We formulate a Bardeen-Cooper-Schriffer (BCS) theory of quasiparticles in a degenerate Fermi gas strongly coupled to photons in a optical cavity. The elementary photonic excitations of the system are cavity polaritons, which consist of a cavity photon and an excitation of an atom within the Fermi sea. The excitation of the atom out of the Fermi sea leaves behind a hole, which together results in a loosely bound Cooper pair, allowing for the system to be written by a BCS wavefunction. As the density of the excitations is increased, the excited atom and hole become more strongly bound, crossing over into the molecular regime. This thus realizes an alternative BCS to BEC crossover scenario, where the participating species are quasiparticle excitations in a Fermi sea consisting of excited atoms and holes.
Quantum nonlinear optics is a quickly growing field with large technological promise, at the same time involving complex and novel many-body phenomena. In the usual scenario, optical nonlinearities originate from the interactions between polaritons, which are hybrid quasi-particles mixing matter and light degrees of freedom. Here we introduce a type of polariton which is intrinsically nonlinear and emerges as the natural quasi-particle in presence quantum degenerate fermionic matter. It is a composite object made of a fermion trapped inside an optical soliton forming a topological defect in a …
Microcavity electron-hole-photon systems in two-dimensions are long anticipated to exhibit a crossover from Bose-Einstein condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluid, when carrier density is tuned to reach the Mott transition density. Yet, theoretical understanding of such a BEC-BCS crossover largely relies on the mean-field framework and the nature of the carriers at the crossover remains unclear to some extent. Here, motivated by the recent demonstration of a BCS polariton laser {[}Hu \textit{et al.}, arXiv:1902.00142{]} and based on a simplified short-range description of…
Bardeen-Cooper-Schrieffer State Representation and Pairing in the Fermionic Tonks-Girardeau Gas
Universitat de Barcelona（巴塞罗那大学）；Institut de Ciències del Cosmos, Universitat de Barcelona（巴塞罗那大学宇宙科学研究所）；Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）
Grassmann Phase Space Theory (GSPT) is applied to the BEC/BCS crossover in cold fermionic atomic gases and used to determine the evolution (over either time or temperature) of the Quantum Correlation Functions (QCF) that specify: (a) the positions of the spin up and spin down fermionic atoms in a single Cooper pair and (b) the positions of the two spin up and two spin down fermionic atoms in two Cooper pairs The first of these QCF is relevant to describing the change in size of a Cooper pair, as the fermion-fermion coupling constant is changed via Feshbach resonance methods through the crossov…
We propose a new type of spatially periodic structure, i.e. polaritonic crystal (PolC), to observe a "slow"/"stopped" light phenomenon due to coupled atom-field states (polaritons) in a lattice. Under the tightbinding approximation, such a system realizes an array of weakly coupled trapped two-component atomic ensembles interacting with optical field in a tunnel-coupled one dimensional cavity array. We have shown that the phase transition to the superfluid Bardeen-Cooper-Schrieffer state, a so-called (BCS)-type state of low branch polaritons, occurs under the strong coupling condition. Such a …
We calculate the phase diagram of the Bose-Fermi Hubbard model on the 3d cubic lattice at fermionic half filling and bosonic unit filling by means of single-site dynamical mean-field theory. For fast bosons, this is equivalent to the Cooper problem in which the bosons can induce s-wave pairing between the fermions. We also find miscible superfluid and canted supersolid phases depending on the interspecies coupling strength. In contrast, slow bosons favor fermionic charge density wave structures for attractive fermionic interactions. These competing instabilities lead to a rich phase diagram wi…
A Bose--Einstein condensate of exciton polaritons coexisting with a Fermi gas of electrons has been recently proposed as a promising system for realisation of room-temperature superconductivity [Phys. Rev. Lett., 104, 106402 (2010)]. In order to find the optimum conditions for exciton and exciton-polariton mediated superconductivity, we study the attractive mechanism between electrons of a Cooper pair mediated by the exciton and exciton-polariton condensate and analyze the gap equation that follows. We specifically address microcavities with embedded n-doped quantum wells as well as coupled qu…
We investigate the quartet correlations in four-component fermionic systems at the thermodynamic limit within a variational many-body theory. The Bardeen-Cooper-Schrieffer (BCS)-type variational wave function is extended to the systems with the coexistence of pair and quartet correlations at zero temperature. Special attention is paid to the application of the present framework to an alpha-particle condensation in symmetric nuclear matter, where the coexistence of deuteron and alpha condensations is anticipated. We also discuss how physical properties, such as quasiparticle dispersion, can be …
Angular momentum of rotating fermionic superfluids by Sagnac phonon interferometry
European Laboratory for Nonlinear Spectroscopy (LENS), University of Florence（欧洲非线性光谱学实验室，佛罗伦萨大学）；Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家光学研究所）；INFN, Sezione di Firenze（意大利国家核物理研究所，佛罗伦萨分部）；Department of Physics, University of Florence（佛罗伦萨大学物理系）
We study the nature of superfluid pairing in imbalanced Fermi mixtures in two spatial dimensions. We present evidence that the combined effect of Fermi surface mismatch and order parameter fluctuations of the superfluid condensate can lead to continuous quantum phase transitions from a normal Fermi mixture to an intermediate Sarma-Liu-Wilczek superfluid with two gapless Fermi surfaces -- even when mean-field theory (incorrectly) predicts a first order transition to a phase-separated "Bardeen-Cooper-Schrieffer plus excess fermions" ground state. We propose a mechanism for non-Fermi liquid behav…
Pairing is the fundamental requirement for fermionic superfluidity and superconductivity. To understand the mechanism behind pair formation is an ongoing challenge in the study of many strongly correlated fermionic systems. Cooper pairs are the key ingredient to BCS theory as the microscopic explanation of conventional superconductivity. They form between particles of opposite spin and momentum at the Fermi surface of the system. Here, we directly observe Cooper pairs in a mesoscopic two-dimensional Fermi gas. We apply an imaging scheme that enables us to extract the full in-situ momentum dist…
We consider a cold two-species atomic Fermi gas confined in a trap. We combine the Hermitian coupling between the states (we assume them to be the states with different spins) with the Cooper pairing of atoms with these different spins. This opens up a new prospect for investigation of interplay between various phenomena involving Raman coupling (e.g., atom lasers, dark-state polaritons) and effects caused by Cooper pairing of particles (e.g., superfluidity). We have obtained a threshold of transition from oscillatory to amplifying behavior of matter waves.
