arXiv subjects

Mariusz Gajda

Publications and source records attributed to Mariusz Gajda.

At least 37 records · Page 2Linked to original sources

arXiv2021

Modelling quantum aspects of disruption of a white dwarf star by a black hole

We study the final stages of the evolution of a binary system consisted of a black hole and a white dwarf star. We implement the quantum hydrodynamic equations and carry out numerical simulations. As a model of a white dwarf star, we consider a zero temperature droplet of attractively interacting degenerate atomic bosons and spin-polarized atomic fermions. Such mixtures are investigated experimentally nowadays. We find that the white dwarf star is stripped off its mass while passing the periastron. Due to nonlinear effects, the accretion disk originated from the white dwarf becomes fragmented and the onset of a quantum turbulence with giant quantized vortices present in the bosonic component of the accretion disk is observed. The binary system ends its life in a spectacular way, revealing quantum features underlying the white dwarf star's structure. We find a charged mass, falling onto a black hole, could be responsible for recently discovered ultraluminous X-ray bursts. The simulations show that the final passage of a white dwarf near a black hole can cause a gamma-ray burst.

astro-ph.HE↗

arXiv2020

Pauli crystals -- interplay of symmetries

Recently observed Pauli crystals are structures formed by trapped ultracold atoms with the Fermi statistics. Interactions between these atoms are switched off, so their relative positions are determined by joined action of the trapping potential and the Pauli exclusion principle. Numericalmodeling is used in this paper to find the Pauli crystals in a two-dimensional isotropic harmonic trap, three-dimensional harmonic trap, and a two-dimensional square well trap. The Pauli crystals do not have the symmetry of the trap -- the symmetry is broken by the measurement of positions and, in many cases, by the quantum state of atoms in the trap. Furthermore, the Pauli crystals are compared with the Coulomb crystals formed by electrically charged trapped particles. The~structure of the Pauli crystals differs from that of the Coulomb crystals, this provides evidence that the exclusion principle cannot be replaced by a two-body repulsive interaction but rather has to be considered to be a specifically quantum mechanism leading to many-particle correlations.

cond-mat.quant-gas↗

arXiv2020

Revisiting a stability problem of two-component droplets

We study the problem of the stability of a two-component droplet. The standard solution known from the literature is based on a particular form of the mean field energy functional, in particular on distinction of hard mode and soft mode contributions. By imposing the constraint on densities of the two species which minimizes the hard mode energy, the problem is reduced to a stability analysis of a one component system. As opposed to this, we address the issue in full generality. Our analysis is valid for arbitrary forms of energy density. We formulate constraints which correspond to the physically relevant situation of a system which has unconstrained volume and may evaporate particles. For the specific case of a two component Bose-Bose droplet we find approximate analytic solutions and compare them to the standard result. We show that the densities of both components of a stable droplet are limited to a range depending on interaction strength, in contrast to the original unique solution.

cond-mat.quant-gas↗

arXiv2020

Bistability of Bose-Fermi mixtures

We study the properties of the Bose-Fermi mixture from the perspective of reaching a state of a self-bound quantum droplet. The variational analysis shows that the system exhibits bistability. For weak repulsion between bosons, one of the equilibrium states, smaller in size, spherically symmetric, and with negative energy, corresponds to quantum droplet, the other with always positive energy represents the elongated droplet-like state immersed in the sea of a fermionic cloud. For stronger repulsion between bosons the bifurcation is seized and only the former state is left. Now it represents an elongated object which, for strong enough boson-fermion attraction, gets negative energy. It becomes an excited Bose-Fermi droplet when the trap is released, what is demonstrated by solving the quantum hydrodynamics equations for the Bose-Fermi system. To depict our ideas we consider the $^{133}$Cs-$^6$Li mixture under ideal conditions, i.e. we assume no losses.

cond-mat.quant-gas↗

arXiv2019

Quantum Bose-Fermi droplets

We study the stability of a zero temperature mixture of attractively interacting degenerate bosons and spin-polarized fermions in the absence of confinement. We demonstrate that higher order corrections to the standard mean-field energy can lead to a formation of Bose-Fermi liquid droplets -- self-bound systems in three-dimensional space. The stability analysis of the homogeneous case is supported by numerical simulations of finite systems by explicit inclusion of surface effects. We discuss the experimental feasibility of formation of quantum droplets and indicate the main obstacle -- inelastic three-body collisions.

cond-mat.quant-gas↗

arXiv2019

Self-bound Bose-Fermi liquids in lower dimensions

We study weakly interacting mixtures of ultracold atoms composed of bosonic and fermionic species in 2D and 1D. When interactions between particles are appropriately tuned, self-bound quantum liquids can be formed. We show that while formation of these droplets in 2D is due to the higher order correction terms contributing to the total energy and originating in quantum fluctuations, in 1D geometry the quantum fluctuations have a negligible role on formation of the self-bound systems. The leading mean-field interactions are then sufficient for droplet formation in 1D. We analyse stability conditions for 2D and 1D systems and predict values of equilibrium densities of droplets.

