Boson Density Research Articles

Influence of a static electric field on a one-dimensional Bose-Fermi mixture confined in a double-well potential

In this study, we conducted a detailed investigation into the time evolution of the probability density within a 1D double-well potential hosting a Bose-Fermi mixture. This system comprised spinless bosons and spin one-half fermions with weak repulsive contact interactions. Notably, even at very low effective coupling constants, periodic probabilities were observed, indicating correlated tunneling of both bosons and fermions, leading to complete miscibility, which disappears when an external electric field is turned on. The electric field accentuated fermion-fermion interactions due to the Pauli exclusion principle, altering both boson density and interactions and leading to spatial redistribution of particles. These findings underscore the complex interplay between interactions, external fields, and spatial distributions within confined quantum systems. Our exploration of higher interaction strengths revealed conditions under which probability density functions are decoupled. Furthermore, we observed that increased fermion interaction, driven by the electric field, led to higher tunneling frequencies for both species because of the repulsive nature of the boson-fermion interaction. Conversely, increased boson-boson interaction resulted in complete tunneling of both species, especially when boson density was high, leading to effective fermion repulsion. Expanding our analysis to scenarios involving four bosons demonstrated that higher interaction values corresponded to increased oscillation frequencies in tunneling probabilities. Finally, by manipulating interaction parameters and activating the electric field, we achieved complete tunneling of both species, further increasing oscillation frequencies and resulting in intervals characterized by overlapping probability functions.

Gaussian-state Ansatz for the non-equilibrium dynamics of quantum spin lattices

The study of non-equilibrium dynamics is one of the most important challenges of modern quantum many-body physics, in relationship with fundamental questions in quantum statistical mechanics, as well as with the fields of quantum simulation and computing. In this work we propose a Gaussian Ansatz for the study of the nonequilibrium dynamics of quantum spin systems. Within our approach, the quantum spins are mapped onto Holstein-Primakoff bosons, such that a coherent spin state - chosen as the initial state of the dynamics - represents the bosonic vacuum. The state of the system is then postulated to remain a bosonic Gaussian state at all times, an assumption which is exact when the bosonic Hamiltonian is quadratic; and which is justified in the case of a nonlinear Hamiltonian if the boson density remains moderate. We test the accuracy of such an Ansatz in the paradigmatic case of the S=1/2S=1/2 transverse-field Ising model, in one and two dimensions, initialized in a state aligned with the applied field. We show that the Gaussian Ansatz, when applied to the bosonic Hamiltonian with nonlinearities truncated to quartic order, is able to reproduce faithfully the evolution of the state, including its relaxation to the equilibrium regime, for fields larger than the critical field for the paramagnetic-ferromagnetic transition in the ground state. In particular the spatio-temporal pattern of correlations reconstructed via the Gaussian Ansatz reveals the dispersion relation of quasiparticle excitations, exhibiting the softening of the excitation gap upon approaching the critical field. Our results suggest that the Gaussian Ansatz correctly captures the essential effects of nonlinearities in quantum spin dynamics; and that it can be applied to the study of fundamental phenomena such as quantum thermalization and its breakdown.

Polarons and bipolarons in a two-dimensional square lattice

Quasiparticles and their interactions are a key part of our understanding of quantum many-body systems. Quantum simulation experiments with cold atoms have in recent years advanced our understanding of isolated quasiparticles, but so far they have provided limited information regarding their interactions and possible bound states. Here, we show how exploring mobile impurities immersed in a Bose-Einstein condensate (BEC) in a two-dimensional lattice can address this problem. First, the spectral properties of individual impurities are examined, and in addition to the attractive and repulsive polarons known from continuum gases, we identify a new kind of quasiparticle stable for repulsive boson-impurity interactions. The spatial properties of polarons are calculated showing that there is an increased density of bosons at the site of the impurity both for repulsive and attractive interactions. We then derive an effective Schrödinger equation describing two polarons interacting via the exchange of density oscillations in the BEC, which takes into account strong impurity-boson two-body correlations. Using this, we show that the attractive nature of the effective interaction between two polarons combined with the two-dimensionality of the lattice leads to the formation of bound states - i.e. bipolarons. The wave functions of the bipolarons are examined showing that the ground state is symmetric under particle exchange and therefore relevant for bosonic impurities, whereas the first excited state is doubly degenerate and odd under particle exchange making it relevant for fermionic impurities. Our results show that quantum gas microscopy in optical lattices is a promising platform to explore the spatial properties of polarons as well as to finally observe the elusive bipolarons.

