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We present an experimental and theoretical study of the phonon mode in a unitary Fermi gas. Using two-photon Bragg spectroscopy, we measure excitation spectra at a momentum of approximately half the Fermi momentum, both above and below the superfluid critical temperature $T_\mathrm{c}$. Below $T_\mathrm{c}$, the dominant excitation is the Bogoliubov-Anderson (BA) phonon mode, driven by gradients in the phase of the superfluid order parameter. The temperature dependence of the BA phonon is consistent with a theoretical model based on the quasiparticle random phase approximation in which the dominant damping mechanism is via collisions with thermally excited quasiparticles. As the temperature is increased above $T_\mathrm{c}$, the phonon evolves into a strongly damped collisional mode, accompanied by an abrupt increase in spectral width. Our study reveals strong similarities between sound propagation in the unitary Fermi gas and liquid helium., Comment: 6 pages, 3 figures

We consider a one-dimensional two component extended Fermi-Hubbard model with nearest neighbor interactions and mass imbalance between the two species. We study the stability of trimers, various observables for detecting them, and expansion dynamics. We generalize the definition of the trimer gap to include the formation of different types of clusters originating from nearest neighbor interactions. Expansion dynamics reveal rapidly propagating trimers, with speeds exceeding doublon propagation in strongly interacting regime. We present a simple model for understanding this unique feature of the movement of the trimers, and we discuss the potential for experimental realization., Comment: 10 pages, 10 figures

We study the transport, decoherence and dissipation of an impurity interacting with a bath of free fermions in a one-dimensional lattice. Numerical simulations are made with the time-evolving block decimation method. We introduce a mass imbalance between the impurity and bath particles and find that the fastest decoherence occurs for a light impurity in a bath of heavy particles. By contrast, the fastest dissipation of energy occurs when the masses are equal. We present a simple model for decoherence in the heavy bath limit, and a linear density response description of the interaction which predicts maximum dissipation for equal masses., Comment: 12 pages, 15 figures

We study the interplay between population imbalance in a two-component fermionic system and nearest-neighbor interaction using matrix product states method. Our analysis reveals the existence of a new type of Fulde-Ferrell-Larkin-Ovchinnikov phase in the presence of competing interactions. Furthermore, we find distinct evidence for the presence of hidden order in the system. We present an effective model to understand the emergent oscillations in the string correlations due to the imbalance, and show how they can become an efficient tool to investigate systems with imbalance.

We analyse a Bose-Einstein condensate (BEC) mixed with a superfluid two-component Fermi gas in the whole BCS-BEC cross-over. Using a quasiparticle random phase approximation combined with Beliaev theory to describe the Fermi superfluid and the BEC respectively, we show that the single particle and collective excitations of the Fermi gas give rise to an induced interaction between the bosons, which varies strongly with momentum and frequency. It diverges at the sound mode of the Fermi superfluid, resulting in a sharp avoided crossing feature and a corresponding sign change of the interaction energy shift in the excitation spectrum of the BEC. In addition, the excitation of quasiparticles in the Fermi superfluid leads to damping of the excitations in the BEC. Besides studying induced interactions themselves, these prominent effects can be used to systematically probe the strongly interacting Fermi gas., Comment: 6 pages, 6 figures

We simulate a balanced attractively interacting two-component Fermi gas in a one-dimensional lattice perturbed with a moving potential well or barrier. Using the time-evolving block decimation method, we study different velocities of the perturbation and distinguish two velocity regimes based on clear differences in the time evolution of particle densities and the pair correlation function. We show that, in the slow regime, the densities deform as particles are either attracted by the potential well or repelled by the barrier, and a wave front of hole or particle excitations propagates at the maximum group velocity. Simultaneously, the initial pair correlations are broken and coherence over different sites is lost. In contrast, in the fast regime, the densities are not considerably deformed and the pair correlations are preserved., Comment: 5 pages, 5 figures

We study collective excitations of a trapped Fermi gas at finite temperature using the Bogoliubov-deGennes mean-field theory in conjunction with the generalized random phase approximation. The collective excitations are analyzed through the density response of a monopole excitation. We show the appearance of several modes at the normal fluid - superfluid phase transition temperature: Higgs mode-like pairing amplitude modulations, analogues of the second sound in the trapped gas, and an edge mode that is also the strongest mode in the response., Comment: 8 pages, 7 figures

We use the T-matrix approach for studying highly polarized homogeneous Fermi gases in one dimension with repulsive or attractive contact interactions. Using this approach, we compute ground state energies and values for the contact parameter that show excellent agreement with exact and other numerical methods at zero temperature, even in the strongly interacting regime. Furthermore, we derive an exact expression for the value of the contact parameter in one dimension at zero temperature. The model is then extended and used for studying the temperature dependence of ground state energies and the contact parameter., Comment: 4 pages, 4 figures, 4 pages of supplementary material

In this paper we study problems related to parabolic partial differential equations in metric measure spaces equipped with a doubling measure and supporting a Poincare' inequality. We give a definition of parabolic De Giorgi classes and compare this notion with that of parabolic quasiminimizers. The main result, after proving the local boundedness, is a scale and location invariant Harnack inequality for functions belonging to parabolic De Giorgi classes. In particular, the results hold true for parabolic quasiminimizers.

