The dynamics of a one-dimensional two-component Fermi gas in the presence of a quasi-periodic optical lattice (OL) is investigated by means of a Density Functional Theory approach. Inspired by the protocol implemented in recent cold-atom experiments, designed to identify the many-body localization transition, we analyze the relaxation of an initially prepared imbalance between the occupation number of odd and of even sites. For quasi-disorder strength beyond the Anderson localization transition, the imbalance survives for long times, indicating the inability of the system to reach local equilibrium. The late time value diminishes for increasing interaction strength. Close to the critical quasi-disorder strength corresponding to the noninteracting (Anderson) transition, the interacting system displays an extremely slow relaxation dynamics, consistent with sub-diffusive behavior. The amplitude of the imbalance fluctuations around its running average is found to decrease with time, and such damping is more effective with increasing interaction strengths. While our study addresses the setup with two equally intense OLs, very similar effects due to interactions have been observed also in recent cold-atom experiments performed in the tight-binding regime, i.e. where one of the two OLs is very deep and the other is much weaker.
We study the attractive and repulsive two-component Fermi gas with spin imbalance in two dimensions. Using a generalized $T$-matrix approximation, we examine the thermodynamic properties of both attractive and repulsive contact interacting Fermi gases. The interaction strength, which is characterized by the bound state energy $E_b=\hbar^2/m a_{2d}^2$ in vacuum, can be adjusted through a Feshbach resonance. We calculate the interaction energy, compressibility and spin susceptibility of the two branches of the Fermi gas. For the repulsive branch, we also find a critical strength of interaction $…
We analyze the dynamics of one-dimensional quantum gases with strongly attractive contact interactions. We specify a class of initial states for which attractive forces effectively act as strongly repulsive ones during the time evolution. Our findings extend the theoretical results on the super-Tonks-Girardeau gas to a highly nonequilibrium dynamics. The novel mechanism is illustrated on the prototypical problem of the domain stability in a two-component Fermi gas. We also discuss nonlocal interactions and analyze universality of the presented results. Moreover, we use our conclusions to argue…
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…
We investigate separations of trapped balanced two-component atomic Fermi gases with repulsive contact interaction. Candidates for ground-state densities are obtained from the imaginary-time evolution of a nonlinear pseudo-Schrödinger equation in three dimensions, rather than from the cumbersome variational equations. With the underlying hydrodynamical approach, gradient corrections to the Thomas-Fermi approximation are conveniently included and are shown to be vital for reliable density profiles. We provide critical repulsion strengths that mark the onset of phase transitions in a harmonic tr…
It was shown [Chin. Phys. Lett. 28, 020503 (2011)] that at zero temperature the ground state of the one-dimensional (1D) $w$-component Fermi gas coincides with that of the spinless Bose gas in the limit $ω\to \infty$. This behaviour was experimentally evidenced through a quasi-1D tightly trapping ultracold ${}^{173}$Yb atoms in the recent paper [Nature Physics 10, 198 (2014)]. However, understanding of low temperature behaviour of the Fermi gases with a repulsive interaction acquires spin-charge separated conformal field theories of an effective Tomonaga-Luttinger liquid and an antiferromagnet…
The ground-state properties of two-component repulsive Fermi gases in two dimensions are investigated by means of fixed-node diffusion Monte Carlo simulations. The energy per particle is determined as a function of the intercomponent interaction strength and of the population imbalance. The regime of universality in terms of the s-wave scattering length is identified by comparing results for hard-disk and for soft-disk potentials. In the large imbalance regime, the equation of state turns out to be well described by a Landau-Pomeranchuk functional for two-dimensional polarons. To fully charact…
Motivated by the recent experiment realizing bidirectional spin-orbit-coupled Bose-Einstein condensates (BEC), we theoretically explore the properties of repulsive fermions in the two-dimensional (2D) optical lattice with such non-Abelian gauge fields. Within the mean-field level, we find a novel phase of topological antiferromagnetic (TAFM) order which incorporates both the non-trivial topology due to spin-flip hopping and spontaneous symmetry breaking (SSB) for the in-plane spin order. We argue that the appearance of such a phase is generic for repulsive fermions in Chern bands achieved thro…
