Unitary Bose Gas Research Articles

Liquid-solid transitions in the three-body hard-core model

We determine the phase diagram for a generalisation of two- and three-dimensional hard spheres: a classical system with three-body interactions realised as a hard cut-off on the mean-square distance for each triplet of particles. Quantum versions of this model are important in the context of the unitary Bose gas, which is currently under close theoretical and experimental scrutiny. In two dimensions, the three-body hard-core model possesses a conventional atomic liquid phase and a peculiar solid phase formed by dimers. These dimers interact effectively as hard disks. In three dimensions, the solid phase consists of isolated atoms that arrange in a simple-hexagonal lattice.

Momentum Distribution of a Dilute Unitary Bose Gas with Three-Body Losses.

Using a combination of Boltzmann's equation and virial expansion, we study the effect of three-body losses and interactions on the momentum distribution of a homogeneous unitary Bose gas in the dilute limit where quantum correlations are negligible. The comparison of our results to the recent measurement made at JILA on a unitary gas of ^{85}Rb allows us to determine an experimental fugacity z=0.5(1).

Monte Carlo simulations of the unitary Bose gas

We investigate the zero-temperature properties of a diluted homogeneous Bose gas made of $N$ particles interacting via a two-body square-well potential by perfor ming Monte Carlo simulations. We tune the interaction strength to achieve arbitrary positive values of the scattering length and compute by Monte Carlo quadrature the energy per particle $E/N$ and the condensate fraction $N_0/N$ of this system by using a Jastrow ansatz for the many-body wave function which avoids the formation of the self-bound ground-state and describes instead a (metastable) gaseous state with uniform den sity. In the unitarity limit, where the scattering length diverges while the range of the inter-atomic potential is much smaller than the average distance between atoms, we find a finite energy per particle ($E/N=0.70\ \hbar^2(6\pi^2n)^{2/3}/2m$, with $n$ th e number density) and a quite large condensate fraction ($N_0/N=0.83$).

Efimov-driven phase transitions of the unitary Bose gas

Initially predicted in nuclear physics, Efimov trimers are bound configurations of three quantum particles that fall apart when any one of them is removed. They open a window into a rich quantum world that has become the focus of intense experimental and theoretical research, as the region of 'unitary' interactions, where Efimov trimers form, is now accessible in cold-atom experiments. Here we use a path-integral Monte Carlo algorithm backed up by theoretical arguments to show that unitary bosons undergo a first-order phase transition from a normal gas to a superfluid Efimov liquid, bound by the same effects as Efimov trimers. A triple point separates these two phases and another superfluid phase, the conventional Bose-Einstein condensate, whose coexistence line with the Efimov liquid ends in a critical point. We discuss the prospects of observing the proposed phase transitions in cold-atom systems.

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.

Universal dynamics of a degenerate unitary Bose gas

Understanding the rich behavior that emerges from systems of interacting quantum particles, such as electrons in materials, nucleons in nuclei or neutron stars, the quark-gluon plasma, and superfluid liquid helium, requires investigation of systems that are clean, accessible, and have tunable parameters. Ultracold quantum gases offer tremendous promise for this application largely due to an unprecedented control over interactions. Specifically, $a$, the two-body scattering length that characterizes the interaction strength, can be tuned to any value. This offers prospects for experimental access to regimes where the behavior is not well understood because interactions are strong, atom-atom correlations are important, mean-field theory is inadequate, and equilibrium may not be reached or perhaps does not even exist. Of particular interest is the unitary gas, where $a$ is infinite, and where many aspects of the system are universal in that they depend only on the particle density and quantum statistics. While the unitary Fermi gas has been the subject of intense experimental and theoretical investigation, the degenerate unitary Bose gas has generally been deemed experimentally inaccessible because of three-body loss rates that increase dramatically with increasing $a$. Here, we investigate dynamics of a unitary Bose gas for timescales that are short compared to the loss. We find that the momentum distribution of the unitary Bose gas evolves on timescales fast compared to losses, and that both the timescale for this evolution and the limiting shape of the momentum distribution are consistent with universal scaling with density. This work demonstrates that a unitary Bose gas can be created and probed dynamically, and thus opens the door for further exploration of this novel strongly interacting quantum liquid.

Stability of a Unitary Bose Gas

We study the stability of a thermal (39)K Bose gas across a broad Feshbach resonance, focusing on the unitary regime, where the scattering length a exceeds the thermal wavelength λ. We measure the general scaling laws relating the particle-loss and heating rates to the temperature, scattering length, and atom number. Both at unitarity and for positive a<<λ we find agreement with three-body theory. However, for a<0 and away from unitarity, we observe significant four-body decay. At unitarity, the three-body loss coefficient, L(3) proportional λ(4), is 3 times lower than the universal theoretical upper bound. This reduction is a consequence of species-specific Efimov physics and makes (39)K particularly promising for studies of many-body physics in a unitary Bose gas.

On the viscosity-to-entropy density ratio for unitary Bose and Fermi gases

We calculate the ratio of the viscosity to the entropy density for both Bose and Fermi gases in the unitary limit using a new approach to the quantum statistical mechanics of gases based on the S-matrix. In the unitary limit the scattering length diverges and the S-matrix equals − 1. For the fermion case, we obtain η/s>4.7 times the proposed lower bound of ℏ/4πkB, which came from the anti-Desitter space/conformal field theory correspondence (AdS/CFT) for gauge theories, consistent with the most recent experiments. For the bosonic case, we present evidence that the gas undergoes a phase transition to a strongly interacting Bose–Einstein condensate and is a more perfect fluid, with η/s<1.3 times the bound.