We propose a scheme to create a metastable state of paired bosonic atoms in an optical lattice. The most salient features of this state are that the wavefunction of each pair is a Bell state and that the pair size spans half the lattice, similar to fermionic Cooper pairs. This mesoscopic state can be created with a dynamical process that involves crossing a quantum phase transition and which is supported by the symmetries of the physical system. We characterize the final state by means of a measurable two-particle correlator that detects both the presence of the pairs and their size.
We study theoretically interspecies Cooper pairing in a fermionic system with SU(2)xSU(6) sym- metry. We show that, with suitable unitary transformations, the order parameter for the ground state can be reduced to only two non-vanishing complex components. The ground state has a large degeneracy. We find that while some Goldstone modes have linear dispersions, others are quadratic at low frequencies. We compare our results with the case of SU(N).
We investigate the superfluid state of repulsively interacting three-component (color) fermionic atoms in optical lattices. When the anisotropy of the three repulsive interactions is strong, atoms of two of the three colors form Cooper pairs and atoms of the third color remain a Fermi liquid. An effective attractive interaction is induced by density fluctuations of the third-color atoms. This superfluid state is stable against changes in filling close to half filling. We determine the phase diagrams in terms of temperature, filling, and the anisotropy of the repulsive interactions.
Topological excitations are found throughout nature, in proteins and DNA, as dislocations in crystals, as vortices and solitons in superfluids and superconductors, and generally in the wake of symmetry-breaking phase transitions. In fermionic systems, topological defects may provide bound states for fermions that often play a crucial role for the system's transport properties. Famous examples are Andreev bound states inside vortex cores, fractionally charged solitons in relativistic quantum field theory, and the spinless charged solitons responsible for the high conductivity of polymers. Howev…
We develop the auxiliary field formalism corresponding to a dilute system of spin-1/2 fermions. This theory represents the Fermi counterpart of the BEC theory developed recently by F. Cooper et al. [Phys. Rev. Lett. 105, 240402 (2010)] to describe a dilute gas of Bose particles. Assuming tunable interactions, this formalism is appropriate for the study of the crossover from the regime of Bardeen-Cooper-Schriffer (BCS) pairing to the regime of Bose-Einstein condensation (BEC) in ultracold fermionic atom gases. We show that when applied to the Fermi case at zero temperature, the leading-order au…
We investigate the Bose-Einstein condensation of fermionic pairs in three different superfluid systems: ultracold and dilute atomic gases, bulk neutron matter, and neutron stars. In the case of dilute gases made of fermionic atoms the average distance between atoms is much larger than the effective radius of the inter-atomic potential. Here the condensation of fermionic pairs is analyzed as a function of the s-wave scattering length, which can be tuned in experiments by using the technique of Feshbach resonances from a small and negative value (corresponding to the Bardeen-Cooper-Schrieffer (B…
The recent experimental realization of spin-orbit coupling (SOC) for ultra-cold atoms opens a completely new avenue for exploring new quantum matter. In experiments, the SOC is implemented simultaneously with a Zeeman field. Such spin-orbit coupled Fermi gases are predicted to support Majorana fermions with non-Abelian exchange statistics in one dimension (1D). However, as shown in recent theory and experiments for 1D spin-imbalanced Fermi gases, the Zeeman field can lead to the long-sought Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids with non-zero momentum Cooper pairings, in contrast …
We report on the observation of the Josephson effect between two strongly interacting fermionic superfluids coupled through a thin tunneling barrier. We prove that the relative population and phase are canonically conjugate dynamical variables, coherently oscillating throughout the entire crossover from molecular Bose-Einstein condensates (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluids. We measure the plasma frequency and we extract the Josephson coupling energy, both exhibiting a non-monotonic behavior with a maximum near the crossover regime. We also observe the transition from coherent…
We extend our previous investigations of fermionic condensation in broad Feshbach resonances by using the two-channel model developed for narrow Feshbach resonances. We investigate two crossovers: the BCS-BEC crossover by changing the s-wave scattering length and the crossover from a narrow to a broad resonance by changing the atom-molecule coupling. At zero temperature we analyze, as a function of both atom-molecule coupling and s-wave scattering length, the chemical potential, the energy gap, and the condensate fraction of atoms. In particular, we predict the contribution of Cooper pairs and…
