BCS-BEC crossover in a two-dimensional Fermi gas

Pseudogap Effects in the Strongly Correlated Regime of the Two-Dimensional Fermi Gas

The two-species Fermi gas with attractive short-range interactions in two spatial dimensions provides a paradigmatic system for the understanding of strongly correlated Fermi superfluids in two dimensions. It is known to exhibit a BEC to BCS crossover as a function of ln(k_{F}a), where a is the scattering length, and to undergo a Berezinskii-Kosterlitz-Thouless superfluid transition below a critical temperature T_{c}. However, the extent of a pseudogap regime in the strongly correlated regime of ln(k_{F}a)∼1, in which pairing correlations persist above T_{c}, remains largely unexplored with controlled theoretical methods. Here, we use finite-temperature auxiliary-field quantum Monte Carlo methods on discrete lattices in the canonical ensemble formalism to calculate thermodynamical observables in the strongly correlated regime. We extrapolate to continuous time and the continuum limit to eliminate systematic errors and present results for particle numbers ranging from N=42 to N=162. We estimate T_{c} by a finite-size scaling analysis, and observe clear pseudogap signatures above T_{c} and below a temperature T^{*} in both the spin susceptibility and free-energy gap. We also present results for the contact, a fundamental thermodynamic property of quantum many-body systems with short-range interactions.

Mechanism for sound dissipation in a two-dimensional degenerate Fermi gas

We numerically study the transport properties of a two-dimensional Fermi gas in a weakly and strongly interacting regimes, in the range of temperatures close to the transition to a superfluid phase. For that we excite sound waves in a fermionic mixture by using the phase imprinting technique, follow their evolution, and finally determine both their speed and attenuation. Our formalism, originated from a density-functional theory, incorporates thermal fluctuations via the grand canonical ensemble description and with the help of Metropolis algoritm. From numerical simulations we extract temperature dependence of the sound velocity and diffusivity as well as the dependence on the interaction strength. We emphasize the role of virtual vortex-antivortex pairs creation in the process of sound dissipation.

Observing the Influence of Reduced Dimensionality on Fermionic Superfluids

Understanding the origins of unconventional superconductivity has been a major focus of condensed matter physics for many decades. While many questions remain unanswered, experiments have found the highest critical temperatures in layered two-dimensional materials. However, to what extent the remarkable stability of these strongly correlated 2D superfluids is affected by their reduced dimensionality is still an open question. Here, we use dilute gases of ultracold fermionic atoms as a model system to directly observe the influence of dimensionality on the stability of strongly interacting fermionic superfluids. We find that the superfluid gap follows the same universal function of the interaction strength regardless of dimensionality, which suggests that there is no inherent difference in the stability of two- and three-dimensional fermionic superfluids. Finally, we compare our data to results from solid state systems and find a similar relation between the interaction strength and the gap for a wide range of two- and three-dimensional superconductors.

Precision Many-Body Study of the Berezinskii-Kosterlitz-Thouless Transition and Temperature-Dependent Properties in the Two-Dimensional Fermi Gas

We perform large-scale, numerically exact calculations on the two-dimensional interacting Fermi gas with a contact attraction. Reaching much larger lattice sizes and lower temperatures than previously possible, we determine systematically the finite-temperature phase diagram of the Berezinskii-Kosterlitz-Thouless (BKT) transitions for interaction strengths ranging from BCS to crossover to BEC regimes. The evolutions of the pairing wave functions and the fermion and Cooper pair momentum distributions with temperature are accurately characterized. In the crossover regime, we find that the contact has a nonmonotonic temperature dependence, first increasing as temperature is lowered, and then showing a slight decline below the BKT transition temperature to approach the ground-state value from above.

