The crossover from weak coupling Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) of tightly bound pairs, as a function of the attractive interaction in Fermi systems, has long been of interest to theoretical physicists. The past decade has seen a series of remarkable experimental developments in ultracold Fermi gases that has realized the BCS-BEC crossover in the laboratory, bringing with it fresh new insights into the very strongly interacting unitary regime in the middle of this crossover. In this review, we start with a pedagogical introduction to the crossover and then focus on recent progress in the strongly interacting regime. While our focus is on new theoretical developments, we also describe three key experiments that probe the thermodynamics, transport and spectroscopy of the unitary Fermi gas. We discuss connections between the unitary regime and other areas of physics -- quark-gluon plasmas, gauge-gravity duality and high temperature superconductivity -- and conclude with open questions about strongly interacting Fermi gases.
We calculate the parameters of the Ginzburg-Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg-Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg-Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical ro…
We investigate the macroscopic quantum tunneling of fermionic superfluids in the two-dimensional BCS-BEC crossover by using an effective tunneling energy which explicitly depends on the condensate fraction and the chemical potential of the system. We compare the mean-field effective tunneling energy with the beyond-mean-field one finding that the mean-field tunneling energy is not reliable in the BEC regime of the crossover. Then we solve the Josephson equations of the population imbalance and the relative phase calculating the frequency of tunneling oscillation both in the linear regime and i…
The theoretical description of the critical temperature Tc of a Fermi superfluid dates back to the work by Gor'kov and Melik-Barkhudarov (GMB), who addressed it for a weakly-coupled (dilute) superfluid in the BCS (weak-coupling) limit of the BCS-BEC crossover. The point made by GMB was that particle-particle (pairing) excitations, which are responsible for superfluidity to occur below Tc, and particle-hole excitations, which give rise to screening also in a normal system, get effectively disentangled from each other in the BCS limit, thus yielding a reduction by a factor 2.2 of the value of Tc…
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. Neverthele…
This report adresses topics and questions of common interest in the fields of ultra-cold gases and nuclear physics in the context of the BCS-BEC crossover. The BCS-BEC crossover has recently been realized experimentally, and essentially in all of its aspects, with ultra-cold Fermi gases. This realization, in turn, has raised the interest of the nuclear physics community in the crossover problem, since it represents an unprecedented tool to test fundamental and unanswered questions of nuclear many-body theory. Here, we focus on the several aspects of the BCS-BEC crossover, which are of broad jo…
We investigate chiral symmetry breaking in a model of Dirac fermions with a complexified coupling constant whose imaginary part represents dissipation. We introduce a chiral chemical potential and observe that for real coupling a relativistic BCS-BEC crossover is realized. We solve the model in the mean-field approximation and construct the phase diagram as a function of the complex coupling. It is found that the dynamical mass increases under dissipation, although the chiral symmetry gets restored if dissipation exceeds a threshold.
We show that the long-distance behavior of the two-body density correlation functions and the Cooper-pair probability density of a balanced mixture of a two-component Fermi gas at $T = 0$, is universal along the BEC-BCS crossover. Our result is demonstrated by numerically solving the mean-field BCS model for different finite short-range atomic interaction potentials. We find an analytic expression for the correlation length in terms of the chemical potential and the energy gap at zero momentum.
BCS-BEC crossover in trapped one-dimensional Fermi-Hubbard chains: entanglement and correlation signatures from DMRG and effective-pairing theory
Charles University（查理大学）；São Paulo State University (UNESP)（圣保罗州立大学）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）；Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）；Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）
We analyze the BCS-BEC crossover transition of a balanced two component mixture of fermions interacting via a finite range potential, within a mean field approach. For the analysis we consider three finite range potentials cases describing the interaction between different Fermi species: a square well, an exponential and a Yukawa potential. The T = 0 thermodynamics analysis along the BCS-BEC crossover allow us to recognize the proper variables, for finite range interactions, that capture the transition from a thermodynamic non-universal behavior at unitarity, to its universal restoration. On t…
We develop a self-consistent theory unifying the description of a quantum Fermi gas in the presence of a Fano-Feshbach resonance in the whole phase diagram ranging from BCS to BEC type of superfluidity and from narrow to broad resonances, including the fluctuations beyond mean field. Our theory covers a part of the phase diagram which is not easily accessible by Quantum Monte Carlo simulations and is becoming interesting for a new class of experiments in cold atoms.
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 experimental closed-channel fraction $Z$ across the BEC-BCS crossover and into the BCS regime of a $^6$Li atomic Fermi gas. We obtain the expected behavior $Z \propto \sqrt{T_F}$ 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 discrepancy between experiments and theory has…
We investigate the three-dimensional BCS-BEC crossover in the presence of a Rabi coupling which strongly affects several properties of the system, such as the chemical potential, the pairing gap and the superfluid density. We determine the critical interaction strength, below which the system is normal also at zero temperature. Finally, we calculate the effect of the Rabi coupling on the critical temperature of the superfluid-to-normal phase transition by using different theoretical schemes.
We study the persistent currents of an attractive Fermi gas confined in a tightly-confining ring trap and subjected to an artificial gauge field all through the BCS-BEC crossover. At weak attractions, on the BCS side, fermions display a parity effect in the persistent currents, ie their response to the gauge field is paramagnetic or diamagnetic depending on the number of pairs on the ring. At resonance and on the BEC side of the crossover we find a doubling of the periodicity of the ground-state energy as a function of the artificial gauge field and disappearance of the parity effect, indicati…
Probing the BCS-BEC crossover with photons in a nonlinear optical fiber
我们提出了一个方案，其中强关联光子内产生的空芯一维光纤填充两个冷原子物种可以用来模拟BCS-BEC交叉。我们首先展示了如何在系统中的平稳轻物质激发（极化激元）可以实现光学可调谐的两个组件的玻色-哈伯德模型，然后分析所需的光学参数制度，以产生一个有效的费米-哈伯德模型的光子表现出库珀配对。由于光子关联的{ \it in situ}可用性，可以有效地观察系统的特征关联相位。
We developed a comprehensive semiclassical theory of solitons in one dimensional systems at BCS-BEC crossover to provide a semiclassical explanation of their excitation spectra. Our semiclassical results agree well with the exact solutions on both the deep BCS and deep BEC side and explain qualitatively the smooth crossover between them. Especially, we showed that the minimum energy of the $S=1/2$ excitation is achieved exactly at the Fermi momentum $k_F=πn/2$, where $nm_F$ ($m_F$ is the mass of the fermionic atom) is the total mass density of the system. This momentum remains unchanged along …
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…
