利用壳模型蒙特卡罗方法研究了零射程两体相互作用下的费米子囚禁系统，给出了平均场论不适用的低粒子数极限下的{ \em ab initio}结果.我们目前的结果为$N$体能量的相互作用强度，粒子数和温度的函数。在有限的模型空间中的重正化的微妙问题的解决和我们的方法的收敛性和跨BCS-BEC交叉的适用性进行了讨论。我们的研究结果表明，非常好的定量结果可以得到BCS侧，而在酉和BEC制度的收敛是不太清楚。比较N=2分析在零和有限的温度，并在文献中的其他计算$N>2$显示非常好的协议。
英文摘要：
We study a trapped system of fermions with a zero-range two-body interaction using the shell-model Monte Carlo method, providing {\em ab initio} results for the low particle number limit where mean-field theory is not applicable. We present results for the $N$-body energies as function of interaction strength, particle number, and temperature. The subtle question of renormalization in a finite model space is addressed and the convergence of our method and its applicability across the BCS-BEC crossover is discussed. Our findings indicate that very good quantitative results can be obtained on the BCS side, whereas at unitarity and in the BEC regime the convergence is less clear. Comparison to N=2 analytics at zero and finite temperature, and to other calculations in the literature for $N>2$ show very good agreement.
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 discuss the derivation of a low-energy effective field theory of phase (Goldstone) and amplitude (Higgs) modes of the pairing field from a microscopic theory of attractive fermions. The coupled equations for Goldstone and Higgs fields are critically analyzed in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover both in three spatial dimensions and in two spatial dimensions. The crucial role of pair fluctuations is investigated, and the beyond-mean-field Gaussian theory of the BCS-BEC crossover is compared with available experimental data of the two-dimensional u…
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 briefly discuss recent experiments on the BCS-BEC crossover with ultracold alkali-metal atoms both in three-dimensional configurations and two-dimensional ones. Then we analyze the quantum-field-theory formalism used to describe an attractive $D$-dimensional Fermi gas taking into account Gaussian fluctuations. Finally, we apply this formalism to obtain a reliable equation of state of the 2D system at low temperaratures in the BEC regime of the crossover by performing a meaningful dimensional regularization of the divergent zero-point energy of collective bosonic excitations.
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.
Based on a simple model of a layered superconductor with strong attractive interaction, we find that the separation of the pair-condensation temperature from the pair-formation temperature becomes more remarkable as the interlayer hopping gets smaller. We propose from this result the BCS-BEC crossover induced by the change in dimensionality, for instance, due to insertion of additional insulating layers or application of uniaxial pressure. The emergence of a pseudogap in the electronic density of states, which supports the idea of the dimensionality-induced BCS-BEC crossover, is also verified.
The Bardeen-Cooper-Schrieffer (BCS) condensation and the Bose-Einstein condensation (BEC) are the two extreme limits of the ground state of the paired fermion systems. We report crossover behavior from the BCS condensation to the BEC realized in the two-dimensional (2D) superconductor, electron doped layered material ZrNCl. The phase diagram, established by simultaneous experiments of resistivity and tunneling spectra under the ionic gating, demonstrates the pseudogap phase at the low doping regime. In the low carrier density limit, $T_{\rm BKT}$ (Berezinskii-Kosterlitz-Thouless transition tem…
The physics of the crossover between weak-coupling Bardeen-Cooper-Schrieffer (BCS) and strong-coupling Bose-Einstein-condensate (BEC) limits gives a unified framework of quantum bound (superfluid) states of interacting fermions. This crossover has been studied in the ultracold atomic systems, but is extremely difficult to be realized for electrons in solids. Recently, the superconducting semimetal FeSe with a transition temperature $T_{\rm c}=8.5$ K has been found to be deep inside the BCS-BEC crossover regime. Here we report experimental signatures of preformed Cooper pairing in FeSe below $T…
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 superconductin…
Effects of superconducting fluctuation (SCF) on thermodynamic properties of electron systems in the so-called BCS-BEC-crossover regime are studied. As the attractive interaction between electrons becomes stronger upon approaching the BCS-BEC-crossover regime, importance of the mode coupling between SCF drastically increases. The enhanced mode coupling leads to lowering of both the zero-field superconducting critical temperature and the depairing field $B_\text{c2} (T)$. Consequently, SCF-induced contributions to the specific heat and the diamagnetic susceptibility can seemingly exceed the corr…
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）
The Bardeen-Cooper-Schrieffer (BCS) condensation and Bose-Einstein condensation (BEC) are the two limiting ground states of paired Fermion systems, and the crossover between these two limits has been a source of excitement for both fields of high temperature superconductivity and cold atom superfluidity. For superconductors, ultra-low doping systems like graphene and LixZrNCl successfully approached the crossover starting from the BCS-side. These superconductors offer new opportunities to clarify the nature of charged-particles transport towards the BEC regime. Here we report the study of vort…
We investigate the dynamical effects of pairing interaction on superconductivity in BCS-BEC crossover by studying the Holstein model at half-filling where the electron-phonon coupling $g$ controls the crossover. The dynamical mean-field theory was employed in combination with the numerical renormalization group technique. The dynamical effects induce distinct features such as absenceof the dispersion back-bending of Bogoliubov quasi-particles, non-monotonous coupling dependence of the pairing gap, and the soft phonon spectrum due to the Goldstone mode of local pair phase fluctuations. Also int…
