On Realization of the Bose-Einstein Condensates and Quantum Superfluids

Abstract

The purpose of this work is twofold. In the first part we describe superfluidity/superconductivity as an emergent phenomenon resulting from two-body correlations in presence of the Bose-Einstein condensation of particles. We briefly discuss the underlying mechanism for bosons as well as fermion pairs and illustrate various realizations of superfluidity emphasizing the recent examples. In the second part we study the glassy liquid of incoherent pairs which might exist above the transition temperature T c in the underdoped regime of cuprate superconductors. In particular, we explore the angular variation of pseudogap within two-dimensional version of the boson-fermion model using for a quantitative analysis the projective method. We find that above T c the pseudogap closes first near the nodal areas restoring there pieces (arcs) of the Fermi surface whereas remaining parts of the large Fermi surface around the antinodal points are still absent due to incoherent pairs. Upon increasing temperature the length of the Fermi arcs enlarges because the superconducting correlations are gradually suppressed. An intriguing death of Fermi surface can thus be closely related to the Bogoliubov quasiparticles whose existence in the pseudogap state has been predicted by us and confirmed recently by the angle resolved photoemission spectroscopy measurements on Bi PreliminariesQuantum statistical mechanics puts a strong emphasis on the crucial distinction between fermions obeying the Pauli exclusion principle and bosons having no upper bounds for occupying any quantum state at hand. Under specific conditions the latter can macroscopically accommodate in the lowest energy level (for instance in q = 0 momentum of the noninteracting uniform gas or the zero frequency oscillator level E 0 = 1 2 ω for the case of magneto-optically trapped atoms). This phenomenon, referred to as the Bose-Einstein condensation (BEC), has been discovered for the first time in the superfluid state of 4 He. At temperatures far below the lambda transition about 8% of helium atoms gets frozen to the condensate. Recently, the development of trapping and cooling techniques enabled production of the artificial condensates for several atoms. Very dilute densities of the trapped atoms ≈ 10 14 cm −3 require that the quantum degeneracy level is reached at ultracold temperatures, below µK. Such stringent conditions have been so far achieved by a dozen of groups worldwide and the presently available experimental conditions allow for condensation of more than 90% of the trapped atoms [1].A direct realization of BEC among fermions is obviously prohibited. However, an equivalent phenomenon can be obtained in two steps. First, one needs to combine the initial fermions (at least some of their states located near the Fermi level) into the pairs (composite bosons). Depending on specific fermions the possible mechanisms can range from e.g. the phonon mediated pairing in classical superconductors to any other effective attractions -some examples will be discussed in Sect. 2.3. ...