Stochastic methods for light propagation and recurrent scattering in saturated and nonsaturated atomic ensembles

Lee, Mark D.; Jenkins, S. D.; Ruostekoski, Janne

doi:10.1103/physreva.93.063803

Cited by 67 publications

(125 citation statements)

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“…In fact, for a model atom such as ours, in the limit of low light intensity, there are no quantum fluctuations in the scattered light. We may have an issue for instance if the light intensity is increased, or if more than one electronic Zeeman ground state is involved [50,59], although observing such quantum fluctuations typically requires delicate experimental setups.…”

Section: B Classical-electrodynamics Solution For Light Propagationmentioning

confidence: 99%

“…The present subsection is mostly a brief summary of Refs. [13,50] that develop a work-around. The idea is that, just as one might solve a Fokker-Planck equation (diffusion equation) numerically using stochastic Langevin equations for individual particles 033835-3 [51], one may solve for the polarization correlations using stochastic classical-electrodynamics simulations.…”

Section: B Classical-electrodynamics Solution For Light Propagationmentioning

confidence: 99%

“…Ref. [50]. Specifically, introduce normally ordered correlation functions for ground-state density and correlations between polarization and ground-state density as…”

Section: A Quantum Theory Of Light Propagation In Dipolar Mediummentioning

confidence: 99%

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

Javanainen

Ruostekoski

et al. 2017

Phys. Rev. A

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We study light propagation through a slab of cold gas using both the standard electrodynamics of polarizable media and massive atom-by-atom simulations of the electrodynamics. The main finding is that the predictions from the two methods may differ qualitatively when the density of the atomic sample ρ and the wave number of resonant light k satisfy ρk −3 1. The reason is that the standard electrodynamics is a mean-field theory, whereas for sufficiently strong light-mediated dipole-dipole interactions the atomic sample becomes strongly correlated. The deviations from mean-field theory appear to scale with the parameter ρk −3 , and we demonstrate noticeable effects already at ρk −3 10 −2 . In dilute gases and in gases with an added inhomogeneous broadening the simulations show shifts of the resonance lines in qualitative agreement with the predicted Lorentz-Lorenz shift and "cooperative Lamb shift," but the quantitative agreement is unsatisfactory. Our interpretation is that the microscopic basis for the local-field corrections in electrodynamics is not fully understood.

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Section: B Classical-electrodynamics Solution For Light Propagationmentioning

confidence: 99%

Section: B Classical-electrodynamics Solution For Light Propagationmentioning

confidence: 99%

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

Javanainen

Ruostekoski

et al. 2017

Phys. Rev. A

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“…Collective scattering of a weakintensity laser off a cold ensemble of rubidium atoms with Zeeman splitting has been recently investigated both theoretically and experimentally [16][17][18][19], with results that partly contradict predictions of the standard cooperative Lamb shift theory. In the context of ensembles of atoms in magnetic fields, a legitimate question is to which extend can the Zeeman splitting be considered independently from the cooperative effects and in particular the collective Lamb shift.…”

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confidence: 99%

Collective radiation spectrum for ensembles with Zeeman splitting in single-photon superradiance

Kong

Pálffy

2017

Phys. Rev. A

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In an ensemble of identical atoms, cooperative effects like sub-or superradiance may alter the decay rates and the energy of specific transitions may be shifted from the single-atom value by the so-called collective Lamb shift. While such effects in ensembles of two-level systems are by now well understood, realistic multi-level systems are more difficult to handle. In this work we show that in a system of atoms or nuclei under the action of an external magnetic field, the collective contribution to the level shifts can amount to seizable deviations from the single-atom Zeeman or magnetic hyperfine splitting picture. We develop a formalism to describe single-photon superradiance in multi-level systems in the small sample limit and quantify the parameter regime for which the collective Lamb shift leads to measurable deviations in the magnetic-field-induced splitting. In particular, we show that this effect should be observable in the nuclear magnetic hyperfine splitting in Mössbauer nuclei embedded in thin-film x-ray cavities. PACS numbers: 78.70.Ck, 42.50.Nn, 76.80.+y 32.30.Dx In 1947, a famous experiment by Lamb and Retherford [1] confirmed that the 2s 1/2 and 2p 1/2 levels in hydrogen are not degenerate, leading to increased efforts in the theoretical understanding of radiation quantization [2,3] and to the development of quantum electrodynamics (QED) [4]. Today, it is known that this small shift has to do with emission and reabsorption of virtual photons within the atom, mainly with selfenergy and vacuum-polarization corrections. Interestingly, it could be shown that an additional contribution arises if many identical atoms are interacting collectively with resonant photons, and virtual photons are exchanged between different atoms [5][6][7][8][9][10]. This additional contribution has been termed in analogy collective Lamb shift, although the exact underlying processes share with the single-atom Lamb shift mechanism only the virtual character of the photons being exchanged.The collective Lamb shift has been investigated theoretically for ensembles of two-level systems in the small and large sample limits [5,[11][12][13][14][15]. Collective scattering of a weakintensity laser off a cold ensemble of rubidium atoms with Zeeman splitting has been recently investigated both theoretically and experimentally [16][17][18][19], with results that partly contradict predictions of the standard cooperative Lamb shift theory. In the context of ensembles of atoms in magnetic fields, a legitimate question is to which extend can the Zeeman splitting be considered independently from the cooperative effects and in particular the collective Lamb shift. In this Letter, we show that in ensembles of atoms or nuclei with magneticfield induced level multiplets, the collective magnetic splitting can show significant deviations of the Zeeman splitting compared to the single-atom behaviour and cannot be justified by mere two-level system collective Lamb shift contributions for each transition independently, as done for instance in Re...

