Fermionic Cloud Research Articles

Fermionic spectral walls in kink collisions

We show that a spectral wall, i.e., an obstacle in the dynamics of a bosonic soliton, which arises due to the transition of a normal mode into the continuum spectrum, exists after coupling the original bosonic model to fermions. This spectral wall can be experienced if the boson or fermion field is in an excited state. Furthermore, while passing through a spectral wall, an incoming kink-fermion bound state can be separated into purely bosonic kink, which continues to move to spatial infinity and a fermionic cloud that spreads in the region before the wall.

Taming Faraday waves in binary fermionic clouds: The effect of Zeeman interaction

This work presents a study of the Faraday instability in a parametrically forced Fermi-Fermi mixture. The condensate is confined in the transversal spatial dimension with a strong parametric confinement potential and in the longitudinal spatial dimension with a weaker potential. The theoretical description is done using the mean-field theory with two amplitude equations that represent each spin state. In order to stabilize the Faraday patterns, a phenomenological damping term is introduced. The influence of the Zeeman interaction is analyzed in detail. In particular, phase diagrams of the existence and stability of the Faraday waves are calculated as a function of the Zeeman interaction, the coupling parameter, and the forcing amplitude. The degree of segregation of the two fields and their synchronization level is also calculated as a function of the Zeeman parameter. In addition, we examine how the pattern wavelength varies as a function of the Zeeman parameter and the forcing frequency.

Anatomy of Z2 fluxes in anyon Fermi liquids and Bose condensates

We study in detail the properties of pi-fluxes embedded in a state with a finite density of anyons that form either a Fermi liquid or a Bose-Einstein condensate. By employing a recently developed exact lattice bosonization in 2D, we demonstrate that such pi-flux remains a fully deconfined quasiparticle with a finite energy cost in a Fermi liquid of emergent fermions coupled to a Z2 gauge field. This pi-flux is accompanied by a screening cloud of fermions, which in the case of a Fermi gas with a parabolic dispersion binds exactly 1/8 of a fermionic hole. In addition there is a long-ranged power-law oscillatory disturbance of the liquid surrounding the pi-flux akin to Friedel oscillations. These results carry over directly to the pi-flux excitations in orthogonal metals. In sharp contrast, when the pi-flux is surrounded by a Bose-Einstein condensate of particles coupled to a Z2 gauge field, it binds a superfluid half-vortex, becoming a marginally confined excitation with a logarithmic energy cost divergence.

Bistability of Bose–Fermi mixtures

We study formation of a Bose–Fermi droplet in realistic experimental setting. We start with a typical experimental arrangement of two atomic species—bosons and fermions in a harmonic axially symmetric confinement. 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 133Cs–6Li mixture under ideal conditions, i.e. we assume no losses.

Breathing Mode of a Bose-Einstein Condensate Immersed in a Fermi Sea.

By analyzing the 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 etal. [Phys. Rev. Lett. 120, 243403 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.243403]. We show that a hydrodynamic description of a domain wall between bosonic and fermionic atoms reproduces the experimental data of Huang etal. [Phys. Rev. A 99, 041602(R) (2019)PLRAAN2469-992610.1103/PhysRevA.99.041602]. 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.

Fermion clouds around z = 0 Lifshitz black holes

In this work, the Dirac equation is studied in the [Formula: see text] Lifshitz black hole ([Formula: see text]LBH) spacetime. The set of equations representing the Dirac equation in the Newman–Penrose (NP) formalism is decoupled into a radial set and an angular set. The separation constant is obtained with the aid of the spin weighted spheroidal harmonics. The radial set of equations, which are independent of mass, is reduced to Zerilli equations (ZEs) with their associated potentials. In the near horizon (NH) region, these equations are solved in terms of the Bessel functions of the first and second kinds arising from the fermionic perturbation on the background geometry. For computing the boxed quasinormal modes (BQNMs) instead of the ordinary quasinormal modes (QNMs), we first impose the purely ingoing wave condition at the event horizon. Then, Dirichlet boundary condition (DBC) and Newmann boundary condition (NBC) are applied in order to get the resonance conditions. For solving the resonance conditions, we follow the Hod’s iteration method. Finally, Maggiore’s method (MM) is employed to derive the entropy/area spectra of the [Formula: see text]LBH which are shown to be equidistant.

