We consider a spin-balanced degenerate gas of spin-1/2 fermions whose dynamics is governed by low-energy $P$-wave interactions, characterized by the scattering volume $a_1$ and effective momentum $r_1$. The energy per particle $\bar{\cal{E}}$ in the many-body system is calculated by resumming the ladder diagrams comprising both particle-particle and hole-hole intermediate states, following the novel advances recently developed by us in Ann.Phys. 437,168741(2022). This allows to obtain a renormalized result for $\bar{\cal{E}}$ within generic cutoff regularization schemes, with $\bar{\cal{E}}$ directly expressed in terms of the scattering parameters $a_1$ and $r_1$, once the cut off is sent to infinity. The whole set of possible values of $a_1$ and $r_1$ is explored for the first time in the literature looking for minima in the energy per particle with $\bar{\cal{E}}$ given as described. They are actually found, but a further inspection reveals that the associated scattering parameters give rise to resonance poles in the complex momentum-plane with positive imaginary part, which is at odds with the Hermiticity of the Hamiltonian. We also determine that these conflictive poles, with a pole-position momentum that is smaller in absolute value than the Fermi momentum of the system, clearly impact the calculation of $\bar{\cal{E}}$. As a result, we conclude that unpolarized spin-1/2 fermionic normal matter interacting in $P$-wave is not stable. We also study three universal parameters around the unitary limit. Finally, the whole set of values for the parameters $a_1$, $r_1$ is characterized according to whether they give rise to unallowed poles and, if so, by attending to their pole positions relative to the Fermi momentum of the system explored.
We calculate the renormalized effective 2-, 3-, and 4-body interactions for N neutral ultracold bosons in the ground state of an isotropic harmonic trap, assuming 2-body interactions modeled with the combination of a zero-range and energy-dependent pseudopotential. We work to third-order in the scattering length a defined at zero collision energy, which is necessary to obtain both the leading-order effective 4-body interaction and consistently include finite-range corrections for realistic 2-body interactions. The leading-order, effective 3- and 4-body interaction energies are U3 = -(0.85576..…
The superfluidity and pairing phenomena in ultracold atomic Fermi gases have been of great interest in recent years, with multiple tunable parameters. Here we study the BCS-BEC crossover behavior of balanced two-component Fermi gases in a one-dimensional optical lattice, which is distinct from the simple three-dimensional (3D) continuum and a fully 3D lattice often found in a condensed matter system. We use a pairing fluctuation theory which includes self-consistent feedback effects at finite temperatures, and find widespread pseudogap phenomena beyond the BCS regime. As a consequence of the l…
Interactions of ultracold atoms with Rashba spin-orbit coupling, currently being studied with simulated (artificial) gauge fields, have nontrivial ultraviolet and infrared behavior. Examining the ultraviolet structure of the Bethe-Salpeter equation, we show that the linear ultraviolet divergence in the bare interaction can be renormalized as usual in terms of low-energy scattering lengths, and that for both bosons and fermions ultraviolet logarithmic divergences are absent. Calculating the leading order effective interaction with full dependence on the spin-orbit coupling strength and the cent…
We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of hopping imbalance. Our analysis is based on dynamical mean-field theory (DMFT) and its real-space generalization at finite temperature. We study the temperature dependence of the transition into the ordered state as a function of the interaction strength and the imbalance parameter in two and three spatial dimensions. We show that below the critical temperature for Néel order mass-imbalanced mixtures also exhibit a charge-density wave, which provides a dir…
We present the complete phase diagram for one-dimensional binary mixtures of bosonic ultracold atomic gases in a harmonic trap. We obtain exact results with direct numerical diagonalization for small number of atoms, which permits us to quantify quantum many-body correlations. The quantum Monte Carlo method is used to calculate energies and density profiles for larger system sizes. We study the system properties for a wide range of interaction parameters. For the extreme values of these parameters, different correlation limits can be identified, where the correlations are either weak or strong…
