The crossover from a BEC (Bose-Einstein condensation) to a BCS (Bardeen-Cooper-Schrieffer) superfluid in dilute gases of ultracold Fermi atoms creates an ideal environment to enrich our knowledge of strongly correlated many-body systems. These experiments are relevant to a wide range of fields from condensed matter to astrophysics. The nature of pairing in strongly interacting Fermi gases can be readily studied, thus aiding our understanding of related problems in high-T_{c} superconductors, whose mechanism is still under debate. These are not well-understood due to the large interaction parameter. Here, we calculate the dynamical properties of a normal, trapped, and strongly correlated Fermi gas, by developing a quantum cluster expansion. In ultra-cold atomic physics one can measure the elementary excitations, using rf or Bragg spectroscopy. Our calculations for the single-particle spectral function agree with the recent measurements, and clearly demonstrate pseudogap pairing in the strongly interacting regime.
We investigate the phase diagram and the BCS-BEC crossover of a homogeneous three-component ultracold Fermi gas with a U(3) invariant attractive interaction. We show that the system at sufficiently low temperatures exhibits population imbalance, as well as fermionic pairing. We describe the crossover in this system, connecting the weakly interacting BCS regime of the partially population-imbalanced fermion pairing state and the BEC limit with three weakly interacting species of molecules, including pairing fluctuations within a t-matrix calculation of the particle self-energies.
We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.
We study the influence of population imbalance on the pairing, spin, and density instabilities of a two component ideal Fermi gas after a sudden quench of interactions near a Feshbach resonance. Over a large region of parameters the pairing instability is dominated by finite momentum pairing, suggesting the possibility of observing FFLO-like states in the unstable initial dynamics. Long-wavelength density instabilities are found on the BCS side of the resonance, and are interpreted as a precursor of the phase separation expected at equilibrium. On the BEC side of the resonance, the pairing ins…
We theoretically investigate magnetic properties of a unitary Fermi gas in a harmonic trap. Including strong pairing fluctuations within the framework of an extended $T$-matrix approximation (ETMA), as well as effects of a trap potential within the local density approximation (LDA), we calculate the local spin susceptibility $χ(T,r)$ above the superfluid phase transition temperature $T_{\rm c}$. We show that the formation of preformed singlet Cooper pairs anomalously suppresses $χ(T,r)$ in the trap center near $T_{\rm c}$. We also point out that, in the unitarity limit, the spin-gap temperatur…
We investigate long-range pairing interactions between ultracold fermionic atoms confined in an optical lattice which are mediated by the coupling to a cavity. In the absence of other perturbations, we find three degenerate pairing symmetries for a two-dimensional square lattice. By tuning a weak local atomic interaction via a Feshbach resonance or by tuning a weak magnetic field, the superfluid system can be driven from a topologically trivial s-wave to topologically ordered, chiral superfluids containing Majorana edge states. Our work points out a novel path towards the creation of exotic su…
The symmetry properties of the Cooper pairing problem for multi-component ultra-cold dipolar molecular systems are investigated. The dipolar anisotropy provides a natural and robust mechanism for both triplet and singlet Cooper pairing to first order in the interaction strength. With a purely dipolar interaction, the triplet $p_z$-like polar pairing is the most dominant. A short-range attractive interaction can enhance the singlet pairing to be nearly degenerate with the triplet pairing. We point out that these two pairing channels can mix by developing a relative phase of $\pm\fracπ{2}$, thus…
We investigate single-particle properties of a strongly interacting ultracold Fermi gas with mass imbalance. Using an extended $T$-matrix theory, we calculate the density of states, as well as the single-particle spectral weight, in the unitarity limit above the superfluid phase transition temperature $T_{\rm c}$. We show that the momentum regions where pairing fluctuations strongly affect single-particle excitations are different between light fermions and heavy fermions, reflecting the difference of the Pauli blocking effects between them. In addition, we obtain different pseudogap phenomena…
We review some recent progresses on the study of ultracold Fermi gases with synthetic spin-orbit coupling. In particular, we focus on the pairing superfluidity in these systems at zero temperature. Recent studies have shown that different forms of spin-orbit coupling in various spatial dimensions can lead to a wealth of novel pairing superfluidity. A common theme of these variations is the emergence of new pairing mechanisms which are direct results of spin-orbit-coupling-modified single-particle dispersion spectra. As different configurations can give rise to single-particle dispersion spectr…
