Bose-Einstein Condensation Crossover Research Articles

Finite-range effect in the two-dimensional density-induced BCS–BEC crossover

Abstract We theoretically investigate the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover in a two-dimensional Fermi gas with the finite-range interaction by using the Hartree–Fock–Bogoliubov theory. Expanding the scattering phase shift in terms of the scattering length and effective range, we discuss the effect of the finite-range interaction on the pairing and thermodynamic properties. By solving the gap equation and the number equation self-consistently, we numerically calculate the effective-range dependence of the pairing gap, chemical potential, and pair size throughout the BCS–BEC crossover. Our results would be useful for further understanding of low-dimensional many-body problems.

Density-wave ordering in a unitary Fermi gas with photon-mediated interactions

A density wave (DW) is a fundamental type of long-range order in quantum matter tied to self-organization into a crystalline structure. The interplay of DW order with superfluidity can lead to complex scenarios that pose a great challenge to theoretical analysis. In the past decades, tunable quantum Fermi gases have served as model systems for exploring the physics of strongly interacting fermions, including most notably magnetic ordering1, pairing and superfluidity2, and the crossover from a Bardeen–Cooper–Schrieffer superfluid to a Bose–Einstein condensate3. Here, we realize a Fermi gas featuring both strong, tunable contact interactions and photon-mediated, spatially structured long-range interactions in a transversely driven high-finesse optical cavity. Above a critical long-range interaction strength, DW order is stabilized in the system, which we identify via its superradiant light-scattering properties. We quantitatively measure the variation of the onset of DW order as the contact interaction is varied across the Bardeen–Cooper–Schrieffer superfluid and Bose–Einstein condensate crossover, in qualitative agreement with a mean-field theory. The atomic DW susceptibility varies over an order of magnitude upon tuning the strength and the sign of the long-range interactions below the self-ordering threshold, demonstrating independent and simultaneous control over the contact and long-range interactions. Therefore, our experimental setup provides a fully tunable and microscopically controllable platform for the experimental study of the interplay of superfluidity and DW order.

Nonequilibrium noise as a probe of pair-tunneling transport in the BCS-BEC crossover.

The detection of elementary carriers in transport phenomena is one of the most important keys to understand nontrivial properties of strongly correlated quantum matter. Here, we propose a method to identify the tunneling current carrier in strongly interacting fermions from nonequilibrium noise in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate crossover. The noise-to-current ratio, the Fano factor, can be a crucial probe for the current carrier. Bringing strongly correlated fermions into contact with a dilute reservoir produces a tunneling current in between. The associated Fano factor increases from one to two as the interaction becomes stronger, reflecting the fact that the dominant conduction channel changes from the quasiparticle tunneling to the pair tunneling.

Isothermal compressibility and effects of multibody molecular interactions in a strongly interacting ultracold Fermi gas

We theoretically investigate the isothermal compressibility $\kappa_{T}$ in the normal state of an ultracold Fermi gas. Including pairing fluctuations, as well as preformed-pair formations, within the framework of the self-consistent $T$-matrix approximation (SCTMA), we evaluate the temperature dependence of this thermodynamic quantity over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. While $\kappa_T$ in the weak-coupling BCS regime is dominated by Fermi atoms near the Fermi surface, correlations between tightly bound Cooper-pair molecules are found to play crucial roles in the strong-coupling BEC regime. In the latter region, besides a two-body molecular interaction, a three-body one is shown to sizably affect $\kappa_T$ near the superfluid phase transition temperature. Our results indicate that the strong-coupling BEC regime of an ultracold Fermi gas would provide a unique opportunity to study multi-body correlations between Cooper-pair molecules.

Excitonic condensation state in the assistance of the adiabatic and anti-adiabatic phonons

The excitonic condensate in semimetal and semiconducting materials with the assistance of the phonons in both the adiabatic and anti-adiabatic regimes has been investigated. In the framework of the random phase approximation, we analyse the static excitonic susceptibility function once the electrons and holes are described in the extended Falicov–Kimball model involving the electron–phonon interaction. The excitonic condensate transition point is detected as a divergence of the susceptibility function. The complex phase diagrams exhibit the significant impact of the adiabatic phonons on the stability of the excitonic condensation state. In contrast, phonons in the anti-adiabatic regime play a less role in the formation and the condensation of the excitons. Depending on the temperature or the external pressure, the excitonic condensate stability and its Bardeen–Cooper–Schrieffer–Bose–Einstein condensation crossover in the systems are also discussed in detail.

