Atomic Fermi Gas Research Articles

Scattering hypervolume of fermions in two dimensions

We define the three-body scattering hypervolume ${D}_{F}$ for identical spin-polarized fermions in two dimensions by considering the wave function of three such fermions colliding at zero energy and zero orbital angular momentum. We derive the asymptotic expansions of such a wave function when three fermions are far apart or one pair and the third fermion are far apart, and ${D}_{F}$ appears in the coefficients of such expansions. For weak-interaction potentials, we derive an approximate formula of ${D}_{F}$ by using the Born expansion. We then study the shift of energy of three such fermions in a large periodic area due to ${D}_{F}$. This shift is proportional to ${D}_{F}$ times the square of the area of the triangle formed by the momenta of the fermions. We also calculate the shifts of energy and of pressure of spin-polarized two-dimensional Fermi gases due to a nonzero ${D}_{F}$ and the three-body recombination rate of spin-polarized ultracold atomic Fermi gases in two dimensions.

Ground states of atomic Fermi gases in a two-dimensional optical lattice with and without population imbalance

We study the ground state phase diagram of population balanced and imbalanced ultracold atomic Fermi gases with a short range attractive interaction throughout the crossover from BCS to Bose-Einstein condensation (BEC), in a two-dimensional optical lattice (2DOL) comprised of two lattice and one continuum dimensions. We find that the mixing of lattice and continuum dimensions, together with population imbalance, has an extraordinary effect on pairing and the superfluidity of atomic Fermi gases. In the balanced case, the superfluid ground state prevails the majority of the phase space. However, for relatively small lattice hopping integral $t$ and large lattice constant $d$, a pair density wave (PDW) emerges unexpectedly at intermediate coupling strength, and the nature of the in-plane and overall pairing changes from particle-like to hole-like in the BCS and unitary regimes, associated with an abnormal increase in the Fermi volume with the pairing strength. In the imbalanced case, the stable polarized superfluid phase shrinks to only a small portion of the entire phase space spanned by $t$, $d$, imbalance $p$ and interaction strength $U$, mainly in the bosonic regime of low $p$, moderately strong pairing, and relatively large $t$ and small $d$. Due to the Pauli exclusion between paired and excessive fermions within the confined momentum space, a PDW phase emerges and the overall pairing evolves from particle-like into hole-like, as the pairing strength grows stronger in the BEC regime. In both cases, the ground state property is largely governed by the Fermi surface topology. These findings are very different from the cases of pure 3D continuum, 3D lattice or 1DOL.

Magic Gap Ratio for Optimally Robust Fermionic Condensation and Its Implications for High-T_{c} Superconductivity.

Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2Δ/k_{B}T_{c}≈6.5 (where Δ is the pairing gap and T_{c} is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N_{0} and the height of the jump δγ(T_{c}) in the coefficient γ of the fermionic specific heat at T_{c} are strongly peaked. In the cuprates, δγ(T_{c}) is peaked at this gap ratio when Δ corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in δγ(T_{c}) also to coincide with a normal state maximum in γ, which is indicative of a pairing fluctuation pseudogap above T_{c}.

Quantum-limited thermometry of a Fermi gas with a charged spin particle

We investigate the sensitivity of an ion sensor in determining the temperature of an atomic Fermi gas. Our study extends to charged impurities the proposal by M. T. Mitchison et al. Phys. Rev. Lett. 125, 080402 (2020), where atomic neutral impurities were used as an in situ thermometer of the quantum gas. We find that the long-range character of the atom-ion interaction enhances the thermometer's sensitivity for certain system parameters. In addition, we investigate the impact of the ion quantum motional state on the sensitivity by assuming that it is confined in a harmonic trap. We observe that the temperature sensitivity of the ion is noticeably influenced by its spatial extension, making the latter a versatile tool to be manipulated for improving the thermometer performance. We finally discuss our findings in the context of current experimental atom-ion mixtures.