On the Accuracy of Random Phase Approximation for Dynamical Structure Factors in Cold Atomic Gases

Many-body physics poses one of the greatest challenges to science in the 21st century. Still more daunting is the problem of accurately calculating the properties of quantum many-body systems in the strongly correlated regime. Cold atomic gases provide an excellent test ground, for both experimentalists and theorists, to study the exotic and sometimes counterintuitive behavior of quantum many-body problems. Of particular interest is the appearance of collective excitations in these systems, such as the famous Goldstone mode and the elusive Higgs mode. It is particularly important to assess the robustness of theoretical and computational techniques to study such excitations. We build on the unprecedented opportunity provided by the fact that, in some cases, exact numerical predictions can be obtained through quantum Monte Carlo. We use these predictions to assess the accuracy of the Random Phase Approximation, which is widely considered to be a method of choice for the study of the collective excitations in a cold atomic Fermi gas modeled with a Fermi–Hubbard Hamiltonian. We found good agreement between the two methodologies for the dynamic properties, particularly for the position of the Goldstone mode. We also explored the possibility of using a renormalized, effective potential in place of the physical potential. We determined that using a renormalized potential is likely too simplistic a method for improving the accuracy of generalized Random Phase Approximation and that a more sophisticated approach is needed.

New mechanism and exact theory of superconductivity from strong repulsive interaction

We introduce a general mechanism for superconductivity in Fermi systems with strong repulsive interaction. Because kinetic terms are small compared to the bare repulsion, the dynamics of charge carriers is constrained by the presence of other nearby carriers. By treating kinetic terms as a perturbation around the atomic limit, we show that pairing can be induced by correlated multiparticle tunneling processes that favor two itinerant carriers to be close together. Our analytically controlled theory provides a quantitative formula relating Tc to microscopic parameters, with maximum Tc reaching about 10% of the Fermi temperature. Our work demonstrates a powerful method for studying strong coupling superconductivity with unconventional pairing symmetry. It also offers a realistic new route to realizing finite angular momentum superfluidity of spin-polarized fermions in optical lattice.

Large phonon time-of-flight fluctuations in expanding flat condensates of cold Fermi gases

We reexamine how quantum density fluctuations in condensates of ultra-cold Fermi gases lead to fluctuations in phonon times-of-flight, an effect that increases as density is reduced. We suggest that these effects should be measurable in pancake-like (two-dimensional) condensates on their release from their confining optical traps, providing their initial (width/thickness) aspect ratio is suitably large.

Clustering of Four-Component Unitary Fermions

Ab initio nuclear physics tackles the problem of strongly interacting four-component fermions. The same setting could foreseeably be probed experimentally in ultracold atomic systems, where two- and three-component experiments have led to major breakthroughs in recent years. Both due to the problem's inherent interest and as a pathway to nuclear physics, in this Letter we study four-component fermions at unitarity via the use of quantum Monte Carlo methods. We explore novel forms of the trial wave function and find one which leads to a ground state of the eight-particle system whose energy is almost equal to that of two four-particle systems. We investigate the clustering properties involved and also extrapolate to the zero-range limit. In addition to being experimentally testable, our results impact the prospects of developing nuclear physics as a perturbation around the unitary limit.

Reaching the Continuum Limit in Finite-Temperature Ab Initio Field-Theory Computations in Many-Fermion Systems

Finite-temperature grand-canonical computations based on field theory are widely applied in areas including condensed matter physics, ultracold atomic gas systems, and the lattice gauge theory. However, these calculations have computational costs scaling as N_{s}^{3} with the size of the lattice or basis set, N_{s}. We report a new approach based on systematically controllable low-rank factorization that reduces the scaling of such computations to N_{s}N_{e}^{2}, where N_{e} is the average number of fermions in the system. In any realistic calculations aiming to describe the continuum limit, N_{s}/N_{e} is large and needs to be extrapolated effectively to infinity for convergence. The method thus fundamentally changes the prospect for finite-temperature many-body computations in correlated fermion systems. Its application, in combination with frameworks to control the sign or phase problem as needed, will provide a powerful tool in ab initio quantum chemistry and correlated electron materials. We demonstrate the method by computing exact properties of the two-dimensional Fermi gas with zero-range attractive interaction as a function of temperature in both the normal and superfluid states.