We investigate the specific heat $C_V$ at constant volume and effects of uniaxial anisotropy of a $p$-wave attractive interaction in the normal state of an ultracold Fermi gas. Within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we evaluate this thermodynamic quantity as a function of temperature, in the whole interaction regime. While the uniaxial anisotropy is not crucial for $C_V$ in the weak-coupling regime, $C_V$ is found to be sensitive to the uniaxial anisotropy in the strong-coupling regime. This originates from the population imbalance among $p_i…
We investigate pseudogap phenomena originating from pairing fluctuations in the BCS-BEC crossover regime of a two-dimensional Fermi gas in a harmonic trap. Including pairing fluctuations within a $T$-matrix theory and effects of a trap within the local density approximation, we calculate the local density of states (LDOS) at the superfluid phase transition temperature $T_{\rm c}$. In the weak-coupling regime, we show that the pseudogap already appears in LDOS around the trap center. The spatial region where the pseudogap can be seen in LDOS becomes wider for a strong pairing interaction. We al…
We investigate the superfluid phase transition and single-particle excitations in the BCS (Bareen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas with mass imbalance. In our recent paper [R. Hanai, et. al., Phys. Rev. A 88, 053621 (2013)], we showed that an extended $T$-matrix approximation (ETMA) can overcome the serious problem known in the ordinary (non-self-consistent) $T$-matrix approximation that it unphysically gives double-valued superfluid phase transition temperature $T_{\rm c}$ in the presence of mass imbalance. However, at the same tim…
Motivated by recent experimental advances in ultracold atomic gases placed in cavities, we study the influence of the atom-cavity coupling on the Fermi gases trapped in optical lattices. By adiabatic elimination of the cavity photon field, the atom-cavity coupling gives rise to effective long-range interactions. It results in a variety of two-body scattering processes, during which the atomic pairs can acquire an additional center-of-mass momentum. This reveals the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids in which the atomic pairing momentum is nonzero. By inspecting …
It is found that all the {\em singlet orbital pairing} instabilities are {\em absent} in a class of spin-polarized multi-orbital systems with quadratic band touching, which opens the way for {\em triplet orbital pairing} order. The ground states are found to be {\em non-Abelian} states with p-wave orbital pairing in checkerboard (away from 1/2 filling) and kagome (above 1/3 filling) lattices with {\em isotropic} attractive interaction which can be realized in ultracold multi-orbital optical lattices. The special property of such systems is generalized to more classes of multi-orbital systems, …
In the mixture of ultracold spin-1 atoms of two different species A and B (e.g., $^{23}$Na (A) and $^{87}$Rb (B)), inter-species singlet-pairing process ${\rm A}_{+1}+{\rm B}_{-1}\rightleftharpoons {\rm A}_{-1}+{\rm B}_{+1}$, can be induced by the spin-dependent inter-atomic interaction, where subscript $\pm 1$ denotes the magnetic quantum number. Nevertheless, one cannot isolate this process from other spin-changing processes by tuning the bias real magnetic field. As a result, so far the singlet-pairing process have not been clearly observed in the experiments, and the measurement of the cor…
The Fulde-Ferrell (FF) superfluid phase, in which fermions form finite-momentum Cooper pairings, is well studied in spin-singlet superfluids in past decades. Different from previous works that engineer the FF state in spinful cold atoms, we show that the FF state can emerge in spinless Fermi gases confined in optical lattice associated with nearest-neighbor interactions. The mechanism of the spinless FF state relies on the split Fermi surfaces by tuning the chemistry potential, which naturally gives rise to finite-momentum Cooper pairings. The phase transition is accompanied by changed Chern n…
We investigate the uniform spin susceptibility $χ_{\rm s}$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation, we show that $χ_{\rm s}$ exhibits non-monotonic temperature dependence in the normal state. In particular, $χ_{\rm s}$ is suppressed near the superfluid phase transition temperature $T_{\rm c}$ due to strong pairing fluctuations. To characterize this anomalous behavior, we introduce the spin-gap temperature $T_{\rm s}$ as the temp…
We reveal that the p-wave superfluid can be realized in a mixture of fermionic and F=1 bosonic gases. We derive a general set of the gap equations for gaps in the s- and p-channels. It is found that the spin-spin bose-fermi interactions favor the p-wave pairing and naturally suppress the pairing in the s-channel. The gap equations for the polar phase of p-wave superfluid fermions are numerically solved. It is shown that a pure p-wave superfluid can be observed in a well-controlled environment of atomic physics.
