Two-dimensional Fermi Gas Research Articles

Collective modes of a two-dimensional Fermi gas at finite temperature

In this work we examine the breathing mode of a strongly interacting two-dimensional Fermi gas and the role of temperature on the anomalous breaking of scale invariance. By calculating the equation of state with different many-body $T$-matrix theories and the virial expansion approach, we obtain a hydrodynamic equation of the harmonically trapped Fermi gas (with trapping frequency $\omega_{0}$) through the local density approximation. By solving the hydrodynamic equation we determine the breathing mode frequencies as functions of interaction strength and temperature. We find that the breathing mode anomaly depends sensitively on both interaction strength and temperature. In particular, in the strongly interacting regime we predict a significant down-shift of the breathing mode frequency, below the scale invariant value of $2\omega_{0}$ for temperatures of order the Fermi temperature.

Pairing fluctuations in a strongly interacting two-dimensional Fermi gas

We theoretically investigate strong-coupling properties of a two-dimensional Fermi gas in the normal phase. Including pairing fluctuations within the framework of a self-consistent T-matrix approximation, we calculate the single-particle density of states (DOS) near the observed Berezinskii-Kosterlitz-Thouless phase transition temperature TBKT. We show that the pseudogap phenomenon associated with strong pairing fluctuations appears as an almost fully gapped single-particle density of states in the strong-coupling regime, indicating that amplitude fluctuations of the order parameter are almost absent and the system is dominated by phase fluctuations of the order parameter, as expected in a two-dimensional system near TBKT. On the other hand, although pairing fluctuations are enhanced by the low-dimensionality of the system, they are found to be still not strong enough to open such a full gap in the intermediate coupling (crossover) regime. In this regime, a dip structure is only seen in DOS around ω = 0, indicating that amplitude of the superfluid order parameter is also fluctuating, in addition to phase fluctuations. In theoretically determining TBKT in a two-dimensional Fermi gas, it is frequently assumed that, while phase fluctuations exist, the amplitude of the superfluid order parameter is fixed. However, our results indicate the necessity of including both amplitude and phase fluctuations of the order parameter in evaluating TBKT in the crossover region. Since the BKT phase transition has recently been reported in a two-dimensional 6Li Fermi gas, our results would be useful for the theoretical study of this observed novel Fermi superfluid and effects of strong low-dimensional pairing fluctuations.

Two-Dimensional Homogeneous Fermi Gases.

We report on the experimental realization of homogeneous two-dimensional (2D) Fermi gases trapped in a box potential. In contrast to harmonically trapped gases, these homogeneous 2D systems are ideally suited to probe local as well as nonlocal properties of strongly interacting many-body systems. As a first benchmark experiment, we use a local probe to measure the density of a noninteracting 2D Fermi gas as a function of the chemical potential and find excellent agreement with the corresponding equation of state. We then perform matter wave focusing to extract the momentum distribution of the system and directly observe Pauli blocking in a near unity occupation of momentum states. Finally, we measure the momentum distribution of an interacting homogeneous 2D gas in the crossover between attractively interacting fermions and bosonic dimers.

Pseudogap Regime of a Two-dimensional Uniform Fermi Gas

We investigate pseudogap phenomena in a two-dimensional Fermi gas. Including pairing fluctuations within a self-consistent $T$-matrix approximation, we determine the pseudogap temperature $T^*$ below which a dip appears in the density of states $\rho(\omega)$ around the Fermi level. Evaluating $T^*$, we identify the pseudogap region in the phase diagram of this system. We find that, while the observed BKT (Berezinskii-Kosterlitz-Thouless) transition temperature $T^{\rm exp}_{\rm BKT}$ in a $^6$Li Fermi gas is in the pseudogap regime, the detailed pseudogap structure in $\rho(\omega)$ at $T^{\rm exp}_{\rm BKT}$ still differs from a fully-gapped one, indicating the importance of amplitude fluctuations in the Cooper channel there. Since the observed $T^{\rm exp}_{\rm BKT}$ in the weak-coupling regime cannot be explained by the recent BKT theory which only includes phase fluctuations, our results may provide a hint about how to improve this BKT theory. Although $\rho(\omega)$ has not been measured in this system, we show that the assessment of our results is still possible by using the observable Tan's contact.

