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arXiv:2002.00653 · Physical Review A

Non-Hermitian BCS-BEC evolution with a complex scattering length

M. Iskin

Published Jan 22, 2021• 22 citations
arXivHTMLPDF

Abstract

Having both elastic and inelastic two-body processes that are characterized by a complex $s$-wave scattering length between $\ensuremath{\uparrow}$ and $\ensuremath{\downarrow}$ fermions in mind, here we apply the non-Hermitian extension of the mean-field theory to the BCS-BEC evolution at zero temperature. We construct the phase diagram of the system, where we find a reentrant superfluid (SF) transition that is intervened by a normal and/or a metastable phase as a function of increasing inelasticity. This transition occurs in a large parameter regime away from the unitarity, i.e., on both the BCS and BEC sides of the resonance, and it is mostly governed by the exceptional points. In addition, except for the strongly inelastic regime, we also show that the SF phase can be well described by the condensation of weakly interacting bosonic pairs in the two-body bound state with a complex binding energy.

DOI
10.1103/physreva.103.013724

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Having both elastic and inelastic two-body processes that are characterized by a complex sss-wave scattering length between \ensuremath↑\ensuremath{\uparrow}\ensuremath↑ and \ensuremath↓\ensuremath{\downarrow}\ensuremath↓ fermions in mind, here we apply the non-Hermitian extension of the mean-field theory to the BCS-BEC evolution at zero temperature. We construct the phase diagram of the system, where we find a reentrant superfluid (SF) transition that is intervened by a normal and/or a metastable phase as a function of increasing inelasticity. This transition occurs in a large parameter regime away from the unitarity, i.e., on both the BCS and BEC sides of the resonance, and it is mostly governed by the exceptional points. In addition, except for the strongly inelastic regime, we also show that the SF phase can be well described by the condensation of weakly interacting bosonic pairs in the two-body bound state with a complex binding energy.
Motivated by recent experimental advances in ultracold atoms, we analyze a non-Hermitian (NH) BCS Hamiltonian with a complex-valued interaction arising from inelastic scattering between fermions. We develop a mean-field theory to obtain a NH gap equation for order parameters, which are different from the standard BCS ones due to the inequivalence of left and right eigenstates in the NH physics. We find unconventional phase transitions unique to NH systems: superfluidity shows reentrant behavior with increasing dissipation, as a consequence of nondiagonalizable exceptional points, lines, and surfaces in the quasiparticle Hamiltonian for weak attractive interactions. For strong attractive interactions, the superfluid gap never collapses but is enhanced by dissipation due to an interplay between the BCS-BEC crossover and the quantum Zeno effect. Our results lay the groundwork for studies of fermionic superfluidity subject to inelastic collisions.
The two-body loss associated with inelastic interactions between fermions plays a significant role in realistic many-body systems. Here we study a two-component non-Hermitian Bardeen-Cooper-Schrieffer superfluidity with spin imbalance and two-body loss characterized by a complex-valued sss-wave interaction in a square lattice. At the mean-field level, we map out the zero-temperature phase diagram and observe a dissipation-induced transition from superfluid to normal phase as well as a distinctive revival of the superfluid state in the weakly interacting regime applicable to both spin-balanced and spin-imbalanced systems. In the spin-imbalanced case, we find that the effective density of states involving weight functions reduces the regions in k\mathbf{k}k space contributing to pairing, hence leading to a pronounced expansion of the normal phase on the phase diagram. Additionally, we analyze the order parameter, condensate energy, quasiparticle spectra, momentum distribution, and compressibility to characterize the presenting phases and phase transitions.
Recently, the influence of dissipation on a quantum system has attracted much attention, particularly on how the non-Hermitian terms modify the energy spectrum, band topology, and phase transition point. Motivated by the recent investigation of non-Hermitian sss-wave superfluidity, we study the non-Hermitian chiral p+ipp+ipp+ip superfluid (SF) with a complex-valued interaction, originating from inelastic scattering between fermions. We reformulate the non-Hermitian mean-field theory for chiral SFs and derive the gap equation in the path integral approach. By numerically solving the gap equation, we obtain the phase diagram of the non-Hermitian p+ipp+ipp+ip SF, characterized by the reentrant SF transition and dissipation-induced SF phase, as a result of the evolution of the exceptional lines. The method can be extended to higher partial-wave chiral SFs, such as d+idd+idd+id and f+iff+iff+if-wave SFs. We further consider such a chiral p+ipp+ipp+ip SF on a square lattice, to investigate the influence of dissipation on topology. We find that the non-Hermitian skin effect is absent in the specific cylinder geometry, in which the topology associated with the edge modes and Chern number is robust to dissipation. Besides, we find that the energies at the robust point nodes and line nodes are pure real. We further verify the conditions of zero winding number in (quasi-) one-dimensional systems, and prove an associated ``no-go'' theorem, which is hopefully applied to explore the geometry dependent skin effect.