Density fluctuations and sub-Poisson distribution in the ultracold Fermi gas of <sup>6</sup>Li

In this paper, we study the spatial noise fluctuations of the density distribution of non-interacting <sup>6</sup>Li ultracold Fermi gases. For ideal ultracold Fermi gases, the Fermi-Dirac statistics governs its quantum distribution. The suppression of density fluctuations at low temperature, due to Pauli exclusion principle, is observed in a large cloud of fermions. To clearly reveal the density noise fluctuations of the ideal Fermi gases, other noises, such as the background noise, imaging laser noise, CCD photon counting noise, are greatly suppressed. The noise fluctuation shows a sub-Poissonian statistics in excess of 10,000 atoms per spin state. The dependence of the spatial atom noise fluctuation on the quantum degeneracy is also investigated by changing the temperature of the degenerated Fermi gases. The Fermi gases with lower temperature exhibit larger suppression of the noise fluctuations. The results may have great applications in measuring the temperature of strongly correlated many-body physics and observing the phase transition of incompressible quantum phases.

Efimov physics in the presence of a Fermi sea

Motivated by recent experiments on $^{6}$Li-$^{133}$Cs atomic mixtures with high mass imbalance, we study the Efimov correlation in atomic system of two heavy bosons ($^{133}$Cs) immersed in a bath of light fermions ($^{6}$Li). Using the Born-Oppenheimer approximation, we identify two different regimes, depending on the Fermi momentum of light fermions ($k_F$) and the boson-fermion scattering length $a_s(<0)$, where the presence of underlying Fermi sea plays distinct roles in the Efimov-type binding of bosons. Namely, in the regime $k_F|a_s|\lesssim 1$ ($k_F|a_s|\gtrsim1$), the Fermi sea induces an attractive (repulsive) effective interaction between bosons and thus favors (disfavors) the formation of bound state, which can be seen as the Efimov trimer dressed by the fermion cloud. Interestingly, this implies a non-monotonic behavior of these bound states as increasing the fermion density (or $k_F$). Moreover, we establish a generalized universal scaling law for the emergence/variation of such dressed Efimov bound states when incorporating a new scale ($k_F$) brought by the Fermi sea. These results can be directly tested in Li-Cs cold atoms experiment by measuring the modified bound state spectrum and the shifted Efimov resonance, which manifest an emergent non-trivial Efimov correlation in a fermionic many-body environment.

Profile of a galactic spherical cloud of self-gravitating fermions

The field which binds a thermal fermionic cloud is defined as a Hartree integral upon its density. In turn, the density results from the field via a Thomas–Fermi occupation of the local phase space. This defines a complete theory of all properties and observables for the cloud. As an application to dark matter halos, comparisons with astronomic data on dwarf spheroidal galaxies are provided and discussed. Estimates of the elementary fermion mass are obtained, serving as a phase-space bound on fermionic dark matter.

Memory effects in a quasiperiodic Fermi lattice

We investigate a system of fermions trapped in a quasi-periodic potential from an open quantum system theory perspective, designing a protocol in which an impurity atom (a two level system) is coupled to a trapped fermionic cloud described by the non-interacting Aubry-Andr\'e model. The Fermi system is prepared in a charge density wave state before it starts its relaxation. In this work we focus our attention on the time evolution of the impurity in such an out of equilibrium environment, and study whether the induced dynamics can be classified as Markovian or non-Markovian. We find how the localised phase of the Aubry-Andr\'{e} model displays evidence of strong and stable memory effects and can be considered as a controllable and robust non-Markovian environment.

Dynamical system modeling fermionic limit

The existence of multiple radial solutions to the elliptic equation modeling fermionic cloud of interacting particles is proved for the limiting Planck constant and intermediate value of mass parameters. It is achieved by considering the related nonautonomous dynamical system for which the passage to the limit can be established due to the continuity of the solutions with respect to the parameter going to zero.