Density and pseudo-spin rotons in a bilayer of soft-core bosons

We study the dynamics of a bilayer system of bosons with repulsive soft-core Rydberg-dressed interactions within the mean-field Bogoliubov-de Gennes approximation. We find roton minima in both symmetric and asymmetric collective density modes of the symmetric bilayer. Depending on the density of bosons in each layer and the spacing between two layers, the homogeneous superfluid phase becomes unstable in either (or both) of these two channels, leading to density and pseudo-spin-density wave instabilities in the system. Breaking the symmetry between two layers, either with a finite counterflow or a density imbalance renormalizes the dispersion of collective modes and makes the system more susceptible to density-wave instability.

Excitation Spectrum in an Ensemble of Hubbard Bosons

An approach that makes it possible to correctly derive equations describing the Bose–Einstein condensation and the spectrum of elementary excitations in the ensemble of Hubbard bosons in the strong correlation regime (U gg {text{|}}{{t}_{{fm}}}{text{|}}) has been developed in the atomic representation using the Dyson method with the introduced indefinite metric. The kinematic Dyson interaction caused by the properties of the commutation relations of dynamic variables plays an important role in such a system. An effective Hamiltonian has been obtained using the operator form of perturbation theory at finite U values. It has been shown that the properties of the ensemble of Hubbard bosons have been determined by the kinematic interaction, correlated hopping, and the attraction between Hubbard bosons. Numerical calculations have demonstrated the effect of these interactions on the characteristics of the energy spectrum of excitations of the ensemble of Hubbard bosons and on the dependence of the density of condensate particles on the density of bosons in the system.

Entanglement criteria for the bosonic and fermionic induced ensembles

We introduce the bosonic and fermionic ensembles of density matrices and study their entanglement. In the fermionic case, we show that random bipartite fermionic density matrices have non-positive partial transposition; hence, they are typically entangled. The similar analysis in the bosonic case is more delicate, due to a large positive outlier eigenvalue. We compute the asymptotic ratio between the size of the environment and the size of the system Hilbert space for which random bipartite bosonic density matrices fail the PPT criterion, being thus entangled. We also relate moment computations for tensor-symmetric random matrices to evaluations of the circuit counting and interlace graph polynomials for directed graphs.

Mediated interaction between polarons in a one-dimensional Bose gas

We study a weakly-interacting one-dimensional Bose gas with two impurities coupled locally to the boson density. We derive analytical results for the induced interaction between the impurities at arbitrary coupling and separation $r$. At $r\lesssim \xi$, where $\xi$ denotes the healing length of the Bose gas, the interaction is well described by the mean-field contribution. Its form changes as the coupling is increased, approaching a linear function of $r$ at short distances in the regime of strong coupling. The mean-field contribution decays exponentially at arbitrary coupling for $r\gg\xi$. At such long distances, however, the effect of quantum fluctuations becomes important, giving rise to a long-ranged quantum contribution to the induced interaction. At longest distances it behaves as $1/r^3$, while at strong coupling we find an intermediate distance regime with a slower decay, $1/r$. The quantum contribution in the crossover regime is also calculated. The induced interaction between impurities (i.e., polarons) is attractive and leads to the formation of their bound state, known as bipolaron. We discuss its binding energy.

Density probabilities of a Bose-Fermi mixture in 1D double well potential

We use the two mode approximation for a interacting one-dimensional spinless soft core bosons and one half spin fermions in a double-well potential with a large central barrier. We include all the on-site boson-boson, fermion-fermion and boson-fermion repulsive contact potential represented by delta-function and considered bosonic and fermionic isotopes of ytterbium(Yb) 170 Yb and 171 Yb respectively. By means of this approximation, we find that in the regime λ BF > λ BB give rise to a immiscible phase and in the regime λ BB ≥ λ BF give rise to a miscible phase, that is characterized by a temporal overlap of the bosonic and fermionic probability densities. We also report that due to the Bose-Fermi interaction, the system presents an apparent destruction of the collapse-revival oscillation of boson density probability at least in the ranges investigated.

