It is shown that a cluster expansion technique, which is usually applied in the high-temperature regime to calcutate virial coefficients, can be applied to evaluate the superfluid transition temperature of the Bardeen-Cooper-Schrieffer (BCS)--Bose-Einstein condensation (BEC) crossover \`a la Lee and Yang. The transition temperature is identified with the emergence of the singularity in the sum of a certain infinite series of cluster functions. In the weak-coupling limit, we reproduce the Thouless criterion and the number equation of Nozi\`eres and Schmitt-Rink, and hence the transition temperature of the BCS theory. In the strong-coupling limit, we reproduce the transition temperature of BEC of noninteracting tightly bound dimers.It is shown that a cluster expansion technique, which is usually applied in the high-temperature regime to calcutate virial coefficients, can be applied to evaluate the superfluid transition temperature of the Bardeen-Cooper-Schrieffer (BCS)--Bose-Einstein condensation (BEC) crossover \`a la Lee and Yang. The transition temperature is identified with the emergence of the singularity in the sum of a certain infinite series of cluster functions. In the weak-coupling limit, we reproduce the Thouless criterion and the number equation of Nozi\`eres and Schmitt-Rink, and hence the transition temperature of the BCS theory. In the strong-coupling limit, we reproduce the transition temperature of BEC of noninteracting tightly bound dimers.

arXiv:1310.4665Physical Review AMar 14, 20147 citations

Universality and novel phases in the BCS-BEC crossover

W. Zwerger

Bulletin of the American Physical SocietyJun 8, 20070 citations

Modified many-body wave function for BCS-BEC crossover in Fermi gases

Shina Tan, Kathryn Levin

We present a many-body formalism for BCS-BEC crossover, which represents a modification of the Bardeen-Cooper-Schrieffer-Leggett ground state to include four-fermion and higher correlations. In the Bose-Einstein condensate regime, we show how our approach contains the four-fermion behavior of Petrov et al. and associated scattering length ${a}_{dd}$ at short distances and, second, reduces to composite-boson Bogoliubov physics at long distances. It reproduces the Lee-Yang term, whose numerical value is also fixed by ${a}_{dd}$ . We have also examined the next term beyond the Lee-Yang correction in a phenomenological fashion, building on cloud size data and collective mode experiments, although one has to view this phenomenological analysis with some caution since experiments are in a state of flux and are performed close to unitarity.We present a many-body formalism for BCS-BEC crossover, which represents a modification of the Bardeen-Cooper-Schrieffer-Leggett ground state to include four-fermion and higher correlations. In the Bose-Einstein condensate regime, we show how our approach contains the four-fermion behavior of Petrov et al. and associated scattering length ${a}_{dd}$ at short distances and, second, reduces to composite-boson Bogoliubov physics at long distances. It reproduces the Lee-Yang term, whose numerical value is also fixed by ${a}_{dd}$. We have also examined the next term beyond the Lee-Yang correction in a phenomenological fashion, building on cloud size data and collective mode experiments, although one has to view this phenomenological analysis with some caution since experiments are in a state of flux and are performed close to unitarity.

arXiv:cond-mat/0506293Physical Review AOct 9, 200610 citations

Pairing Fluctuations Approach to the BCS–BEC Crossover

Giancarlo Calvanese Strinati

Lecture notes in physicsOct 19, 20119 citations

Criteria of off-diagonal long-range order in Bose and Fermi systems based on the Lee-Yang cluster expansion method

Naoyuki Sakumichi, Norio Kawakami, Masahito Ueda

The quantum-statistical cluster expansion method of Lee and Yang is extended to investigate off-diagonal long-range order (ODLRO) in one-component and multicomponent mixtures of bosons or fermions. Our formulation is applicable to both a uniform system and a trapped system without local-density approximation and allows systematic expansions of one-particle and multiparticle reduced density matrices in terms of cluster functions, which are defined for the same system with Boltzmann statistics. Each term in this expansion can be associated with a Lee-Yang graph. We elucidate a physical meaning of each Lee-Yang graph; in particular, for a mixture of ultracold atoms and bound dimers, an infinite sum of the ladder-type Lee-Yang 0-graphs is shown to lead to Bose-Einstein condensation of dimers below the critical temperature. In the case of Bose statistics, an infinite series of Lee-Yang 1-graphs is shown to converge and gives the criteria of ODLRO at the one-particle level. Applications to a dilute Bose system of hard spheres are also made. In the case of Fermi statistics, an infinite series of Lee-Yang 2-graphs is shown to converge and gives the criteria of ODLRO at the two-particle level. Applications to a two-component Fermi gas in the tightly bound limit are also made.The quantum-statistical cluster expansion method of Lee and Yang is extended to investigate off-diagonal long-range order (ODLRO) in one-component and multicomponent mixtures of bosons or fermions. Our formulation is applicable to both a uniform system and a trapped system without local-density approximation and allows systematic expansions of one-particle and multiparticle reduced density matrices in terms of cluster functions, which are defined for the same system with Boltzmann statistics. Each term in this expansion can be associated with a Lee-Yang graph. We elucidate a physical meaning of each Lee-Yang graph; in particular, for a mixture of ultracold atoms and bound dimers, an infinite sum of the ladder-type Lee-Yang 0-graphs is shown to lead to Bose-Einstein condensation of dimers below the critical temperature. In the case of Bose statistics, an infinite series of Lee-Yang 1-graphs is shown to converge and gives the criteria of ODLRO at the one-particle level. Applications to a dilute Bose system of hard spheres are also made. In the case of Fermi statistics, an infinite series of Lee-Yang 2-graphs is shown to converge and gives the criteria of ODLRO at the two-particle level. Applications to a two-component Fermi gas in the tightly bound limit are also made.

arXiv:1112.5768Physical Review AApr 2, 20123 citations

{a}_{dd}

at short distances and, second, reduces to composite-boson Bogoliubov physics at long distances. It reproduces the Lee-Yang term, whose numerical value is also fixed by

{a}_{dd}

. We have also examined the next term beyond the Lee-Yang correction in a phenomenological fashion, building on cloud size data and collective mode experiments, although one has to view this phenomenological analysis with some caution since experiments are in a state of flux and are performed close to unitarity.