We consider the density response of a trapped two-component Fermi gas. Combining the Bogoliubov-deGennes method with the random phase approximation allows the study of both collective and single particle excitations. Calculating the density response across a wide range of interactions, we observe a crossover from a weakly interacting pair vibration mode to a strongly interacting Goldstone mode. The crossover is associated with a depressed collective mode frequency and an increased damping rate, in agreement with density response experiments performed in strongly interacting atomic gases., Comment: 14 pages, 8 figures

The Hartree energy shift is calculated for a unitary Fermi gas. By including the momentum dependence of the scattering amplitude explicitly, the Hartree energy shift remains finite even at unitarity. Extending the theory also for spin-imbalanced systems allows calculation of polaron properties. The results are in good agreement with more involved theories and experiments., Comment: 31 pages, many figures

We study a three-component superfluid Fermi gas in a spherically symmetric harmonic trap using the Bogoliubov-deGennes method. We predict a coexistence phase in which two pairing field order parameters are simultaneously nonzero, in stark contrast to studies performed for trapped gases using local density approximation. We also discuss the role of atom number conservation in the context of a homogeneous system., Comment: Text revised, added two figures and three references

We present real-space dynamical mean-field theory calculations for attractively interacting fermions in three-dimensional lattices with elongated traps. The critical polarization is found to be 0.8, regardless of the trap elongation. Below the critical polarization, we find unconventional superfluid structures where the polarized superfluid and Fulde-Ferrell-Larkin-Ovchinnikov-type states emerge across the entire core region.

Some thoughts regarding pairing in atomic Fermi gases were considered, meant for starting discussion on the topic., Comment: The draft paper has been withdrawn by the author

We consider spectroscopies of strongly interacting atomic gases, and we propose a model for describing the coupling between quasiparticles and gapless phonon-like modes. Our model explains features in a wide range of different experiments in both fermionic and bosonic atom gases in various spectroscopic methods., Comment: Minor revision. Added 2 pages and 2 figures

We study many-body contributions to the effective interaction between fermions in a three-component Fermi mixture. We find that effective interactions induced by the third component can lead to a phase diagram different from that predicted if interactions with the third component are neglected. As a result, in a confining potential a superfluid shell structure can arise even for equal populations of the components. We also find a critical temperature for the BCS transition in a 6Li mixture which can deviate strongly from the one in a weakly interacting two-component system., Comment: 4 pages, 5 figures

We study Bragg spectroscopy of a strongly interacting Bose-Einstein condensate using time-dependent Hartree-Fock-Bogoliubov theory. We include approximatively the effect of the momentum dependent scattering amplitude which is shown to be the dominant factor in determining the spectrum for large momentum Bragg scattering. The condensation of the Bragg scattered atoms is shown to significantly alter the observed excitation spectrum by creating a novel pairing channel of mobile pairs., Comment: 11 pages, 4 figures

We propose a pairing-based method for cooling an atomic Fermi gas. A three component (labels 1, 2, 3) mixture of Fermions is considered where the components 1 and 2 interact and, for instance, form pairs whereas the component 3 is in the normal state. For cooling, the components 2 and 3 are coupled by an electromagnetic field. Since the quasiparticle distributions in the paired and in the normal states are different, the coupling leads to cooling of the normal state even when initially $T_{paired}\geq T_{normal}$ (notation $T_S\geq T_N$). The cooling efficiency is given by the pairing energy and by the linewidth of the coupling field. No superfluidity is required: any type of pairing, or other phenomenon that produces a suitable spectral density, is sufficient. In principle, the paired state could be cooled as well but this requires $T_N

We consider pairing in a two-component atomic Fermi gas, in a three-dimensional optical lattice, when the components have unequal densities, i.e. the gas is polarized. We show that a superfluid where the translational symmetry is broken by a finite Cooper pair momentum, namely an FFLO-type state, minimizes the Helmholtz free energy of the system. We demonstrate that such a state is clearly visible in the observable momentum distribution of the atoms, and analyze the dependence of the order parameter and the momentum distribution on the filling fraction and the interaction strength., Comment: 18 pages, 17 figures, replaced with published version, also available at http://stacks.iop.org/1367-2630/8/179

