Repulsive Bosons Research Articles

Thermodynamic properties and performance improvements of fractional Otto heat engine with repulsive bosons

This study presents calculations of a multiparticle system within the framework of fractional quantum mechanics. We specifically explore the energy levels of a bosonic system with repulsive interactions confined in a hard-wall box. The impacts of fractional parameters on the system’s thermodynamic properties are meticulously analyzed. Furthermore, utilizing this model, we construct a quantum Otto cycle and discover that the system exhibits Bose–Fermi duality under varying fractional parameters. Intriguingly, the introduction of fractional parameters enables to optimize the performance of the quantum heat engine, edging it closer to the Carnot efficiency.

Sorting of dynamical crystallization from dynamical fermionization: A quantum many-body approach

Dynamical fermionization refers to the phenomenon when the momentum distribution of impenetrable bosons asymptotically reaches that of non interacting fermions on sudden release from the trap. Whereas on sudden change in trap frequency results to Bose-Fermi oscillation which has been experimentally confirmed in the case of the Lieb-Liniger model in the Tonks-Girardeau (TG) regime. Crystallization happens for sufficiently strongly interacting repulsive bosons with dipolar interactions in one spatial dimension. Crystallization resembles fermionization but distinctly different due to long-range interaction. The present work aims to distinguish dynamical crystallization from dynamical fermionization in the expansion and breathing dynamics of N=4 strongly interacting bosons in TG limit. Our results suggest that the N-fold complete splitting in one-body density for dipolar bosons makes a clear signature of crystallization in the Bose-Fermi oscillation. We investigate the many-body dynamics by employing multiconfigurational time-dependent Hartree method for bosons which solve the N-body time-dependent Schrödinger equation numerically exactly.

Virialized profiles and oscillations of self-interacting fuzzy dark matter solitons

We investigate the effect of self-interactions on the shape and oscillations of the solitonic core profile of condensed fuzzy dark matter systems without the backdrop of a halo, revealing universal features in terms of an appropriately scaled interaction strength characterizing the crossover between the weakly and strongly interacting regimes. Our semianalytical results are further confirmed by spherically symmetric simulations of the Gross-Pitaevskii-Poisson equations. Inverting our obtained relations, we highlight a degeneracy that could significantly affect constraints on the boson mass in the presence of repulsive boson self-interactions and propose the simultaneous extraction of static and dynamical solitonic features as a way to uniquely constrain both the boson mass and self-interactions. Published by the American Physical Society 2024

First and Second Sound in Two-Dimensional Bosonic and Fermionic Superfluids

We review our theoretical results of the sound propagation in two-dimensional (2D) systems of ultracold fermionic and bosonic atoms. In the superfluid phase, characterized by the spontaneous symmetry breaking of the U(1) symmetry, there is the coexistence of first and second sound. In the case of weakly-interacting repulsive bosons, we model the recent measurements of the sound velocities of 39K atoms in 2D obtained in the weakly-interacting regime and around the Berezinskii–Kosterlitz–Thouless (BKT) superfluid-to-normal transition temperature. In particular, we perform a quite accurate computation of the superfluid density and show that it is reasonably consistent with the experimental results. For superfluid attractive fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover. In the low-temperature regime, we reproduce the recent measurements of first-sound speed with 6Li atoms. We also predict that there is mixing between sound modes only in the finite-temperature BEC regime.

Artificial atoms from cold bosons in one dimension

We investigate the ground-state properties of weakly repulsive one-dimensional bosons in the presence of an attractive zero-range impurity potential. First, we derive mean-field solutions to the problem on a finite ring for the two asymptotic cases: (i) all bosons are bound to the impurity and (ii) all bosons are in a scattering state. Moreover, we derive the critical line that separates these regimes in the parameter space. In the thermodynamic limit, this critical line determines the maximum number of bosons that can be bound by the impurity potential, forming an artificial atom. Second, we validate the mean-field results using the flow equation approach and the multi-layer multi-configuration time-dependent Hartree method for atomic mixtures. While beyond-mean-field effects destroy long-range order in the Bose gas, the critical boson number is unaffected. Our findings are important for understanding such artificial atoms in low-density Bose gases with static and mobile impurities.