Three-body crossover from a Cooper triple to a bound trimer state in three-component Fermi gases near a triatomic resonance

We theoretically investigate ground-state properties of a three-component Fermi gas with pairwise contact interactions between different components near a triatomic resonance where bound trimers are about to appear. Using variational equations for in-medium two- and three-body cluster states in three dimensions, we elucidate the competition of pair and triple formations due to the Fermi surface effects. We present the ground-state phase diagram that exhibits transition from a Cooper pair to Cooper triple state and crossover from a Cooper triple to tightly bound trimer state at negative scattering lengths. This three-body crossover is analogous to the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover observed in a two-component Fermi gas. We predict that the threshold scattering length $a_{-}$ for three-body states can be shifted towards the weak-coupling side due to the emergence of Cooper triples.

Resonant multi-gap superconductivity at room temperature near a Lifshitz topological transition in sulfur hydrides

The maximum critical temperature for superconductivity in pressurized hydrides appears at the top of superconducting domes in Tc vs pressure curves at a particular pressure, which is not predicted by standard superconductivity theories. The high-order anisotropic Van Hove singularity near the Fermi level observed in band-structure calculations of pressurized sulfur hydride, typical of a supermetal, has been associated with the array of metallic hydrogen wire modules forming a nanoscale heterostructure at an atomic limit called the superstripe phase. Here, we propose that pressurized sulfur hydrides behave as a heterostructure made of a nanoscale superlattice of interacting quantum wires with a multicomponent electronic structure. We present first-principles quantum calculation of a universal superconducting dome where Tc amplification in multi-gap superconductivity is driven by the Fano–Feshbach resonance due to a configuration interaction between open and closed pairing channels, i.e., between multiple gaps in the BCS regime, resonating with a single gap in the BCS–Bose–Einstein condensation crossover regime. In the proposed three dimensional phase diagram, the critical temperature shows a superconducting dome where Tc is a function of two variables: (i) the Lifshitz parameter (η) measuring the separation of the chemical potential from the Lifshitz transition normalized by the inter-wire coupling and (ii) the effective electron–phonon coupling (g) in the appearing new Fermi surface including phonon softening. The results will be of help for material design of room-temperature superconductors at ambient pressure.

Mechanisms of screening or enhancing the pseudogap throughout the two-band Bardeen-Cooper-Schrieffer to Bose-Einstein condensate crossover

We demonstrate the rise-and-fall of multiple pseudogaps in the Bardeen-Cooper-Schrieffer-Bose-Einstein-condensation (BCS-BEC) crossover in two-band fermionic systems having different pairing strengths in the deep band and in the shallow band. The striking features of this phenomenon are an unusual many-body screening of pseudogap state and the importance of pair-exchange couplings, which induces multiple pseudogap formation in the two bands. The multi-band configuration suppresses pairing fluctuations and the pseudogap opening in the strongly-interacting shallow band at small pair-exchange couplings by screening effects, with possible connection to the pseudogap phenomenology in iron based superconductors. On the other hand, the multiple pseudogap mechanism accompanies with the emergence of binary preformed Cooper pairs originating from interplay between intra-band and pair-exchange couplings.

Josephson dynamics of strongly interacting superfluid Fermi gases in double-well potentials

In this work, we study the nonlinear Josephson dynamics of Fermi superfluids in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a molecular Bose-Einstein condensate (BEC) in a double-well potential. Under a two-mode approximation, we derive a full two-mode (fTM) model including all interaction energy terms. By solving the fTM model numerically, we study the zero-phase and [Formula: see text]-phase modes of Josephson oscillations in the BCS–BEC crossover. We find that in the strongly interacting regime the cross interaction terms not appearing in the two-mode model cannot be easily ignored. The cross interactions can alter the behaviors of Josephson dynamics substantially, and interestingly the alterations for the zero-phase and [Formula: see text]-phase modes are just opposite.

