144
R. Röhlsberger and J. Evers
the experimentally recorded intensity as function of the time after excitation and
the detuning of the single line absorber. (b) shows the corresponding theoretical fit,
which agrees very well. The white dashed lines indicate the position of the dynamical
beats expected without pulse delay. It can be seen that close to resonance D = 0,
the dynamical beat minima observed in the experiment are systematically shifted
to later times, as expected for slow light. To illustrate this further, (c) shows cuts
through (a) and (b) for D = 0.56γ and D = 46.1γ , respectively. For the lower
detuning, the spectrally narrow x-ray pulse experiences the steep linear dispersion,
and thus is slowed down. The higher detuning is outside the steep linear dispersion
region and does not lead to slow light. As a result, at late times, the two data sets
are essentially identical, except for a temporal delay indicated by the black arrow.
Note that at early times the two curves differ, because of the residual contribution of
light which did not interact with the single line absorber. Finally, panel (d) shows the
experimentally observed delay τ as function of detuning D . The solid line shows
the corresponding theoretical prediction. We find that our cavity allows to induce
delays exceeding 35 ns, which corresponds to group velocities below 10
−4 c [36].
These results constitute another proof of the possibility of manipulating the x-ray
optical response of nuclei embedded in cavities to one’s desire. Further theoretical
calculations predict that with a suitable time-dependent manipulation of the applied
magnetic fields, also a complete stopping of the x-ray pulse could be achieved [97].
Possible applications of such techniques include the delay and synchronization of
x-ray photons, and the coherence-based enhanced of nonlinear interactions between
x-rays and nuclei [72].
3.8 Collective Strong Coupling of Nuclei in Coupled
Cavities and Superlattices
A central subject of quantum optics is to manipulate the interaction of light and matter.
To achieve this, two important parameters must be controlled. One is the strength
of the light-matter interaction. It has to be strong enough that emitted photons have
a chance to act back on their emitters. This is the so-called strong-coupling limit
in quantum optics [98]. It can be achieved in special environments into which the
emitters are embedded. Strong coupling is used in the optical and infrared regimes,
for instance, to produce non-classical states of light, enhance optical nonlinearities
even at relatively low intensities [99] and control quantum states [100]. The other
parameter is the number of modes of the electromagnetic field that the resonant
system interacts within this environment. If the number of these modes is too large,
the emitted photons might get irreversibly lost when they are distributed over these
modes. Strong coupling has been achieved for a variety of systems and energy ranges,
but until now not with X-rays. Here we report about the first observation of collective
strong coupling of hard X-rays at the nuclear resonance of
57 Fe.
R. Röhlsberger and J. Evers
the experimentally recorded intensity as function of the time after excitation and
the detuning of the single line absorber. (b) shows the corresponding theoretical fit,
which agrees very well. The white dashed lines indicate the position of the dynamical
beats expected without pulse delay. It can be seen that close to resonance D = 0,
the dynamical beat minima observed in the experiment are systematically shifted
to later times, as expected for slow light. To illustrate this further, (c) shows cuts
through (a) and (b) for D = 0.56γ and D = 46.1γ , respectively. For the lower
detuning, the spectrally narrow x-ray pulse experiences the steep linear dispersion,
and thus is slowed down. The higher detuning is outside the steep linear dispersion
region and does not lead to slow light. As a result, at late times, the two data sets
are essentially identical, except for a temporal delay indicated by the black arrow.
Note that at early times the two curves differ, because of the residual contribution of
light which did not interact with the single line absorber. Finally, panel (d) shows the
experimentally observed delay τ as function of detuning D . The solid line shows
the corresponding theoretical prediction. We find that our cavity allows to induce
delays exceeding 35 ns, which corresponds to group velocities below 10
−4 c [36].
These results constitute another proof of the possibility of manipulating the x-ray
optical response of nuclei embedded in cavities to one’s desire. Further theoretical
calculations predict that with a suitable time-dependent manipulation of the applied
magnetic fields, also a complete stopping of the x-ray pulse could be achieved [97].
Possible applications of such techniques include the delay and synchronization of
x-ray photons, and the coherence-based enhanced of nonlinear interactions between
x-rays and nuclei [72].
3.8 Collective Strong Coupling of Nuclei in Coupled
Cavities and Superlattices
A central subject of quantum optics is to manipulate the interaction of light and matter.
To achieve this, two important parameters must be controlled. One is the strength
of the light-matter interaction. It has to be strong enough that emitted photons have
a chance to act back on their emitters. This is the so-called strong-coupling limit
in quantum optics [98]. It can be achieved in special environments into which the
emitters are embedded. Strong coupling is used in the optical and infrared regimes,
for instance, to produce non-classical states of light, enhance optical nonlinearities
even at relatively low intensities [99] and control quantum states [100]. The other
parameter is the number of modes of the electromagnetic field that the resonant
system interacts within this environment. If the number of these modes is too large,
the emitted photons might get irreversibly lost when they are distributed over these
modes. Strong coupling has been achieved for a variety of systems and energy ranges,
but until now not with X-rays. Here we report about the first observation of collective
strong coupling of hard X-rays at the nuclear resonance of
57 Fe.