Functional-renormalization-group approach to strongly coupled Bose-Fermi mixtures in two dimensions

We study theoretically the phase diagram of strongly coupled two-dimensional Bose-Fermi mixtures interacting with attractive short-range potentials as a function of the particle densities. We focus on the limit where the size of the bound state between a boson and a fermion is small compared to the average interboson separation and develop a functional-renormalization-group approach that accounts for the bound-state physics arising from the extended Fr\"ohlich Hamiltonian. By including three-body correlations we are able to reproduce the polaron-to-molecule transition in two-dimensional Fermi gases in the extreme limit of vanishing boson density. We predict frequency- and momentum-resolved spectral functions and study the impact of three-body correlations on quasiparticle properties. At finite boson density, we find that when the bound-state energy exceeds the Fermi energy by a critical value, the fermions and bosons can form a fermionic composite with a well-defined Fermi surface. These composites constitute a Fermi sea of dressed Feshbach molecules in the case of ultracold atoms, while in the case of atomically thin semiconductors a trion liquid emerges. As the boson density is increased further, the effective energy gap of the composites decreases, leading to a transition into a strongly correlated phase where polarons are hybridized with molecular degrees of freedom. We highlight the universal connection between two-dimensional semiconductors and ultracold atoms, and we discuss perspectives for further exploring the rich structure of strongly coupled Bose-Fermi mixtures in these complementary systems.

Gravitational Radius in view of Existence and Uniqueness Theorem

Talking about a black hole, one has in mind the process of unlimited self-compression of gravitating matter with a mass greater than critical. With a mass greater than the critical one, the elasticity of neutron matter cannot withstand gravitational compression. However, compression cannot be unlimited, because with increasing pressure, neutrons turn into some other “more elementary” particles. These can be bosons of the Standard Model of elementary particles. The wave function of the condensate of neutral bosons at zero temperature is a scalar field. If instead of the constraint det gik < 0 we use a weaker condition of regularity (all invariants of the metric tensor gik are finite), then there is a regular static spherically symmetric solution to Klein-Gordon and Einstein equations, claiming to describe the state to which the gravitational collapse leads. With no restriction on total mass. In this solution, the metric component grr changes its sign twice: g rr (r) = 0 at r=rg and r=rh > rg . Between these two gravitational radii the signature of the metric tensor gik is (+, +, -, -). Gravitational radius rg inside the gravitating body ensures regularity in the center. Within the framework of the phenomenological model “λψ4 ”, relying on the existence and uniqueness theorem, the main properties of a collapsed black hole are determined. At r = rg a regular solution to Klein-Gordon and Einstein equations exists, but it is not a unique one. Gravitational radius rg is the branch point at which, among all possible continuous solutions, we have to choose a proper one, corresponding to the problem under consideration. We are interested in solutions that correspond to a finite mass of a black hole. It turns out that the density value of bosons is constant at r < rg. It depends only on the elasticity of a condensate, and does not depend on the total mass. The energy-momentum tensor at r ⩽ rg corresponds to the ultra relativistic equation of state p = ɛ/3. In addition to the discrete spectrum of static solutions with a mass less than the critical one (where grr < 0 does not change sign), there is a continuous spectrum of equilibrium states with grr(r) changing sign twice, and with no restriction on mass. Among the states of continuous spectrum, the maximum possible density of bosons depends on the mass of the condensate and on the rest mass of bosons. The rest energy of massive Standard Model bosons is about 100 GeV. In this case, for the black hole in the center of our Milky Way galaxy, the maximum possible density of particles should not exceed 3 × 1081 cm-3.

Massless charged particles tunneling radiation from a RN-dS horizon and the linear and quadratic GUP

In this paper, we investigate the massless Reissner–Nordstrom de Sitter metric in the context of minimal length scenarios. We prove not only the confinement of the energy density of massless charged particles, both fermions and bosons, but also their ability to tunnel through the cosmological horizon. These massless particles might be interacting with Dirac sea and in this case they will appear outside the cosmological horizon in the context of dS/CFT holography. This result may formulate a fundamental reason for the expansion of the Dirac sea. Therefore, a spacetime Big Crunch may occur.

