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Journal of Physics A Mathematical and General

Phase diagram of ultracold strongly coupled plasmas

Genri E. Norman

Published Apr 7, 2006• 12 citations
Publisher

Abstract

The results of recent experiments and simulation for ultracold plasmas are related to the criterion of the thermodynamic stability. Different approaches for the equation of state of strongly coupled plasmas are used: second virial coefficient, electrolyte-like and van der Waals-like approximations. Three areas of ultracold plasma parameters are distinguished: thermodynamically stable, labile and metastable.

DOI
10.1088/0305-4470/39/17/s42

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The results of recent experiments and simulation for ultracold plasmas are related to the criterion of the thermodynamic stability. Different approaches for the equation of state of strongly coupled plasmas are used: second virial coefficient, electrolyte-like and van der Waals-like approximations. Three areas of ultracold plasma parameters are distinguished: thermodynamically stable, labile and metastable.
We show the existence of the liquid-vapor phase coexistence and a critical point for strongly coupled ions in ultracold neutral (UCN) plasmas. Expressions for the free energy of UCN plasmas and an equation of state for the ions are obtained in the mean field approximation. A van der Waals-like isotherm shows the existence of a critical point in UCN plasmas. Depending on the ion temperature, the ions are shown to exist in a mixed vapor-liquid phase for a range of the ion Coulomb coupling parameter Γ(i) (defined by the ratio between the ion interaction and the ion kinetic energies), and in a strongly coupled liquid state for values of Γ(i) above this range. The estimates of critical constants show that it may be possible to observe these phenomena in the present day UCN plasmas.
The theoretical interpretation of recent experiments on the time evolution of the temperature in freely expanding, ultracold plasma clouds released from a magneto-optical trap is discussed. The most interesting result of those experiments was the asymptotic behavior T e ∝ t −(1,2±0.1), instead of the behavior proportional to t −2, which was expected for a rarefied monatomic gas in the inertial expansion stage. It is shown that such a substantially slower temperature fall can be well explained by the specific properties of the equation of state of ultracold plasma with a large Coulomb coupling parameter; whereas the heat release in inelastic processes (in particular, three-body recombination) turns out to be relatively unimportant in the first approximation. This conclusion is confirmed by approximate analytic estimates from the model of virializing the energies of charged particles and also by the results of ab initio computer simulations; moreover, the computations demonstrate that the law of decrease in the electron temperature is established very rapidly, when the virialization criterion begins to be satisfied only to within a factor of order unity.
We present a theoretical interpretation of the recently revealed features of temperature evolution in the ultracold plasma clouds released from a magneto-optical trap, namely: (a) its independence at the sufficiently large times on the initial plasma parameters and (b) the asymptotics close to t^{-1} instead of t^{-2}, expected for a rarefied ideal gas. It is shown that both these properties can be well explained by the model of virialization of the charged particle velocities in the regime of strong electron-ion correlations, while heating due to inelastic processes (e.g. three-body recombination) should be of secondary importance. These conclusions are confirmed also by the results of ab initio computer simulations.
For interacting many-body systems the two most natural energy scales are the average energy per particle and the average energy per particle and the average nearest-neighbor potential energy. When the ratio of the nearest-neighbor potential energy to the kinetic energy is greater than 1, we say that the system is "strongly coupled," where strong coupling is characterized by the parameter Γ. This dimensionless parameter describes the complete thermodynamic state of a system, making it possible to study the fundamental behavior of strongly coupled systems as manifested in high energy-density plasmas using low energy table-top experiments. In our experiments, we are working with plasmas in this exotic regime. In this paper we report on the progress of an experiment in laser-cooled calcium designed to increase the strong coupling of an ultracold neutral plasma by promoting the plasma ions to the second ionization state. We report preliminary measurements of the change in the Ca+ ion temperature due to the second ionization.
Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe Ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.