Atomic Gases at Negative Kinetic Temperature

We show that thermalization of the motion of atoms at negative temperature is possible in an optical lattice, for conditions that are feasible in current experiments. We present a method for reversibly inverting the temperature of a trapped gas. Moreover, a negative-temperature ensemble can be cooled (reducing $|T|$) by evaporation of the lowest-energy particles. This enables the attainment of the Bose-Einstein condensation phase transition at negative temperature.

Figure 1

Band structure of the one-dimensional Mathieu equation. White area: Bands, gray area: gaps. Dotted line: $q=0.559$, dashed line: $q=0.936$; see text.

Figure 2

Valence and conduction bands of a 1D optical lattice at $q=0.936$. Grey area: Gaps, white area: Bands.

Figure 3

Density of states $\rho (E)$ in a three-dimensional lattice with $\overline{\alpha }=-{10}^{-3}$. The energy $E$ is taken with respect to the top of the first (valence) band.

Figure 4

Method for reversibly transforming a positive-temperature gas (a) into a negative-temperature gas (f). Each step is reversible; see text. (a) trapped gas at positive $T$. (b) a strong optical lattice, (c) a strong optical lattice without trap, (d) a strong optical lattice with changed $a_{\mathrm{sc}}$, (e) a strong optical lattice with negative trap, (f) an optical lattice at $q=0.936$ with a negative-temperature gas.