a) Atomic 3-level system, that appears to be transparent on the 1 -> 3 transition when an intense control laser couples the metastable level 2 with the excited state 3. b) Black line: Absorption spectrum for the transition 1 -> 3 without coupling of levels 2 and 3 (control laser off). Red line: Switching the control laser on leads to a deep minimum at in the absorption spectrum where the system appears to be transparent.
Electromagnetically Induced Transparency at X-ray Energies
Electromagnetically induced transparency (EIT) is a key technique in quantum optics through which an opaque medium becomes transparent near an atomic resonance by the coupling of two laser fields to the same excited state [1]. This technique facilitates to employ light to control the optical properties of matter and has resulted in numerous applications like nonlinear optics at the few-photon level [2], light speed reduction to a few m/s [3], lasing without inversion [4] and others. We have shown that EIT is possible in the regime of hard x-rays by exploiting the collective emission from ensembles of 57Fe Mössbauer nuclei embedded in a planar cavity. This opens new routes to exploit EIT and its applications at x-ray energies, effectively establishing the field of nuclear quantum optics.
The phenomenon of EIT arises from the competition of two laser fields simultaneously exciting an upper state |3> from both the ground state |1> and a third metastable state |2>. If the field that resonantly couples the states |2> and |3> is very strong it blocks the absorption of light that is tuned to the |1> → |3> transition, see Fig. 1. As a result, this light can propagate without absorption – the material appears to be transparent. This concept is well established in optical sciences since several decades [1] and currently receives renewed interest because it holds promises, e.g., for quantum information processing at the level of single quanta of light and matter [5].
Here we extend the concept of EIT into the x-ray regime by employing the Mössbauer isotope 57Fe which is a nuclear two-level system with a transition energy of 14.4 keV and a natural linewidth of 4.7 neV. At first sight it seems to be unclear how to achieve nuclear EIT because nuclear three-level systems with a metastable level are not available to establish conventional EIT schemes. Therefore, the possibility to employ a single field of hard x-rays for EIT with a nuclear two-level system is highly desirable.
The key to the realization of nuclear EIT is cooperative emission from ensembles of Mössbauer nuclei that are properly placed in a planar cavity for hard x-rays. The physics of cooperative emission from atoms in cavities bears a multitude of interesting phenomena. This applies even in the linear regime where the atom - cavity interaction can be treated in the weak-coupling limit which is typically the case at x-ray wavelengths. Due to its high resonant cross section the 14.4 keV transition of 57Fe is a well-suited two-level system for such studies. This isotope was recently employed to explore superradiant emission and the collective Lamb shift LN for a single ensemble of atoms located in an antinode of the field within a planar cavity [6]. Fig. 2a shows the calculated energy spectrum of the reflectivity of such a cavity that is excited in its third-order mode at a grazing angle of ϕ = 3.5 mrad.
Calculated reflectivity spectra of different cavity configurations. Sample geometry (top row), and spectral response (reflectivity around the 14.4 keV nuclear resonance energy, bottom row) of planar cavities for x-rays, containing 2 nm thick layers of 57Fe nuclei (red). The cavities are excited in the third-order mode under grazing angle phi = 3.5 mrad. The graphs in the top row show the standing wave intensity of the electromagnetic field in the cavities. (a) For a single layer in the center of the cavity, the collective decay width is broadened due to superradiant enhancement and exibits a shift, the collective Lamb shift LN (b) If the cavity contains two 57Fe layers placed in a node and an antinode of the standing wave field one observes a pronounced dip in the spectral response, indicative of an EIT transparency window. (c) The transparency window vanishes if the 57Fe layers are arranged in the sequence antinode - node as viewed from the top of the planar cavity.
A qualitatively new situation is encountered when two resonant 57Fe layers instead of one are placed in a cavity. A pronounced dip in the spectral response appears when one of the 57Fe layers is placed in a node, the other one in an antinode of the standing wave in the cavity, see Fig. 2b. This dip is the spectral fingerprint of EIT. It depends sensitively on the distance and the location of the two resonant layers within the cavity. For example, the EIT effect completely vanishes if the two layers occupy the sequence antinode - node instead of node - antinode if seen from the top surface of the cavity, see Fig. 2c.
Cooperative emission plays a crucial role for EIT in this system. While the layer in the antinode exhibits a very fast superradiant decay, the layer located in the antinode remains subradiant with a slow decay, thus representing the metastable state in the three-level scheme of EIT. Effectively, the cavity renders the nuclei to behave as three-level systems, see Fig. 3. Eventually, the radiation field in the cavity mixes the two upper levels and the resulting quantum interference leads to a pronounced transparency at the exact resonance energy of the nuclei where the system is completely opaque otherwise.
For an experimental verification of the EIT effect we have prepared two planar x-ray cavities consisting of a (3nm Pt)/(38nm C)/(10nm Pt) layer structure with two 3 nm thick 57Fe layers embedded in the C guiding layer as shown in Fig. 2b,c. The magnetic hyperfine interaction splits the nuclear resonance into four well-separated lines. The experiments were performed at the beamline P01 of PETRA III in the 40-bunch mode of operation. To determine the energy spectrum of the cavity reflectivity from the time-resolved data we have employed a resonant energy analyzer foil mounted on a Doppler drive to vary the energy detuning Δ around the resonance [7]. The results are shown in Fig. 4 for two samples with the 57Fe layers arranged in the sequence node- antinode (sample A) and antinode - node (sample B). Sample A shows striking evidence for EIT as predicted. Its spectral response exhibits transparency dips (indicated by the arrows) that are particularly pronounced at the outer (and strongest) resonance lines of the hyperfine-split spectrum at detunings of Δ = +/- 51 Γ0. As expected, in sample B the EIT effect vanishes due to the reversal of the layer sequence in node and antinode of the cavity field.
References
1. M. Fleischhauer, A. Imamoglu, J. P. Marangos, “Electromagnetically induced transparency : Optics in coherent media”, Rev. Mod. Phys. 77, 633 - 672 (2005).
2. H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearity obtained by electromagnetically induced transparency”, Opt. Lett. 21, 1936 – 1938 (1996).
3. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas”, Nature 397, 594 - 598 (1999).
4. M. O. Scully and M. Fleischhauer, “Lasers without inversion”, Science 263, 337-338 (1994).
5. M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity“, Nature 465, 755 (2010).
6. R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet and R. Rüffer, “Collective Lamb shift in single photon superradiance“, Science 328, 1248-1251 (2010).
7. R. Callens, R. Coussement, T. Kawakami, J. Ladriére, S. Nasu, T. Ono, I. Serdons, K. Vyvey, T. Yamada, Y. Yoda, and J. Odeurs, “Principles of stroboscopic detection of nuclear forward scattered synchrotron radiation”, Phys. Rev. B 67, 104423 (2003).