BCS-BEC crossover of atomic Fermi superfluid in a spherical bubble trap

We present a theory of a two-component atomic Fermi gas with tunable attractive contact interactions on a spherical shell going through the Bardeen-Cooper-Schrieffer (BCS) - Bose Einstein condensation (BEC) crossover, inspired by the realizations of spherical bubble traps for ultracold atoms in microgravity. The derivation follows the BCS-Leggett theory to obtain the gap and number equations. The BCS-BEC crossover can be induced by tuning the interaction, and the properly normalized gap and chemical potential exhibit universal behavior regardless of the planar or spherical geometry. Nevertheless, the spherical-shell geometry introduces another way of inducing the crossover by the curvature. The curvature-induced BCS-BEC crossover is made possible by fixing the particle number and interaction strength while shrinking the sphere, causing a reduction to the ratio of the pairing and kinetic energies and pushing the system towards the BCS limit. The saturation of the superfluid density further confirms the ground state is a Fermi superfluid.

Pairing Phenomena and Superfluidity of Atomic Fermi Gases in a Two‐Dimensional Optical Lattice: Unusual Effects of Lattice‐Continuum Mixing

AbstractThe superfluid behavior of ultracold atomic Fermi gases with a short range attractive interaction in a two‐dimensional optical lattice (2DOL) is studied using a pairing fluctuation theory, within the context of BCS‐BEC crossover. It is found that the mixing of lattice and continuum dimensions leads to exotic phenomena. For relatively large lattice constant d and small hopping integral t, the superfluid transition temperature exhibits a remarkable reentrant behavior as a function of the interaction strength, and leads to a pair density wave ground state, where vanishes, for a range of intermediate coupling strength. In the unitary and BCS regimes, the nature of the in‐plane and overall pairing changes from particle‐like to hole‐like, with an unexpected nonmonotonic dependence of the chemical potential on the pairing strength. The Bose–Einstein condensation asymptotic behaviors exhibit distinct power law dependencies on the interaction strength compared to cases of pure 3D lattice, 3D continuum, and 1DOL. These predictions can be tested in future experiments.

Mobile ion in a Fermi sea

The remarkable single particle control of individual ions combined with the versatility of ultracold atomic gases makes hybrid ion-atom system an exciting new platform for quantum simulation of few- and many-body quantum physics. Here, we study theoretically the properties of a mobile ion immersed in a quantum degenerate gas of fermionic atoms. Using an effective low-energy atom-ion interaction together with a well established approach that includes exactly two-body correlations, we calculate the full spectral response of the ion and demonstrate the existence of several quasiparticle branches, which are charged analogues of the Fermi polaron observed in neutral atomic gases. Due to the long-range nature of the atom-ion interaction, these ionic Fermi polarons have several properties distinct from their neutral counterparts such as the simultaneous presence of several stable states and smooth transitions from repulsive to attractive polarons with increasing interaction strength. Surprisingly, the residue of the ionic polaron is shown to increase with the Fermi density for fixed interaction strength, which is in marked contrast to the neutral polaron. The properties of the ionic polaron approach that of the neutral polaron only in the low density limit where the average interparticle spacing is larger than the characteristic length of the atom-ion interaction. We finally analyse the effects of the Fermi gas on the molecular ions, which are bound atom-dimer states.

Second sound attenuation near quantum criticality.

Second sound attenuation, a distinctive dissipative hydrodynamic phenomenon in a superfluid, is crucial for understanding superfluidity and elucidating critical phenomena. Here, we report the observation of second sound attenuation in a homogeneous Fermi gas of lithium-6 atoms at unitarity by performing Bragg spectroscopy with high energy resolution in the long-wavelength limit. We successfully obtained the temperature dependence of second sound diffusivity [Formula: see text] and thermal conductivity κ. Furthermore, we observed a sudden rise-a precursor of critical divergence-in both [Formula: see text] and κ at a temperature of about 0.95 superfluid transition temperature [Formula: see text]. This suggests that the unitary Fermi gas has a much larger critical region than does liquid helium. Our results pave the way for determining the universal critical scaling functions near quantum criticality.