We study a one-dimensional system of interacting spinless fermions subject to a localized loss, where the interplay of gapless quantum fluctuations and particle interactions leads to an incarnation of the quantum Zeno effect of genuine many-body nature. This model constitutes a non-equilibrium counterpart of the paradigmatic Kane-Fisher potential barrier problem, and it exhibits strong interaction effects due to the gapless nature of the system. As a central result, we show that the loss probability is strongly renormalized near the Fermi momentum as a realization of the quantum Zeno effect, r…
We describe the behavior of a system of fermionic atoms loaded in a bipartite one-dimensional optical lattice that is under the action of an external time-periodic driving force. By using Floquet theory, an effective model with renormalized hopping coefficients is derived. The insulating behavior characterizing the system at half-filling in the absence of driving is dynamically suppressed and for particular values of the driving parameter the system becomes either a standard metal or an unconventional metal with four Fermi points. We use the bosonization technique to investigate the effect of …
We present our experimental setup to produce ultracold strongly correlated fermionic superfluids made of a two-component spin-mixture of $^6$Li atoms. Employing standard cooling techniques, we achieve quantum degeneracy in a single-beam optical dipole trap. Our setup is capable of generating spin-balanced samples at temperatures as low as $T/T_F = 0.1$ containing up to $5 \times 10^4$ atomic pairs. We can access different superfluid regimes by tuning the interparticle interactions close to a broad magnetic Feshbach resonance. In particular, we are able to explore the crossover from the molecul…
We study a balanced two-component system of ultracold fermions in one dimension with attractive interactions and subject to a spin-dependent optical lattice potential of opposite sign for the two components. We find states with different types of modulated pairing order parameters which are conceptually similar to pi-phases discussed for superconductor-ferromagnet heterostructures. Increasing the lattice depth induces sharp transitions between states of different parity. While the origin of the order parameter oscillations is similar to the FFLO phase for paired states with spin imbalance, the…
We investigate single-particle properties of a mass-imbalanced Fermi gas in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. In the presence of mass imbalance, we point out that the ordinary $T$-matrix approximation, which has been extensively used to clarify various BCS-BEC crossover physics in the mass-balanced case, unphysically gives a double-valued solution in terms of the superfluid phase transition temperature $T_{\rm c}$ in the crossover region. To overcome this serious problem, we include higher order strong-coupling corrections beyond the $T$-mat…
We theoretically investigate a supersymmetric collective mode called Goldstino in a Bose-Fermi mixture. The explicit supersymmetry breaking, which is unavoidable in cold atom experiments, is considered. We derive the Gell-Mann--Oakes-Renner (GOR) relation for the Goldstino, which gives the relation between the energy gap at the zero momentum and the explicit breaking term. We also numerically evaluate the gap of Goldstino above the Bose-Einstein condensation temperature within the random phase approximation (RPA). While the gap obtained from the GOR relation coincides with that in the RPA for …
We report on the creation of homogeneous Fermi gases of ultracold atoms in a uniform potential. In the momentum distribution of a spin-polarized gas, we observe the emergence of the Fermi surface and the saturated occupation of one particle per momentum state. This directly confirms Pauli blocking in momentum space. For the spin-balanced unitary Fermi gas, we observe spatially uniform pair condensates. For thermodynamic measurements, we introduce a hybrid potential that is harmonic in one dimension and uniform in the other two. The spatially resolved compressibility reveals the superfluid tran…
Motivated by a recent experiment [Revelle et al. Phys. Rev. Lett. 117, 235301 (2016)] that characterized the one- to three-dimensional crossover in a spin-imbalanced ultracold gas of $^6$Li atoms trapped in a two-dimensional array of tunnel-coupled tubes, we calculate the phase diagram for this system using Hartree-Fock Bogoliubov-de Gennes mean-field theory, and compare the results with experimental data. Mean-field theory predicts fully spin-polarized normal, partially spin-polarized normal, spin-polarized superfluid, and spin-balanced superfluid phases in a homogeneous system. We use the lo…
Properties of the ground state and the spectrum of elementary excitations are investigated for the low density ultracold spinor 3D Bose gas of particles with arbitrary nonzero spin. Gross-Pitaevskii equations are derived. Within the framework of the considering interaction Hamiltonian it is shown that the ground state spin structure and spin part of the chemical potential is determined by the renormalized interaction, being defined by the contribution of the virtual large momenta. The ferromagnetic structure of the ground state, and the equation of the phase, density, and spin dynamics are obt…