We discuss theoretically the non-Hermitian superfluid phase transition in one-dimensional two-component Fermi gases near the ppp-wave Feshbach resonance accompanied by the two-body loss associated with dipolar relaxation. We point out that this system gives us an opportunity to explore the interplay among various nontrivial properties such as universal thermodynamics at divergent ppp-wave scattering lengths, the topological phase transition at vanishing chemical potential, and the non-Hermitian Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) transition, in a unified manner. In the BCS phase, the loss-induced superfluid-normal transition occurs when the exceptional point appears in the effective non-Hermitian Hamiltonian. In the BEC phase, the diffusive gapless mode can be regarded as a precursor of the instability of the superfluid state. Moreover, we show that the superfluid state is fragile against the two-body loss near the topological phase transition point.
This thesis focuses on the analysis of Bardeen-Cooper-Schrieffer (BCS) \nto Bose-Einstein condensation (BEC) evolution in ultracold superfluid \nFermi gases when the interaction between atoms is varied. The tuning of \nattractive interactions permits the ground state of the system to evolve from a weak \nfermion attraction BCS limit of loosely bound and largely overlapping Cooper pairs \nto a strong fermion attraction limit of tightly bound small bosonic molecules \nwhich undergo BEC. \nThis evolution is accompanied by anomalous behavior of many superfluid \nproperties, and reveals several quantum phase transitions. \nThis thesis has two parts: \nIn the first part, I analyze zero and nonzero orbital angular momentum \npairing effects, and show that a quantum phase transition occurs for \nnonzero angular momentum pairing, unlike the sss-wave case where the BCS \nto BEC evolution is just a crossover. \nIn the second part, I analyze two-species fermion mixtures with mass and \npopulation imbalance in continuum, trap and lattice models. In contrast with \nthe crossover physics found in the mass and population balanced mixtures, \nI demonstrate the existence of phase transitions between normal and \nsuperfluid phases, as well as phase separation between superfluid (paired) \nand normal (excess) fermions in imbalanced mixtures as a function of scattering \nparameter and mass and population imbalance.
The problem of the evolution from BCS theory with cooperative Cooper pairing to the formation and condensation of composite bosons has attracted considerable attention for the past several decades. It has gained renewed impetus in the mid-eighties with the discovery of the high-Tc superconductors, which have a coherence length comparable to the interparticle spacing. More recently, this subject has spurred a great deal of research activity in connection with experiments involving dilute atomic gases of fermionic atoms. The initial objective of this work will be to use functional integral techniques to analyze the low-temperature BCS-to-BEC evolution of d-wave superconductors within the saddle point (mean field) approximation for a continuum model. Then, the same mathematical formalism will be applied to the problem of the BCS-to-BEC evolution of fully spin-polarized p-wave Fermi gases in two dimensions. We find that a quantum phase transition occurs for both systems as they are driven from the BCS-like regime of weakly interacting fermionic pairs to the opposite BEC-like regime of strongly interacting bosonic molecules. This is in contrast to the smooth crossover predicted and observed in systems that exhibit s-wave pairing symmetry. We calculate several spectroscopic and thermodynamic properties that signal the occurrence of this phase transition, and suggest some possible experimental realizations. Finally, fluctuations about the saddle point solution are included in the calculations, and the effects of such correction are analyzed in the low (T~0) and high (T~Tc) temperature limits. We conclude that, at high temperatures, the bosonic degrees of freedom that arise from two-particle bound states become essential to describe the strong coupling limit,\nas the saddle point approximation alone becomes unreliable.