Superconductivity and superfluidity of fermions require, within the BCS theory, matching of the Fermi energies of the two interacting Fermion species. Difference in the number densities of the two species leads either to a normal state, to phase separation, or - potentially - to exotic forms of superfluidity such as FFLO-state, Sarma state or breached pair state. We consider ultracold Fermi gases with polarization, i.e. spin-density imbalance. We show that, due to the gases being trapped and isolated from the environment in terms of particle exchange, exotic forms of superfluidity appear as a shell around the BCS-superfluid core of the gas and, for large density imbalance, in the core as well. We obtain these results by describing the effect of the trapping potential by using the Bogoliubov-de Gennes equations. For comparison to experiments, we calculate also the condensate fraction, and show that, in the center of the trap, a polarized superfluid leads to a small dip in the central density difference. We compare the results to those given by local density approximation and find qualitatively different behavior., Comment: Extended and revised, 13 pages, 13 figures

We consider density-imbalanced Fermi gases of atoms in the strongly interacting, i.e. unitarity, regime. The Bogoliubov-deGennes equations for a trapped superfluid are solved. They take into account the finite size of the system, as well as give rise to both phase separation and FFLO type oscillations in the order parameter. We show how radio-frequency spectroscopy reflects the phase separation, and can provide direct evidence of the FFLO-type oscillations via observing the nodes of the order parameter., Comment: Added one reference. Published in PRL

We study the sound velocity in cubic and non-cubic three-dimensional optical lattices. We show how the van Hove singularity of the free Fermi gas is smoothened by interactions and eventually vanishes when interactions are strong enough. For non-cubic lattices, we show that the speed of sound (Bogoliubov-Anderson phonon) shows clear signatures of dimensional crossover both in the 1D and 2D limits., Comment: 16 pages, 9 figures, replaced with the published version

We study RF-spectroscopy of ultracold Fermi gas by going beyond the linear response in the field-matter interaction. Higher order perturbation theory allows virtual processes and energy conservation beyond the single particle level. We formulate an effective higher order theory which agrees quantitatively with experiments on the pairing gap, and is consistent with the absence of the mean-field shift in the spin-flip experiment., Comment: 4 pages, 3 figures. Text revised, new figures

We consider trapped atomic Fermi gases with Feshbach-resonance enhanced interactions in pseudogap and superfluid temperatures. We calculate the spectrum of RF(or laser)-excitations for transitions that transfer atoms out of the superfluid state. The spectrum displays the pairing gap and also the contribution of unpaired atoms, i.e. in-gap excitations. The results support the conclusion that a superfluid, where pairing is a many-body effect, was observed in recent experiments on RF spectroscopy of the pairing gap., Comment: Journal version

We consider atomic Fermi gases where Feshbach resonances can be used to continuously tune the system from weak to strong interaction regime, allowing to scan the whole BCS-BEC crossover. We show how a probing field transferring atoms out of the superfluid can be used to detect the onset of the superfluid transition in the high-$T_c$ and BCS regimes. The number of transferred atoms, as a function of the energy given by the probing field, peaks at the gap energy. The shape of the peak is asymmetric due to the single particle excitation gap. Since the excitation gap includes also a pseudogap contribution, the asymmetry alone is not a signature of superfluidity. Incoherent nature of the non-condensed pairs leads to broadening of the peak. The pseudogap and therefore the broadening decay below the critical temperature, causing a drastic increase in the asymmetry. This provides a signature of the transition., Comment: Revised version, accepted to Phys. Rev. Letters. Figures changed, explanations added

We have fabricated and measured superconducting single-electron transistors with Al leads and Nb islands. At bias voltages below the gap of Nb we observe clear signatures of resonant tunneling of Cooper pairs, and of Coulomb blockade of the subgap currents due to linewidth broadening of the energy levels in the superconducting density of states of Nb. The experimental results are in good agreement with numerical simulations., Comment: 4 pages, 3 figures

Single-electron transistors have been proposed to be used as a read-out device for Cooper pair charge qubits. Here we show that a coupled superconducting transistor at a threshold voltage is much more effective in measuring the state of a qubit than a normal-metal transistor at the same voltage range. The effect of the superconducting gap is to completely block the current through the transistor when the qubit is in the logical state 1, compared to the mere diminishment of the current in the normal-metal case. The time evolution of the system is solved when the measuring device is driven out of equilibrium and the setting is analysed numerically for parameters accessible by lithographic aluminium structures., Comment: 4 pages, 3 figures, submitted to Phys.Rev.Lett., RevTex4