Exactly solvable model of two interacting Rydberg-dressed atoms confined in a two-dimensional harmonic trap

Exactly solvable model of two Rydberg-dressed atoms moving in a quasi-two-dimensional harmonic trap is introduced and its properties are investigated. Depending on the strength of inter-particle interactions and the critical range of the potential, the two-particle eigenstates are classified with respect to the excitations of the center-of-mass motion, relative angular momentum, and relative distance variable. Having these solutions in hand, we discuss inter-particle correlations as functions of interaction parameters. We also present a straightforward prescription of how to generalize obtained solutions to higher dimensions.

Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid

Quantum anomalies are violations of classical scaling symmetries caused by divergences that appear in the quantization of certain classical theories. Although they play a prominent role in the quantum field theoretical description of many-body systems, their influence on experimental observables is difficult to discern. In this study, we discovered a distinctive manifestation of a quantum anomaly in the momentum-space dynamics of a two-dimensional (2D) Fermi superfluid of ultracold atoms. The measured pair momentum distributions of the superfluid during a breathing mode cycle exhibit a scaling violation in the strongly interacting regime. We found that the power-law exponents that characterize long-range phase correlations in the system are modified by the quantum anomaly, emphasizing the influence of this effect on the critical properties of 2D superfluids.

Reduced Quantum Anomaly in a Quasi-Two-Dimensional Fermi Superfluid: Significance of the Confinement-Induced Effective Range of Interactions

A two-dimensional (2D) harmonically trapped interacting Fermi gas is anticipated to exhibit a quantum anomaly and possesses a breathing mode at frequencies different from a classical scale-invariant value ω_{B}=2ω_{⊥}, where ω_{⊥} is the trapping frequency. The predicted maximum quantum anomaly (∼10%) has not been confirmed in experiments. Here, we theoretically investigate the zero-temperature density equation of state and the breathing mode frequency of an interacting Fermi superfluid at the dimensional crossover from three to two dimensions. We find that the simple model of a 2D Fermi gas with a single s-wave scattering length is not adequate to describe the experiments in the 2D limit, as commonly believed. A more complete description of quasi-2D leads to a much weaker quantum anomaly, consistent with the experimental observations. We clarify that the reduced quantum anomaly is due to the significant confinement-induced effective range of interactions.

Quantum Anomaly and 2D-3D Crossover in Strongly Interacting Fermi Gases

We present an experimental investigation of collective oscillations in harmonically trapped Fermi gases through the crossover from two to three dimensions. Specifically, we measure the frequency of the radial monopole oscillation or breathing mode in highly oblate gases with tunable interactions. The breathing mode frequency is set by the adiabatic compressibility and probes the thermodynamic equation of state. In 2D, a dynamical scaling symmetry for atoms interacting via a δ potential predicts the breathing mode to occur at exactly twice the harmonic confinement frequency. However, a renormalized quantum treatment introduces a new length scale which breaks this classical scale invariance resulting in a so-called quantum anomaly. Our measurements deep in the 2D regime lie above the scale-invariant prediction for a range of interaction strengths providing evidence for the quantum anomaly and signifying the breakdown of an elementary δ-potential model of atomic interactions. By varying the atom number we can tune the chemical potential and see the breathing mode frequency evolve smoothly between the 2D to 3D thermodynamic limits.

