Effective photon-photon interaction in a two-dimensional "photon fluid"
Effective photon-photon interaction in a two-dimensional "photon fluid"
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DOI：
10.1103/physreva.69.063816
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发表时间：
2004-06-01
影响因子：
2.9
通讯作者：
Viefers, S
中科院分区：
文献类型：
--
作者：
Chiao, RY;Hansson, TH;Viefers, S
本文建立了一个有效的理论，研究了法布里-珀罗腔中二维光子流体中原子介导的光子-光子相互作用。用一组非简谐洛仑兹振子模拟原子，有效相互作用在耦合常数（非简谐参数）中被估计为二阶。相互作用具有重整化二维δ函数势的形式，重整化尺度由系统的物理参数确定，例如原子密度和光子相对于原子共振频率的失谐。对于实际的参数值，微扰级数必须进行图解，有效相互作用变得与非谐项的“裸”强度无关。由此产生的非线性克尔极化率的表达式是参数相等的一个发现较早的稀释气体的二能级原子。使用我们的结果的有效相互作用参数，我们推导出的条件，形成的光子流体，里德伯原子在微波腔和碱金属原子在光学腔。
We formulate an effective theory for the atom-mediated photon-photon interactions in a two-dimensional "photon fluid" confined in a Fabry-Perot resonator. With the atoms modeled by a collection of anharmonic Lorentz oscillators, the effective interaction is evaluated to second order in the coupling constant (the anharmonicity parameter). The interaction has the form of a renormalized two-dimensional delta-function potential, with the renormalization scale determined by the physical parameters of the system, such as density of atoms and the detuning of the photons relative to the resonance frequency of the atoms. For realistic values of the parameters, the perturbation series has to be resummed, and the effective interaction becomes independent of the "bare" strength of the anharmonic term. The resulting expression for the nonlinear Kerr susceptibility is parametrically equal to the one found earlier for a dilute gas of two-level atoms. Using our result for the effective interaction parameter, we derive conditions for the formation of a photon fluid, both for Rydberg atoms in a microwave cavity and for alkali atoms in an optical cavity.