Virial coefficients of one-dimensional and two-dimensional Fermi gases by stochastic methods and a semiclassical lattice approximation

Virial coefficients of one-dimensional and two-dimensional Fermi gases by stochastic methods and a semiclassical lattice approximation

Kosterlitz-Thouless transition and vortex-antivortex lattice melting in two-dimensional Fermi gases with p - or d -wave pairing

We present a theoretical study of the finite-temperature Kosterlitz-Thouless (KT) and vortex-antivortex lattice (VAL) melting transitions in two-dimensional Fermi gases with $p$- or $d$-wave pairing. For both pairings, when the interaction is tuned from weak to strong attractions, we observe a quantum phase transition from the Bardeen-Cooper-Schrieffer (BCS) superfluidity to the Bose-Einstein condensation (BEC) of difermions. The KT and VAL transition temperatures increase during this BCS-BEC transition and approach constant values in the deep BEC region. The BCS-BEC transition is characterized by the non-analyticities of the chemical potential, the superfluid order parameter, and the sound velocities as functions of the interaction strength at both zero and finite temperatures; however, the temperature effect tends to weaken the non-analyticities comparing to the zero temperature case. The effect of mismatched Fermi surfaces on the $d$-wave pairing is also studied.

Accurate computations of Rashba spin-orbit coupling in interacting systems: From the Fermi gas to real materials

We describe the treatment of Rashba spin-orbit coupling (SOC) in interacting many-fermion systems within the auxiliary-field quantum Monte Carlo framework, and present a set of illustrative results. These include numerically exact calculations on the ground-state properties of the spin-balanced, attractive two-dimensional Fermi gas, as well as a study of a tight-binding Hamiltonian with repulsive interaction. These systems are formally connected via the Hubbard Hamiltonian plus SOC, but cover different physics ranging from superfluidity and triplet pairing to SOC in real materials in the presence of strong interactions in localized orbitals. We carry out detailed benchmark studies of the method in the latter case when an approximation is needed to control the sign problem for repulsive Coulomb interactions. The methods presented here provide an approach for predictive computations in materials to study the interplay of SOC and strong correlation.

High-temperature pairing in a strongly interacting two-dimensional Fermi gas.

The nature of the normal phase of strongly correlated fermionic systems is an outstanding question in quantum many-body physics. We used spatially resolved radio-frequency spectroscopy to measure pairing energy of fermions across a wide range of temperatures and interaction strengths in a two-dimensional gas of ultracold fermionic atoms. We observed many-body pairing at temperatures far above the critical temperature for superfluidity. In the strongly interacting regime, the pairing energy in the normal phase considerably exceeds the intrinsic two-body binding energy of the system and shows a clear dependence on local density. This implies that pairing in this regime is driven by many-body correlations, rather than two-body physics. Our findings show that pairing correlations in strongly interacting two-dimensional fermionic systems are remarkably robust against thermal fluctuations.

Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations

Experiments with ultracold atoms provide a highly controllable laboratory setting with many unique opportunities for precision exploration of quantum many-body phenomena. The nature of such systems, with strong interaction and quantum entanglement, makes reliable theoretical calculations challenging. Especially difficult are excitation and dynamical properties, which are often the most directly relevant to experiment. We carry out exact numerical calculations, by Monte Carlo sampling of imaginary-time propagation of Slater determinants, to compute the pairing gap in the two-dimensional Fermi gas from first principles. Applying state-of-the-art analytic continuation techniques, we obtain the spectral function and the density and spin structure factors providing unique tools to visualize the BEC-BCS crossover. These quantities will allow for a direct comparison with experiments.

