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We study a mixture of a repulsive dipolar condensate and a degenerate Fermi gas in a quasi-one-dimensional geometry. We demonstrate that the presence of fermions, which attract bosons, drastically changes the behavior of the dipolar condensate. For strong enough boson-fermion attraction, a dipolar Bose-Fermi droplet appears in the mixture, and as the attraction becomes stronger, a roton excitation develops in the Bogoliubov spectrum, leading to the formation of a supersolid, and eventually a crystal of isolated droplets. We describe the system by coupled extended Gross-Pitaevskii (bosons) and Hartree-Fock (fermions) equations. We study the excitation spectrum of the system and identify a number of Goldstone and Higgs modes in the supersolid regime., Comment: 10 pages, 11 figures

We present a theoretical analysis of phase separations between two repulsively interacting components in an ultracold fermionic gas, occurring at the dimensional crossover in a harmonic trap with varying aspect ratios. A tailored kinetic energy functional is derived and combined with a density-potential functional approach to develop a framework that is benchmarked with the orbital-based method. We investigate the changes in the density profile of the phase-separated gas under different interaction strengths and geometries. The analysis reveals the existence of small, partially polarized domains in certain parameter regimes, which is similar to the purely two-dimensional limit. However, the density profile is further enriched by a shell structure found in anisotropic traps. We also track the transitions that can be driven by either a change in interaction strength or trap geometry. The developed framework is noted to have applications for other systems with repulsive interactions that combine continuous and discrete degrees of freedom., Comment: 15 pages, 5 figures

We investigate electromagnetic and gravitational radiation generated during a process of the tidal stripping of a white dwarf star circulating a black hole. We model a white dwarf star by a Bose-Fermi droplet at zero temperature and use the quantum hydrodynamic equations to simulate evolution of a black hole-white dwarf binary system. While going through the periastron, the white dwarf looses a small fraction of its mass. The mass falling onto a black hole is a source of powerful electromagnetic and gravitational radiation. Bursts of ultraluminous radiation are flared at each periastron passage. This resembles the recurrent flaring of X-ray sources discovered recently by Irwin et al.. Gravitational energy bursts occur mainly through emission at very low frequencies. The accretion disc, formed due to stripping of a white dwarf, starts at some point to contribute continuously to radiation of both electromagnetic and gravitational type., Comment: 9 pages, 5 figures. Just minor text corrections to avoid text overlap with our previous article arXiv:1907.12419. Submitted to Phys. Rev. D

We develop a model of a binary fermionic mixture, consisting of large number of atoms, applicable at nonzero temperatures, in the normal phase. We use this approach to study dynamics of degenerate Fermi systems under various perturbations. For example, we analyze spin-dipole oscillations of a two-component fermionic mixture, demonstrating that the ferromagnetic phase shows up at stronger repulsion between components while the temperature raises. We study as well the radial oscillations of weakly interacting repulsive Fermi gases. We obtain a good agreement with experimental data when available. Otherwise, we compare our results with the outcome of the Hartree-Fock orbital calculations done for the system with small number of fermions., Comment: 7 pages, 3 figures, extended discussion

We predict the phase separations of two-dimensional Fermi gases with repulsive contact-type interactions between two spin components. Using density-potential functional theory with systematic semiclassical approximations, we address the long-standing problem of itinerant ferromagnetism in realistic settings. We reveal a universal transition from the paramagnetic state at small repulsive interactions towards ferromagnetic density profiles at large interaction strengths, with intricate particle-number dependent phases in between. Building on quantum Monte Carlo results for uniform systems, we benchmark our simulations against Hartree-Fock calculations for a small number of trapped fermions. We thereby demonstrate that our employed corrections to the mean-field interaction energy and especially to the Thomas-Fermi kinetic energy functional are necessary for reliably predicting properties of trapped mesoscopic Fermi gases. The density patterns of the ground state survive at low finite temperatures and confirm the Stoner-type polarization behavior across a universal interaction parameter, albeit with substantial quantitative differences that originate in the trapping potential and the quantum-corrected kinetic energy. We also uncover a zoo of metastable configurations that are energetically comparable to the ground-state density profiles and are thus likely to be observed in experiments. We argue that our density-functional approach can be easily applied to interacting multi-component Fermi gases in general., Comment: 23 pages, 8 figures

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., Comment: 6 pages, 5 figures