Distinguishing noisy boson sampling from classical simulations

Giving a convincing experimental evidence of the quantum supremacy over classical simulations is a challenging goal. Noise is considered to be the main problem in such a demonstration, hence it is urgent to understand the effect of noise. Recently found classical algorithms can efficiently approximate, to any small error, the output of boson sampling with finite-amplitude noise. In this work it is shown analytically and confirmed by numerical simulations that one can efficiently distinguish the output distribution of such a noisy boson sampling from the approximations accounting for low-order quantum multiboson interferences, what includes the mentioned classical algorithms. The number of samples required to tell apart the quantum and classical output distributions is strongly affected by the previously unexplored parameter: density of bosons, i.e., the ratio of total number of interfering bosons to number of input ports of interferometer. Such critical dependence is strikingly reminiscent of the quantum-to-classical transition in systems of identical particles, which sets in when the system size scales up while density of particles vanishes.

Superfluidity of non-condensate bosons in Bose–Einstein condensed systems

We present a general theory for superfluidity of non-condensate bosons in Bose–Einstein condensed systems. Considering a system enclosed in a cylindrical vessel rotating about its axis, the superfluid density is determined by analyzing the response of the system to an inertial force field specified by a vector potential in the frame rotating together with the vessel. We derive a general formula for the superfluid density of non-condensate bosons expressed in terms of Green’s functions. It is shown that the superfluidity of non-condensate bosons is caused by the anomalous self-energy describing the pairing correlation between them. The total superfluid density is given by the sum of the condensate density and the superfluid density of non-condensate bosons, reducing to the Landau formula within mean-field approximations neglecting the damping of quasiparticles. We generalize the linear relation between the current and inertial vector potential to satisfy the gauge invariance, introducing the pairing wave function for the superfluid component of non-condensate bosons. We find that the phase of the pairing wave function is twice that of the condensate wave function and the circulation is still quantized in units of 2π∕m even in the presence of the pairing current of non-condensate bosons.

Unified ballistic transport relation for anisotropic dispersions and generalized dimensions

An analytical formula is derived for particle and energy densities of fermions and bosons, and their ballistic momentum and energy currents for anisotropic energy dispersions in generalized dimensions. The formulation considerably simplifies the comparison of the statistical properties and ballistic particle and energy transport currents of electrons, acoustic phonons, and photons in various dimensions in a unified manner. Assorted examples of its utility are discussed, ranging from blackbody radiation to Schottky diodes and ballistic transistors, quantized electrical and thermal conductance, generalized ballistic Seebeck and Peltier coefficients, their Onsager relations, the generalized Wiedemann-Franz law and the robustness of the Lorenz number, and ballistic thermoelectric power factors, all of which are obtained from the single formula. The new formulation predicts a thermoelectric power factor behaviour of 3D Dirac bands which has not been observed yet.

Quantum Monte Carlo study of the hardcore bosons with finite-range interactions in one-dimensional optical lattices

Using Quantum Monte Carlo algorithm, we study the quantum behaviors of the hardcore bosons with finite-range interactions in one-dimensional optical lattices, such finite-range interactions were realized in Rydberg-dressed alkali atoms loaded into optical lattices. With the choice of the hardcore boson density ρ=0.75 and finite-interaction range rc=4, the ground-state of the system is expected to be degenerate due to the cluster formation. With the increase of interaction strength V/t, we find the system switches from the superfluid phase to supersolid phase and finally to CDW phase. The finite temperature effect and the finite size effect are also carefully examined.

Density profile of a semi-infinite one-dimensional Bose gas and bound states of the impurity

We study the effect of the boundary on a system of weakly interacting bosons in one dimension. It strongly influences the boson density which is completely suppressed at the boundary position. Away from it, the density is depleted over the distances on the order of the healing length at the mean-field level. Quantum fluctuations modify the density profile considerably. The local density approaches the average one as an inverse square of the distance from the boundary. We calculate an analytic expression for the density profile at arbitrary separations from the boundary. We then consider the problem of localization of a foreign quantum particle (impurity) in the potential created by the inhomogeneous boson density. At the mean-field level, we find exact results for the energy spectrum of the bound states, the corresponding wave functions, and the condition for interaction-induced localization. The quantum contribution to the boson density gives rise to small corrections of the bound state energy levels. However, it is fundamentally important for the existence of a long-range Casimir-like interaction between the impurity and the boundary.