Itinerant ferromagnetism of two-dimensional repulsive fermions with Rabi coupling

We study a two-dimensional fermionic cloud of repulsive alkali-metal atoms characterized by two hyperfine states which are Rabi coupled. Within a variational Hartree–Fock scheme, we calculate analytically the ground-state energy of the system. Then we determine the conditions under which there is a quantum phase transition with spontaneous symmetry breaking from a spin-balanced configuration to a spin-polarized one, an effect known as itinerant ferromagnetism. Interestingly, we find that the transition appears when the interaction energy per particle exceedes both the kinetic energy per particle and the Rabi coupling energy. The itinerant ferromagnetism of the polarized phase is analyzed, obtaining the population imbalance as a function of interaction strength, Rabi coupling, and number density. Finally, the inclusion of a external harmonic confinement is investigated by adopting the local density approximation. We predict that a single atomic cloud can display population imbalance near the center of the trap and a fully balanced configuration at the periphery.

Finite-temperature quantum fluctuations in two-dimensional Fermi superfluids

In two-dimensional systems with a continuous symmetry the Mermin-Wagner-Hohenberg theorem precludes spontaneous symmetry breaking and condensation at finite temperature. The Berezinskii-Kosterlitz-Thouless critical temperature marks the transition from a superfluid phase characterized by quasi-condensation and algebraic long-range order to a normal phase, where vortex proliferation completely destroys superfluidity. As opposed to conventional off-diagonal long-range order typical of three-dimensional superfluid systems, algebraic long-range order is driven by quantum and thermal fluctuations strongly enhanced in reduced dimensionality. Motivated by this unique scenario and by the very recent experimental realization of trapped quasi-two-dimensional fermionic clouds, we include one-loop Gaussian fluctuations in the theoretical description of resonant Fermi superfluids in two dimensions demonstrating that first sound, second sound and also critical temperature are strongly renormalized, away from their mean-field values. In particular, we prove that in the intermediate and strong coupling regimes these quantities are radically different when Gaussian fluctuations are taken into account. Our one-loop theory shows good agreement with very recent experimental data on the Berezinskii-Kosterlitz-Thouless critical temperature [Phys. Rev. Lett. 115, 010401 (2015)] and on the first sound velocity, giving novel predictions for the second sound as a function of interaction strength and temperature, open for experimental verification.

Kohn-Sham theory of a rotating dipolar Fermi gas in two dimensions

A two-dimensional dipolar Fermi gas in harmonic trap under rotation is studied by solving "ab initio" Kohn-Sham equations. The physical parameters used match those of ultracold gas of fermionic $^{23}Na^{40}K$ molecules, a prototype system of strongly interacting dipolar quantum matter, which has been created very recently. We find that, as the critical rotational frequency is approached and the system collapses into the lowest Landau level, an array of tightly packed quantum vortices develops, in spite of the non-superfluid character of the system. In this state the system looses axial symmetry, and the fermionic cloud boundaries assume an almost perfect square shape. At higher values of the filling factor the vortex lattice disappears, while the system still exhibits square-shaped boundaries. At lower values of the filling factor the fermions become instead localized in a "Wigner cluster" structure.

Drag dynamics in one-dimensional Fermi systems

We study drag dynamics of several fermions in a fermion cloud in one-dimensional continuous systems, with particular emphasis on the non-trivial quantum many-body effects in systems whose parameters change gradually in real time. We adopt the Fermi--Hubbard model and the time-dependent density matrix renormalization group method to calculate the drag force on a trapped fermion cluster in a cloud of another fermion species with contact interaction. The simulation result shows that a non-trivial peak in the resistance force is observed in the high cloud density region, which implies a criterion of effective ways in diffusive transport in a fermion cloud. We compare the DMRG simulation result with a mean-field result, and it is suggested that some internal degrees of freedom have a crucial role in the excitation process when the cloud density is high. This work emphasizes the difference between the full-quantum calculation and the semiclassical calculation, which is the quantum effects, in slow dynamics of many-body systems bound in a fermion cloud.

