Two-body and three-body contacts for identical Bosons near unitarity.

In a recent experiment with ultracold trapped Rb85 atoms, Makotyn et al. studied a quantum-degenerate Bose gas in the unitary limit where its scattering length is infinitely large. We show that the observed momentum distributions are compatible with a universal relation that expresses the high-momentum tail in terms of the two-body contact C2 and the three-body contact C3. We determine the contact densities for the unitary Bose gas with number density n to be C2 ≈ 20 n(4/3) and C3 ≈ 2n(5/3). We also show that the observed atom loss rate is compatible with that from 3-atom inelastic collisions, which gives a contribution proportional to C3, but the loss rate is not compatible with that from 2-atom inelastic collisions, which gives a contribution proportional to C2. We point out that the contacts C2 and C3 could be measured independently by using the virial theorem near and at unitarity, respectively.

Efimov physics from a renormalization group perspective.

We discuss the physics of the Efimov effect from a renormalization group viewpoint using the concept of limit cycles. Furthermore, we discuss recent experiments providing evidence for the Efimov effect in ultracold gases and its relevance for nuclear systems.

Universal relations for identical bosons from three-body physics.

Systems consisting of identical bosons with a large scattering length satisfy universal relations determined by 2-body physics that are similar to those for fermions with two spin states. They require the momentum distribution to have a large-momentum 1/k(4) tail and the radio-frequency transition rate to have a high-frequency 1/ω(3/2) tail, both of which are proportional to the 2-body contact. Identical bosons also satisfy additional universal relations that are determined by 3-body physics and involve the 3-body contact, which measures the probability of 3 particles being very close together. The coefficients of the 3-body contact in the 1/k(5) tail of the momentum distribution and in the 1/ω(2) tail of the radio-frequency transition rate are log-periodic functions of k and ω that depend on the Efimov parameter.

Short-time operator product expansion for rf spectroscopy of a strongly interacting Fermi gas.

Universal relations that hold for any state provide powerful constraints on systems consisting of fermions with two spin states interacting with a large scattering length. In radio-frequency (rf) spectroscopy, the mean shift in the rf frequency and the large-frequency tail of the rf transition rate are proportional to the contact, which measures the density of pairs with small separations. We show that these universal relations can be derived and extended by using the short-time operator product expansion of quantum field theory. This is a general method for identifying aspects of many-body physics that are controlled by few-body physics.

Three-body recombination of 6Li atoms with large negative scattering lengths.

The three-body recombination rate at threshold for distinguishable atoms with large negative pair scattering lengths is calculated in the zero-range approximation. The only parameters in this limit are the 3 scattering lengths and the Efimov parameter, which can be complex-valued. We provide semianalytic expressions for the cases of 2 or 3 equal scattering lengths, and we obtain numerical results for the general case of 3 different scattering lengths. Our general result is applied to the three lowest hyperfine states of 6Li atoms. Comparisons with recent experiments provide indications of loss features associated with Efimov trimers near the 3-atom threshold.

Exact relations for a strongly interacting fermi gas from the operator product expansion.

The momentum distribution in a Fermi gas with two spin states and a large scattering length has a tail that falls off like 1/k4 at large momentum k, as pointed out by Tan. He used novel methods to derive exact relations between the coefficient of the tail in the momentum distribution and various other properties of the system. We present simple derivations of these relations using the operator product expansion for quantum fields. We identify the coefficient as the integral over space of the expectation value of a local operator that measures the density of pairs.