Quantum gas microscopy of an attractive Fermi–Hubbard system

The attractive Fermi-Hubbard model is the simplest theoretical model for studying pairing and superconductivity of fermions on a lattice. Although its s-wave pairing symmetry excludes it as a microscopic model for high-temperature superconductivity, it exhibits much of the relevant phenomenology, including a short-coherence length at intermediate coupling and a pseudogap regime with anomalous properties. Here we study an experimental realization of this model using a two-dimensional (2D) atomic Fermi gas in an optical lattice. Our site-resolved measurements on the normal state reveal checkerboard charge-density-wave correlations close to half-filling. A "hidden" SU(2) pseudo-spin symmetry of the Hubbard model at half-filling guarantees superfluid correlations in our system, the first evidence for such correlations in a single-band Hubbard system of ultracold fermions. Compared to the paired atom fraction, we find the charge-density-wave correlations to be a much more sensitive thermometer, useful for optimizing cooling into superfluid phases in future experiments.

Effective-range dependence of two-dimensional Fermi gases

The Feshbach resonance provides precise control over the scattering length and effective range of interactions between ultracold atoms. We propose the ultratransferable pseudopotential to model effective interaction ranges $\ensuremath{-}1.5\ensuremath{\le}{k}_{\mathrm{F}}^{2}{R}_{\mathrm{eff}}^{2}\ensuremath{\le}0$, where ${R}_{\mathrm{eff}}$ is the effective range and ${k}_{\text{F}}$ is the Fermi wave vector, describing narrow to broad Feshbach resonances. We develop a mean-field treatment and exploit the pseudopotential to perform a variational and diffusion Monte Carlo study of the ground state of the two-dimensional Fermi gas, reporting on the ground-state energy, contact, condensate fraction, momentum distribution, and pair-correlation functions as a function of the effective interaction range across the BEC-BCS crossover. The limit ${k}_{\mathrm{F}}^{2}{R}_{\mathrm{eff}}^{2}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ is a gas of bosons with zero binding energy, whereas $ln({k}_{\mathrm{F}}a)\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ corresponds to noninteracting bosons with infinite binding energy.

Superconductivity in a two-dimensional repulsive Rashba gas at low electron density

We study the superconducting instability and the resulting superconducting states in a two-dimensional repulsive Fermi gas with Rashba spin–orbit coupling at low electron density (namely the Fermi energy EF is lower than the energy ER of the Dirac point induced by Rashba coupling). We find that superconductivity is enhanced as the dimensionless Fermi energy () decreases, due to two reasons. First, the density of states at increases as . Second, the particle–hole bubble becomes more anisotropic, resulting in an increasing effective attraction. The superconducting state is always in the total angular momentum (or ) channel with Chern number C = 4 (or ), breaking time reversal symmetry spontaneously. Although a putative Leggett mode is expected due to the two-gap nature of the superconductivity, we find that it is always damped. More importantly, once a sufficiently large Zeeman coupling is applied to the superconducting state, the Chern number can be tuned to be ±1 and Majorana zero modes exist in the vortex cores.

Two-dimensional Bose and Fermi gases beyond weak coupling

Using a formalism based on the two-body S-matrix we study two-dimensional Bose and Fermi gases with both attractive and repulsive interactions. Approximate analytic expressions, valid at weak coupling and beyond, are developed and applied to the Berezinskii–Kosterlitz–Thouless (BKT) transition. We successfully recover the correct logarithmic functional form of the critical chemical potential and density for the Bose gas. For fermions, the BKT critical temperature is calculated in BCS and BEC regimes through consideration of Tan’s contact.

Thermodynamic equivalence of two-dimensional imperfect attractive Fermi and repulsive Bose gases

We consider two-dimensional imperfect attractive Fermi and repulsive Bose gases consisting of spinless point particles whose total interparticle interaction energy is represented by $a{N}^{2}/2V$ with $a=\ensuremath{-}{a}_{F}\ensuremath{\le}0$ for fermions and $a={a}_{B}\ensuremath{\ge}0$ for bosons. We show that, in spite of the attraction, the thermodynamics of a $d=2$ imperfect Fermi gas remains well defined for $0\ensuremath{\le}{a}_{F}\ensuremath{\le}{a}_{0}={h}^{2}/2\ensuremath{\pi}m$, and is exactly the same as the one of the repulsive imperfect Bose gas with ${a}_{B}={a}_{0}\ensuremath{-}{a}_{F}$. In particular, for ${a}_{F}={a}_{0}$ one observes the thermodynamic equivalence of the attractive imperfect Fermi gas and the ideal Bose gas.

