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arXiv 1409.6074cond-mat.quant-gas
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双凝体中涨落的标度

Scaling of Fluctuations in a Trapped Binary Condensate

R. N. Bisset, R. M. Wilson, C. Ticknor

备注：
7 pages, 3 figures
发表信息：
Phys. Rev. A 91, 053613 (2015)
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摘要：

我们证明，有限细胞内的数量波动的测量提供了一个直接的手段来研究波动标度在一个被困的两组分冷凝。该量子系统支持由对磁波动的发散敏感性驱动的可混溶（共空间）和不可混溶（磁破碎）状态之间的二阶相变。由于过渡接近从混溶侧的磁化率被发现强烈依赖于观察细胞的几何形状和取向。然而，只要拟合排除了临界点附近的区域，就可以为所有考虑的单元恢复与均匀气体（$γ= 1$）一致的标度指数。当从不混溶侧接近过渡时，磁涨落表现出非平凡的标度指数$γ\simeq 1.30$。实验上，可以通过考虑各个成像像素或通过组合像素以形成更大的单元来形成观察单元，并且可以通过重复的\emph{in situ}图像来获得波动统计。有趣的是，在过渡的两侧，我们发现最好使用覆盖一半捕获系统的观察单元来提取指数。这意味着相对低分辨率的\emph{in situ}成像将足以研究这些指数。我们还研究了能隙，发现在可混溶侧的指数$νz$ = 0.505，并且出乎意料地，对于不混溶相，指数$νz$ = 0.60（3）。

英文摘要：

We demonstrate that measurements of number fluctuations within finite cells provide a direct means to study fluctuation scaling in a trapped two-component condensate. This quantum system supports a second-order phase transition between miscible (co-spatial) and immiscible (symmetry-broken) states that is driven by a diverging susceptibility to magnetic fluctuations. As the transition is approached from the miscible side the magnetic susceptibility is found to depend strongly on the geometry and orientation of the observation cell. However, a scaling exponent consistent with that for the homogenous gas ($γ= 1$) can be recovered, for all cells considered, as long as the fit excludes the region in the immediate vicinity of the critical point. As the transition is approached from the immiscible side, the magnetic fluctuations exhibit a non-trivial scaling exponent $γ\simeq 1.30$. Experimentally, the observation cells may be formed either by considering individual imaging pixels or by combining pixels to form larger cells, and fluctuation statistics can be obtained by repeated \emph{in situ} images. Interestingly, on both sides of the transition, we find it best to extract the exponents using an observation cell that covers half of the trapped system. This implies that relatively low-resolution \emph{in situ} imaging will be adequate for the investigation of these exponents. We also investigate the gap energy and find exponents $νz$ = 0.505 on the miscible side and, unexpectedly, $νz$ = 0.60(3) for the immiscible phase.

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