Remarkable effects occur upon the resonant interaction of light with matter, if the radiating atoms themselves are embedded in resonant structures like cavities or waveguides: When the incident radiation couples to a resonant mode of the cavity, one can observe a substantial decrease in the radiative lifetime, if the atoms are located in an antinode of the standing wave. This is caused by a strong modification of the photonic density of states in the vicinity of reflecting boundaries. As already discussed by Purcell in 1946 [1], this leads to an enhancement of the spontaneous emission rate of the radiating atoms. The fundamental interest in this phenomenon and the potential applications in optical information technology have led to intense research activities, constituting the field of cavity quantum electrodynamics. Experiments in this field are typically performed in the microwave or optical regime of the electromagnetic spectrum. Due to a growing interest in the study of ultrafast processes using pulsed X-ray sources, it is appealing to study the effect of confining environments on the spontaneous emission of X-rays as well. With decreasing wavelength of the radiation, however, the coupling efficiency of the spontaneous radiation into the cavity modes drastically decreases, so that the effect on the spontaneous emission rate is negligibly small. This situation improves significantly if the emission is highly directional with a wavevector k0 that coincides with a wavevector of a cavity mode. In general, such a situation occurs when an ensemble of resonant emitters, rather than a single atom, is excited coherently by a directional radiation pulse with wavevector k0. Due to the collective nature of the excitation, the subsequent radiative decay of this state proceeds into the direction of the incident wavevector k0. The excitation of Mössbauer nuclei by pulses of synchrotron radiation allows one to prepare such a collectively excited state with a well-defined wavevector k0 in the X-ray regime. This provides a very efficient mechanism to funnel the spontaneous (re)emission of X-rays into a selected photonic mode of a waveguide or cavity where the resonant nuclei are located

Fig. 4: Coherent enhancement of the specular reflectivity from a 57Fe probe layer that is embedded in a waveguide [2], as sketched in the inset. At 4.4 mrad the first-order guided mode is excited. The solid red line is a theoretical simulation. For comparison, the dashed red line displays the angular dependence of any incoherent signal from the 57Fe nuclei, e.g., fluorescence radiation.

In this experiment we have studied the influence of a planar single-mode waveguide on the radiative decay of an ensemble of 57Fe nuclei. These nuclei are located as an ultrathin layer in the centre of the guiding layer. The sample used here is sketched in the inset of Figure 4. The guided mode is excited at an incidence angle of m = 4.4 mrad, where a strong boost of the radiation resonantly reflected from the 57Fe nuclei is observed. This is a result of the strong enhancement of the photonic density of states in the waveguide [2]. To investigate the effect of the cavity resonance on the nuclear lifetime, time spectra at different angular positions around the guided mode were recorded. A selection of these spectra is shown in Figure 5a where a drastic variation of the decay constant on the angle of incidence is visible. (The oscillation period reflects the energetic separation of the hyperfine transitions that results from a magnetic hyperfine field of B = 33.1 T at the nucleus.) Figure 5b shows the dependence of the nuclear decay rate on the angle of incidence. The 6-fold acceleration of the decay at the peak position and the overall shape of the curve is well described by the simulation shown in Figure 4 (solid line).

Fig. 5: (a) Time spectra of the specular reflection recorded at different angular positions around the peak in Figure 4; (b) The angular dependence of the nuclear decay rate (normalised to the natural decay rate) as derived from the time spectra, together with a theoretical simulation (solid red line).

The phenomena described here rely on the mode structure of the vacuum field as it is modified by the medium that surrounds the radiating atoms. The corresponding temporal alteration of the photon-matter interaction might be particularly relevant for time-resolved studies of dynamics in nanoscale structures using short-pulsed X-ray sources with pulse durations in the range of ps to fs. Since these phenomena are final state effects of the scattered photon field, they do not require a high number of photons per mode in the incident beam.

 

References

[1] E. M. Purcell, Phys. Rev. 69, 681 (1946).
[2] R. Röhlsberger, T. Klein, K. Schlage, O. Leupold, and R. Rüffer, Phys. Rev. B 69, 235412 (2004).

Principal Publication and Authors

R. Röhlsberger (a), K. Schlage (b), T. Klein (b), O. Leupold (a), Phys. Rev. Lett. 95, 097601 (2005).
(a) DESY, Hamburg (Germany)
(b) Universität Rostock, Institut für Physik (Germany)