Spatial emergence of off-diagonal long-range order throughout the BCS-BEC crossover

Year: 2022

Authors: Pisani L.; Pieri P.; Strinati G.C.

Autors Affiliation: Univ Camerino, Phys Div, Sch Sci & Technol, I-62032 Camerino, MC, Italy; Univ Bologna, Dipartimento Fis & Astron, I-40127 Bologna, BO, Italy; Ist Nazl Fis Nucl, Sez Bologna, I-40127 Bologna, BO, Italy; Ist Nazl Fis Nucl, Sez Perugia, I-06123 Perugia, PG, Italy; CNR INO, Ist Nazl Ott, Sede Firenze, I-50125 Florence, FI, Italy.

Abstract: In a superfluid system, off-diagonal long-range order is expected to be exhibited in the appropriate reduced density matrices when the relevant particles (either bosons or fermion pairs) are considered to recede sufficiently far apart from each other. This concept is usually exploited to identify the value of the condensate density, without explicit concern, however, as to the spatial range over which this asymptotic condition can effectively be achieved. Here, based on a diagrammatic approach that includes beyond-mean-field pairing fluctuations in the broken-symmetry phase at the level of the t-matrix also with the inclusion of the Gorkov-Melik-Barkhudarov (GMB) correction, we present a systematic study of the two-particle reduced density matrix for a superfluid fermionic system undergoing the BCS-BEC crossover, when the entities to recede far apart from each other evolve with continuity from largely overlapping Cooper pairs in the BCS limit to dilute composite bosons in the BEC limit. By this approach, we not only provide the coupling and temperature dependence of the condensate density at the level of our diagrammatic approach, which includes the GMB correction, but we also obtain the evolution of the spatial dependence of the two-particle reduced density matrix, from a power law at low temperature to an exponential dependence at high temperature in the superfluid phase, when the interparticle coupling spans the BCS-BEC crossover. Our results put limitations on the minimum spatial extent of a finite-size system for which superfluid correlations can effectively be established.

Journal/Review: PHYSICAL REVIEW B

Volume: 105 (5)      Pages from: 054505-1  to: 054505-20

KeyWords: Bose-condensation; momentum distribution; superconductivity; evolution; quantum
DOI: 10.1103/PhysRevB.105.054505

ImpactFactor: 3.700
Citations: 6
data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-24
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