We investigate strong-coupling effects on normal state properties of an ultracold Fermi gas. Within the framework of $T$-matrix approximation in terms of pairing fluctuations, we calculate the single-particle density of states (DOS), as well as the spectral weight, over the entire BCS-BEC crossover region above the superfluid phase transition temperature $T_{\rm c}$. Starting from the weak-coupling BCS regime, we show that the so-called pseudogap develops in DOS above $T_{\rm c}$, which becomes remarkable in the crossover region. The pseudogap structure continuously changes into a fully gapped…
We investigate the photoemission-type spectrum in a cold Fermi gas which was recently measured by JILA group [J. T. Stewart {\it et al}., Nature \textbf{454}, 744 (2008)]. This quantity gives us very useful information about single-particle properties in the BCS-BEC crossover. In this letter, including pairing fluctuations within a $T$-matrix theory, as well as effects of a harmonic trap within the local density approximation, we show that spatially inhomogeneous pairing fluctuations due to the trap potential is an important key to understand the observed spectrum. In the crossover region, whi…
We theoretically investigate strong-coupling properties of an ultracold Fermi gas in the BCS-BEC crossover regime in the non-equilibrium steady state, being coupled with two fermion baths. By developing a non-equilibrium strong-coupling theory based on the combined $T$-matrix approximation with the Keldysh Green's function technique, we show that the chemical potential bias applied by the two baths gives rise to the anomalous enhancement of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing fluctuations (although the system has no spin imbalance), resulting in the re-entrant behavior of the …
We investigate single-particle excitations and strong-coupling effects in a two-dimensional Fermi gas. Including pairing fluctuations within a Gaussian fluctuation theory, we calculate the density of states $ρ(ω)$ near the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature $T_{\rm BKT}$. Near $T_{\rm BKT}$, we show that superfluid fluctuations induce a pseudogap in $ρ(ω)$. The pseudogap structure is very similar to the BCS superfluid density of states, although the superfluid order parameter is absent in the present two-dimensional case. Since a two-dimensional $^{40}$K Fermi gas has…
A model of two 1D ideal Bose gases A and B with strong AB attractions induced by a p-wave AB Feshbach resonance is studied. The model is solved exactly by a Bose-Bose duality mapping, and it is shown that there is no A-component or B-component Bose-Einstein condensation and no AB-pair off-diagonal long-range order (ODLRO), but both AA-pair and BB-pair ODLRO. After generalization by adding even-wave AA and BB repulsion and reducing the strength of the odd-wave AB attraction by Feshbach resonance detuning, a quantum phase transition occurs between a phase with AB contact nodes and one with no su…
We theoretically investigate the response of a two component Fermi gas to vector potentials which couple separately to the two spin components. Such vector potentials may be implemented in ultracold atomic gases using optically dressed states. Our study indicates that light-induced gauge potentials may be used to probe the properies of the interacting ultracold Fermi gas, providing. amongst other things, ways to measure the superfluid density and the strength of pairing.