By analyzing breathing mode of a Bose-Einstein condensate repulsively interacting with a polarized fermionic cloud, we further the understanding of a Bose-Fermi mixture recently realized by Lous et al. [\textit{Phys. Rev. Lett.} \textbf{120}, 243403]. We show that a hydrodynamic description of a domain wall between bosonic and fermionic atoms reproduces experimental data of Huang et al. [\textit{Phys. Rev. A} \textbf{99}, 041602(R)]. Two different types of interaction renormalization are explored, based on lowest order constrained variational and perturbation techniques. In order to replicate nonmonotonic behavior of the oscillation frequency observed in the experiment, temperature effects have to be included. We find that the frequency down-shift is caused by the fermion-induced compression and rethermalization of the bosonic species as the system is quenched into the strongly interacting regime., Comment: 7 pages + Supplemental Materials

We study spin-dipole oscillations of a binary fermionic mixture at nonzero temperatures. We apply the atomic-orbital method combined with the Monte Carlo technique based sampling to probe finite temperatures. Our results agree quantitatively with recent experiment, G. Valtolina et al., Nat. Phys. 13, 704 (2017), showing the appearance of the ferromagnetic phase at stronger repulsion between components when the temperature is increased., Comment: 5 pages, 4 figures

We calculate frequencies of collective oscillations of two-component Fermi gas that is kept on the repulsive branch of its energy spectrum. Not only is a paramagnetic phase explored, but also a ferromagnetically separated one. Both in-, and out-of-phase perturbations are investigated, showing contributions from various gas excitations. Additionally, we compare results coming from both time-dependent Hartree-Fock and density-functional approaches., Comment: 16 pages, 4 figures, Resubmission to SciPost

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., Comment: 14 pages, 7 figures. Corresponding author -> MN email: m.nikolajuk@uwb.edu.pl; Printed in Scientific Reports

We report a formation of sharp, solitonlike structures in an experimentally accessible ultracold Fermi gas, as a quantum carpet solution is analyzed in a many body system. The effect is perfectly coherent in a noninteracting gas, but in the presence of repulsive interaction in a two-component system, the structures vanish at a finite time. As they disappear, the system enters a dynamical equilibrium, in which kinetic energies of atoms tend to the same average value. The coherence is revived in a strong interaction regime, with the onset of phase separation, and with a double quantum carpet appearing., Comment: 12 pages, 8 figures

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., Comment: Modified analysis in 2D and new results in 1D; 5 pages, 6 figures

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., Comment: Resubmission to SciPost

We study a binary spin-mixture of a zero-temperature repulsively interacting $^6$Li atoms using both the atomic-orbital and the density functional approaches. The gas is initially prepared in a configuration of two magnetic domains and we determine the frequency of the spin-dipole oscillations which are emerging after the repulsive barrier, initially separating the domains, is removed. We find, in agreement with recent experiment (G. Valtolina et al., arXiv:1605.07850 (2016)), the occurrence of a ferromagnetic instability in an atomic gas while the interaction strength between different spin states is increased, after which the system becomes ferromagnetic. The ferromagnetic instability is preceded by the softening of the spin-dipole mode., Comment: 5 pages, 2 figures

We numerically analyze the impact of a single Rydberg electron onto a Bose-Einstein condensate. Both $S-$ and $D-$ Rydberg states are studied. The radial size of $S-$ and $D-$states are comparable, hence the only difference is due to the angular dependence of the wavefunctions. We find the atom losses in the condensate after the excitation of a sequence of Rydberg atoms. Additionally, we investigate the mechanical effect in which the Rydberg atoms force the condensate to oscillate. Our numerical analysis is based on the classical fields approximation. Finally, we compare numerical results to experimental data., Comment: 6 pages, 4 figures, 4 tables

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., Comment: 21 pages, 7 figures

We show that the momentum distribution of a nonlinear matter wave suddenly released with a finite velocity in a speckle potential converges, after an out-of-equilibrium evolution, to a universal Rayleigh-Jeans thermal distribution. By exploring the complete phase diagram of the equilibrated wave, we discover that for low but nonzero values of the disorder strength, a large-scale structure -a condensate- appears in the equilibrium distribution., Comment: 5 pages, 3 figures. Supplementary material added

The quantum mechanical states of electrons in atoms and molecules are distinct orbitals, which are fundamental for our understanding of atoms, molecules and solids. Electronic orbitals determine a wide range of basic atomic properties, allowing also for the explanation of many chemical processes. Here, we propose a novel technique to optically image the shape of electron orbitals of neutral atoms using electron-phonon coupling in a Bose-Einstein condensate. To validate our model we carefully analyze the impact of a single Rydberg electron onto a condensate and compare the results to experimental data. Our scheme requires only well-established experimental techniques that are readily available and allows for the direct capture of textbook-like spatial images of single electronic orbitals in a single shot experiment., Comment: New J. Phys., accepted