Understanding the magnetic response of the normal state of the cuprates is considered a key piece in solving the puzzle of their high-temperature superconductivity. The essential physics of these materials is believed to be captured by the Fermi-Hubbard model, a minimal model that has been realized with cold atoms in optical lattices. Here we report on site-resolved measurements of the Fermi-Hubbard model in a spin-imbalanced atomic gas, allowing us to explore the response of the system to large effective magnetic fields. We observe short-range canted antiferromagnetism at half-filling with st…
Recent realization of well-controlled quantum simulators of the triangular-lattice Fermi-Hubbard model, including the triangular optical lattices loaded with ultracold Fermions and the heterostructures of the transition-metal dichalcogenides, as well as the more advanced techniques to probe them, pave the way for studying frustrated Fermi-Hubbard physics. Here, we theoretically predict asymmetric photoemission and tunneling spectroscopies for a lightly hole-doped and electron-doped triangular Mott antiferromagnet, and reveal two distinct types of magnetic polarons: a \emph{lightly} renormalize…
We investigate a mixture of ultracold fermionic $^{40}$K atoms and weakly bound $^{6}$Li$^{40}$K dimers on the repulsive side of a heteronuclear atomic Feshbach resonance. By radio-frequency spectroscopy we demonstrate that the normally repulsive atom-dimer interaction is turned into a strong attraction. The phenomenon can be understood as a three-body effect in which two heavy $^{40}$K fermions exchange the light $^{6}$Li atom, leading to attraction in odd partial-wave channels (mainly p-wave). Our observations show that mass imbalance in a fermionic system can profoundly change the character…
Motivated by recent experiments in ultracold gases, we focus on the properties of the center of mass coordinate of an interacting one dimensional Fermi gas, displaying several distinct phases. While the variance of the center of mass vanishes in insulating phases such as phase separated and charge density wave phases, it remains finite in the metallic phase, which realizes a Luttinger liquid. By combining numerics with bosonization, we demonstrate that the autocorrelation function of the center of mass coordinate is universal throughout the metallic phase. It exhibits persistent oscillations a…
We explore the interspecies interaction quench dynamics of ultracold spin-polarized few-body mass balanced Fermi-Fermi mixtures confined in a double-well with an emphasis on the beyond Hartree-Fock correlation effects. It is shown that the ground state of particle imbalanced mixtures exhibits a symmetry breaking of the single-particle density for strong interactions in the Hartree-Fock limit, which is altered within the many-body approach. Quenching the interspecies repulsion towards the strongly interacting regime the two species phase separate within the Hartree-Fock approximation while rema…
We study the spin mixing dynamics of ultracold spin-1 atoms in a weak non-uniform magnetic field with field gradient $G$, which can flip the spin from +1 to -1 so that the magnetization $m=ρ_{+}-ρ_{-}$ is not any more a constant. The dynamics of $m_F=0$ Zeeman component $ρ_{0}$, as well as the system magnetization $m$, are illustrated for both ferromagnetic and polar interaction cases in the mean-field theory. We find that the dynamics of system magnetization can be tuned between the Josephson-like oscillation similar to the case of double well, and the interesting self-trapping regimes, i.e. …
Although gauge invariance is a postulate in fundamental theories of nature such as quantum electrodynamics, in quantum-simulation implementations of gauge theories it is compromised by experimental imperfections. In a recent work [Halimeh and Hauke, \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.030503}{Phys. Rev. Lett. \textbf{125}, 030503 (2020)}], it has been shown in finite-size spin-$1/2$ quantum link lattice gauge theories that upon introducing an energy-penalty term of sufficiently large strength $V$, unitary gauge-breaking errors at strength $λ$ are suppressed $\pr…
We show that ultradilute quantum liquids can be formed with ultracold bosonic dipolar atoms in a bilayer geometry. Contrary to previous realizations of ultradilute liquids, there is no need for stabilizing the system with an additional repulsive short-range potential. The advantage of the proposed system is that dipolar interactions on their own are sufficient for creation of a self-bound state and no additional short-range potential is needed for the stabilization. We perform quantum Monte Carlo simulations and find a rich ground-state phase diagram that contains quantum phase transitions bet…