We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal phase. In the three-dimensional case, it has been shown that the so-called pseudogap phenomena can be well described by a (non-self-consistent) $T$-matrix approximation (TMA). In the two-dimensional case, while this strong coupling theory can explain the pseudogap phenomenon in the strong-coupling regime, it unphysically gives large pseudogap size in the crossover region, as well as in the weak-coupling regime. We show that this difficulty can be overcome when one improve TMA to include higher orde…
We theoretically investigate magnetic properties of a trapped ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation (ETMA), as well as effects of a harmonic trap in the local density approximation (LDA), we calculate the local spin susceptibility $χ_{\rm t}(r,T)$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that pairing fluctuations cause non-monotonic temperature dependence of $χ_{\rm t}(r,T)$. Although this behavior looks similar to the spin-gap phenomenon associated with pairing f…
We investigate strong-coupling corrections to the specific heat $C_V$ in the normal state of an ultracold Fermi gas in the BCS-BEC crossover region. A recent experiment on a $^6$Li unitary Fermi gas [M. J. H. Ku, {\it et. al.}, Science {\bf 335}, 563 (2012)] shows that $C_V$ is remarkably amplified near the superfluid phase transition temperature $T_{\rm c}$, being similar to the well-known $λ$-structure observed in liquid $^4$He. Including pairing fluctuations within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we show that strong pairing fluctuations ar…
Correlation properties in ultracold Fermi gas with negative scattering length and its impact on the three-body recombination is analyzed. We find that Cooper pairing enhances the recombination rate in contrast to the decrease of this rate accompanying Bose-Einstein condensation in a Bose gas. This trend is characteristic for all interval of temperatures T<Tc.
We theoretically investigate strong-coupling properties of an ultracold Fermi gas with an orbital Feshbach resonance (OFR). Including tunable pairing interaction associated with an OFR within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink (NSR), we examine the occupation of the closed channel. We show that, although the importance of the closed channel is characteristic of the system with an OFR, the occupation number of the closed channel is found to actually be very small at the superfluid phase transition temperature $T_{\rm c}$, in the whole BCS (Bardeen…
"Bottom-up" approaches to the many-body physics of fermions have demonstrated recently precise number and site-resolved preparations with tunability of interparticle interactions in single-well, SW, and double-well, DW, nano-scale confinements created by manipulating ultracold fermionic atoms with optical tweezers. These experiments emulate an analogue-simulator mapping onto the requisite microscopic hamiltonian, approaching realization of Feynman's vision of quantum simulators that "will do exactly the same as nature". Here we report on exact benchmark configuration-interaction computational …
We theoretically investigate the shear viscosity $η$ in the BCS-BEC crossover regime of an ultracold Fermi gas with a Feshbach resonance. Within the framework of the strong-coupling self-consistent $T$-matrix approximation, we examine how a strong pairing interaction associated with a Feshbach resonance affects this transport coefficient, in the normal state above the superfluid phase transition temperature $T_{\rm c}$. We show that, while $η$ diverges in both the weak-coupling BCS and strong-coupling BEC limits, it becomes small in the unitary regime. The minimum of $η$ is obtained, not at th…
We investigate superfluid properties of a one-component Fermi gas with a uniaxially anisotropic $p$-wave pairing interaction, $U_x>U_y=U_z$ (where $U_i$ ($i=x,y,z)$ is a $p_i$-wave pairing interaction). This type of interaction is considered to be realized in a $^{40}$K Fermi gas. Including pairing fluctuations within a strong-coupling $T$-matrix theory, we determine the $p_x$-wave superfluid phase transition temperature $T^{p_x}_{\rm c}$, as well as the other phase transition temperature $T_{\rm c}^{p_x+ip_y}$ ($<T_{\rm c}^{p_x}$), below which the superfluid order parameter has the $p_x+ip_y$…
Ultracold two-component Fermi gases with a tunable population imbalance have provided an excellent opportunity for studying the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, which have been of great interest in condensed matter physics. However, the FFLO states have not been observed experimentally in Fermi gases in three dimensions (3D), possibly due to their small phase space volume and extremely low temperature required for an equal-mass Fermi gas. Here we explore possible effects of mass imbalance, mainly in a $^6$Li--$^{40}$K mixture, on the one-plane-wave FFLO phases for a 3D ho…
We investigate the specific heat at constant volume $C_V$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature $T_{\rm c}$. Within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while $C_V(T\gesim T_{\rm c})$ in the unitary regime is remarkably enhanced by {\it metastable} preformed Cooper pairs or pairing fluctuations, it is well described b…
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…
We investigate single-particle properties of a one-component Fermi gas with a tunable p-wave interaction. Including pairing fluctuations associated with this anisotropic interaction within a $T$-matrix theory, we calculate the single-particle density of states, as well as the spectral weight, above the superfluid transition temperature $T_{\rm c}$. Starting from the weak-coupling regime, we show that the so-called pseudogap first develops in these quantities with increasing the interaction strength. However, when the interaction becomes strong to some extent, the pseudogap becomes obscure to e…
We consider finite-momentum pairing of superfluid phase in ultracold Fermi gas with spin-orbit coupling when subjected to an effective Zeeman field. Based on our two body and mean field many body calculations, we show that the Fulde-Ferrell type superfluid dominates in zero and finite temperature phase diagram. We examine the origin and properties of this novel phase systematically.
