A unique feature of ultracold atoms is the separation of length scales, r_{0}≪k_{F}^{-1}, where k_{F} and r_{0} are the Fermi momentum characterizing the average particle distance and the range of interaction between atoms, respectively. For s-wave scattering, Shina Tan discovered that such diluteness leads to universal thermodynamic relations governed by contact. Here, we show that the concept of contact can be generalized to an arbitrary partial-wave scattering. Contact of all partial-wave scatterings forms a contact spectrum, which establishes universal thermodynamic relations with notable differences from those in the presence of s-wave scattering alone. Such a contact spectrum is particularly useful for characterizing many-body correlations in atomic quantum Hall states (QHSs). It has an interesting connection with a special bipartite entanglement spectrum of QHSs and enables an intrinsic probe of atomic QHSs using short-range two-body correlations.A unique feature of ultracold atoms is the separation of length scales, r_{0}≪k_{F}^{-1}, where k_{F} and r_{0} are the Fermi momentum characterizing the average particle distance and the range of interaction between atoms, respectively. For s-wave scattering, Shina Tan discovered that such diluteness leads to universal thermodynamic relations governed by contact. Here, we show that the concept of contact can be generalized to an arbitrary partial-wave scattering. Contact of all partial-wave scatterings forms a contact spectrum, which establishes universal thermodynamic relations with notable differences from those in the presence of s-wave scattering alone. Such a contact spectrum is particularly useful for characterizing many-body correlations in atomic quantum Hall states (QHSs). It has an interesting connection with a special bipartite entanglement spectrum of QHSs and enables an intrinsic probe of atomic QHSs using short-range two-body correlations.

arXiv:1506.01640Physical Review LettersJan 26, 201663 citations

Ultracold Atoms as Strongly Correlated Systems

Roberto Onofrio, Luca Salasnich

Lecture notes in physicsJan 1, 20240 citations

Universality in phase transitions for ultracold fermionic atoms

Sebastian Diehl, CHRISTOF WETTERICH

We describe the gas of ultracold fermionic atoms by a functional integral for atom and molecule fields. The crossover from Bose-Einstein condensation (BEC) to BCS-type superfluidity shows universal features in terms of a concentration parameter for the ratio between scattering length and average interatomic distance. We discuss the relevance of the Yukawa coupling between atoms and molecules, establish an exact narrow resonance limit, and show that renormalized quantities are independent of the Yukawa coupling for the broad resonance and BCS and BEC limits. Within our functional integral formalism we compute the atom scattering in vacuum and the molecular binding energy. This connects the universal concentration parameter to the magnetic field of a given experiment. Beyond mean-field theory we include the fluctuations of the molecule field and the renormalization effects for the atom-molecule coupling. We find excellent agreement with the observed fraction of bare molecules in $^{6}\mathrm{Li}$ and qualitative agreement with the condensate fraction in $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$ . In addition to the phase diagram and condensate fraction we compute the correlation length for molecules, the in-medium scattering length for molecules and atoms, and the sound velocity.We describe the gas of ultracold fermionic atoms by a functional integral for atom and molecule fields. The crossover from Bose-Einstein condensation (BEC) to BCS-type superfluidity shows universal features in terms of a concentration parameter for the ratio between scattering length and average interatomic distance. We discuss the relevance of the Yukawa coupling between atoms and molecules, establish an exact narrow resonance limit, and show that renormalized quantities are independent of the Yukawa coupling for the broad resonance and BCS and BEC limits. Within our functional integral formalism we compute the atom scattering in vacuum and the molecular binding energy. This connects the universal concentration parameter to the magnetic field of a given experiment. Beyond mean-field theory we include the fluctuations of the molecule field and the renormalization effects for the atom-molecule coupling. We find excellent agreement with the observed fraction of bare molecules in $^{6}\mathrm{Li}$ and qualitative agreement with the condensate fraction in $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$. In addition to the phase diagram and condensate fraction we compute the correlation length for molecules, the in-medium scattering length for molecules and atoms, and the sound velocity.

arXiv:cond-mat/0502534Physical Review AMar 17, 200651 citations

Strongly correlated states in ultracold atoms

Dalla Torre, G Emanuele

Jan 1, 20110 citations

Scaling Properties of Universal Tetramers

M. R. Hadizadeh, Marcelo Takeshi Yamashita, Lauro Tomio +2 more

We evidence the existence of a universal correlation between the binding energies of successive four-boson bound states (tetramers), for large two-body scattering lengths (a), related to an additional scale not constrained by three-body Efimov physics. Relevant to ultracold atom experiments, the atom-trimer relaxation peaks for |a|→∞ when the ratio between the tetramer and trimer energies is ≃4.6 and a new tetramer is formed. The new scale is also revealed for a < 0 by the prediction of a correlation between the positions of two successive peaks in the four-atom recombination process.We evidence the existence of a universal correlation between the binding energies of successive four-boson bound states (tetramers), for large two-body scattering lengths (a), related to an additional scale not constrained by three-body Efimov physics. Relevant to ultracold atom experiments, the atom-trimer relaxation peaks for |a|→∞ when the ratio between the tetramer and trimer energies is ≃4.6 and a new tetramer is formed. The new scale is also revealed for a < 0 by the prediction of a correlation between the positions of two successive peaks in the four-atom recombination process.

arXiv:1101.0378Physical Review LettersSep 23, 201179 citations

^{6}\mathrm{Li}

and qualitative agreement with the condensate fraction in

^{6}\mathrm{Li}

and

^{40}\mathrm{K}

. In addition to the phase diagram and condensate fraction we compute the correlation length for molecules, the in-medium scattering length for molecules and atoms, and the sound velocity.