cond-mat.quant-gas↗

arXiv2018

Quantum Bose-Bose droplets at a dimensional crossover

We study a liquid quantum droplets in a mixture of two-component Bose-Einstein condensates under a variable confinement introduced along one or two spatial dimensions. Despite the atom-atom scattering has a three-dimensional character, discreetness of the available modes in the reduced dimension(s) strongly influences the zero-point energy -- the Lee-Huang-Yang term. In a weakly interaction limit, it is the leading correction to the mean-field energy at the crossover from three to two dimensions, or from three to one dimension. We analyze the properties of the droplets at the dimensional crossovers, and provide the demanding conditions for accessing quasi-low dimensions. We predict new kinds of droplets which are formed only due to the quantum fluctuations when the mean-field interaction vanishes. Our results pave the way for exploring new states of quantum matter, and are important for experiments with liquid quantum droplets in reduced dimensions.

cond-mat.quant-gas↗

arXiv2017

Experimentally accessible invariants encoded in interparticle correlations of harmonically trapped ultra-cold few-fermion mixtures

System of a two-flavor mixture of ultra-cold fermions confined in a one-dimensional harmonic trap is studied in the frame of the center of mass. We present a numerical method of obtaining energetic spectra in this frame for an arbitrary mass ratio of fermionic species. We identify a specific invariant encoded in many-body correlations which enable one to determine an eigenstate of the Hamiltonian and to label excitations of the center of mass. The tool presented may be particularly useful in experimental analysis of the interparticle interactions which do not affect the center of mass excitations in a harmonic potential.

cond-mat.quant-gas↗

arXiv2017

Unified way for computing dynamics of Bose-Einstein condensates and degenerate Fermi gases

In this work we present a very simple and efficient numerical scheme which can be applied to study the dynamics of bosonic systems like, for instance, spinor Bose-Einstein condensates with nonlocal interactions but equally well works for Fermi gases. The method we use is a modification of well known Split Operator Method (SOM). We carefully examine this algorithm in the case of $F=1$ spinor Bose-Einstein condensate without and with dipolar interactions and for strongly interacting two-component Fermi gas. Our extension of the SOM method has many advantages: it is fast, stable, and keeps constant all the physical constraints (constants of motion) at high level.

cs.CE↗

arXiv2017

On the observability of Pauli crystals

The best known manifestation of the Fermi-Dirac statistics is the Pauli exclusion principle: no two identical fermions can occupy the same one-particle state. This principle enforces high order correlations in systems of many identical fermions and is responsible for a particular geometric arrangement of trapped particles even when all mutual interactions are absent [1]. These geometric structures, called Pauli crystals, are predicted for a system of $N$ identical atoms trapped in a harmonic potential. They emerge as the most frequent configurations in a collection of single-shot pictures of the system. Here we study how fragile Pauli crystals are when realistic experimental limitations are taken into account. The influence of the number of single-shots pictures available to analysis, thermal fluctuations and finite efficiency of detection are considered. The role of these sources of noise on the possibility of experimental observation of Pauli crystals is shown and conditions necessary for the detection of the geometrical arrangements of particles are identified.

cond-mat.quant-gas↗

arXiv2016

Single-shot simulations of dynamics of quantum dark solitons

Eigenstates of Bose particles with repulsive contact interactions in one-dimensional space with periodic boundary conditions can be found with the help of the Bethe ansatz. The type~II excitation spectrum identified by E. H. Lieb, reproduces the dispersion relation of dark solitons in the mean-field approach. The corresponding eigenstates possess translational symmetry which can be broken in measurements of positions of particles. We analyze emergence of single and double solitons in the course of the measurements and investigate dynamics of the system. In the weak interaction limit, the system follows the mean-field prediction for a short period of time. Long time evolution reveals many-body effects that are related to an increasing uncertainty of soliton positions. In the strong interaction regime particles behave like impenetrable bosons. Then, the probability densities in the configuration space become identical to the probabilities of non-interacting fermions but the wave-functions themselves remember the original Bose statistics. Especially, the phase flips that are key signatures of the solitons in the weak interaction limit, can be observed in the time evolution of the strongly interacting bosons.