This paper gives a survey of a diagrammatic approach for fermionic pairing fluctuations, which are relevant to the BCS-BEC crossover realized with ultracold Fermi gases. Emphasis will be given to the physical intuition about the relevant physical processes that can be associated with this approach. Specific results will be presented for thermodynamic and dynamical quantities, where a critical comparison with alternative diagrammatic approaches will also be attempted.
We investigate the pairing physics in a three-component Fermi-Fermi mixture, where a few impurities are immersed in a non-interacting spin-$\frac{1}{2}$ Fermi gas with synthetic spin-orbit coupling (SOC), and interact attractively with one spin species in the Fermi gas. Due to the interplay of SOC and spin-selective interaction, the molecular state intrinsically acquires a non-zero center-of-mass momentum, which results in a new type of Fulde-Ferrell (FF) pairing in spin-orbit coupled Fermi systems. The existence of the Fermi sea can also lead to the competition between FF-like molecular state…
We study the ground-state properties of a two-component fermionic mixture effectively confined in a one-dimensional harmonic trap. We consider scenarios when numbers of particles in components are the same but particles have different masses. We examine whether it is possible to detect signatures of an unconventional pairing between opposite-spin fermions in the presence of attractive interactions. For this purpose, we perform the exact diagonalization of the many-body Hamiltonian and study the two-particle reduced density matrix. In agreement with expectations, we confirm that the many-body g…
We consider bosons in a Hubbard lattice with an SU($\cal N$) pseudospin degree of freedom which is made dynamical via a coherent transfer term. It is shown that, in the basis which diagonalizes the pseudospin coupling, a generic hopping process affects the spin state, similar to a spin-orbit coupling. This results, for the system in the Mott phase, in a ferromagnetic phase with variable quantization axis. In extreme cases, it can even give rise to antiferromagnetic order.
Pairing of mobile charge carriers in doped antiferromagnets plays a key role in the emergence of unconventional superconductivity. In these strongly correlated materials, the pairing mechanism is often assumed to be mediated by magnetic correlations, in contrast to phonon-mediated interactions in conventional superconductors. A precise understanding of the underlying mechanism in real materials is, however, still lacking, and has been driving experimental and theoretical research for the past 40 years. Early theoretical studies established the emergence of binding among dopants in ladder syste…
We analyze how the presence of the bound state on top of strong intercomponent contact repulsion affects the dynamics of a two-component ultracold Fermi gas confined in a one-dimensional harmonic trap. By performing full many-body numerical calculations, we retrieve dynamics of an initially phase separated state that has been utilized to excite the spin-dipole mode in experimental settings. We observe an appearance of pairing correlations at the domain wall, heralding the onset of a molecular faction at the interlayer between the components. We find that such a mechanism can be responsible for…
Physical properties of an ultracold Fermi gas in the temperature-coupling phase diagram can be characterized by the contact intensity C, which enters the pair-correlation function at short distances and describes how the two-body problem merges into its surrounding. We show that the local order established by pairing fluctuations about the critical temperature Tc of the superfluid transition considerably enhances the contact C in a temperature range where pseudogap phenomena are maximal. Our ab initio results for C in a trap compare well with recently available experimental data over a wide co…
Radio frequency spectra of a trapped unitary 6Li gas are reported and analyzed in terms of a theoretical approach that includes both final-state and trap effects. Final-state effects play a crucial role in evidencing two main peaks both above and below the critical temperature Tc as being associated with two distinct phases that reside in different trap regions. These are the pairing-gap and pseudo-gap phases below Tc, which evolve into the pseudo-gap and no-gap phases above Tc. In this way, a long standing puzzle about the interpretation of rf spectra for 6Li in a trap is solved.