Anomalous Breaking of Scale Invariance in a Two-Dimensional Fermi Gas

The frequency of the breathing mode of a two-dimensional Fermi gas with zero-range interactions in a harmonic confinement is fixed by the scale invariance of the Hamiltonian. Scale invariance is broken in the quantized theory by introducing the two-dimensional scattering length as a regulator. This is an example of a quantum anomaly in the field of ultracold atoms and leads to a shift of the frequency of the collective breathing mode of the cloud. In this work, we study this anomalous frequency shift for a two-component Fermi gas in the strongly interacting regime. We measure significant upwards shifts away from the scale-invariant result that show a strong interaction dependence. This observation implies that scale invariance is broken anomalously in the strongly interacting two-dimensional Fermi gas.

Quantum Anomaly and Thermodynamics of One-Dimensional Fermions with Three-Body Interactions

We show that a system of three species of one-dimensional fermions, with an attractive three-body contact interaction, features a scale anomaly directly related to the anomaly of two-dimensional fermions with two-body contact forces. We show, furthermore, that those two cases (and their multispecies generalizations) are the only nonrelativistic systems with contact interactions that display a scale anomaly. While the two-dimensional case is well known and has been under study both experimentally and theoretically for years, the one-dimensional case presented here has remained unexplored. For the latter, we calculate the impact of the anomaly on the equation of state, which appears through the generalization of Tan's contact for three-body forces, and determine the pressure at finite temperature. In addition, we show that the third-order virial coefficient is proportional to the second-order coefficient of the two-dimensional two-body case.

Observation of Quantum-Limited Spin Transport in Strongly Interacting Two-Dimensional Fermi Gases

We measure the transport properties of two-dimensional ultracold Fermi gases during transverse demagnetization in a magnetic field gradient. Using a phase-coherent spin-echo sequence, we are able to distinguish bare spin diffusion from the Leggett-Rice effect, in which demagnetization is slowed by the precession of a spin current around the local magnetization. When the two-dimensional scattering length is tuned to be comparable to the inverse Fermi wave vector k_{F}^{-1}, we find that the bare transverse spin diffusivity reaches a minimum of 1.7(6)ℏ/m, where m is the bare particle mass. The rate of demagnetization is also reflected in the growth rate of the s-wave contact, observed using time-resolved spectroscopy. The contact rises to 0.28(3)k_{F}^{2} per particle, which quantifies how scaling symmetry is broken by near-resonant interactions, unlike in unitary three-dimensional systems. Our observations support the conjecture that, in systems with strong scattering, the local relaxation rate is bounded from above by k_{B}T/ℏ.

Weakly parametrized Jastrow ansatz for a strongly correlated Bose system

We consider the Jastrow pair-product wavefunction for strongly correlated Bose systems, in our case liquid helium-4. An ansatz is proposed for the pair factors which consist of a numeric solution to a modified and parametrized pair scattering equation. We consider a number of such simple one-variable parametrizations. Additionally, we allow for a parametrizeable cutoff of the pair factors and for the addition of a long-range phonon tail. This approach results in many-body wavefunctions that have between just one and three variational parameters. Calculation of observables is carried with the variational Monte Carlo method. We find that such a simple parametrization is sufficient to produce results that are comparable in quality to the best available two-body factors for helium. For the two-parameter wavefunction, we find variational energies of -6.04 K per particle for a system of one thousand particles. It is also shown that short-range two-body correlations are reproduced in good detail by the two- and three-parameter functions.

Rashba Spin-Orbit Coupling, Strong Interactions, and the BCS-BEC Crossover in the Ground State of the Two-Dimensional Fermi Gas

The recent experimental realization of spin-orbit coupled Fermi gases provides a unique opportunity to study the interplay between strong interaction and spin-orbit coupling (SOC) in a tunable, disorder-free system. We present here precision ab initio numerical results on the two-dimensional, unpolarized, uniform Fermi gas with attractive interactions and Rashba SOC. Using the auxiliary-field quantum Monte Carlo method and incorporating recent algorithmic advances, we carry out exact calculations on sufficiently large system sizes to provide accurate results systematically as a function of experimental parameters. We obtain the equation of state, the momentum distributions, the pseudospin correlations, and the pair wave functions. Our results help illuminate the rich pairing structure induced by SOC, and provide benchmarks for theory and guidance to future experimental efforts.