Doping-controlled transition from excitonic insulator to semimetal in Ta2NiSe5

Excitonic insulator (EI) is an intriguing insulating phase of matter, where electrons and holes are bonded into pairs, so called excitons, and form a phase-coherent state via Bose-Einstein Condensation (BEC). Its theoretical concept has been proposed several decades ago, but the followed research is very limited, due to the rare occurrence of EI in natural materials and the lack of manipulating method of excitonic condensation. In this paper, we report the realization of a doping-controlled EI-to-semi-metal transition in Ta$_2$NiSe$_5$ using $in$-$situ$ potassium deposition. Combining with angle-resolved photoemission spectroscopy (ARPES), we delineate the evolution of electronic structure through the EI transition with unprecedented precision. The results not only show that Ta$ _2 $NiSe$ _5 $ (TNS) is an EI originated from a semi-metal non-interacting band structure, but also resolve two sequential transitions, which could be attributed to the phase-decoherence and pair-breaking respectively. Our results unveil the Bardeen-Cooper-Schrieffer (BCS)-BEC crossover behavior of TNS and demonstrate that its band structure and excitonic binding energy can be tuned precisely via alkali-metal deposition. This paves a way for investigations of BCS-BEC crossover phenomena, which could provide insights into the many-body physics in condensed matters and other many-body systems.

Superconductivity of the FeSe/SrTiO3 Interface in View of BCS–BEC Crossover**Supported by the National Key R&D Program of China under Grant Nos 2017YFA0303600, 2016YFA0300600 and 2016YFA0202300, the National Natural Science Foundation of China under Grant No 11634016, the Strategic Priority Research Program (B) of Chinese Academy of Sciences under Grant No XDB07030100, the Research Program of Beijing Academy of Quantum Information

In paired Fermi systems, strong many-body effects exhibit in the crossover regime between the Bardeen–Cooper–Schrieffer (BCS) and the Bose–Einstein condensation (BEC) limits. The concept of the BCS–BEC crossover, which is studied intensively in the research field of cold atoms, has been extended to condensed matters. Here by analyzing the typical superconductors within the BCS–BEC phase diagram, we find that FeSe-based superconductors are prone to shift their positions in the BCS–BEC crossover regime by charge doping or substrate substitution, since their Fermi energies and the superconducting gap sizes are comparable. Especially at the interface of single-layer FeSe on SrTiO3 substrate, the superconductivity is relocated closer to the crossover unitary than other doped FeSe-based materials, indicating that the pairing interaction is effectively modulated. We further show that hole-doping can drive the interfacial system into the phase with possible pre-paired electrons, demonstrating its flexible tunability within the BCS–BEC crossover regime.

Collective oscillation modes of a superfluid Bose–Fermi mixture

In this work, we present a theoretical study for the collective oscillation modes, i.e. quadrupole, radial and axial mode, of a mixture of Bose and Fermi superfluids in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a molecular Bose–Einstein condensate (BEC) in harmonic trapping potentials with cylindrical symmetry of experimental interest. To this end, we start from the coupled superfluid hydrodynamic equations for the dynamics of Bose–Fermi superfluid mixtures and use the scaling theory that has been developed for a coupled system. The collective oscillation modes of Bose–Fermi superfluid mixtures are found to crucially depend on the overlap integrals of the spatial derivations of density profiles of the Bose and Fermi superfluids at equilibrium. We not only present the explicit expressions for the overlap density integrals, as well as the frequencies of the collective modes provided that the effective Bose–Fermi coupling is weak, but also test the valid regimes of the analytical approximations by numerical calculations in realistic experimental conditions. In the presence of a repulsive Bose–Fermi interaction, we find that the frequencies of the three collective modes of the Bose and Fermi superfluids are all upshifted, and the change speeds of the frequency shifts in the BCS–BEC crossover can characterize the different groundstate phases of the Bose–Fermi superfluid mixtures for different trap geometries.

Impurity-induced Shiba bound state in the BCS–BEC crossover regime of two-dimensional Fermi superfluid**Project supported by the National Key R&D Program of China (Grant No. 2017YFA0206302).

For a two-dimensional ultra-cold Fermi superfluid with an effective static magnetic impurity, we theoretically investigated the variation of the Yu–Shiba–Rusinov (YSR) bound state in the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover regime. Within the framework of mean-field theory, analytical results of the YSR bound state energy were obtained as a function of the interaction parameters. First, when the background Fermi superfluid system stays in the weakly interacting BCS regime, we found that the YSR bound state energy is linearly dependent on the gap parameter with its coefficient slightly different from previous results. Second, we discovered re-entrance phenomena for the YSR state and an upper bound of the strength of the interaction between the paired atoms. By carefully analyzing the bound state energy as a function of the interaction parameters, we obtained a phase diagram showing the existence of the YSR state. Finally, we concluded that the re-entrance phenomena and the critical point can be easily experimentally detected through measurement of radio-frequency spectroscopy and density of states using current experimental techniques.