We investigate magnetic properties and effects of pairing fluctuations in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Recently, Liu and Hu, and Parish, pointed out that the strong-coupling theory developed by Nozières and Schmitt-Rink (NSR), which has been extensively used to successfully clarify various physical properties of cold Fermi gases, unphysically gives negative spin susceptibility in the BCS-BEC crossover region. The same problem is found to also exist in the ordinary non-self-consistent T-matrix approximation. In …
We investigate magnetic properties of an ultracold Fermi gas with population imbalance. In the presence of population imbalance, the strong-coupling theory developed by Nozieres and Schmitt-Rink (which is frequently referred to as the NSR theory, or Gaussian fluctuation theory) is known to give unphysical results in the BCS-BEC crossover region. We point out that this problem comes from how to treat pseudogap effects originating from pairing fluctuations and many-body corrections to the spin susceptibility. We also clarify how to overcome this problem by including higher order fluctuations bey…
We consider a localized impurity atom that interacts with a cloud of fermions in the paired state. We develop an effective scattering length description of the interaction between an impurity and a fermionic atom using their vacuum scattering length. Treating the pairing of fermions at the mean-field level, we show that the impurity atom acts like a magnetic impurity in the condensed matter context, and leads to the formation of a pair of Shiba bound states inside the superconducting gap. In addition, the impurity atom can lead to the formation of deeply bound states below the Fermi sea.
We present an $\textit{ab initio}$, numerically exact study of attractive fermions in square lattices with Rashba spin-orbit coupling. The ground state of this system is a supersolid, with co-existing charge and superfluid order. The superfluid is composed of both singlet and triplet pairs induced by spin-orbit coupling. We perform large-scale calculations using auxiliary-field quantum Monte Carlo to provide the first full, quantitative description of the charge, spin, and pairing properties of the system. In addition to characterizing the exotic physics, our results will serve as essential hi…
In this paper, we study the effect of population imbalance and its interplay with pairing strength and lattice effect in atomic Fermi gases in a one-dimensional optical lattice. We compute various phase diagrams as the system undergoes BCS-BEC crossover, using the same pairing fluctuation theory as in Part I. We find widespread pseudogap phenomena beyond the BCS regime and intermediate temperature superfluid states for relatively low population imbalances. The Fermi surface topology plays an important role in the behavior of $T_\text{c}$. For large $d$ and/or small $t$, which yield an open Fer…
We investigate strong-coupling properties of a trapped two-dimensional normal Fermi gas. Within the framework of a combined $T$-matrix theory with the local density approximation, we calculate the local density of states, as well as the photoemission spectrum, to see how two-dimensional pairing fluctuations affect these single-particle quantities. In the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region, we show that the local density of states exhibits a dip structure in the trap center, which is more remarkable than the three-dimensional case. This pseudogap p…
We study non-equilibrium dynamics of ultracold two-component Fermi gases in low-dimensional geometries after the interactions are quenched from weakly interacting to strongly interacting regime. We develop a T-matrix formalism that takes into account the interplay between Pauli blocking and tight confinement in low-dimensional geometries. We employ our formalism to study the formation of molecules in quasi-two-dimensional Fermi gases near Feshbach resonance and show that the rate at which molecules form depends strongly on the transverse confinement. Furthermore, Pauli blocking gives rise to a…
We investigate an ultracold Fermi gas at unitarity confined in a periodic box $V=L^3$ using renormalization group (RG) techniques. Within this approach we can quantitatively assess the long range bosonic order parameter fluctuations which dominate finite-size effects. We determine the finite-size and particle-number dependence of universal quantities, such as the Bertsch parameter and the fermion gap. Moreover, we analyze how these universal observables respond to the variation of an external pairing source. Our results indicate that the Bertsch parameter saturates rather quickly to its value …
We investigate properties of spin-imbalanced ultracold Fermi gas in a large range of spin polarizations at low temperatures. We present results of microscopic calculations based on mean-field and density functional theory approaches, with no symmetry constraints. At low polarization values we predict the structure of the system as consisting of several spin-polarized droplets. As the polarization increases, the system self-organizes into a disordered structures similar to liquid crystals, and energetically they can compete with ordered structures such as grid-like domain walls. At higher polar…
