Universal equation of state for wave turbulence in a quantum gas.

Boyle's 1662 observation that the volume of a gas is, at constant temperature, inversely proportional to pressure, offered a prototypical example of how an equation of state (EoS) can succinctly capture key properties of a many-particle system. Such relationships are now cornerstones of equilibrium thermodynamics1. Extending thermodynamic concepts to far-from-equilibrium systems is of great interest in various contexts, including glasses2,3, active matter4-7 and turbulence8-11, but is in general an open problem. Here, using a homogeneous ultracold atomic Bose gas12, we experimentally construct an EoS for a turbulent cascade of matter waves13,14. Under continuous forcing at a large length scale and dissipation at a small one, the gas exhibits a non-thermal, but stationary, state, which is characterized by a power-law momentum distribution15 sustained by a scale-invariant momentum-space energy flux16. We establish the amplitude of the momentum distribution and the underlying energy flux as equilibrium-like state variables, related by an EoS that does not depend on the details of the energy injection or dissipation, or on the history of the system. Moreover, we show that the equations of state for a wide range of interaction strengths and gas densities can be empirically scaled onto each other. This results in a universal dimensionless EoS that sets benchmarks for the theory and should also be relevant for other turbulent systems.

Can Three-Body Recombination Purify a Quantum Gas?

Three-body recombination in quantum gases is traditionally associated with heating, but it was recently found that it can also cool the gas. We show that in a partially condensed three-dimensional homogeneous Bose gas three-body loss could even purify the sample, that is, reduce the entropy per particle and increase the condensed fraction η. We predict that the evolution of η under continuous three-body loss can, depending on small changes in the initial conditions, exhibit two qualitatively different behaviors-if it is initially above a certain critical value, η increases further, whereas clouds with lower initial η evolve towards a thermal gas. These dynamical effects should be observable under realistic experimental conditions.

Universal Scaling Laws in the Dynamics of a Homogeneous Unitary Bose Gas.

We study the dynamics of an initially degenerate homogeneous Bose gas after an interaction quench to the unitary regime at a magnetic Feshbach resonance. As the cloud decays and heats, it exhibits a crossover from degenerate- to thermal-gas behavior, both of which are characterized by universal scaling laws linking the particle-loss rate to the total atom number N. In the degenerate and thermal regimes, the per-particle loss rate is ∝N^{2/3} and N^{26/9}, respectively. The crossover occurs at a universal kinetic energy per particle and at a universal time after the quench, in units of energy and time set by the gas density. By slowly sweeping the magnetic field away from the resonance and creating a mixture of atoms and molecules, we also map out the dynamics of correlations in the unitary gas, which display a universal temporal scaling with the gas density, and reach a steady state while the gas is still degenerate.