Thermometry and cooling of a Bose gas to 0.02 times the condensation temperature

Abstract

Trapped quantum gases can be cooled to impressively low temperatures 1,2 , but it is unclear whether their entropy is low enough to realize phenomena such as d-wave superconductivity and magnetic ordering 3 . Estimated critical entropies per particle for quantum magnetic ordering are ∼0.3k B and ∼0.03k B for bosons in three-and two-dimensional lattices, respectively 4 , with similar values for Néel ordering of latticetrapped Fermi gases 5 . Here we report reliable single-shot temperature measurements of a degenerate Rb gas by imaging the momentum distribution of thermalized magnons, which are spin excitations of the atomic gas. We record average temperatures fifty times lower than the Bose-Einstein condensation temperature, indicating an entropy per particle of ∼0.001k B at equilibrium, nearly two orders of magnitude lower than the previous best in a dilute atomic gas 2,6 and well below the critical entropy for antiferromagnetic ordering of a Bose-Hubbard system. The magnons can reduce the temperature of the system by absorbing energy during thermalization and by enhancing evaporative cooling, allowing the production of low-entropy gases in deep traps.In many experiments on strongly interacting atomic-gas systems, the low-entropy regime is reached by first preparing a weakly interacting bulk Bose gas at the lowest possible temperature, and then slowly transforming the system to become strongly interacting 7-11 . To discern whether the transformation is adiabatic and to determine indirectly the thermodynamic properties of the strongly interacting system, the system is returned to the weakly interacting regime where relations between temperature, entropy and other properties are known. Therefore, methods to lower entropies and measure temperatures of weakly interacting gases are important for the study of both weakly and strongly interacting atomic-gas systems.In this Letter, we report cooling a Bose gas to a few per cent of the condensation temperature, T c , corresponding to an entropy per particle S/N ≈ 1 × 10 −3 k B , where k B is the Boltzmann constant. Surprisingly, we achieve this low entropy using a standard technique: forced evaporation in an optical dipole trap, which we find remains effective in a previously uncharacterized regime. The lowest temperatures we report are achieved at very shallow final trap depths, as low as 20 nK, set by stabilizing the optical intensity with a longterm fractional reproducibility better than 10 −2 . In addition, we demonstrate and characterize a method of cooling that lowers the entropy without changing the trap depth, possibly allowing the lowentropy regime to be reached or maintained in systems where the trap depth is constrained.Both thermometry and cooling require a means of distinguishing thermal excitations. For example, forced evaporative cooling 12,13 depends on the ability to selectively expel high-energy excitations from the system. Similarly, thermometry of a degenerate quantum gas requires one to identify the excitations that distinguish a zero-temperature from...

Stepwise Bose-Einstein Condensation in a Spinor Gas

“…Previous experimental works exploring finite temperatures in spinor gases mostly studied spin dynamics in thermal gases [23][24][25][26], or demonstrated cooling of a majority Zeeman component by selective evaporation of the minority components [27,28]. The realization of dipolar spinor gases with free magnetization [15] was limited to the study of spin-polarized condensed phases in equilibrium due to dipolar relaxation.…”

Hartree-Fock Approach for Rotating Bose-Einstein Condensation in One-dimensional Deep Optical Lattice

“…Thus, it is important to determine and investigate the entropy-temperature curves [32]. The behavior of these curves is used in analyzing the process of adiabatic cooling [19,33,34]. For the rotating condensate in an optical lattice, the normalized entropy per particle is given by Blakie [32] (25)…”

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Calorimetry of a harmonically trapped Bose gas

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