Equation of State of Ultracold Fermions in the 2D BEC-BCS Crossover Region

We report the experimental measurement of the equation of state of a two-dimensional Fermi gas with attractive s-wave interactions throughout the crossover from a weakly coupled Fermi gas to a Bose gas of tightly bound dimers as the interaction strength is varied. We demonstrate that interactions lead to a renormalization of the density of the Fermi gas by several orders of magnitude. We compare our data near the ground state and at finite temperature with predictions for both fermions and bosons from quantum Monte Carlo simulations and Luttinger-Ward theory. Our results serve as input for investigations of close-to-equilibrium dynamics and transport in the two-dimensional system.

Thermodynamics of an Attractive 2D Fermi Gas

Thermodynamic properties of matter are conveniently expressed as functional relations between variables known as equations of state. Here we experimentally determine the compressibility, density, and pressure equations of state for an attractive 2D Fermi gas in the normal phase as a function of temperature and interaction strength. In 2D, interacting gases exhibit qualitatively different features to those found in 3D. This is evident in the normalized density equation of state, which peaks at intermediate densities corresponding to the crossover from classical to quantum behavior.

Quasicondensation in Two-Dimensional Fermi Gases

In this paper we follow the analysis and protocols of recent experiments, combined with simple theory, to arrive at a physical understanding of quasi-condensation in two dimensional Fermi gases. A key signature of quasi-condensation, which contains aspects of Berezinskiĭ-Kosterlitz-Thouless behavior, is a strong zero momentum peak in the pair momentum distribution. Importantly, this peak emerges at a reasonably well defined onset temperature. The resulting phase diagram, pair momentum distribution, and algebraic power law decay are compatible with recent experiments throughout the continuum from BEC to BCS.

Pressure, compressibility, and contact of the two-dimensional attractive fermi gas

Using ab initio lattice methods, we calculate the finite temperature thermodynamics of homogeneous two-dimensional spin-1/2 fermions with attractive short-range interactions. We present results for the density, pressure, compressibility, and quantum anomaly (i.e., Tan's contact) for a wide range of temperatures (mostly above the superfluid phase, including the pseudogap regime) and coupling strengths, focusing on the unpolarized case. Within our statistical and systematic uncertainties, our prediction for the density equation of state differs quantitatively from the prediction by Luttinger-Ward theory in the strongly coupled region of parameter space, but otherwise agrees well with it. We also compare our calculations with the second- and third-order virial expansion, with which they are in excellent agreement in the low-fugacity regime.

Spin-imbalanced quasi-two-dimensional Fermi gases

We measure the density profiles for a Fermi gas of (6)Li containing N(1) spin-up atoms and N(2) spin-down atoms, confined in a quasi-two-dimensional geometry. The spatial profiles are measured as a function of spin imbalance N(2)/N(1) and interaction strength, which is controlled by means of a collisional (Feshbach) resonance. The measured cloud radii and central densities are in disagreement with mean-field Bardeen-Cooper-Schrieffer theory for a true two-dimensional system. We find that the data for normal-fluid mixtures are reasonably well fit by a simple two-dimensional polaron model of the free energy. Not predicted by the model is a phase transition to a spin-balanced central core, which is observed above a critical value of N(2)/N(1). Our observations provide important benchmarks for predictions of the phase structure of quasi-two-dimensional Fermi gases.