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“…The metamolecules respond as linear classical harmonic oscillators, driven by a coherent field, and are therefore different from two-level entangled single-excitation molecules or strongly driven nonlinear quantum states [28]. However, two-level systems, such as atoms, also behave as classical harmonic oscillators in the low light intensity limit when driven by a field in a coherent state [29,30], illustrating the generality of the phenomenon across different physical systems [27].…”

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confidence: 99%

Many-Body Subradiant Excitations in Metamaterial Arrays: Experiment and Theory

et al. 2017

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Subradiant excitations, originally predicted by Dicke, have posed a long-standing challenge in physics owing to their weak radiative coupling to environment. Here we engineer massive coherently driven classical subradiance in planar metamaterial arrays as a spatially extended eigenmode comprising over 1000 metamolecules. By comparing the near-and far-field response in large-scale numerical simulations with those in experimental observations we identify strong evidence for classically correlated multimetamolecule subradiant states that dominate the total excitation energy. We show that similar spatially extended many-body subradiance can also exist in plasmonic metamaterial arrays at optical frequencies. DOI: 10.1103/PhysRevLett.119.053901 The classic example of neutrons and magnetic dipole radiation by Dicke [1] over 60 years ago describes the collective super-radiant and subradiant response of emitters at high density. Super-radiance, where the emission is enhanced due to constructive interference, has been experimentally observed in a variety of systems [2]. For subradiant states the emission is suppressed owing to the destructive interference of the radiation from the emitters. Because of the inherently weak coupling of the subradiant states to external electromagnetic (EM) fields, their experimental studies have been limited. In the early experiments subradiant emission was observed for two trapped ions [3] as well as for two trapped molecules [4]. Two-particle subradiant and super-radiant states have an analogy with the gerade (even) and ungerade (odd) symmetry states of homonuclear molecular dimers, and subradiant states have also been created in weakly bound ultracold Sr 2 [5] and Yb 2 [6] molecules. Super-radiant states in dimers represent excitations via strong electric dipole transitions, while subradiant states may, e.g., be produced by weak magnetic dipole or electric quadrupole transitions.Similar effects have been investigated in the context of plasmonics, where the analogy between nanostructured plasmonic resonators and molecular states encountered in natural media has lead to a plasmon hybridization theory [7]. Excitations in such systems, reminiscent of molecular wave functions, have consequently resulted in an analysis of dark and bright modes, with subradiant and super-radiant characteristics, respectively. Narrow Fano resonances in the transmitted field or subradiant and super-radiant excitations were experimentally observed in plasmonic resonators consisting of three or four nanorods [8,9], and in plasmonic heptamers [10][11][12], while efforts to increase the mode complexity of the resonators are attracting considerable attention [13,14]. Recent theoretical work also highlighted that the connection between transmission resonances and the existence of subradiant excitations is less obvious than commonly recognized, since narrow Fano resonances are also produced by the interference of nonorthogonal modes even in the absence of subradiance [15,16].Experiments on EM field transmission in lar...

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Stochastic methods for light propagation and recurrent scattering in saturated and nonsaturated atomic ensembles

Cited by 67 publications

References 67 publications

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

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

Collective radiation spectrum for ensembles with Zeeman splitting in single-photon superradiance

Many-Body Subradiant Excitations in Metamaterial Arrays: Experiment and Theory

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