Recent experiments have revitalized the interest in a Fermi gas of ultracold atoms with strong repulsive interactions. In spite of its seeming simplicity, this system exhibits a complex behavior, resulting from the competing action of two distinct instabilities: ferromagnetism, which promotes spin anticorrelations and domain formation; and pairing, that renders the repulsive fermionic atoms unstable towards forming weakly bound bosonic molecules. The breakdown of the homogeneous repulsive Fermi liquid arising from such concurrent mechanisms has been recently observed in real time through pump-…
We consider two-dimensional imperfect attractive Fermi and repulsive Bose gases consisting of spinless point particles whose total interparticle interaction energy is represented by $a N^2/2 V$ with $a=-a_{F}\leq 0$ for fermions, and $a=a_{B}\geq 0$ for bosons. We show that in spite of the attraction the thermodynamics of $d=2$ imperfect Fermi gas remains well defined for $0 \leq a_{F}\leq a_{0}=h^2/2πm$, and is exactly the same as the one of the repulsive imperfect Bose gas with $a_{B}=a_{0}-a_{F}$. In particular, for $a_{F}=a_{0}$ one observes the thermodynamic equivalence of the attractive …
We exploit a time-resolved pump-probe spectroscopic technique to study the out-of-equilibrium dynamics of an ultracold two-component Fermi gas, selectively quenched to strong repulsion along the upper branch of a broad Feshbach resonance. For critical interactions, we find the rapid growth of short-range anti-correlations between repulsive fermions to initially overcome concurrent pairing processes. At longer evolution times, these two competing mechanisms appear to macroscopically coexist in a short-range correlated state of fermions and pairs, unforeseen thus far. Our work provides fundament…
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 be…
Unconventional strongly correlated phases of the repulsive Fermi-Hubbard model, which could be emulated by ultracold vapors loaded in optical lattices, are investigated by means of energy minimizations with quantum number projection before variation and without any assumed order parameter. In a tube-like geometry of optical plaquettes to realize the four-leg ladder Hubbard Hamiltonian, we highlight the intertwining of spin-, charge-, and pair-density waves embedded in a uniform d-wave superfluid background. As the lattice filling increases, this phase emerges from homogenous states exhibiting …
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 $\frac{a}{2} N^2 \, ω^d$, where $N$ is the number of particles, $ω$ - 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 sma…
Repulsive fermions and shell effects on the surface of a sphere
Università di Padova（帕多瓦大学）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova（意大利国家核物理研究所（INFN）帕多瓦分部）；Istituto Nazionale di Ottica (INO) del Consiglio Nazionale delle Ricerche (CNR)（意大利国家研究委员会光学研究所（INO））
Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose-Fermi and Fermi-Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron …
Due to the vast growth of the many-body level density with excitation energy, its smoothed form is of central relevance for spectral and thermodynamic properties of interacting quantum systems. We compute the cumulative of this level density for confined one-dimensional continuous systems with repulsive short-range interactions. We show that the crossover from an ideal Bose gas to the strongly correlated, fermionized gas, i.e., partial fermionization, exhibits universal behavior: Systems with very few up to many particles share the same underlying spectral features. In our derivation we supple…
We investigate the metastable repulsive branch of a mobile impurity coupled to a degenerate Fermi gas via short-range interactions. We show that the quasiparticle lifetime of this repulsive Fermi polaron can be experimentally probed by driving Rabi oscillations between weakly and strongly interacting impurity states. Using a time-dependent variational approach, we find that we can accurately model the impurity Rabi oscillations that were recently measured for repulsive Fermi polarons in both two and three dimensions. Crucially, our theoretical description does not include relaxation processes …
Path-integral analyses originally pioneered in the study of the complex-phase problem afflicting lattice calculations of finite-density quantum chromodynamics are generalized to non-relativistic Fermi gases with repulsive interactions. Using arguments similar to those previously applied to relativistic theories, we show that the analogous problem in nonrelativistic systems manifests itself naturally in Tan's contact as a nontrivial cancellation between terms with varied dependence on extensive thermodynamic quantities. We analyze that case under the assumption of gaussian phase distribution, w…