Relativistic Quantum Information of Anyons

In this paper, a method is developed to investigate the relativistic quantum information of anyons. Anyons are particles with intermediate statistics ranging between Bose-Einstein and Fermi-Dirac statistics, with a parameter $\alpha$ ($0<\alpha<1$) characteristic of this intermediate statistics. A density matrix is also introduced as a combination of the density matrices of bosons and fermions with a continuous parameter, $\alpha$, that represents the behavior of anyons. This density matrix reduces to bosonic and fermionic density matrices in the limits $\alpha\rightarrow 0$ and $\alpha\rightarrow 1$,respectively. We compute entanglement entropy, negativity, and coherency for anyons in non-inertial frames as a function of $\alpha$. We also computed quantum fisher information for these particles. Semions, which are particles with $\alpha = 0.5$, were found to have minimum quantum fisher information with respect to $\alpha$ than those with other values of fractional parameter.

Enhanced visibility of the Fulde-Ferrel-Larkin-Ovchinnikov state in one-dimensional Bose-Fermi mixtures near the immiscibility point

Based on the matrix product states method, we investigate numerically the ground state properties of one-dimensional mixtures of repulsive bosons and spin-imbalanced attractive fermions, the latter being in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, where Cooper pairs condense at a finite momentum $k=k_{FFLO}$. We find that the visibility of such a state is dramatically enhanced as the repulsive Bose-Fermi mixture is brought close to the phase-separation point. In particular, large amplitude self-induced oscillations with wave-vector $2k_{FFLO}$ appear in both the fermion total density and the boson density profiles, leaving sharp fingerprints in the corresponding static structure factors. We show that these features remain well visible in cold atoms systems trapped longitudinally by a smooth flat-bottom potential. Hence bosons can be used to directly reveal the modulated Fermi superfluid in experiments.

Observation of Spin-Spin Fermion-Mediated Interactions between Ultracold Bosons.

Interactions in an ultracold boson-fermion mixture are often manifested by elastic collisions. In a mixture of a condensed Bose gas (BEC) and spin polarized degenerate Fermi gas (DFG), fermions can mediate spin-spin interactions between bosons, leading to an effective long-range magnetic interaction analogous to Ruderman-Kittel-Kasuya-Yosida [Phys. Rev. 96, 99 (1954); Prog. Theor. Phys. 16, 45 (1956); Phys. Rev. 106, 893 (1957)] interaction in solids. We used Ramsey spectroscopy of the hyperfine clock transition in a ^{87}Rb BEC to measure the interaction mediated by a ^{40}K DFG. By controlling the boson density we isolated the effect of mediated interactions from mean-field frequency shifts due to direct collision with fermions. We measured an increase of boson spin-spin interaction by a factor of η=1.45±0.05^{stat}±0.13^{syst} in the presence of the DFG, providing clear evidence of spin-spin fermion mediated interaction. Decoherence in our system was dominated by inhomogeneous boson density shift, which increased significantly in the presence of the DFG, again indicating mediated interactions. We also measured a frequency shift due to boson-fermion interactions in accordance with a scattering length difference of a_{bf_{2}}-a_{bf_{1}}=-5.36±0.44^{stat}±1.43^{syst}a_{0} between the clock-transition states, a first measurement beyond the low-energy elastic approximation [R. Côté, A. Dalgarno, H. Wang, and W. C. Stwalley, Phys. Rev. A 57, R4118 (1998); A. Dalgarno and M. Rudge, Proc. R. Soc. A 286, 519 (1965)] in this mixture. This interaction can be tuned with a future use of a boson-fermion Feshbach resonance.Fermion-mediated interactions can potentially give rise to interesting new magnetic phases and extend the Bose-Hubbard model when the atoms are placed in an optical lattice.

Quantum Monte Carlo study of the superfluid density in quasi-one-dimensional systems of hard-core bosons: Effect of the suppression of phase slippage

We study the superfluid density of hard-core bosons on quasi-one-dimensional lattices using the quantum Monte Carlo method. Because of phase slippage, the superfluid density drops quickly to zero at finite temperatures with increasing the system length $\ell$ and the superfluid transition temperature is zero in one spatial dimension and also in quasi-one dimension in the limit of $\ell\rightarrow\infty$. We calculate the superfluid density of a model where no phase slippage is allowed and show that the superfluid density remains finite at finite temperatures even in the one-dimensional limit. We also discuss how finite superfluid density can be observed in a quasi-one-dimensional system using a torsional oscillator.