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Photon-Atom Coupling with Parabolic Mirrors

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Engineering the Atom-Photon Interaction

Part of the book series: Nano-Optics and Nanophotonics ((NON))

Abstract

Efficient coupling of light to single atomic systems has gained considerable attention over the past decades. This development is driven by the continuous growth of quantum technologies. The efficient coupling of light and matter is an enabling technology for quantum information processing and quantum communication. And indeed, in recent years much progress has been made in this direction. But applications aside, the interaction of photons and atoms is a fundamental physics problem. There are various possibilities for making this interaction more efficient, among them the apparently ‘natural’ attempt of mode-matching the light field to the free-space emission pattern of the atomic system of interest. Here we will describe the necessary steps of implementing this mode-matching with the ultimate aim of reaching unit coupling efficiency. We describe the use of deep parabolic mirrors as the central optical element of a free-space coupling scheme, covering the preparation of suitable modes of the field incident onto these mirrors as well as the location of an atom at the mirror’s focus. Furthermore, we establish a robust method for determining the efficiency of the photon-atom coupling.

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Notes

  1. 1.

    There is no state of the light field, more intense than a single photon, which will transform into a single photon state when projecting onto a certain mode function. Such a projection is equivalent to attenuation.

  2. 2.

    If not explicitly mentioned otherwise, the term atom is used to designate any kind of single quantum target.

  3. 3.

    We consciously neglect effects related to a nonzero detuning between the incident field and the atomic resonance.

  4. 4.

    The half solid angle case corresponds to \(h/f=1\).

  5. 5.

    This is of course also true for other focusing optics or dipole configurations and correspondingly other suitable ‘standard’ field modes as e.g. a fundamental Gaussian mode, see [24] for some examples.

  6. 6.

    The Strehl ratio defines the maximum intensity in the focal region for a focusing system exhibiting aberrations as a fraction of the intensity obtained without aberrations [48]. Whereas in the latter reference a plane wave is considered, we apply this figure of merit for the case of a doughnut mode.

  7. 7.

    The phase shift of the light scattered by an atom, i.e. the response of a driven harmonic oscillator, has been measured recently [52].

  8. 8.

    Values for the scattering ratio exceeding unity might seem unphysical at first sight because one might suspect a violation of energy conservation. Here we argue that this is not the case. Energy is always associated with the total field not with individual interfering components. One might write a propagating field as the sum of two fields \(E_1\) and \(E_2\), one 180\(^\circ \) out of phase with respect to the other. The total energy has of course a well defined value. But the individual fields \(E_{1,2}\) are not well defined. You can choose a field with a larger \(E_1\) as long as the amplitude of field \(E_2\) is also increased such that the sum is as before.

    In the specific problem of elastic scattering of a beam resonant with the atomic transition it can even be required that the scattered power has to be larger than the incident one. Due to the 180\(^\circ \) phase shift between the scattered and the transmitted incident light there would otherwise be a net loss of energy under efficient-coupling conditions, since in elastic scattering no energy is transferred onto the atom.

  9. 9.

    The decreasing components should of course be observable for any incident pulse with non-zero temporal overlap \(\eta _t\).

  10. 10.

    It can be shown in a fully quantum-mechanical calculation that an exponentially rising pulse with proper time-constant indeed leads to full excitation of the atom [66].

  11. 11.

    YbIII has been created by electron-impact ionization from a cloud of trapped YbII ions [67]. We recently accomplished the controlled photo-ionization from YbII to YbIII.

  12. 12.

    A similar technique employing electro-optic modulation is reported in [69]. In contrast to this, other authors directly modulate the waveform of a single photon upon receiving a trigger signal from a heralding photon, see [70], and the chapter by Chuu and Du. Last but not least, in a recent experiment single-photon Fock states with increasing exponential envelope have been achieved by manipulating a heralding photon with an asymmetric cavity prior to detection [71]. Both photons originated from a cascaded decay in a cold atomic ensemble.

  13. 13.

    This expression arises from the fact that the power scattered into the first diffraction order of the AOM is proportional to the sine of the acoustic power establishing the diffraction grating.

  14. 14.

    Similar efficiencies where obtained recently in experiments for microwave pulses [74, 75].

  15. 15.

    The cooling laser beam at 370  nm that enters through an auxiliary opening of the parabolic mirror (cf. Fig. 3.9) is blocked during the saturation measurements.

  16. 16.

    This reasoning assumes that the quantization axis is parallel to the optical axis of the parabola. But one can show that for any orientation of the quantization axis the same correction factor has to be applied when treating a \(S_{1/2}\rightarrow P_{1/2}\) transition.

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Acknowledgments

We gratefully acknowledge the contributions of Marianne Bader, Benoit Chalopin, Martin Fischer, Andrea Golla, Simon Heugel and Robert Maiwald to our experimental endeavours. We thank the Deutsche Forschungsgemeinschaft for financial support. G.L. also acknowledges financial support from the European Research Council under the Advanced Grant ‘PACART’.

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Authors and Affiliations

  1. Department of Physics, University of Erlangen-Nuremberg, Staudtstr. 7/B2, 91058, Erlangen, Germany

    Markus Sondermann & Gerd Leuchs

  2. Max Planck Institute for the Science of Light, Guenther-Scharowsky-Str. 1/Bldg. 24, 91058, Erlangen, Germany

    Gerd Leuchs

  3. Department of Physics, University of Ottawa, Ottawa, ON, K1N 6N5, Canada

    Gerd Leuchs

Authors
  1. Markus Sondermann
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Correspondence to Markus Sondermann .

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Editors and Affiliations

  1. Experimental Physics, University of Innsbruck, Innsbruck, Austria

    Ana Predojević

  2. ICFO - Institut de Ciències Fotòniques, ICREA - Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain

    Morgan W. Mitchell

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Sondermann, M., Leuchs, G. (2015). Photon-Atom Coupling with Parabolic Mirrors. In: Predojević, A., Mitchell, M. (eds) Engineering the Atom-Photon Interaction. Nano-Optics and Nanophotonics. Springer, Cham. https://doi.org/10.1007/978-3-319-19231-4_3

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