cond-mat.quant-gas↗

arXiv2016

Single shot imaging of trapped Fermi gas

Recently developed techniques allow for simultaneous measurements of the positions of all ultra cold atoms in a trap with high resolution. Each such single shot experiment detects one element of the quantum ensemble formed by the cloud of atoms. Repeated single shot measurements can be used to determine all correlations between particle positions as opposed to standard measurements that determine particle density or two-particle correlations only. In this paper we discuss the possible outcomes of such single shot measurements in case of cloud of ultra-cold non-interacting Fermi atoms. We show that the Pauli exclusion principle alone leads to correlations between particle positions that originate from unexpected spatial structures formed by the atoms.

cond-mat.quant-gas↗

arXiv2016

Competition between Bose Einstein Condensation and spin dynamics

We study the impact of spin-exchange collisions on the dynamics of Bose-Einstein condensation, by rapidly cooling a chromium multi-component Bose gas. Despite relatively strong spin-dependent interactions, the critical temperature for Bose-Einstein condensation is reached before the spin-degrees of freedom fully thermalize. The increase in density due to Bose-Einstein condensation then triggers spin dynamics, hampering the formation of condensates in spin excited states. Small metastable spinor condensates are nevertheless produced, and manifest strong spin fluctuations.

cond-mat.quant-gas↗

arXiv2016

Diffusion in a system of a few distinguishable fermions in a one-dimensional double-well potential

Dynamical properties of a few ultra-cold fermions confined in a double-well potential is studied. We show that the dynamics, which is governed by single-particle tunnelings for vanishing interactions, is completely different for strong interactions. Depending on the details of the configuration, for sufficiently strong interactions (repulsions or attractions) the particle flow through the barrier can be accelerated or slowed down. This effect cannot be explained with the single-particle picture. It is clarified with direct inspection to the spectrum of the few-body Hamiltonian.

cond-mat.quant-gas↗

arXiv2016

Two-flavor mixture of a few fermions of different mass in a one-dimensional harmonic trap

A system of two species of fermions of different mass confined in a one-dimensional harmonic trap is studied with an exact diagonalization approach. It is shown independently on the number of particles that a mass difference between fermionic species induces a separation in the lighter flavor system. The mechanism of emerging of separated phases is explained phenomenologically and confirmed with the help of a direct inspection of the ground-state of the system. Finally, it is shown that the separation driven by a mass difference, in contrast to the separation induced by a difference of populations, is robust to the interactions with thermal environment.

cond-mat.quant-gas↗

arXiv2015

Density fluctuations in a quasi-one-dimensional Bose gas as observed in free expansion

We study, within a framework of the classical fields approximation, the density correlations of a weakly interacting expanding Bose gas for the whole range of temperatures across the Bose-Einstein condensation threshold. We focus on elongated quasi-one-dimensional systems where there is a huge discrepancy between the existing theory and experimental results (A. Perrin et al., Nature Phys. 8, 195 (2012)). We find that the density correlation function is not reduced for temperatures below the critical one as it is predicted for the ideal gas or for a weakly interacting system within the Bogoliubov approximation. This behavior of the density correlations agrees with the above mentioned experiment with the elongated system. Although the system was much larger then studied here we believe that the behavior of the density correlation function found there is quite generic. Our theoretical studies indicate also large density fluctuations in the trap in the quasicondensate regime where only phase fluctuations were expected. We argue that the enhanced density fluctuations can originate in the presence of interactions in the system, or more precisely in the existence of spontaneous dark solitons in the elongated gas at thermal equilibrium.

cond-mat.quant-gas↗

arXiv2015

Pairing in a system of a few attractive fermions in a harmonic trap

We study a strongly attractive system of a few spin-1/2 fermions confined in a one-dimensional harmonic trap, interacting via two-body contact potential. Performing exact diagonalization of the Hamiltonian we analyze the ground state and the thermal state of the system in terms of one-- and two--particle reduced density matrices. We show how for strong attraction the correlated pairs emerge in the system. We find that the fraction of correlated pairs depends on temperature and we show that this dependence has universal properties analogous to the gap function known from the theory of superconductivity. In contrast to the standard approach based on the variational ansatz and/or perturbation theory, our predictions are exact and are valid also in a strong attraction limit. Our findings contribute to the understanding of strongly correlated few-body systems and can be verified in current experiments on ultra-cold atoms.

cond-mat.quant-gas↗

arXiv2014

Non-standard Hubbard models in optical lattices: a review

Originally, the Hubbard model has been derived for describing the behaviour of strongly-correlated electrons in solids. However, since over a decade now, variations of it are also routinely being implemented with ultracold atoms in optical lattices. We review some of the rich literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighboring sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation on the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, also the effects related to higher Bloch bands become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher $p$-orbitals, as well as models that couple dynamically spin and orbital degrees of freedom. Finally, we review mean-field nonlinear-Schrödinger models of the Salerno type that share with the non-standard Hubbard models the nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of the consideration. We conclude by listing some future open problems.

cond-mat.quant-gas↗