We study experimentally and numerically the quasi-bidimensional transport of a $^{87}$Rb Bose-Einstein condensate launched with a velocity $v_0$ inside a disordered optical potential created by a speckle pattern. A time-of-flight analysis reveals a pronounced enhanced density peak in the backscattering direction $-v_0$, a feature reminiscent of coherent backscattering. Detailed numerical simulations indicate however that other effects also contribute to this enhancement, including a "backscattering echo" due to the position-momentum correlations of the initial wave packet., Comment: 5 pages, 4 figures

Using analytical and numerical methods, it is shown that the momentum distribution of a matter wave packet launched in a random potential exhibits a pronounced coherent backscattering (CBS) peak. By analyzing the momentum distribution, key transport times can be directly measured. The CBS peak can be used to prove that transport occurs in the phase-coherent regime, and measuring its time dependence permits monitoring the transition from classical diffusion to Anderson localization., Comment: 4 pages, 4 figures

We consider a simple experimental setup, based on a harmonic confinement, where a Bose-Einstein condensate and a thermal cloud of weakly interacting alkali atoms are trapped in two different vessels connected by a narrow channel. Using the classical field approximation, as described in J. Phys. B 40, R1 (2007) and optimized in Phys. Rev. A 81, 013629 (2010) for an arbitrary trapping potential, we theoretically investigate the analog of the celebrated superfluid helium fountain effect. We show that this thermo-mechanical effect might indeed be observed in this system. By analyzing the dynamics of the system, we are able to identify the superfluid and normal components of the flow as well as to distinguish the condensate fraction from the superfluid component. We show that the superfluid component can easily flow from the colder vessel to the hotter one while the normal component is practically blocked in the latter., Comment: 13 pages, 11 figures, 3 tables

We optimize the classical field approximation of the version described in J. Phys. B 40, R1 (2007) for the oscillations of a Bose gas trapped in a harmonic potential at nonzero temperatures, as experimentally investigated by Jin et al. [Phys. Rev. Lett. 78, 764 (1997)]. Similarly to experiment, the system response to external perturbations strongly depends on the initial temperature and on the symmetry of perturbation. While for lower temperatures the thermal cloud follows the condensed part, for higher temperatures the thermal atoms oscillate rather with their natural frequency, whereas the condensate exhibits a frequency shift toward the thermal cloud frequency (m=0 mode), or in the opposite direction (m=2 mode). In the latter case, for temperatures approaching critical, we find that the condensate begins to oscillate with the frequency of the thermal atoms, as in the m=0 mode. A broad range of frequencies of the perturbing potential is considered., Comment: 10 pages, 9 figures, added references, changed content, improved English

We study the instability of multiply charged vortices in the presence of thermal atoms and find various scenarios of splitting of such vortices. The onset of the decay of a vortex is always preceded by the increase of a number of thermal (uncondensed) atoms in the system and manifests itself by the sudden rise of the amplitude of the oscillations of the quadrupole moment. Our calculations show that the decay time gets shorter when the multiplicity of a vortex becomes higher., Comment: 4 pages, 6 figures

We consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases confined in a three-dimensional elongated harmonic trap. The Bose and Fermi atoms are assumed to effectively attract each other whereas bosonic atoms repel each other. Strong enough attraction between bosonic and fermionic components can change the character of the interaction within the bosonic cloud from repulsive to attractive making thus possible the generation of bright solitons in the mixture. On the other hand, such structures might be in danger due to the collapse phenomenon existing in attractive gases. We show, however, that under some conditions (defined by the strength of the Bose-Fermi components attraction) the structures which neither spread nor collapse can be generated. For elongated enough traps the formation of solitons is possible even at the ``natural'' value of the mutual Bose-Fermi ($^{87}$Rb -$^{40}$K in our case) scattering length., Comment: 6 pages, 6 figures, 1 table

We analyze the ground state of the two--component gas of trapped ultracold fermionic atoms. We neglect the forces between atoms in the same hyperfine state (the same component). For the case when the forces between distinguishable atoms (i.e., atoms in different hyperfine states) are repulsive (positive mutual scattering length), we find the existence of critical interaction strength above which one atomic fraction expels the other from the center of the trap. When atoms from different components attract each other (negative mutual scattering length) the ground state of the system dramatically changes its structure for strong enough attraction -- the Cooper pairs built of atoms in different hyperfine states appear., Comment: 10 pages, 14 figures

We show that the phase imprinting method is capable of generating vortices in a one-component gas of neutral fermionic atoms at zero and finite temperatures. We find qualitative differences in dynamics of vortices in comparision with the case of Bose-Einstein condensate. The results of the imprinting strongly depend on the geometry of the trap, e.g., in asymmetric traps no single vortex state exists. The observations could be considered as a signature of Cooper-pair based superfluidity in a Fermi gas., Comment: 4 pages, 4 figures