BCS – BEC crossover, collective excitations, and hydrodynamics of superfluid quantum liquids and gases

A Fermi gas described within the Bardeen–Cooper–Schrieffer (BCS) theory can be converted into a Bose–Einstein condensate (BEC) of composite molecules (dimers) by adiabatically tuning the interaction. The sequence of states that emerge in the process of such a conversion is referred to as the BCS–BEC crossover. We here review the theoretical and experimental results obtained for the BCS–BEC crossover in three- and quasi-two-dimensional quantum gases in the limiting geometry of traps and on optical lattices. We discuss nontrivial phenomena in the hydrodynamics of superfluid quantum gases and fluids, including the collective excitation spectrum in the BCS–BEC crossover, the hydrodynamics of rotating Bose condensates containing a large number of quantized vortices, and the intriguing problem of the chiral anomaly in the hydrodynamics of superfluid Fermi systems with an anisotropic p-wave pairing. We also analyze spin-imbalanced quantum gases and the potential to realize the triplet p-wave pairing via the Kohn–Luttinger mechanism in those gases. Recent results on two-dimensional Fermi-gas preparation and the observation of fluctuation phenomena related to the Berezinskii–Kosterlitz–Thouless transition in those gases are also reviewed. We briefly discuss the recent experimental discovery of the BCS–BEC crossover and anomalous superconductivity in bilayer graphene and the role of graphene, other Dirac semimetals (for example, bismuth), and 2D optical lattices as potential reference systems that exhibit all of the effects reviewed here.

Temperature Dependence of Paramagnetic Critical Magnetic Field in Disordered Attractive Hubbard Model

Within the generalized DMFT+$\Sigma$ approach we study disorder effects in the temperature dependence of paramagnetic critical magnetic field $H_{cp}(T)$ for Hubbard model with attractive interaction. We consider the wide range of attraction potentials $U$ - from the weak coupling limit, when superconductivity is described by BCS model, up to the limit of very strong coupling, when superconducting transition is related to Bose - Einstein condensation (BEC) of compact Cooper pairs. The growth of the coupling strength leads to the rapid growth of $H_{cp}(T)$ at all temperatures. However, at low temperatures paramagnetic critical magnetic field $H_{cp}$ grows with $U$ much slower, than the orbital critical field, and in BCS limit the main contribution to the upper critical magnetic filed is of paramagnetic origin. The growth of the coupling strength also leads to the disappearance of the low temperature region of instability towards type I phase transition and Fulde - Ferrell - Larkin - Ovchinnikov (FFLO) phase, characteristic for BCS weak coupling limit. Disordering leads to the rapid drop of $H_{cp}(T)$ in BCS weak coupling limit, while in BCS - BEC crossover region and BEC limit $H_{cp}(T\to 0)$ dependence on disorder is rather weak. Within DMFT+$\Sigma$ approach disorder influence on $H_{cp}(T)$ is of universal nature at any coupling strength and related only to disorder widening of the conduction band. In particular, this leads to the drop of the effective coupling strength with disorder, so that disordering restores the region of type I transition in the intermediate coupling region.

Super Efimovian expansions of superfluid Fermi gases in the BCS–BEC crossover

We study the super Efimovian expansions of a superfluid Fermi gas in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC), by using superfluid hydrodynamic equations with the equation of state fitting from the experimental data and a scaling approach. We find that in an isotropic trap, the super Efimovian expansion of the Fermi superfluid in the unitary limit is characterized by the double-log periodicity, while for an axially symmetric trap, the double-log periodicity only emerges in the longer direction for a large anisotropy of the trapping frequencies. Away from unitarity where the scale invariance is broken, the super Efimovian expansions of the superfluid Fermi gases deviate from the double-log oscillations. The oscillations in the BCS regime deviate upward from the double-log oscillations, whereas the oscillations in the BEC regime deviate downward and the deviation in the BEC limit is the most significant. This difference can be used to discriminate different superfluid regimes.