Two-dimensional Fermi gas in antiparallel magnetic fields

We study a two-dimensional Fermi gas with an attractive interaction subjected to synthetic magnetic fields assumed to be mutually antiparallel for two different spin components. By employing the mean-field approximation, we find that its phase diagram at zero temperature consists of pair superfluid and quantum spin Hall insulator phases and closely resembles that of the Bose-Hubbard model. The resulting two phases are separated by a second-order quantum phase transition classified into the universality class of either the dilute Bose gas or the XY model. We also show that the pairing gap can be enhanced significantly by the antiparallel magnetic fields as a consequence of magnetic catalysis, which may facilitate the realization of the pair superfluid in two dimensions by ultracold atom experiments.

Core structure of two-dimensional Fermi gas vortices in the BEC-BCS crossover region

We report $T=0$ diffusion Monte Carlo results for the ground-state and vortex excitation of unpolarized spin-1/2 fermions in a two-dimensional disk. We investigate how vortex core structure properties behave over the BEC-BCS crossover. We calculate the vortex excitation energy, density profiles, and vortex core properties related to the current. We find a density suppression at the vortex core on the BCS side of the crossover, and a depleted core on the BEC limit. Size-effect dependencies in the disk geometry were carefully studied.

Effect of weak disorder on the BCS–BEC crossover in a two-dimensional Fermi gas

In this paper, we study the two-dimensional (2D) ultracold Fermi gas with weak impurity in the framework of mean-field theory where the impurity is introduced through Gaussian fluctuations. We have investigated the role of the impurity by studying the experimentally accessible quantities such as condensate fraction and equation of state of the ultracold systems. Our analysis reveals that at the crossover, the disorder enhances superfluidity, which we attribute to the unique nature of the unitary region and to the dimensional effect.

Vortices and antivortices in two-dimensional ultracold Fermi gases

Vortices are commonly observed in the context of classical hydrodynamics: from whirlpools after stirring the coffee in a cup to a violent atmospheric phenomenon such as a tornado, all classical vortices are characterized by an arbitrary circulation value of the local velocity field. On the other hand the appearance of vortices with quantized circulation represents one of the fundamental signatures of macroscopic quantum phenomena. In two-dimensional superfluids quantized vortices play a key role in determining finite-temperature properties, as the superfluid phase and the normal state are separated by a vortex unbinding transition, the Berezinskii-Kosterlitz-Thouless transition. Very recent experiments with two-dimensional superfluid fermions motivate the present work: we present theoretical results based on the renormalization group showing that the universal jump of the superfluid density and the critical temperature crucially depend on the interaction strength, providing a strong benchmark for forthcoming investigations.

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.

Signature of the universal super Efimov effect: Three-body contact in two-dimensional Fermi gases

A new class of universal "three-body" bound states has been recently predicted theoretically for identical fermions interacting at p-wave resonance in two dimensions. This phenomenon is called the super Efimov effect since the binding energies of the states follow a intriguing double exponential scaling. However, experimental resolution of this scaling is expected to meet formidable challenges. In this work, we introduce a new thermodynamic quantity, the three-body contact $C_\theta$, to quantify three-body correlations in a two dimensional gas composed of the resonantly interacting fermions; the contact $C_\theta$ is the consequence of the underlying universal super Efimov effect in the many-body context. We show how $C_\theta$ affects physical observables such as the radio-frequency spectrum, the momentum distribution and the atom loss rate. Signature of the elusive super Efimov effect in the thermodynamic system can be pinned down by the detection of the three-body contact $C_\theta$ via these observables.