Spontaneous Symmetry Breaking in a Coherently Driven Nanophotonic Bose-Hubbard Dimer.

We report on the first experimental observation of spontaneous mirror symmetry breaking (SSB) in coherently driven-dissipative coupled optical cavities. SSB is observed as the breaking of the spatial or mirror Z_{2} symmetry between two symmetrically pumped and evanescently coupled photonic crystal nanocavities, and manifests itself as random intensity localization in one of the two cavities. We show that, in a system featuring repulsive boson interactions (U>0), the observation of a pure pitchfork bifurcation requires negative photon hopping energies (J<0), which we have realized in our photonic crystal molecule. SSB is observed over a wide range of the two-dimensional parameter space of driving intensity and detuning, where we also find a region that exhibits bistable symmetric behavior. Our results pave the way for the experimental study of limit cycles and deterministic chaos arising from SSB, as well as the study of nonclassical photon correlations close to SSB transitions.

Loop parametric scattering of cavity polaritons

Within the framework of the mean-field approximation, a coherently excited two-dimensional system of weakly repulsive bosons is predicted to show a giant loop scattering when the rotational symmetry is reduced. The considered process combines (i) the parametric decay of the driven condensate into different k-states and (ii) their massive back scattering owing to spontaneous synchronization of several four-wave mixing channels. The hybridization of the direct and inverse scattering processes, which are different and thus do not balance each other, makes the condensate oscillate under constant one-mode excitation. In particular, the amplitude of a polariton condensate excited by a resonant electromagnetic wave in a uniform polygonal GaAs-based microcavity is expected to oscillate in the sub-THz frequency domain.

A bosonic bright soliton in a mixture of repulsive Bose–Einstein condensate and polarized ultracold fermions under the influence of pressure evolution

Repulsive Bose–Einstein condensates, where short-range interaction is included up to the third order by the interaction radius, demonstrate the existence of bright solitons in a narrow interval of parameters. These solitons are studied here for the boson–fermion mixture, where spin-1/2 fermions are considered in the regime of full-spin polarization. The influence of fermions on bosonic bright solitons via the boson–fermion interaction is considered up to the third order by the interaction radius. Fermions themselves are considered within the hydrodynamic model, which includes the kinetic pressure-evolution equation. The interactions between fermions are also considered. The first order by the interaction radius makes a zero contribution to the Euler equation and the kinetic pressure evolution equation for fermions, but the third order by the interaction radius provides nonzero contributions to both equations. The repulsive (attractive) boson–fermion interaction leads to bright (dark) fermionic solitons.

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.

Exact results for persistent currents of two bosons in a ring lattice

We study the ground state of two interacting bosonic particles confined in a ring-shaped lattice potential and subjected to a synthetic magnetic flux. The system is described by the Bose-Hubbard model and solved exactly through a plane-wave Ansatz of the wave function. We obtain energies and correlation functions of the system both for repulsive and attractive interactions. In contrast with the one-dimensional continuous theory described by the Lieb-Liniger model, in the lattice case we prove that the center of mass of the two particles is coupled with its relative coordinate. Distinctive features clearly emerge in the persistent current of the system. While for repulsive bosons the persistent current displays a periodicity given by the standard flux quantum for any interaction strength, in the attractive case the flux quantum becomes fractionalized in a manner that depends on the interaction. We also study the density after the long time expansion of the system which provides an experimentally accessible route to detect persistent currents in cold atom settings. Our results can be used to benchmark approximate schemes for the many-body problem.

Scaling properties of Tan's contact: Embedding pairs and correlation effect in the Tonks-Girardeau limit

We study the Tan's contact of a one dimensional quantum gas of N repulsive identical bosons confined in a harmonic trap at finite temperature. This canonical ensemble framework corresponds to the experimental conditions, the number of particles being fixed for each experimental sequence. We show that, in the strongly interacting regime, the contact rescaled by the contact at the Tonks-Girardeau limit is an universal function of two parameters, the rescaled interaction strength and temperature. This means that all pair and correlation effects in the Tan's contact are embedded in the Tan's contact in the Tonks-Girardeau limit.

