3 Quantum Optical Phenomena in Nuclear Resonant Scattering
151
waves within the band gaps [116, 123], much as the quantum optical model of this
chapter. A system resembling a bichromatic array of quantum wells was examined in
[102]; although that paper has a different focus, the observed phenomena resemble
those presented here.
3.8.2 Rabi Oscillations via Strong Coupling of Two Nuclear
Cavities
In the regime of strong coupling, the reversible exchange of photons between a cavity mode and an electromagnetic resonance leads to an oscillatory energy transfer
between the two systems, the so-called Rabi oscillations. Collective strong coupling
of X-rays and nuclei has recently been demonstrated in a periodic multilayer [39], as
described in the previous section. The mode splitting and anticrossing dispersion typical of strong coupling was observed in energy-resolved reflectivity measurements.
However, the Zeeman splitting of the Mössbauer resonance into several resonance
lines together with dissipation and structural imperfections of the layer system prevented a clear detection of Rabi oscillations. Moreover, a conclusive proof of strong
coupling requires that the splitting of the resonance is solely due to the interaction
between the ensembles and is not affected by Lamb shift contributions. This requires
a particular arrangement of the resonant ensembles, as explained in the following.
The central requirement for the strong coupling regime is that the coupling of the
mode and the resonant layer be larger than their decay rates given by the the spectral
width of the cavity (that is, the inverse of the time a photon is stored in the cavity)
and the decay width of the nuclear ensemble. For a single thin-film cavity system, the
coupling strength, although larger than the nuclear decay width, is still much smaller
than the cavity linewidth. We circumvent this difficulty by introducing a novel double
cavity setup (Fig. 3.21), which is described by an effective Hamiltonian fulfilling
the desired strong coupling conditions. This ansatz follows the general approach
of simulating a complex physical system that mimics a simple Hamiltonian that
cannot be implemented straightforwardly. Similar approaches are used extensively
in contemporary research, for example to observe the Dicke phase transition [124,
125] or in the use of ultracold quantum gases to simulate magnetism [126] and
correlated materials [127, 128].
In the following we discuss a quantum optical description of the double cavity
setup in order to show that it indeed fulfills the conditions to observe Rabi oscillations
between the two nuclear layers. The interaction between the X-ray field and the two
nuclear layers embedded in the double cavity can be described by means of a recently
developed quantum-optical model [29, 79] adapted to the particular sample geometry.
The Hamiltonian of this interaction is given by
151
waves within the band gaps [116, 123], much as the quantum optical model of this
chapter. A system resembling a bichromatic array of quantum wells was examined in
[102]; although that paper has a different focus, the observed phenomena resemble
those presented here.
3.8.2 Rabi Oscillations via Strong Coupling of Two Nuclear
Cavities
In the regime of strong coupling, the reversible exchange of photons between a cavity mode and an electromagnetic resonance leads to an oscillatory energy transfer
between the two systems, the so-called Rabi oscillations. Collective strong coupling
of X-rays and nuclei has recently been demonstrated in a periodic multilayer [39], as
described in the previous section. The mode splitting and anticrossing dispersion typical of strong coupling was observed in energy-resolved reflectivity measurements.
However, the Zeeman splitting of the Mössbauer resonance into several resonance
lines together with dissipation and structural imperfections of the layer system prevented a clear detection of Rabi oscillations. Moreover, a conclusive proof of strong
coupling requires that the splitting of the resonance is solely due to the interaction
between the ensembles and is not affected by Lamb shift contributions. This requires
a particular arrangement of the resonant ensembles, as explained in the following.
The central requirement for the strong coupling regime is that the coupling of the
mode and the resonant layer be larger than their decay rates given by the the spectral
width of the cavity (that is, the inverse of the time a photon is stored in the cavity)
and the decay width of the nuclear ensemble. For a single thin-film cavity system, the
coupling strength, although larger than the nuclear decay width, is still much smaller
than the cavity linewidth. We circumvent this difficulty by introducing a novel double
cavity setup (Fig. 3.21), which is described by an effective Hamiltonian fulfilling
the desired strong coupling conditions. This ansatz follows the general approach
of simulating a complex physical system that mimics a simple Hamiltonian that
cannot be implemented straightforwardly. Similar approaches are used extensively
in contemporary research, for example to observe the Dicke phase transition [124,
125] or in the use of ultracold quantum gases to simulate magnetism [126] and
correlated materials [127, 128].
In the following we discuss a quantum optical description of the double cavity
setup in order to show that it indeed fulfills the conditions to observe Rabi oscillations
between the two nuclear layers. The interaction between the X-ray field and the two
nuclear layers embedded in the double cavity can be described by means of a recently
developed quantum-optical model [29, 79] adapted to the particular sample geometry.
The Hamiltonian of this interaction is given by