Collective effects between multiple nuclear ensembles in an x-ray cavity-QED setup

Heeg, Kilian Peter; Evers, Jörg

doi:10.1103/physreva.91.063803

Cited by 30 publications

(169 citation statements)

References 31 publications

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“…The interaction between atoms can be measured by the EIT spectra. Compared with the EIT-like schemes with a static coupling in atomic ensembles [15,17,40,42,44], the local dynamical modulation of the transition frequencies of the atoms introduces a tunable detuning for the coupling field. Therefore, our scheme contains all the ingredients of EIT.…”

Section: Discussionmentioning

confidence: 99%

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Electromagnetically induced transparency with superradiant and subradiant states

et al. 2017

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We construct the electromagnetically induced transparency (EIT) by dynamically coupling a superradiant state with a subradiant state. The superradiant and subradiant states with enhanced and inhibited decay rates act as the excited and metastable states in EIT, respectively. Their energy difference determined by the distance between the atoms can be measured by the EIT spectra, which renders this method useful in subwavelength metrology. The scheme can also be applied to many atoms in nuclear quantum optics, where the transparency point due to counter-rotating wave terms can be observed.

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Section: Discussionmentioning

confidence: 99%

“…[40,44] to calculate the x-ray reflection coefficient R of the planar cavity as sketched in the main text Fig. 3,…”

Section: Appendix D Derivation Of the Cavity Reflection Coefficientmentioning

confidence: 99%

Electromagnetically induced transparency with superradiant and subradiant states

et al. 2017

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“…This clearly reflects the importance of interference. In the framework of thin-film x-ray cavities, this interference effect reminding of EIT has been investigated experimentally [35,36] and theoretically [37][38][39]. For significant energy difference φ, in the limit x 1, the poles can be approximately written as [33] …”

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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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“…Both the Parratt formalism and the computer package CONUSS can successfully predict the scattering spectra starting from the structure but cannot be easily used for the inverse problem. A phenomenological quantum model for x-ray cavities was developed several years ago [35,36] and used to model experimental data for specific cases. While quite versatile for single-layer cavities [35], the original model had difficulties to accurately describe more complicated structures, and an extension including multiple modes in the cavity was required to correctly reproduce experimental data for cavities with two embedded nuclear layers [36].…”

Section: Introductionmentioning

confidence: 99%

“…While Refs. [35,36] focus on the regime of single excitations, a situation which corresponds to the studied case of synchrotron radiation driving nuclear transitions, the case of stronger excitation up to population inversion is discussed in Ref. [37].…”

Section: Introductionmentioning

confidence: 99%

Green's-function formalism for resonant interaction of x rays with nuclei in structured media

2020

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The resonant interaction between x-ray photons and nuclei is one of the most exciting subjects in the burgeoning field of x-ray quantum optics. A resourceful platform used to date is thin-film x-ray cavities with embedded layers or Mössbauer nuclei such as 57 Fe. A quantum optical model based on the classical electromagnetic Green's function is developed to investigate theoretically the nuclear response inside the x-ray cavity. The model is versatile and provides an intuitive picture about the influence of the cavity structure on the resulting spectra. We test its predictive powers with the help of the semiclassical coherent scattering formalism simulations and discuss our results on increasing complexity of layer structures.

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Collective effects between multiple nuclear ensembles in an x-ray cavity-QED setup

Cited by 30 publications

References 31 publications

Electromagnetically induced transparency with superradiant and subradiant states

Electromagnetically induced transparency with superradiant and subradiant states

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

Green's-function formalism for resonant interaction of x rays with nuclei in structured media

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