Extensive theoretical and experimental investigation has been conducted on fermion pair condensation and exciton condensation as distinct classes of Bose-Einstein-like condensation. In our work, the fermion-exciton condensate (FEC), a single quantum state in which character of both fermion pair and exciton condensates coexist, is introduced and explored. Using the signatures of fermion and exciton condensation—obtained via analysis of system reduced density matrices—, we establish the existence of FECs computationally in the small-particle-number limit and theoretically in the large-N thermodynamic limit, predicting that the FEC wave function arises from the entanglement of fermion-pair and exciton wave functions. We then capture the FEC through a model Hamiltonian that can recreate the physics of this new class of highly-correlated condensation phenomena; this Hamiltonian provides insights into the required forces for generating a fermion-exciton condensate and hence will likely be invaluable for the realization of such condensations in realistic materials. Utilizing prior insights, we finally prepare a variety of fermion-exciton condensate states on quantum computers—realizing strongly-correlated FEC states on current, noisy intermediate-scale quantum devices—and verify the presence of the dual condensate via post-measurement analysis.  The quantum computing results verify the form of the dual condensate wave function and suggest that such a state may potentially be realizable in physical systems such as twisted graphene bilayers in which forces favoring exciton condensation and superconducting, respectively, are in fierce competition. FEC states may demonstrate properties hybridizing the superconductivity of fermion-pair condensates and the dissipationless flow of energy of exciton condensates with possible applications in energy transport and electronics.  Future experimental and computational exploration of this new class of condensate is anticipated.

Entangled phase of simultaneous fermion and exciton condensations realized

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ACS Fall 2022

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