操纵光晶格中的原子：分数费米子数及其光学量子测量
Manipulating atoms in an optical lattice: Fractional fermion number and its optical quantum measurement
摘要：
我们提供了一个详细的分析，我们以前提出的计划[物理。88，180401，（2002）]来设计1D光晶格中原子气体的跳跃幅度的分布，使得粒子数变为分数。我们考虑一个构造系统的两个组分的费米子原子的稀释气体耦合通过一个相干的电磁场与拓扑非平凡的相位轮廓。我们展示了如何在一个准备好的二聚光晶格的交替跳跃振幅的图案中的缺陷，所得的原子哈密顿量表现出分数费米子数的解析和数值。特别地，在低能极限下，我们证明了原子哈密顿量等价于描述量子场论中分数化的相对论狄拉克哈密顿量。扩展我们以前的论点[物理。91，150404（2003）]我们展示了如何通过光散射检测粒子数算子的分数本征值。特别是，我们展示了如何散射的远距离共振光可以传达信息的计数统计的原子在光晶格，包括状态选择性的原子密度分布和原子数的波动。光学探测可以提供一个真正的量子力学测量的粒子数分馏在一个稀释的原子气体。
英文摘要：
We provide a detailed analysis of our previously proposed scheme [Phys. Rev. Lett. 88, 180401, (2002)] to engineer the profile of the hopping amplitudes for atomic gases in a 1D optical lattice so that the particle number becomes fractional. We consider a constructed system of a dilute two-species gas of fermionic atoms where the two components are coupled via a coherent electromagnetic field with a topologically nontrivial phase profile. We show both analytically and numerically how the resulting atomic Hamiltonian in a prepared dimerized optical lattice with a defect in the pattern of alternating hopping amplitudes exhibits a fractional fermion number. In particular, in the low-energy limit we demonstrate the equivalence of the atomic Hamiltonian to a relativistic Dirac Hamiltonian describing fractionalization in quantum field theory. Expanding on our earlier argument [Phys. Rev. Lett. 91, 150404 (2003)] we show how the fractional eigenvalues of the particle number operator can be detected via light scattering. In particular, we show how scattering of far-off resonant light can convey information about the counting statistics of the atoms in an optical lattice, including state-selective atom density profiles and atom number fluctuations. Optical detection could provide a truly quantum mechanical measurement of the particle number fractionalization in a dilute atomic gas.
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