Multicomponent quantum gases are ideal platforms to study fundamental phenomena arising from the mutual interaction between different constituents. Particularly, due to the repulsive interactions between two species, the system may exhibit a phase separation. We develop a mean-field-based theory for a two-component Bose mixture, which is equivalent to the Hartree-Fock-Bogoliubov approximation, and derive analytical expressions for the phase boundary and miscibility. The majority of existing theories, which are valid only for weakly interacting Bose gases, predict that the phase boundary is det…
Repulsive Bose-Einstein condensate, where the short-range interaction is included up to the third order by the interaction radius, demonstrates existence of a bright soliton in a narrow interval of parameters. This soliton is studied here for the boson-fermion mixture, where spin-1/2 fermions are consider in the regime of full spin polarization. Influence of fermions via the boson-fermion interaction is considered up to the third order by the interaction radius. Fermions themselves are considered by hydrodynamic model including the pressure evolution equation. Interaction between fermions is c…
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.
We study the effective Bloch-wave scattering of a spinless Fermi gas in one-dimensional (1D) optical lattices. By tuning the odd-wave scattering length, we find multiple resonances of Bloch-waves scattering at the bottom (and the top) of the lowest band, beyond which an attractive (and a repulsive) two-body bound state starts to emerge. These resonances exhibit comparable widths in the deep lattice limit, and the finite interaction range plays an essential role in determining their locations. Based on the exact two-body solutions, we construct an effective microscopic model for the low-energy …
Recent LENS experiment on a 3D Fermi gas has reported a negative effective mass ($m^*<0$) of Fermi polarons in the strongly repulsive regime. There naturally arise a question whether the negative $m^*$ is a precursor of the instability towards phase separation (or itinerant ferromagnetism). In this work, we make use of the exact solutions to study the ground state and excitation properties of repulsive Fermi polarons in 1D, which can also exhibit a negative $m^*$ in the super Tonks-Girardeau regime. By analyzing the total spin, quasi-momentum distribution and pair correlations, we conclude tha…
We investigate the zero-temperature ferromagnetic behavior of a two-component repulsive Fermi gas in the presence of a correlated random field that represents an optical speckle pattern. The density is tuned so that the (noninteracting) Fermi energy is close to the mobility edge of the Anderson localization transition. We employ quantum Monte Carlo simulations to determine various ground-state properties, including the equation of state, the magnetic susceptibility, and the energy of an impurity immersed in a polarized Fermi gas (repulsive polaron). In the weakly interacting limit, the magneti…
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 s…
Universal relations are important for understanding strongly interacting Fermi gases, the study of which have been mostly limited to cases with a single scattering channel. Here we discover a series universal relations for strongly interacting Fermi gases with multiple scattering channels. Unlike its counterpart across a single channel wide magnetic Feshbach resonance, a new kind of contact which we call the cross-channel contact naturally appears in this system, this contact is related to varies thermodynamic quantities as well as short range correlation functions.
We study the propagation of dispersive waves in superfluid Fermi gases in the BEC-BCS crossover. Unlike in other superfluid systems, where dispersive waves have already been studied and observed, Fermi gases can exhibit a subsonic dispersion relation for which the dispersive wave pattern appears at the tail of the wave front. We show that this property can be used to distinguish between a subsonic and a supersonic dispersion relation at unitarity.
We derive the phonon damping rate due to the four-phonon Landau-Khalatnikov process in low temperature strongly interacting Fermi gases using quantum hydrodynamics, correcting and extending the original calculation of Landau and Khalatnikov [ZhETF, 19 (1949) 637]. Our predictions can be tested in state-of-the-art experiments with cold atomic gases in the collisionless regime.