Collective dipole oscillations in a mixture of Bose and Fermi superfluids in the BCS–BEC crossover

We present a study for the collective dipole oscillations of a mixture of Bose and Fermi superfluids in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a molecular Bose–Einstein condensate (BEC) in the ENS experimental setup (Ferrier-Barbut et al 2014 Science 345 1035). The dynamics of the double superfluidity is described by coupled time-dependent order-parameter equations, which are Gross–Pitaevskii equations for the Bose superfluid, coupled to the order-parameter equation including the equation of state fitting from the experimental data for the Fermi superfluid in the BCS–BEC crossover. The numerical simulations show that due to the boson–fermion interaction, the frequencies of the dipole oscillations of the Bose and Fermi superfluids are both downshifted and the frequency shifts increase monotonically from the BCS side to BEC side, which are in agreement with the experiment. We further study the dependencies of the frequency shifts on the oscillation amplitudes and the nonlinear effects, in which the Bose and Fermi superfliuds show different features. The frequency shifts of the Bose superfluid increase linearly as the oscillation amplitudes increase, while the frequency shifts of the Fermi superfluid show a quadratical increase. It is found that the intrinsic dipole oscillations of the Bose (Fermi) superfluid can be triggered by only boosting the Fermi (Bose) superfluid.

Closed-channel contribution in the BCS-BEC crossover regime of an ultracold Fermi gas with an orbital Feshbach resonance

We theoretically investigate strong-coupling properties of an ultracold Fermi gas with an orbital Feshbach resonance (OFR). Including tunable pairing interaction associated with an OFR within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink (NSR), we examine the occupation of the closed channel. We show that, although the importance of the closed channel is characteristic of the system with an OFR, the occupation number of the closed channel is found to actually be very small at the superfluid phase transition temperature Tc, in the whole BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region, when we use the scattering parameters for an ultracold 173Yb Fermi gas. The occupation of the closed channel increases with increasing the temperature above Tc, which is more remarkable for a stronger pairing interaction. We also present a prescription to remove effects of an experimentally inaccessible deep bound state from the NSR formalism, which we meet when we theoretically deal with a 173Yb Fermi gas with an OFR.

Temperature Dependence of the Upper Critical Field in Disordered Hubbard Model with Attraction

We study disorder effects upon the temperature behavior of the upper critical magnetic field in attractive Hubbard model within the generalized $DMFT+\Sigma$ approach. We consider the wide range of attraction potentials $U$ - from the weak coupling limit, where superconductivity is described by BCS model, up to the strong coupling limit, where superconducting transition is related to Bose - Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures significantly higher than superconducting transition temperature, as well as the wide range of disorder - from weak to strong, when the system is in the vicinity of Anderson transition. The growth of coupling strength leads to the rapid growth of $H_{c2}(T)$, especially at low temperatures. In BEC limit and in the region of BCS - BEC crossover $H_{c2}(T)$ dependence becomes practically linear. Disordering also leads to the general growth of $H_{c2}(T)$. In BCS limit of weak coupling increasing disorder lead both to the growth of the slope of the upper critical field in the vicinity of transition point and to the increase of $H_{c2}(T)$ in low temperature region. In the limit of strong disorder in the vicinity of the Anderson transition localization corrections lead to the additional growth of $H_{c2}(T)$ at low temperatures, so that the $H_{c2}(T)$ dependence becomes concave. In BCS - BEC crossover region and in BEC limit disorder only slightly influences the slope of the upper critical field close to $T_{c}$. However, in the low temperature region $H_{c2}(T)$ may significantly grow with disorder in the vicinity of the Anderson transition, where localization corrections notably increase $H_{c2}(T=0)$ also making $H_{c2}(T)$ dependence concave.

Spin susceptibility and effects of a harmonic trap in the BCS-BEC crossover regime of an ultracold Fermi gas

We theoretically investigate magnetic properties of a trapped ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation (ETMA), as well as effects of a harmonic trap in the local density approximation (LDA), we calculate the local spin susceptibility $\chi_{\rm t}(r,T)$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that pairing fluctuations cause non-monotonic temperature dependence of $\chi_{\rm t}(r,T)$. Although this behavior looks similar to the spin-gap phenomenon associated with pairing fluctuations in a {\it uniform} Fermi gas, the trapped case is found to also be influenced by the temperature-dependent density profile, in addition to pairing fluctuations. We demonstrate how to remove this extrinsic effect from $\chi_{\rm t}(r,T)$, to study the interesting spin-gap phenomenon purely originating from pairing fluctuations. Since experiments in cold atom physics are always done in a trap, our results would be useful for the assessment of preformed pair scenario, from the viewpoint of spin-gap phenomenon.