Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction

Abstract

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 non-diagonalizable 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 connection between multiple prices of an Option at a given time with single prices defined at different times: The concept of weak-value in quantum finance

“…One typical example happens in condensed maatter physics where interesting physical effects related to the phenomena of superfluidity appear. In [11], it was demonstrated that unconventional phase transitions might occur when non-Hermitian BCS Hamiltonians are used for describing ultracold atoms. There exists experimental evidence about this and the details can be found in [11].…”

“…This is a consequence of the fact that the Financial market is not an isolated system, but it is rather an open system with permanent input and output of information. It is well-known that Open systems are modeled with non-Hermitian Hamiltonians and this does not violate any Quantum principle [8][9][10][11][12][13]. Given the non-Hermitian character of the system (without any imposed symmetry), the eigenvalues of the financial Hamiltonians are in general complex numbers and the evolution of the system is not necessarily unitary.…”

Perspective on topological states of non-Hermitian lattices

“…The interest in non-Hermitian Hamiltonians was originally focused in  -symmetric Hamiltonians [23] as a generalization of quantum mechanics where the Hermiticity constraint could be removed while keeping a real spectra. Today, this has shifted to non-Hermitian Hamiltonians regarded as an effective description of, for example, open quantum systems [24,25], where the finite lifetime introduced by electronelectron or electron-phonon interactions [26][27][28], or disorder [29], is modeled through a non-Hermitian term, or in the physics of lasing [30][31][32][33][34]. An additional source of momentum in this field comes from the study of systems where the quantum mechanical description is used after mapping to a Schrödinger-like equation, as in systems with gain and loss (as found in optics and photonics [35][36][37][38]), surface Maxwell waves [39], and topoelectrical circuits [40,41].…”

Untying links through anti-parity-time-symmetric coupling

“…The types of non-Hermiticities and their manners of appearance are important for the non-Hermitian topological systems [34,54]. If the non-Hermiticity is = (0, 0, γ ), the topological phase transition and the existence of the edge state are unaltered because of the pseudo-anti-Hermiticity protection [34]; the topological properties of the non-Hermitian system are inherited by the EPs (exceptional rings or exceptional surfaces in 2D or 3D) [60][61][62][63][64][65][66][67]. If the non-Hermiticity is = (0, γ , 0), the non-Hermitian skin effect occurs under open boundary condition [54][55][56][57][58][59][68][69][70][71][72][73][74][75][76][77][78], the non-Hermitian Aharonov-Bohm effect under periodical boundary condition invalidates the conventional bulk-boundary correspondence [54], and the non-Bloch band theory is developed for topological characterization [77][78][79][80][81][82].…”