insulator transition driven by the fermion concentration, and the formation of com…
We calculate the phase diagrams for a harmonically trapped ideal gas mixture of fermionic atoms and bosonic molecules in chemical and thermal equilibrium, where the internal energy of the molecules can be adjusted relative to that of the atoms by use of a tunable Feshbach resonance. We plot the molecule fraction and the fraction of Bose-condensed molecules as functions of the temperature and internal molecular energy. We show the paths traversed in the phase diagrams when the molecular energy is varied either suddenly or adiabatically. Our model calculation helps to interpret the {\it{adiabati…
We investigate the production efficiency of ultracold molecules in bosonic $^{85}$Rb and fermionic $^{40}$K when the magnetic field is swept across a Feshbach resonance. For adiabatic sweeps of the magnetic field, the conversion efficiency of each species is solely determined by the phase space density of the atomic cloud, in contrast to a number of theoretical predictions. Our novel model for the adiabatic pairing process, developed from general physical principles, accurately predicts the conversion efficiency for {\it both} ultracold gases of bosons and of fermions. In the non-adiabatic reg…
Using the Lindblad master equation approach, we investigate the structure of steady-state solutions of open integrable quantum lattice models, driven far from equilibrium by incoherent particle reservoirs attached at the boundaries. We identify a class of boundary dissipation processes which permits to derive exact steady-state density matrices in the form of graded matrix-product operators. All the solutions factorize in terms of vacuum analogues of Baxter's Q-operators which are realized in terms of non-unitary representations of certain finite dimensional subalgebras of graded Yangians. We …
In terms of spinless fermions and spin waves, we describe magnetic properties of a spin-1/2 ferromagnetic-antiferromagnetic bond-alternating chain which behaves as a Haldane-gap antiferromagnet. On one hand, we employ the Jordan-Wigner transformation and treat the fermionic Hamiltonian within the Hartree-Fock approximation. On the other hand, we employ the Holstein-Primakoff transformation and modify the conventional spin-wave theory so as to restore the sublattice symmetry. We calculate the excitation gap, the specific heat, the magnetic susceptibility, magnetization curves, and the nuclear s…
An effective coherent state path integral for super-symmetric pair condensates is investigated with specification on the nontrivial coset integration measure. The nontrivial coset integration measure, determined by the square root of the super-determinant of the coset metric tensor, is eliminated by the inverse square root of this coset metric tensor; this results into Euclidean path integration variables for the pair condensate fields. According to the transformation to 'flat' anomalous path integration variables, first order variations of fields can be performed for classical equations with …
In terms of spinless fermions via the Jordan-Wigner transformation along a snake-like path and spin waves modified so as to restore the sublattice symmetry, we investigate static and dynamic properties of two-leg antiferromagnetic Heisenberg ladders. The specific heat is finely reproduced by the spinless fermions, whereas the magnetic susceptibility is well described by the modified spin waves. The nuclear spin-lattice relaxation rate is discussed in detail with particular emphasis on its novel field dependence.
We investigate the dynamics of bound states of two interacting particles, either bosons or fermions, performing a continuous-time quantum walk on a one-dimensional lattice. We consider the situation where the distance between both particles has a hard bound, and the richer situation where the particles are bound by a smooth confining potential. The main emphasis is on the velocity characterizing the ballistic spreading of these bound states, and on the structure of the asymptotic distribution profile of their center-of-mass coordinate. The latter profile generically exhibits many internal fron…
In this work we study fluctuations and dissipation of a string in a deformed anti-de Sitter (AdS) space at finite temperature and density. The deformed AdS space is a charged black hole solution of the Einstein-Maxwell-Dilaton action. In this background we take into account the backreaction on the horizon function from an exponential deformation of the AdS space. From this model we compute the admittance and study the influence of the temperature and the chemical potential on it. We calculate the two-point correlations functions, and the mean square displacement for bosonic and fermionic cases…
By means of full exact diagonalization, we study level statistics and the structure of the eigenvectors of one-dimensional gapless bosonic and fermionic systems across the transition from integrability to quantum chaos. These systems are integrable in the presence of only nearest-neighbor terms, whereas the addition of next-nearest neighbor hopping and interaction may lead to the onset of chaos. We show that the strength of the next-nearest neighbor terms required to observe clear signatures of nonintegrability is inversely proportional to the system size. Interestingly, the transition to chao…
We consider a model of quantum-wire junctions where the latter are described by conformal-invariant boundary conditions of the simplest type in the multicomponent compactified massless scalar free field theory representing the bosonized Luttinger liquids in the bulk of wires. The boundary conditions result in the scattering of charges across the junction with nontrivial reflection and transmission amplitudes. The equilibrium state of such a system, corresponding to inverse temperature $β$ and electric potential $V$, is explicitly constructed both for finite and for semi-infinite wires. In the …
