标题： 冷量子气体中的粒子数涨落 显示英文标题

标题： Number fluctuations in cold quantum gases

摘要： 在超冷气体中，许多实验使用原子成像作为基本可观测量。 所得图像是对多个实现进行平均的，并且通常只使用这个平均值。 只有最近才测量了噪声以提取物理信息。 在本文中，我们研究了零温下这些气体中出现的量子噪声。 我们仅限于均匀情况，并研究气体中给定体积内的粒子数波动，特别是半径为$R$的球体内的波动。 我们表明，零温下的波动不是广延的，主导项在三维（或一维）系统中按球体半径$R$的$R^2\ln R$（或$\ln R$）比例变化。 我们系统地计算了这一主导项之后的下一个项。 我们首先考虑可压缩超流体的一般情况。 然后我们研究了整个玻色-爱因斯坦凝聚（BEC）-BCS转变过程，并特别研究了弱相互作用玻色气体和自由费米气体的极限情况。 显示英文摘要

摘要： In ultracold gases many experiments use atom imaging as a basic observable. The resulting image is averaged over a number of realizations and mostly only this average is used. Only recently the noise has been measured to extract physical information. In the present paper we investigate the quantum noise arising in these gases at zero temperature. We restrict ourselves to the homogeneous situation and study the fluctuations in particle number found within a given volume in the gas, and more specifically inside a sphere of radius $R$. We show that zero-temperature fluctuations are not extensive and the leading term scales with sphere radius $R$ as $R^2\ln R$ (or $\ln R$) in three- (or one-) dimensional systems. We calculate systematically the next term beyond this leading order. We consider first the generic case of a compressible superfluid. Then we investigate the whole Bose-Einstein-condensation (BEC)-BCS crossover crossover, and in particular the limiting cases of the weakly interacting Bose gas and of the free Fermi gas.