Shifts of a Resonance Line in a Dense Atomic Sample

Abstract

We study the collective response of a dense atomic sample to light essentially exactly using classicalelectrodynamics simulations. In a homogeneously broadened atomic sample there is no overt LorentzLorenz local field shift of the resonance, nor a collective Lamb shift. However, the addition of inhomogeneous broadening restores the usual mean-field phenomenology. DOI: 10.1103/PhysRevLett.112.113603 PACS numbers: 42.50.Nn, 32.70.Jz, 42.25.Bs Textbook arguments [1,2] tell us that in a dielectric medium the local electric field E l seen by an atom (molecule) is different from the macroscopic electric field E by an amount proportional to the polarization P of the medium, E l ¼ E þ P=3ϵ 0 . This is the origin of the localfield corrections in electrodynamics embodied in the Clausius-Mossotti and Lorentz-Lorenz relations. As a result, the frequency dependence of the microscopic polarizability and the macroscopic susceptibility are different. If the polarizability has a Lorentzian line shape then so does the susceptibility, but the resonance is shifted by what is known as the Lorentz-Lorenz (LL) shift [3]. The LL shift serves as the generic frequency scale for other density dependent phenomena in an atomic sample such as collisional self-broadening of absorption lines [4,5] and collective Lamb shift (CLS) [6][7][8][9][10].Local-field corrections are a standard workhorse in solid and liquid media. On the other hand, in a resonant atomic gas a density conducive to LL shift and CLS results in an optically thick sample, which might explain the sparsity of laser spectroscopy era experiments. There are careful experiments on related phenomenology that agree with the respective theory [8,9,[11][12][13], but except for the nuclear-physics experiment of Ref.[9] the published experiments we know of deal with inhomogeneously broadened samples with a substantial line broadening due to the motion of the atoms. Atomic-physics experiments with cold and dense clouds such as those in Ref. [14] are presently underway [15]. Optically thick samples are needed for a good quantum interface between photons and matter [16], so that local-field effects, and, more generally, cooperative response of matter to light, are likely to become issues in the quest toward quantum technologies.Here we study the cooperative response of a dense atomic sample to light in the limit of low excitation essentially exactly [17] using classical-electrodynamics simulations [18][19][20][21][22][23][24][25] in a slab geometry analogously to theory [6] and experiments [8] on CLS. In these simulations with an unprecedentedly large scale, we have discovered that a homogeneously broadened sample with fixed atomic positions in fact does not exhibit the expected LorentzLorenz or collective Lamb shifts. However, when we add inhomogeneous broadening [24] to the atomic samples, the traditional phenomenology of local-field corrections together with density-dependent collective effects reemerges. Basically, in a homogeneously broadened sample the correlations between nearby ...

Exact electrodynamics versus standard optics for a slab of cold dense gas

“…This MFT treats the radiative interactions between the atoms in the average sense, and the position-dependent correlations of the pointlike atoms are lost-even when the system is entirely classical without any quantum effects. The inhomogeneous broadening washes out these correlations, which explains the validity of the standard MFT phenomenology in such systems [17] and indicates that the usual EDPM is an emergent phenomenon where strong correlation effects are suppressed by thermal motion or dissipation. The origin of macroscopic electromagnetism from microscopic principles consequently is inherently related to the meaning of cooperative light-atom interactions [18,40] and the limits of the predictive power of EDPM.…”

“…III we discuss concepts such as coherent and incoherent scattering and cooperative line shifts and linewidths by presenting analytically solvable examples that were not covered in Refs. [17,18]. Even if the examples are simple, they demonstrate the subtlety of the concept of cooperation.…”

“…Delving into the problem deeper, we discovered that the standard electrodynamics of polarizable media (EDPM) [42,43] and the resulting standard optics may fail qualitatively in cold, dense atomic samples [17,18]. However, adding inhomogeneous broadening that mimics the Doppler shifts of thermal atoms restored the behavior of standard EDPM.…”

“…The present work started with our chance observation in numerical light propagation simulations that the densitydependent Lorentz-Lorenz (LL) shift of the atomic resonance [41], a quintessential local-field correction, is absent in cold, dense atomic samples [17]. Delving into the problem deeper, we discovered that the standard electrodynamics of polarizable media (EDPM) [42,43] and the resulting standard optics may fail qualitatively in cold, dense atomic samples [17,18].…”

“…The growing throughput of computers available to researchers is making such a plan practical. These methods, whether called classicalelectrodynamics simulations or coupled-dipole simulations, are now a routine theoretical tool [2,4,7,8,[14][15][16][17][18][19][20][21][22][23][24][25][26]. Closely related numerical techniques based on the analysis of the eigenstates of the coupled system of the light and the atoms [15,[27][28][29][30][31][32] or density matrices and quantum trajectories [33][34][35] are also widely used today.…”