Sorting Fermionization from Crystallization in Many-Boson Wavefunctions

Fermionization is what happens to the state of strongly interacting repulsive bosons interacting with contact interactions in one spatial dimension. Crystallization is what happens for sufficiently strongly interacting repulsive bosons with dipolar interactions in one spatial dimension. Crystallization and fermionization resemble each other: in both cases – due to their repulsion – the bosons try to minimize their spatial overlap. We trace these two hallmark phases of strongly correlated one-dimensional bosonic systems by exploring their ground state properties using the one- and two-body density matrix. We solve the N-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) and for fermions (MCTDHF) methods. Using the one- and two-body density, fermionization can be distinguished from crystallization in position space. For N interacting bosons, a splitting into an N-fold pattern in the one-body and two-body density is a unique feature of both, fermionization and crystallization. We demonstrate that this splitting is incomplete for fermionized bosons and restricted by the confinement potential. This incomplete splitting is a consequence of the convergence of the energy in the limit of infinite repulsion and is in agreement with complementary results that we obtain for fermions using MCTDHF. For crystalline bosons, in contrast, the splitting is complete: the interaction energy is capable of overcoming the confinement potential. Our results suggest that the spreading of the density as a function of the dipolar interaction strength diverges as a power law. We describe how to distinguish fermionization from crystallization experimentally from measurements of the one- and two-body density.

Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

We analyze, analytically and numerically, the position, momentum, and in particular the angular-momentum variance of a Bose–Einstein condensate (BEC) trapped in a two-dimensional anisotropic trap for static and dynamic scenarios. Explicitly, we study the ground state of the anisotropic harmonic-interaction model in two spatial dimensions analytically and the out-of-equilibrium dynamics of repulsive bosons in tilted two-dimensional annuli numerically accurately by using the multiconfigurational time-dependent Hartree for bosons method. The differences between the variances at the mean-field level, which are attributed to the shape of the BEC, and the variances at the many-body level, which incorporate depletion, are used to characterize position, momentum, and angular-momentum correlations in the BEC for finite systems and at the limit of an infinite number of particles where the bosons are 100 % condensed. Finally, we also explore inter-connections between the variances.

Two-dimensional Bose polaron using diffusion Monte Carlo method

We investigate the properties of a mobile impurity immersed in a two-dimensional (2D) Bose gas at zero temperature using quantum Monte Carlo (QMC) methods. The repulsive boson–boson and impurity-boson interactions are modeled by hard-disk potentials with positive scattering lengths a and b, respectively, taken to be equal to the scattering lengths. We calculate the polaron energy and effective mass for the density parameter na2 [Formula: see text] 1 and the ratio a/b. We find that at low densities perturbation theory adequately describes the simulation results. As the impurity-boson interaction strength increases, the polaron mass is enhanced. Additionally, we calculate the structural properties of the Bose system, such as the impurity-boson pair-correlation function and the change of the density profile around the impurity.

Ground state of weakly repulsive soft-core bosons on a sphere

We study a system of penetrable bosons embedded in a spherical surface. Under the assumption of weak interaction between the particles, the ground state of the system is, to a good approximation, a pure condensate. We employ thermodynamic arguments to investigate, within a variational ansatz for the single-particle state, the crossover between distinct finite-size "phases" in the parameter space spanned by the sphere radius and the chemical potential. In particular, for radii up to a few interaction ranges we examine the stability of the fluid phase with respect to a number of crystal-like arrangements having the symmetry of a regular or semi-regular polyhedron. We find that, while quantum fluctuations keep the system fluid at low density, upon compression it eventually becomes inhomogeneous, i.e., particles gather together in clusters. As the radius increases, the nature of the high-density aggregate varies and we observe a sequence of transitions between different cluster phases ("solids"), whose underlying rationale is to maximize the coordination number of clusters, while ensuring at the same time the proper distance between each neighboring pair. We argue that, at least within our mean-field description, every cluster phase is supersolid.

Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps

We discuss thermodynamic properties of harmonically trapped imperfect quantum gases. The spatial inhomogeneity of these systems imposes a redefinition of the mean-field interparticle potential energy as compared to the homogeneous case. In our approach, it takes the form , where N is the number of particles, —the harmonic trap frequency, d—system’s dimensionality, and a is a parameter characterizing the interparticle interaction. We provide arguments that this model corresponds to the limiting case of a long-ranged interparticle potential of vanishingly small amplitude. This conclusion is drawn from a computation similar to the well-known Kac scaling procedure, which is presented here in a form adapted to the case of an isotropic harmonic trap. We show that within the model, the imperfect gas of trapped repulsive bosons undergoes the Bose–Einstein condensation provided d > 1. The main result of our analysis is that in d = 1 the gas of attractive imperfect fermions with is thermodynamically equivalent to the gas of repulsive bosons with provided the parameters and fulfill the relation . This result supplements similar recent conclusion about thermodynamic equivalence of two-dimensional (2D) uniform imperfect repulsive Bose and attractive Fermi gases.

Bose-Fermi duality in a quantum Otto heat engine with trapped repulsive bosons

Quantum heat engine with ideal gas has been well studied, yet the role of interaction was seldom explored. We construct a quantum Otto heat engine with N repulsive Bosonic particles in a 1D hard wall box. With the advantage of exact solution using Bethe Ansatz, we obtain not only the exact numerical result of efficiency in all interacting strength c, but also analytical results for strong interaction. We find the efficiency \eta recovers to the one of non-interacting case $\eta_{\mathrm{non}}=1-(L_{1}/L_{2})^{2}$ for strong interaction with asympotic behavior $\eta\sim\eta_{\mathrm{non}}-4(N-1)L_{1}\left(L_{2}-L_{1}\right)/(cL_{2}^{3})$. Here, $L_{1}$ and $L_{2}$ are two trap sizes during the cycle. Such recovery reflects the duality between 1D strongly repulsive Bosons and free Fermion. We observe and explain the appearance of a minimum efficiency at a particular interacting strength c, and study its dependence on the temperature.

Trapping collapse: Infinite number of repulsive bosons trapped by a generic short-range potential

Weak potential wells (or traps) in one and two dimensions, and the potential wells slightly deeper than the critical ones in three dimensions, feature shallow bound states with localization length much larger than the well radii. We address a simple fundamental question of how many repulsively interacting bosons can be localized by such traps. We find that under rather generic conditions, for both weakly and strongly repulsive particles, in two and three dimensions---but not in one-dimension---the potential well will trap infinitely many bosons. For example, even hard-core repulsive interactions do not prevent this ``trapping collapse'' phenomenon from taking place. A quantum system acquires the phenomenon along with the universal (asymptotically exact) classical-field behavior at large distances, allowing generic description by the Gross-Pitaevskii equation. We also discuss the possibility of having a transition between the infinite and finite number of trapped particles when strong repulsive interparticle correlations are increased.

Ground-state phase diagram of the one-dimensional t−J model with pair hopping terms

The $t$-$J$ model is a standard model of strongly correlated electrons, often studied in the context of high-$T_c$ superconductivity. However, most studies of this model neglect three-site terms, which appear at the same order as the superexchange $J$. As these terms correspond to pair-hopping, they are expected to play an important role in the physics of superconductivity when doped sufficiently far from half-filling. In this paper we present a density matrix renormalisation group study of the one-dimensional $t$-$J$ model with the pair hopping terms included. We demonstrate that that these additional terms radically change the one-dimensional ground state phase diagram, extending the superconducting region at low fillings, while at larger fillings, superconductivity is completely suppressed. We explain this effect by introducing a simplified effective model of repulsive hardcore bosons.

Superfluid Boson–Fermion Mixture: Structure Formation and Collective Periodic Motion

Multiple periodic domain formation due to a modulation instability in a boson–fermion mixture superfluid in the unitary regime has been studied. The periodicity of the structure evolves with time. At the early stage of evolution, bosonic domains show the periodic nature, whereas the periodicity in the fermionic (Cooper pair) domains appears at the late stage of evolution. The nature of interatomic interspecies interactions affects the domain formation. In a harmonic trap, the mixture executes an undamped oscillation. The frequency of the oscillation depends on the relative coupling strength between boson–fermion and fermion–fermion. The repulsive boson–fermion interaction reduces the oscillation frequency, whereas the attractive interaction enhances the frequency significantly.