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arXiv:cond-mat/0606281 · New Journal of Physics

A primary noise thermometer for ultracold Bose gases

Rudolf Gati, Jérôme Estève, Boerge Hemmerling, T. B. Ottenstein, J. Appmeier, A Weller, Markus K. Oberthaler

Published Sep 12, 2006• 65 citations
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Abstract

We discuss in detail the experimental investigation of thermally induced fluctuations of the relative phase between two weakly coupled Bose–Einstein condensates (BECs). In analogy to superconducting Josephson junctions, the weak coupling originates from a tunnelling process through a potential barrier which is obtained by trapping the condensates in an optical double-well potential. The observed fluctuations of the relative phase are in quantitative agreement with a many body two mode model at finite temperature. The agreement demonstrates the possibility of using the phase fluctuation measurements in a bosonic Josephson junction (BJJ) as a primary thermometer. This new method allows for measuring temperatures far below the critical temperature where standard methods based on time of flight measurements fail. We employ this new thermometer to probe the heat capacity of a degenerate Bose gas as a function of temperature.

DOI
10.1088/1367-2630/8/9/189

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We discuss in detail the experimental investigation of thermally induced fluctuations of the relative phase between two weakly coupled Bose–Einstein condensates (BECs). In analogy to superconducting Josephson junctions, the weak coupling originates from a tunnelling process through a potential barrier which is obtained by trapping the condensates in an optical double-well potential. The observed fluctuations of the relative phase are in quantitative agreement with a many body two mode model at finite temperature. The agreement demonstrates the possibility of using the phase fluctuation measurements in a bosonic Josephson junction (BJJ) as a primary thermometer. This new method allows for measuring temperatures far below the critical temperature where standard methods based on time of flight measurements fail. We employ this new thermometer to probe the heat capacity of a degenerate Bose gas as a function of temperature.
Here we report on the experimental investigation of thermally induced fluctuations of the relative phase between two Bose-Einstein condensates which are coupled via tunneling. The experimental control over the coupling strength and the temperature of the thermal background allows for the quantitative analysis of the phase fluctuations. Furthermore, we demonstrate the application of these measurements for thermometry in a regime where standard methods fail. With this we confirm that the heat capacity of an ideal Bose gas deviates from that of a classical gas as predicted by the third law of thermodynamics.
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Abstract In the framework of the stochastic projected Gross–Pitaevskii equation we investigate finite-temperature dynamics of a bosonic Josephson junction (BJJ) formed by a Bose–Einstein condensate of atoms in a two-well trapping potential. We extract the characteristic properties of the BJJ from the stationary finite-temperature solutions and compare the dynamics of the system with the resistively shunted Josephson model. Analyzing the decay dynamics of the relative population imbalance we estimate the effective normal conductance of the junction induced by thermal atoms. The calculated normal conductance at various temperatures is then compared with predictions of the noise-less model and the model of ballistic transport of thermal atoms.
We realize a one-dimensional Josephson junction using quantum degenerate Bose gases in a tunable double well potential on an atom chip. Matter wave interferometry gives direct access to the relative phase field, which reflects the interplay of thermally driven fluctuations and phase locking due to tunneling. The thermal equilibrium state is characterized by probing the full statistical distribution function of the two-point phase correlation. Comparison to a stochastic model allows us to measure the coupling strength and temperature and hence a full characterization of the system.
Bosonic Josephson junctions can be realized by confining ultracold gases of bosons in multiwell traps and studied theoretically with the MMM-site Bose-Hubbard model. We show that canonical equilibrium states of the MMM-site Bose-Hubbard model may be approximated by mixtures of coherent states, provided the number of atoms is large and the total energy is comparable to kBT{k}_{B}TkB​T. Using this approximation, we study thermal fluctuations in bosonic Josephson junctions in the mean-field regime. Statistical estimates of the fluctuations of relative phase and number, obtained by averaging over many replicates of an experiment, can be used to estimate the temperature and the tunneling parameter or to test whether the experimental procedure is effectively sampling from a canonical thermal equilibrium ensemble.