A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential

We calculate Bardeen–Cooper–Schrieffer (BCS) state of a unitary Fermi gas of atoms interacting with the finite-ranged Jost-Kohn potential which has been recently shown to account for the resonant interactions (2019 J. Phys. B: At. Mol. Opt. Phys. 52 165004). Using exact scattering solution of the potential, we derive two-body T-matrix element which is employed to construct the BCS Hamiltonian in momentum space. We present results on the energy- and range-dependence of the pairing gap and superfluid density and the range-dependence of the chemical potential for a wide variation of the scattering length including the unitary regime. In the zero range limit our calculated gap at the Fermi energy is found to be nearly equal to that calculated in mean-field theory with contact potential. The mean gap averaged over the full width at half maximum of the gap function in the zero range and unitary limits is found to be 0.42E F which is quite close to the recent result of the quantum Monte-Carlo simulation (2018 Phys. Rev. A 97 013601). The chemical potential in the zero range limit also agrees well with that for the contact potential.

Second sound in the crossover from the Bose-Einstein condensate to the Bardeen-Cooper-Schrieffer superfluid

Second sound is an entropy wave which propagates in the superfluid component of a quantum liquid. Because it is an entropy wave, it probes the thermodynamic properties of the quantum liquid. Here, we study second sound propagation for a large range of interaction strengths within the crossover between a Bose-Einstein condensate (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superfluid, extending previous work at unitarity. In particular, we investigate the strongly-interacting regime where currently theoretical predictions only exist in terms of an interpolation in the crossover. Working with a quantum gas of ultracold fermionic 6Li atoms with tunable interactions, we show that the second sound speed varies only slightly in the crossover regime. By varying the excitation procedure, we gain deeper insight on sound propagation. We compare our measurement results with classical-field simulations, which help with the interpretation of our experiments.

Pauli blocking of light scattering in degenerate fermions.

Pauli blocking of spontaneous emission is responsible for the stability of atoms. Electrons cannot decay to lower-lying internal states that are already occupied. Pauli blocking also occurs when free atoms scatter light elastically (Rayleigh scattering) and the final external momentum states are already populated. This was predicted more than 30 years ago but is challenging to realize experimentally. Here, we report on Pauli blocking of light scattering in a dense quantum-degenerate Fermi gas of ultracold lithium atoms. When the Fermi momentum is larger than the photon recoil, most final momentum states are within the Fermi surface. At low temperature, we find that light scattered even at large angles is suppressed by 37% compared with higher temperatures, where atoms scatter at the single-atom Rayleigh scattering rate.

Pauli blocking of atom-light scattering.

Transition rates between coupled states in a quantum system depend on the density of available final states. The radiative decay of an excited atomic state has been suppressed by reducing the density of electromagnetic vacuum modes near the atomic transition. Likewise, reducing the density of available momentum modes of the atomic motion when it is embedded inside a Fermi sea will suppress spontaneous emission and photon scattering rates. Here we report the experimental demonstration of suppressed light scattering in a quantum degenerate Fermi gas. We systematically measured the dependence of the suppression factor on the temperature and Fermi energy of a strontium quantum gas and achieved suppression of scattering rates by up to a factor of 2 compared with a thermal gas.

Observation of Pauli blocking in light scattering from quantum degenerate fermions.

The Pauli exclusion principle forbids indistinguishable fermions from occupying the same quantum mechanical state. The implications of this are profound; for example, it accounts for the electronic shell structure of atoms. Here, we performed measurements on the scattering of light from ultracold ensembles of atoms. For a Fermi gas in the quantum degenerate regime, we observed a marked suppression in scattering compared with a similarly prepared Bose gas. The observed decrease in fluorescence and the corresponding increase in light transmission results from Pauli blocking, where Fermi-Dirac statistics limits the number of accessible states for a scattering atom in a large Fermi sea. Our work confirms a fundamental result on the optical response of quantum gases and may contribute to cooling and thermometry schemes.

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.

Scattering hypervolume of spin-polarized fermions

We analyze the collision of three identical spin-polarized fermions at zero collision energy, assuming arbitrary finite-range potentials, and define the corresponding three-body scattering hypervolume ${D}_{F}$. The scattering hypervolume $D$ was first defined for identical bosons in 2008. It is the three-body analog of the two-body scattering length. We solve the three-body Schr\"odinger equation asymptotically when the three fermions are far apart or one pair and the third fermion are far apart, deriving two asymptotic expansions of the wave function. Unlike the case of bosons for which $D$ has the dimension of length to the fourth power, here the ${D}_{F}$ we define has the dimension of length to the eighth power. We then analyze the interaction energy of three such fermions with momenta $\ensuremath{\hbar}{\mathbf{k}}_{1}$, $\ensuremath{\hbar}{\mathbf{k}}_{2}$, and $\ensuremath{\hbar}{\mathbf{k}}_{3}$ in a large periodic cubic box. The energy shift due to ${D}_{F}$ is proportional to ${D}_{F}/{\mathrm{\ensuremath{\Omega}}}^{2}$, where $\mathrm{\ensuremath{\Omega}}$ is the volume of the box. We also calculate the shifts of energy and pressure of spin-polarized Fermi gases due to a nonzero ${D}_{F}$ and the three-body recombination rate of spin-polarized ultracold atomic Fermi gases at finite temperatures.

Observation of a superradiant quantum phase transition in an intracavity degenerate Fermi gas.

Coupling Bose-Einstein condensates to optical cavities has enabled the study of many-body states with long-range interactions. However, equivalent experiments with ultracold Fermi gases have remained largely unexplored. Here, we report an experimental realization of a superradiant quantum phase transition of a degenerate Fermi gas in a transversely pumped optical cavity. The self-ordering checkerboard density pattern of Fermi gases and superradiant transitions of the cavity field spontaneously emerge by increasing the pumping intensity above a threshold value. The effects of Fermi statistics are manifested by an inverse square root scaling of the threshold with atom number and the slow dynamics of low–atomic momentum states. Our work provides an ideal platform for studying nonequilibirium dynamics of many-body states for long-range interacting Fermi gases.

Spin-imbalanced homogeneous atomic fermi gas in two dimensions

Spin-imbalanced homogeneous atomic fermi gas in two dimensions

Observation of the BEC-BCS crossover in a degenerate Fermi gas of lithium atoms

We observe characteristic atomic behaviors in the Bose–Einstein-condensation-Bardeen–Cooper–Schrieffer (BECBCS) crossover, by accurately tuning the magnetic field across the Feshbach resonance of lithium atoms. The magnetic field is calibrated by measuring the Zeeman shift of the optical transition. A non-monotonic anisotropic expansion is observed across the Feshbach resonance. The density distribution is explored in different interacting regimes, where a condensate of diatomic molecules forms in the BEC limit with the indication of a bimodal distribution. We also measure the three-body recombination atom loss in the BEC-BCS crossover, and find that the magnetic field of the maximum atom loss is in the BEC limit and gets closer to the Feshbach resonance when decreasing the atom temperature, which agrees with previous experiments and theoretical prediction. This work builds up a controllable platform for the study on the strongly interacting Fermi gas.

A generalized molecule approach capturing the Feshbach-induced pairing physics in the BEC–BCS crossover

By including the effect of a trap with characteristic energy given by the Fermi temperature T F in a two-body two-channel model for Feshbach resonances, we reproduce the measured binding energy of ultracold molecules in a 40K atomic Fermi gas. We also reproduce the experimental closed-channel fraction Z across the BEC–BCS crossover and into the BCS regime of a 6Li atomic Fermi gas. We obtain the expected behavior at unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of the Z dependency on T F on the BCS side, where a significant quantitative discrepancy between experimental data and theory’s predictions has been repeatedly reported. In order to contrast with future experiments we report the proportionality constant at unitarity between Z and predicted by our model for a 40K atomic Fermi gas.

Exotic Vortex States with Discrete Rotational Symmetry in Atomic Fermi Gases with Spin-Orbital-Angular-Momentum Coupling.

We investigate the superfluidity of a two-component Fermi gas with spin-orbital-angular-momentum coupling (SOAMC). Because of the intricate interplay of SOAMC, two-photon detuning and atom-atom interaction, a family of vortex ground states emerges in a broad parameter regime of the phase diagram, in contrast to the usual case where an external rotation or magnetic field is generally required. More strikingly, an unprecedented vortex state, which breaks the continuous rotational symmetry to a discrete one spontaneously, is predicted to occur. The underlying physics are elucidated and verified by numerical simulations. The unique density distributions of the predicted vortex states enable a direct observation in experiment.