Stoner ferromagnetism in a thermal pseudospin-1/2 Bose gas

We compute the finite-temperature phase diagram of a pseudospin-1/2 Bose gas with contact interactions, using two complementary methods: the random-phase approximation and self-consistent Hartree-Fock theory. We show that the spin-dependent interactions, which break the (pseudo-) spin-rotational symmetry of the Hamiltonian, generally lead to the appearance of a magnetically ordered phase at temperatures above the superfluid transition. In three dimensions, we predict a normal easy-axis (easy-plane) ferromagnet for sufficiently strong repulsive (attractive) interspecies interactions, respectively. The normal easy-axis ferromagnet is the bosonic analog of Stoner ferromagnetism known in electronic systems. For the case of interspecies attraction, we also discuss the possibility of a bosonic analog of the Cooper-paired phase. This state is shown to significantly lose in energy to the transverse ferromagnet in three dimensions, but is more energetically competitive in lower dimensions. Extending our calculations to a spin-orbit-coupled Bose gas with equal Rashba and Dresselhaus-type couplings (as recently realized in experiment), we investigate the possibility of stripe ordering in the normal phase. Within our approximations, however, we do not find an instability towards stripe formation, suggesting that the stripe order melts below the condensation temperature, which is consistent with the experimental observations of Ji et al. [Ji et al., Nat. Phys. 10, 314 (2014)].

Universal equation of state and pseudogap in the two-dimensional Fermi gas

We determine the thermodynamic properties and the spectral function for a homogeneous two-dimensional Fermi gas in the normal state using the Luttinger-Ward, or self-consistent T-matrix, approach. The density equation of state deviates strongly from that of the ideal Fermi gas even for moderate interactions, and our calculations suggest that temperature has a pronounced effect on the pressure in the crossover from weak to strong coupling, consistent with recent experiments. We also compute the superfluid transition temperature for a finite system in the crossover region. There is a pronounced pseudogap regime above the transition temperature: the spectral function shows a Bogoliubov-like dispersion with backbending, and the density of states is significantly suppressed near the chemical potential. The contact density at low temperatures increases with interaction and compares well with both experiment and zero-temperature Monte Carlo results.

Ground-state pressure of quasi-2D Fermi and Bose gases

Using an ultracold gas of atoms, we have realized a quasi-two-dimensional Fermi system with widely tunable s-wave interactions nearly in a ground state. Pressure and density are measured. The experiment covers physically different regimes: weakly and strongly attractive Fermi gases and a Bose gas of tightly bound pairs of fermions. In the Fermi regime of weak interactions, the pressure is systematically above a Fermi-liquid-theory prediction, maybe due to mesoscopic effects. In the opposite Bose regime, the pressure agrees with a bosonic mean-field scaling in a range beyond simplest expectations. In the strongly interacting regime, measurements disagree with a purely 2D model. Reported data may serve for sensitive testing of theoretical methods applicable across different quantum physics disciplines.

Pair correlations in the two-dimensional Fermi gas

We consider the two-dimensional Fermi gas at finite temperature with attractive short-range interactions. Using the virial expansion, which provides a controlled approach at high temperatures, we determine the spectral function and contact for the normal state. Our calculated spectra are in qualitative agreement with recent photoemission measurements [M. Feld et al., Nature (London) 480, 75 (2011).], thus suggesting that the observed pairing gap is a feature of the high-temperature gas rather than being evidence of a pseudogap regime just above the superfluid transition temperature. We further argue that the strong pair correlations result from the fact that the crossover to bosonic dimers occurs at weaker interactions than previously assumed.

Apparent low-energy scale invariance in two-dimensional Fermi gases

Recent experiments on a 2D Fermi gas find an undamped breathing mode at twice the trap frequency over a wide range of parameters. To understand this seemingly scale-invariant behavior in a system with a scale, we derive two exact results valid across the entire Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover at all temperatures. First, we relate the shift of the mode frequency from its scale-invariant value to γ(d)≡(1+2/d)P-ρ(∂P/∂ρ)(s) in d dimensions. Next, we relate γ(d) to dissipation via a new low-energy bulk viscosity sum rule. We argue that 2D is special, with its logarithmic dependence of the interaction on density, and thus γ(2) is small in both the BCS-BEC regimes, even though P-2ε/d, sensitive to the dimer binding energy that breaks scale invariance, is not.

