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arXiv:hep-ph/0510302 · Surveys In High Energy Physics

Unusual condensates in quark and atomic systems†

B. Kerbikov

Published Jan 1, 2006• 9 citations
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Abstract

In these lectures, we discuss condensates which are formed in quark matter when it is squeezed and in a gas of fermionic atoms when it is cooled. The behavior of these two seemingly very different systems reveals striking simularities. In particular, in both systems the Bose–Einstein condensate to Bardeen–Cooper–Schrieffer (BEC–BCS) crossover takes place.

DOI
10.1080/01422410500424519

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In these lectures, we discuss condensates which are formed in quark matter when it is squeezed and in a gas of fermionic atoms when it is cooled. The behavior of these two seemingly very different systems reveals striking simularities. In particular, in both systems the Bose–Einstein condensate to Bardeen–Cooper–Schrieffer (BEC–BCS) crossover takes place.
This chapter presents the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly-correlated pairs of fermions to the Bose-Einstein condensation (BEC) of diatomic molecules in the atomic Fermi gas. Our aim is to provide a pedagogical review of the BCS-BEC crossover, with an emphasis on the basic concepts, particularly those that are not generally known or are difficult to find in the literature. We shall not attempt to give an exhaustive survey of current research in the limited space here; where possible, we will direct the reader to more extensive reviews.
The crossover from weak-coupling Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) of tightly bound pairs, as a function of the attractive interaction in Fermi systems, has long been of interest to theoretical physicists. The past decade has seen a series of remarkable experimental developments in ultracold Fermi gases that have realized the BCS-BEC crossover in the laboratory, bringing with it fresh new insights into the very strongly interacting unitary regime in the middle of this crossover. In this review, we start with a pedagogical introduction to the crossover and then focus on recent progress in the strongly interacting regime. Although our focus is on new theoretical developments, we also describe three key experiments that probe the thermodynamics, transport, and spectroscopy of the unitary Fermi gas. We discuss connections between the unitary regime and other areas of physics—quark-gluon plasmas, gauge-gravity duality, and high-temperature superconductivity—and conclude with open questions about strongly interacting Fermi gases.
This study presents a simple idea and a conceptual understandingof the crossover from the Bardeen Cooper (BCS) state of weakly-correlatedpairs of fermions to the Bose{Einstein condensation (BEC) of diatomicmolecules in the atomic Fermi gas. In the context of ultra cold Fermi gases,a BCS-BEC crossover means that by tuning the interaction strength, onegoes from a BCS state to a BEC state without encountering a phase transition.BEC state is a Bose-Einstein condensate of two-atom molecules (boundfermions), while the BCS state is made up of pair of atoms. The differencebetween the pairs and the molecules is that the molecules are localized inthe real space, whereas the BCS pairs are made of two particles with oppositemomenta in the momentum space.
In our recent experiments at MIT, superfluidity has been observed in a strongly interacting atomic Fermi gas. These systems constitute a novel form of matter with model character: One can vary the temperature, density and dimensionality, the number of “spin up” versus “spin down” fermions, and, most remarkably, the interactions can be precisely controlled over an enormous range. This allows to study the crossover of a Bose-Einstein condensate of tightly bound molecules to a Bardeen-Cooper-Schrieffer superfluid of long-range Cooper pairs. Superfluidity in this crossover regime is demonstrated by setting the gas under rotation and observing ordered lattices of quantized vortices [1]. Thanks to its strong interactions, the gas is a high-temperature superfluid: Scaled to the density of electrons in a metal, superfluidity would occur already far above room temperature. A new regime is entered when the number of spin up versus spin down atoms is imbalanced. In this case, not every spin up atom can find a spin down partner. The ground state of such a system has been under debate for over 40 years. We observe the breakdown of superfluidity at a critical imbalance, the Chandrasekhar-Clogston limit [2]. The superfluid gives way to an intriguing, strongly-interacting Fermi gas with unequal spin populations [3, 4].
The crossover from weak coupling Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) of tightly bound pairs, as a function of the attractive interaction in Fermi systems, has long been of interest to theoretical physicists. The past decade has seen a series of remarkable experimental developments in ultracold Fermi gases that has realized the BCS-BEC crossover in the laboratory, bringing with it fresh new insights into the very strongly interacting unitary regime in the middle of this crossover. In this review, we start with a pedagogical introduction to the crossover and then focus on recent progress in the strongly interacting regime. While our focus is on new theoretical developments, we also describe three key experiments that probe the thermodynamics, transport and spectroscopy of the unitary Fermi gas. We discuss connections between the unitary regime and other areas of physics -- quark-gluon plasmas, gauge-gravity duality and high temperature superconductivity -- and conclude with open questions about strongly interacting Fermi gases.