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Since N ′ saturates for N > N c, as shown in Fig. 3, associating the critical point with a small but nonzero N 0 does not introduce any errors.
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Since N ′ saturates for N > N c, as shown in Fig. 3, associating the critical point with a small but nonzero N 0 does not introduce any errors.
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This conclusion is also compatible with an earlier estimate based on analyzing just the shape of the thermal ToF profiles at ∼ 100 nK [17].
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Our absolute atom-number calibration is obtained by measuring N c in a harmonic trap [15]. The systematic uncertainty in V is due to the inherent difficulties in imaging small and dense clouds. Note that it corresponds to about one CCD pixel uncertainty in the linear cloud size.
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N c could also be slightly reduced by weak disorder in the optical potential [27]. By directly imaging our trapping beams, we assess the disorder in our trap to be up to a few percent of U 0.
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N c could also be slightly reduced by weak disorder in the optical potential [27]. By directly imaging our trapping beams, we assess the disorder in our trap to be up to a few percent of U 0.
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We estimate that the total change in T due to the change in the interaction energy per particle could at most be ∼ 3 nK, which is comparable to our experimental data scatter. Moreover, note that for a > 0 the drop in the interaction energy should lead to slight heating rather than cooling of the gas.
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We estimate that the total change in T due to the change in the interaction energy per particle could at most be ∼ 3 nK, which is comparable to our experimental data scatter. Moreover, note that for a > 0 the drop in the interaction energy should lead to slight heating rather than cooling of the gas.
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For a classical gas, c JT can be estimated, to within an order of magnitude, by using the van der Waals approximation for the equation of state.
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