Two-dimensional Fermi liquid with attractive interactions

We realize and study an attractively interacting two-dimensional Fermi liquid. Using momentum-resolved photoemission spectroscopy, we measure the self-energy, determine the contact parameter of the short-range interaction potential, and find their dependence on the interaction strength. We successfully compare the measurements to a theoretical analysis, properly taking into account the finite temperature, harmonic trap, and the averaging over several two-dimensional gases with different peak densities.

Polaron-to-polaron transitions in the radio-frequency spectrum of a quasi-two-dimensional Fermi gas

We measure radio-frequency spectra for a two-component mixture of a 6Li atomic Fermi gas in a quasi-two-dimensional regime with the Fermi energy comparable to the energy level spacing in the tightly confining potential. Near the Feshbach resonance, we find that the observed resonances do not correspond to transitions between confinement-induced dimers. The spectral shifts can be fit by assuming transitions between noninteracting polaron states in two dimensions.

Quantum anomaly, universal relations, and breathing mode of a two-dimensional Fermi gas

In this Letter, we show that the classical SO(2,1) symmetry of a harmonically trapped Fermi gas in two dimensions is broken by quantum effects. The anomalous correction to the symmetry algebra is given by a two-body operator that is well known as the contact. Taking into account this modification, we are able to derive the virial theorem for the system and a universal relation for the pressure of a homogeneous gas. The existence of an undamped breathing mode is associated with the classical symmetry. We provide an estimate for the anomalous frequency shift of this oscillation at zero temperature and compare the result with a recent experiment by [E. Vogt et al., Phys. Rev. Lett. 108, 070404 (2012)]. Discrepancies are attributed to finite temperature effects.

Scale invariance and viscosity of a two-dimensional Fermi gas

We investigate collective excitations of a harmonically trapped two-dimensional Fermi gas from the collisionless (zero sound) to the hydrodynamic (first sound) regime. The breathing mode, which is sensitive to the equation of state, is observed with an undamped amplitude at a frequency 2 times the dipole mode frequency for a large range of interaction strengths and different temperatures. This provides evidence for a dynamical SO(2,1) scaling symmetry of the two-dimensional Fermi gas. Moreover, we investigate the quadrupole mode to measure the shear viscosity of the two-dimensional gas and study its temperature dependence.

Clock shift in a strongly interacting two-dimensional Fermi gas

We derive universal relations for the rf spectroscopy of a two-dimensional Fermi gas consisting of two spin states interacting through an S-wave scattering length. The rf transition rate has a high-frequency tail that is proportional to the contact and displays logarithmic scaling violations, decreasing asymptotically like 1/(ω2ln2ω). Its coefficient is proportional to ln2'(a'(2D)/a(2D)), where a(2D) and a'(2D) are the two-dimensional scattering lengths associated with initial-state and final-state interactions. The clock shift is proportional to the contact and to ln(a'(2D)/a(2D)). If |ln(a'(2D)/a(2D))| >> 1, the clock shift arises as a cancellation between much larger contributions proportional to ln2(a'(2D)/a(2D)) from bound-bound and bound-free rf transitions.

Evolution of fermion pairing from three to two dimensions

We follow the evolution of fermion pairing in the dimensional crossover from three-dimensional to two-dimensional as a strongly interacting Fermi gas of ^{6}Li atoms becomes confined to a stack of two-dimensional layers formed by a one-dimensional optical lattice. Decreasing the dimensionality leads to the opening of a gap in radio-frequency spectra, even on the Bardeen-Cooper-Schrieffer side of a Feshbach resonance. The measured binding energy of fermion pairs closely follows the theoretical two-body binding energy and, in the two-dimensional limit, the zero-temperature mean-field Bose-Einstein-condensation to Bardeen-Cooper-Schrieffer crossover theory.