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 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.
Highlights
Fermionic superfuidity is one of the most striking quantum many-body phenomena, which has been a subject of intensive investigation in condensed matter physics [39]
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
Summary
Leads to some intriguing dynamics in the NH superfluid. In Fig. 2(b), the imaginary part of the quasiparticle energy takes a positive finite value only in between the exceptional lines or surfaces, amplifying quasiparticle distribution in the particular region of the Brillouin zone through the time evolution. The metastable superfluid undergoes an unconventional quantum phase transition due to exceptional points in the case of weak attractions, leading to the disappearance of the superfluid state in the yellow region. For weak attraction U1, the superfluid undergoes an unconventional phase transition to the normal state due to the exceptional points. For a detailed discussion including the relevant timescales, see Supplemental Material [59] These NH superfluids are expected to be realized with ultracold atoms under inelastic collisions. For weak attraction, it has been revealed that the superfluidity breaks down with increasing dissipation but shows reentrant behavior as dissipation is further increased These phase transitions are accompanied by distinctive features of the non-Hermiticity, i.e. the emergence of exceptional points, lines and surfaces in the quasiparticle Hamiltonian for one-, two- and three-dimensions. Quantum liquids: Bose condensation and Cooper pairing in condensed-matter systems (Oxford university press, 2006)
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