We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low-temperature region, we observe a second-order transition from a Fermi liquid to a color superfluid (CSF), where atoms from two of the three colors form Cooper pairs. In the strong attractive region, we observe a first-order transition from a CSF to a trionic state, where three atoms with different colors form singlet bound states. A crossover between a Fermi liquid …
Fermionic functional renormalization group (FRG) is applied to describe the superfluid phase transition of the two-component fermionic system with attractive contact interaction. Connection between the fermionic FRG approach and the Bardeen-Cooper-Schrieffer (BCS) theory with its Gorkov and Melik-Barkhudarov (GMB) correction is made clear, and the FRG flow of the fermion self-energy is also studied to go beyond the BCS+GMB theory. The superfluid transition temperature and the associated chemical potential are calculated in the region of the negative scattering length using fermionic FRG.
Comparative study of quartet superfluid state: Quartet Bardeen-Cooper-Schrieffer theory and generalized Nambu-Gor'kov formalism
RIKEN Nishina Center for Accelerator-Based Science（理化学研究所西村加速器科学中心）；Department of Physics, Graduate School of Science, The University of Tokyo（东京大学理学研究科物理学系）；Quark Nuclear Science Institute, The University of Tokyo（东京大学夸克核科学研究所）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论数学科学中心）
We show how Cooper-pair-assisted transport, which describes the stimulated transport of electrons in the presence of Cooper-pairs, can be engineered and controlled with cold atoms, in regimes that are difficult to access for condensed matter systems. Our model is a channel connecting two cold atomic gases, and the mechanism to generate such a transport relies on the coupling of the channel to a molecular BEC, with diatomic molecules of fermionic atoms. Our results are obtained using a Floquet-Redfield master equation that accounts for an exact treatment of the interaction between atoms in the …
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 cou…
We theoretically study the ground-state properties and the condensations of exciton-like Cooper pairs and biexciton-like Cooper quartets in an electron-hole system. Applying the variational approach associated based on the quartet Bardeen-Cooper-Schrieffer (BCS) model to the four-component fermionic system consisting of spin-1/2 electrons and spin-1/2 holes, we show how Cooper pairs and quartet correlations appear in the equation of state at the thermodynamic limit. The biexciton-like four-body correlations survive even at the high-density regime as a many-body BCS-like state of Cooper quartet…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, a superconducting state with non-zero total momentum Cooper pairs in a large magnetic field, was first predicted about 50 years ago, and since then became an important concept in many branches of physics. Despite intensive search in various materials, unambiguous experimental evidence for the FFLO phase is still lacking in experiments. In this paper, we show that both FF (uniform order parameter with plane-wave phase) and LO phase (spatially varying order parameter amplitude) can be observed using fermionic cold atoms in spin-orbit coupled opt…
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids, Cooper pairings with finite momentum, and Majorana fermions (MFs), quasiparticles with non-Abelian exchange statistics, are two topics under intensive investigation in the past several decades, but unambiguous experimental evidences for them have not been found yet in any physical system. Here we show that the recent experimentally realized cold atom shaken optical lattice provides a new pathway to realize FFLO superfluids and MFs. By tuning shaken lattice parameters (shaking frequency and amplitude), various coupling between the s- and p-or…
A possibility of the condensation of excitations with a non-zero momentum in rectilinearly moving and rotating superfluid bosonic and fermionic (with Cooper pairing) media is considered in terms of a phenomenological order-parameter functional at zero and non-zero temperature. The results might be applicable to the description of bosonic systems like superfluid $^4$He, ultracold atomic Bose gases, charged pion and kaon condensates in rotating neutron stars, and various superconducting fermionic systems with pairing, like proton and color-superconducting components in compact stars, metallic su…
We investigate single-particle properties of a mass-imbalanced Fermi gas in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. In the presence of mass imbalance, we point out that the ordinary $T$-matrix approximation, which has been extensively used to clarify various BCS-BEC crossover physics in the mass-balanced case, unphysically gives a double-valued solution in terms of the superfluid phase transition temperature $T_{\rm c}$ in the crossover region. To overcome this serious problem, we include higher order strong-coupling corrections beyond the $T$-mat…
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_BT_c ~ 6.5 (where Δis the pairing gap and Tc is the transition temperature) at which paired fermion condensates bec…
Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly …
