Unitary Limit Research Articles

Third- and fourth-order virial coefficients of harmonically trapped fermions in a semiclassical approximation

Using a leading-order semiclassical approximation, we calculate the third- and fourth-order virial coefficients of nonrelativistic spin-1/2 fermions in a harmonic trapping potential in arbitrary spatial dimensions, and as functions of temperature, trapping frequency and coupling strength. Our simple, analytic results for the interaction-induced changes $\Delta b_3$ and $\Delta b_4$ agree qualitatively, and in some regimes quantitatively, with previous numerical calculations for the unitary limit of three-dimensional Fermi gases.

Effects of finite-range interactions on the one-electron spectral properties of TTF-TCNQ

The electronic dispersions of the quasi-one-dimensional organic conductor TTF-TCNQ are studied by angle-resolved photoelectron spectroscopy (ARPES) with higher angular resolution and accordingly smaller step width than in previous studies. Our experimental results suggest that a refinement of the single-band 1D Hubbard model that includes finite-range interactions is needed to explain these photoemission data. To account for the effects of these finite-range interactions we employ a mobile quantum impurity scheme that describes the scattering of fractionalized particles at energies above the standard Tomonaga-Luttinger liquid limit. Our theoretical predictions agree quantitatively with the location in the $(k,\omega)$ plane of the experimentally observed ARPES structures at these higher energies. The nonperturbative microscopic mechanisms that control the spectral properties are found to simplify in terms of the exotic scattering of the charge fractionalized particles. We find that the scattering occurs in the unitary limit of (minus) infinite scattering length, which limit occurs within neutron-neutron interactions in shells of neutron stars and in the scattering of ultracold atoms but not in perturbative electronic condensed-matter systems. Our results provide important physical information on the exotic processes involved in the finite-range electron interactions that control the high-energy spectral properties of TTF-TCNQ. Our results also apply to a wider class of 1D and quasi-1D materials and systems that are of theoretical and potential technological interest.

Critical Josephson current in BCS-BEC–crossover superfluids

We develop a microscopic model to describe the Josephson dynamics between two superfluid reservoirs of ultracold fermionic atoms which accounts for the dependence of the critical current on both the barrier height and the interaction strength along the crossover from BCS to BEC. Building on a previous study [F. Meier & W. Zwerger, Phys. Rev. A, 64 033610 (2001)] of weakly-interacting bosons, we derive analytic results for the Josephson critical current at zero temperature for homogeneous and trapped systems at arbitrary coupling. The critical current exhibits a maximum near the unitarity limit which arises from the competition between the increasing condensate fraction and a decrease of the chemical potential along the evolution from the BCS to the BEC limit. Our results agree quantitatively with numerical simulations and recent experimental data.

Zero-range Fermi gas along the BCS-BEC crossover

Properties of the ground state of an unpolarized ultracold Fermi gas along the BCS-BEC crossover are investigated by the variational and diffusion Monte Carlo methods. We apply the Wigner-Bethe-Peierls boundary condition in our calculations to avoid any bias from using an interatomic potential with finite effective range. Properties for several values of the scattering length are studied in the range $\ensuremath{-}8\ensuremath{\le}1/a{k}_{F}\ensuremath{\le}4$, including the unitary limit. The contact parameters as a function of scattering length are obtained by fitting the pair distribution functions for particles with different spins. The energies and contact parameters are in very good agreement with experimental data reported in the literature.

Embedding nuclear physics inside the unitary-limit window

The large values of the singlet and triplet scattering lengths locate the two-nucleon system close to the unitary limit, the limit in which these two values diverge. As a consequence, the system shows a continuous scale invariance which strongly constrains the values of the observables, a well-known fact already noticed a long time ago. The three-nucleon system shows a discrete scale invariance that can be observed by correlations of the triton binding energy with other observables as the doublet nucleon-deuteron scattering length or the alpha-particle binding energy. The low-energy dynamics of these systems is universal; it does not depend on the details of the particular way in which the nucleons interact. Instead, it depends on a few control parameters, the large values of the scattering lengths and the triton binding energy. Using a potential model with variable strength set to give values to the control parameters, we study the spectrum of $A=2,3,4,6$ nuclei in the region between the unitary limit and their physical values. In particular, we analyze how the binding energies emerge from the unitary limit forming the observed levels.

Tev-scale thermal WIMPs: Unitarity and its consequences

We re-examine unitarity bounds on the annihilation cross section of thermal-WIMP dark matter. For high-mass pointlike dark matter, it is generic to form WIMP bound states, which, together with Sommerfeld enhancement, affects the relic abundance. We show that these effects lower the unitarity bound from 139 TeV to below 100 TeV for non-self-conjugate dark matter and from 195 TeV (the oft-quoted value of 340 TeV assumes $\Omega_{DM} h^2 = 1$) to 140 TeV for the self-conjugate case. For composite dark matter, for which the unitarity limit on the radius was thought to be mass-independent, we show that the largest allowed mass is 1 PeV. In addition, we find important new effects for annihilation in the late universe. For example, while the production of high-energy light fermions in WIMP annihilation is suppressed by helicity, we show that bound-state formation changes this. Coupled with rapidly improving experimental sensitivity to TeV-range gamma rays, cosmic rays, and neutrinos, our results give new hope to attack the thermal-WIMP mass range from the high-mass end.

Weak coupling to unitarity crossover in Bose-Fermi mixtures: Mixing-demixing transition and spontaneous symmetry breaking in trapped systems

The usual treatment of a Bose-Fermi mixture relies on weak-coupling Gross-Pitaevskii (GP) and density-functional (DF) Lagrangians, often including the more realistic {perturbative} Lee-Huang-Yang (LHY) corrections. We suggest analytic {non-perturbative} beyond-mean-field Bose and Fermi Lagrangians valid along the crossover from weak- to strong-coupling limits of intra-species interactions consistent with the LHY corrections and the strong-coupling (unitarity) limit for small and large scattering lengths $|a|$, respectively, and use these to study the Bose-Fermi mixture. We study numerically mixing-demixing and spontaneous symmetry breaking in Bose-Fermi mixtures in spherically-symmetric and quasi-one-dimensional traps while the intra-species Bose and Fermi interactions are varied from weak-coupling to strong-coupling limits.The LHY correction is appropriate for medium to weak atomic interactions and diverges for stronger interactions (large scattering length $|a|$), whereas the present beyond-mean-field Lagrangian is finite in the unitarity limit ($|a|\to \infty$). We illustrate our results using the Bose-Fermi $^7$Li-$^6$Li mixture under a spherically-symmetric and a quasi-one-dimensional trap. The results obtained with the present model for density distribution of the Bose-Fermi mixture along the crossover could be qualitatively different from the usual GP-DF Lagrangian with or without LHY corrections. Specifically, we identified spontaneous symmetry breaking and demixing in the present model not found in the usual model with the same values of the parameters.

Unitary limit and linear scaling of neutrons in harmonic trap with tuned CD-Bonn and square-well interactions

We study systems of finite-number neutrons in a harmonic trap at the unitary limit. Two very different types of neutron-neutron interactions are applied, namely, the meson-theoretic CD-Bonn potential and hard-core square-well interactions, all tuned to possess an infinite scattering length, and with effective ranges comparable to the trap size. The potentials are renormalized to equivalent, scattering-length preserving low-momentum potentials, Vlow−k, with which the particle-particle hole-hole ring diagrams are summed to all orders to yield the ground-state energy E0 of the finite neutron system. We find the ratio E0/E0free (where E0free denotes the ground-state energy of the corresponding non-interacting system) to be remarkably independent from variations of the harmonic trap parameter, the type and effective range of the unitarity interaction, and the decimation momentum of Vlow−k. Our results support a special linear scaling relation of E0 versus the trap parameter ħω. Certain properties of Landau's quasi-particles for trapped neutrons at the unitary limit are also discussed.