Pair condensation of polarized fermions in the BCS–BEC crossover

We investigate a two-component Fermi gas with unequal spin populations along the BCS–BEC crossover. By using the extended BCS equations and the concept of off-diagonal-long-range-order we derive a formula for the condensate number of Cooper pairs as a function of energy gap, average chemical potential, imbalance chemical potential and temperature. Then we study the zero-temperature condensate fraction of Cooper pairs by varying interaction strength and polarization, finding a depletion of the condensate fraction by increasing the population imbalance. We also consider explicitly the presence of an external harmonic confinement and we study, within the local-density approximation, the phase separation between superfluid (SF) and normal phase regions of the polarized fermionic cloud. In particular, we calculate both condensate density profiles and total density profiles from the inner SF core to the normal region passing for the interface, where a finite jump in the density is a clear manifestation of this phase-separated regime. Finally, we compare our theoretical results with the available experimental data on the condensate fraction of polarized 6Li atoms (Zwierlein et al 2006 Science 311 492). These experimental data are in reasonable agreement with our predictions in a suitable range of polarizations, but only in the BCS side of the crossover up to unitarity.

Universal quantum behavior of interacting fermions in one-dimensional traps: From few particles to the trap thermodynamic limit

We investigate the ground-state properties of trapped fermion systems described by the Hubbard model with an external confining potential. We discuss the universal behaviors of systems in different regimes: from few particles, i.e. in dilute regime, to the trap thermodynamic limit. The asymptotic trap-size (TS) dependence in the dilute regime (increasing the trap size l keeping the particle number N fixed) is described by a universal TS scaling controlled by the dilute fixed point associated with the metal-to-vacuum quantum transition. This scaling behavior is numerically checked by DMRG simulations of the one-dimensional (1D) Hubbard model. In particular, the particle density and its correlations show crossovers among different regimes: for strongly repulsive interactions they approach those of a spinless Fermi gas, for weak interactions those of a free Fermi gas, and for strongly attractive interactions they match those of a gas of hard-core bosonic molecules. The large-N behavior of systems at fixed N/l corresponds to a 1D trap thermodynamic limit. We address issues related to the accuracy of the local density approximation (LDA). We show that the particle density approaches its LDA in the large-l limit. When the trapped system is in the metallic phase, corrections at finite l are O(l^{-1}) and oscillating around the center of the trap. They become significantly larger at the boundary of the fermion cloud, where they get suppressed as O(l^{-1/3}) only. This anomalous behavior arises from the nontrivial scaling at the metal-to-vacuum transition occurring at the boundaries of the fermion cloud.

Emulating Solid-State Physics with a Hybrid System of Ultracold Ions and Atoms

We propose and theoretically investigate a hybrid system composed of a crystal of trapped ions coupled to a cloud of ultracold fermions. The ions form a periodic lattice and induce a band structure in the atoms. This system combines the advantages of high fidelity operations and detection offered by trapped ion systems with ultracold atomic systems. It also features close analogies to natural solid-state systems, as the atomic degrees of freedom couple to phonons of the ion lattice, thereby emulating a solid-state system. Starting from the microscopic many-body Hamiltonian, we derive the low energy Hamiltonian, including the atomic band structure, and give an expression for the atom-phonon coupling. We discuss possible experimental implementations such as a Peierls-like transition into a period-doubled dimerized state.

Component separation of two-component fermion clouds in a spin-dependent external potential by spin-density-functional theory

We investigate the component separation in one-dimensional two-component fermion clouds in a spin-dependent external potential. The density distributions and the state diagram are studied by means of spin-dependent density-functional theory. The component separation between spin-up and spin-down atoms is induced by the interplay of the spin-dependent harmonic confinement and the strong repulsive interaction between the inter-components. We find the existence of a threshold repulsive interaction strength above which the component separation evolves. Different state diagrams are mapped out numerically, from which two regions are distinguished, i.e., the phase-mixed region with both spin-up and spin-down mixtures in the center of the trap and the phase-separated region with only spin-up atoms remaining in the center.

Dynamical arrest of ultracold lattice fermions.

We theoretically investigate the thermodynamics of an interacting inhomogeneous two-component Fermi gas in an optical lattice. Motivated by a recent experiment by L. Hackermüller et al., Science 327, 1621 (2010), we study the effect of the interplay between thermodynamics and strong correlations on the size of the fermionic cloud. We use dynamical mean-field theory to compute the cloud size, which in the experiment shows an anomalous expansion behavior upon increasing attractive interaction. We confirm this qualitative effect but, assuming adiabaticity, we find quantitative agreement only for weak interactions. For strong interactions we observe significant nonequilibrium effects which we attribute to a dynamical arrest of the particles due to increasing correlations.