3 Quantum Optical Phenomena in Nuclear Resonant Scattering
145
3.8.1 Strong Coupling of X-Rays and Nuclei in Photonic
Lattices: Normal-Mode Splitting
The usual route to strong coupling between light and resonant atoms is to insert the
atoms into a cavity, the Q-factor of which is on the order or larger than that of the
atomic resonance [98]. A good cavity restricts the interaction with the light to the one
mode allowed by the cavity; furthermore, the intensity of the light within the cavity is
large, leading to an enhanced interaction. The strong interaction leads to the coupling
of two degrees of freedom; two normal modes form, which are superpositions of the
otherwise uncoupled components of the system. If the cavity is probed, for instance
by monitoring its reflectivity or transmissivity, its spectral signature shows two dips,
which are detuned from the sample resonance and the cavity mode. Upon varying the
detuning between cavity mode and resonance, it turns out that the dips undergo a very
well-known anti-crossing dispersion; the minimal distance between the branches of
the dispersion relation is given by the interaction strength.
While X-ray cavities have been successfully applied to realize quantum optical
concepts in the linear regime, fabricating a cavity of sufficient quality to reach the
strong coupling regime is not possible yet in the X-ray range. Even in the angular
range of grazing incidence, the reflectivity of the cladding mirrors is ∼ 95% only.
Compared to the reflectivity achieved for microwave and visible light cavities of
99.999% this is not sufficient. The problem is rooted in the fact that the spectral
width of the cavity is much larger than the coupling strength. Essentially, the two
dispersive dips mentioned above cannot be resolved [27, 79].
This points the way to another method of coherent control. Since our nuclear
exciton interacts with only one mode anyway, we can focus on enlarging the interaction without making use of a cavity, but by enlarging the number of nuclei that
contribute to the nuclear exciton, as the collective interaction strength depends on
that number. In the following, we will focus our attention on periodic multilayers
or periodic resonant systems. These, often referred to as resonant photonic crystals
or resonant optical lattices, also restrict the number of modes the resonant matter
interacts with.
The propagation of light through periodic arrays of resonant media such as optical
lattices or multiple quantum wells has opened intriguing possibilities to control the
interaction of light and matter [102–105]. One of the most interesting features of these
systems is the appearance and dispersion of bandgaps [106–109], see Fig. 3.17.
Here we describe an optical lattice-like structure with bandgaps in the regime
of hard X-rays, consisting of a multilayer with alternating layers of non-resonant
56 Fe and nuclear-resonant
57 Fe. The electronic part of the index of refraction is
identical for both isotopes. The system can thus be modelled as having a uniform
background refractive index, with a periodic resonant refractive index superimposed.
The resulting bandgap can be observed by measuring the spectrally resolved Xray reflectivity of the sample close to the Bragg angle of the multilayer. Although
similar isotopic multilayer structures have been discussed before [110–113], mainly
the angular dependence of the reflectivity has been studied instead of its spectral
145
3.8.1 Strong Coupling of X-Rays and Nuclei in Photonic
Lattices: Normal-Mode Splitting
The usual route to strong coupling between light and resonant atoms is to insert the
atoms into a cavity, the Q-factor of which is on the order or larger than that of the
atomic resonance [98]. A good cavity restricts the interaction with the light to the one
mode allowed by the cavity; furthermore, the intensity of the light within the cavity is
large, leading to an enhanced interaction. The strong interaction leads to the coupling
of two degrees of freedom; two normal modes form, which are superpositions of the
otherwise uncoupled components of the system. If the cavity is probed, for instance
by monitoring its reflectivity or transmissivity, its spectral signature shows two dips,
which are detuned from the sample resonance and the cavity mode. Upon varying the
detuning between cavity mode and resonance, it turns out that the dips undergo a very
well-known anti-crossing dispersion; the minimal distance between the branches of
the dispersion relation is given by the interaction strength.
While X-ray cavities have been successfully applied to realize quantum optical
concepts in the linear regime, fabricating a cavity of sufficient quality to reach the
strong coupling regime is not possible yet in the X-ray range. Even in the angular
range of grazing incidence, the reflectivity of the cladding mirrors is ∼ 95% only.
Compared to the reflectivity achieved for microwave and visible light cavities of
99.999% this is not sufficient. The problem is rooted in the fact that the spectral
width of the cavity is much larger than the coupling strength. Essentially, the two
dispersive dips mentioned above cannot be resolved [27, 79].
This points the way to another method of coherent control. Since our nuclear
exciton interacts with only one mode anyway, we can focus on enlarging the interaction without making use of a cavity, but by enlarging the number of nuclei that
contribute to the nuclear exciton, as the collective interaction strength depends on
that number. In the following, we will focus our attention on periodic multilayers
or periodic resonant systems. These, often referred to as resonant photonic crystals
or resonant optical lattices, also restrict the number of modes the resonant matter
interacts with.
The propagation of light through periodic arrays of resonant media such as optical
lattices or multiple quantum wells has opened intriguing possibilities to control the
interaction of light and matter [102–105]. One of the most interesting features of these
systems is the appearance and dispersion of bandgaps [106–109], see Fig. 3.17.
Here we describe an optical lattice-like structure with bandgaps in the regime
of hard X-rays, consisting of a multilayer with alternating layers of non-resonant
56 Fe and nuclear-resonant
57 Fe. The electronic part of the index of refraction is
identical for both isotopes. The system can thus be modelled as having a uniform
background refractive index, with a periodic resonant refractive index superimposed.
The resulting bandgap can be observed by measuring the spectrally resolved Xray reflectivity of the sample close to the Bragg angle of the multilayer. Although
similar isotopic multilayer structures have been discussed before [110–113], mainly
the angular dependence of the reflectivity has been studied instead of its spectral