Modeling B19 as a B17−n−n three-body system in the unitary limit

We present a model description of the bound $^{17}$B isotope in terms of a $^{17}$B-n-n three-body system where the two-body subsystems $^{17}$B-n and n-n are unbound (virtual) states close to the unitary limit. The $^{17}$B ground state is well described in terms of two-body potentials only, and two low-lying resonances are predicted. Their eventual link with the Efimov physics is discussed. This model can be naturally used to describe the recently discovered resonant states in $^{20,21}$B.

Viscosity bound violation in viscoelastic Fermi liquids

The anti-de Sitter/conformal field theory correspondence (AdS/CFT) has been used to determine a lower bound on the ratio of shear viscosity to entropy density (s) for strongly-coupled field theories with a gravity dual. The conjectured universal lower bound, given as , is a measure of interaction strength in a quantum fluid where equality indicates a perfect quantum fluid. In this paper we study η/s in a Fermi gas in the unitary limit. We show that in addition to a local minimum for η/s at which obeys the lower bound, a more interesting result exists in the violation of the η/s lower bound due to the superfluid fluctuations above Tc. To conclude, we examine the viscoelastic properties of the unitary Fermi gas. Previous work brought to light the connection between violation of the η/s bound and a viscoelastic response in the context of holographic solids. We ultimately find that, in addition to holographic solids, all Fermi liquids with a viscoelastic response produced by superfluid fluctuations can violate the universal η/s lower bound.

Four-Boson Continuous Scale Symmetry Breaking

We show that the homogeneous Faddeev–Yakubovski formalism for the bound state of four identical bosons with zero-range interaction in the unitary limit (infinite two-body scattering length) presents scale invariance in the ultraviolet (UV) region. By resorting to an approximate form of the integral equations in the UV limit (considering exclusively an attractive pairwise zero-range interaction), we demonstrate that a pair of log-periodic solutions, with a cycle distinct from the three-boson one, exists with a four-body scale required to define the phase between them.

Breakdown of the Fermi polaron description near Fermi degeneracy at unitarity

We theoretically investigate attractive and repulsive Fermi polarons in three dimensions at finite temperature and impurity concentration through the many-body T-matrix theory and high-temperature virial expansion. By using the analytically continued impurity Green’s function, we calculate the direct rf spectroscopy of attractive polarons in the unitary regime. Taking the peak value of the rf spectroscopy as the polaron energy and the full width half maximum as the polaron lifetime, we determine the temperature range of validity for the quasi-particle description of Fermi polarons in the unitary limit.

Strong-Coupling Effects on Specific Heat in the BCS–BEC Crossover

We theoretically investigate strong-coupling effects on specific heat at constant volume $C_{\rm V}$ in a superfluid Fermi gas with a tunable interaction associated with Feshbach resonance. Including fluctuations of the superfluid order parameter within the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we calculate the temperature dependence of $C_{\rm V}$ at the unitarity limit in the superfluid phase. We show that, in the low temperature region, $T^3$-behavior is shown in the temperature dependence of $C_{\rm V}$. This result indicates that the low-lying excitations are dominated by the gapless Goldstone mode, associated with the phase fluctuations of the superfluid order parameter. Since the Goldstone mode is one of the most fundamental phenomena in the Fermionic superfluidity, our results are useful for further understanding how the pairing fluctuations affects physical properties in the BCS-BEC crossover physics below the superfluid transition temperature.

Confinement-induced resonances in two-center problem via a pseudopotential approach

We study confined scattering of a quantum particle by two centers fixed on the longitudinal axis of a harmonic-waveguide-like trap. The conditions of confinement-induced resonances (CIRs) appearing in these systems, when scattering cross section approaches the unitary limit, are derived for a regularized pseudopotential describing particle interaction with scattering centers. In the limit of a single center, the position of CIR for an even state tends to the well-known result obtained by Olshanii [Phys. Rev. Lett. 81, 938 (1998)]. Our result can be applicable to confined atomic scattering by fixed impurities, such as ions or Rydberg atoms, with possible extension to $N$ impurities, or by two-atomic molecules.

Symmetry obstruction to Fermi liquid behavior in the unitary limit

We show that a Fermi gas, in three dimensions, at temperatures above the superconducting phase transition but below the Fermi temperature, can not be described by Fermi Liquid Theory (FLT) in the unitary limit where the scattering length diverges. The result follows by showing that the there are no effective field theory descriptions that both behave like a Fermi liquid and properly non-linearly realize the spontaneously broken boost and conformal invariance of the system.

Multi-body Correlations in SU(3) Fermi Gases

We investigate strong-coupling effects in a three-component atomic Fermi gas. It is a promising candidate for simulating quantum chromodynamics (QCD), and furthermore, the emergence of various phenomena such as color superfluidity and Efimov effect are anticipated in this system. In this paper, we study the effects of two-body and three-body correlations by means of the many-body $T$-matrix approximation (TMA) as well as the Skorniakov-Ter-Martirosian (STM) equation with medium corrections. We investigate the effects of finite temperature and chemical potential on the trimer binding energy at the superfluid critical point of the unitarity limit.

Direct signals from electroweak singlets through the Higgs portal

We review predictions and constraints for nuclear recoil signals from Higgs portal dark matter under the assumption of standard thermal creation from freeze-out. Thermally created scalar and vector Higgs portal dark matter masses are constrained to be in the resonance region near half the Higgs mass, [Formula: see text], or above several TeV. The resonance region for these models will be tested by XENONnT and LZ. The full mass range up to the unitarity limit can be tested by DarkSide-20k and DARWIN. Fermionic Higgs portal dark matter with a pure CP odd coupling is constrained by the Higgs decay width, but has strongly suppressed recoil cross sections which cannot be tested with upcoming experiments. Fermionic Higgs portal dark matter with a combination of CP even and odd Higgs couplings can be constrained by the direct search experiments.

Renormalisation group analysis of electromagnetic couplings in the pionless effective field theory

.The Wilsonian renormalisation group is applied to a system of two nonrelativistic particles interacting via short-range forces and coupled to an external EM field. By demanding that a fully off-shell one-particle-irreducible 5-point amplitude is independent of the cutoff, a renormalisation group equation is derived for the interaction current density. This is solved to obtain the fixed point corresponding to the unitary limit. The scaling behaviour of perturbations around this point is analysed. Some of these terms are related by gauge invariance to terms in the effective-range expansion; others describe short-range physics that is not included in the two-body potential. We construct observables including the bound-state form factor and show how the scaling of the terms in the interaction current is reflected in the power counting for their contributions to observables.

Transversal modes and Higgs bosons in electroweak vector-boson scattering at the LHC

Processes where W and Z bosons scatter into pairs of electroweak bosons W, Z, and Higgs, are sensitive probes of new physics in the electroweak sector. We study simplified models that describe typical scenarios of new physics and parameterize the range of possible LHC results between the standard-model prediction and unitarity limits. Extending the study beyond purely longitudinal scattering, we investigate the role of transversally polarized gauge bosons. Unitarity becomes an essential factor, and limits on parameters matched to the naive perturbative low-energy effective theory turn out to be necessarily model-dependent. We discuss the implications of our approach for the interpretation of LHC data on vector-boson scattering and Higgs-pair production.

Pair Breaking, Pseudogap, and Superconducting Tc of Hole-Doped Cuprates: Interrelations and Implications

Irrespective of the class they belong to, all the hole doped high-Tc cuprate superconductors show an anti-correlation between the superconducting transition temperature and the characteristic pseudogap energy in the underdoped region. The doping dependent pseudogap in the quasiparticle spectral density is believed to remove low-energy electronic states and thereby reduce the superconducting condensate. Impurities within the CuO2 plane, on the other hand, break Cooper pairs in the unitarity limit and diminish superfluid density. Both pseudogap in pure cuprates and impurity scattering in disordered cuprates reduces Tc very effectively. In this study we have compared and contrasted the mechanisms of Tc degradation due to pseudogap and impurity scattering in hole doped cuprates. We have suggested a framework where both these factors can be treated on somewhat equal footing. Beside impurity and pseudogap dependent superconducting transition temperature, the proposed scenario has been employed to investigate the disorder and hole content dependent isotope exponent in high-Tc cuprates in this work.