142
R. Röhlsberger and J. Evers
temporally long response of the nuclei, and correspondingly to a narrow spectral
absorption resonance which will become the desired spectrally narrow x-ray pulse.
Note that because of the thickness of the single line absorber, dynamical beats appear
in the time domain, which will turn out to be crucial for the analysis of the experiment.
Afterwards, the x-rays pulse is polarized, which does not lead to notable changes
because of the natural polarization of the synchrotron radiation, but improves the
purity of the polarimetry setup. Next, the x-rays interact with the cavity. As explained
below, the nuclei in the cavity are operated in such a way that they slow down and
delay the narrow pulse component by a time τ , and at the same time rotate the
polarization of part of the scattered light. The analyzer is operated in crossed setting,
such that only light with rotated polarization may pass. As a consequence, only light
which interacted with the nuclei in the cavity can pass the analyzer. The light seen
by the detector thus contains two parts. The first part interacted with the cavity, but
not with the single line analyzer. The second part interacted with the cavity and the
single line analyzer. At late times, the latter signal dominates, because it is delayed
by both the single line analyzer and the cavity, and it comprises the desired signal of
a spectrally narrow x-ray pulse which interacted with the cavity. As the lower right
panel of Fig. 3.15 shows, this signal in the time domain approximately is a copy of
the input pulse, but delayed by τ . This delay is easily visualized independent of the
total count rate by the position of the dynamical beat minima.
In order to implement the steep dispersion, we used a variety of the cavity featuring spontaneously generated coherences (see Sect. 3.7.3) optimized for the linear
dispersion. Both EIT (see Sect. 3.7.2) and SGC may feature transparency windows
and steep linear dispersion, and in fact are related [35, 37]. The advantage of the
SGC cavities is the simpler design, and that previous experiments [29] had already
demonstrated the possibility to reach almost perfect transparency, see Fig. 3.14.
Furthermore, the SGC cavities rely on the magnetic substructure of the nuclei in a
way which allows to rotate the polarization of the scattered light as required for the
polarimetry method to generate spectrally narrow x-ray pulses.
To analyze light propagation in the cavity setting, in analogy to the procedure leading to Eq. (3.55), we expand the cavity response R(ω) around the transparency resonance ω 0 in linear order. We find R(ω) ≈ R(ω 0 )e
i(ω−ω 0 )τ , where τ =
∂
∂ω
arg[R(ω 0 )].
The action of the cavity on an input pulse E in (t) with spectrum E in (ω) is therefore
given by
E out (t) ∝
E in (ω)R(ω)e
−iωt dω
≈ R(ω 0 )e
−iω 0 τ
E in (ω)e
−iω(t−τ ) dω
∝ E in (t − τ ) .
(3.57)
We thus find that the input pulse preserves its shape, but is delayed by the time τ ,
as desired for slow light. The expression of τ can be understood by noting that in a
cavity setting, the real and imaginary parts of the medium susceptibility are in fact
R. Röhlsberger and J. Evers
temporally long response of the nuclei, and correspondingly to a narrow spectral
absorption resonance which will become the desired spectrally narrow x-ray pulse.
Note that because of the thickness of the single line absorber, dynamical beats appear
in the time domain, which will turn out to be crucial for the analysis of the experiment.
Afterwards, the x-rays pulse is polarized, which does not lead to notable changes
because of the natural polarization of the synchrotron radiation, but improves the
purity of the polarimetry setup. Next, the x-rays interact with the cavity. As explained
below, the nuclei in the cavity are operated in such a way that they slow down and
delay the narrow pulse component by a time τ , and at the same time rotate the
polarization of part of the scattered light. The analyzer is operated in crossed setting,
such that only light with rotated polarization may pass. As a consequence, only light
which interacted with the nuclei in the cavity can pass the analyzer. The light seen
by the detector thus contains two parts. The first part interacted with the cavity, but
not with the single line analyzer. The second part interacted with the cavity and the
single line analyzer. At late times, the latter signal dominates, because it is delayed
by both the single line analyzer and the cavity, and it comprises the desired signal of
a spectrally narrow x-ray pulse which interacted with the cavity. As the lower right
panel of Fig. 3.15 shows, this signal in the time domain approximately is a copy of
the input pulse, but delayed by τ . This delay is easily visualized independent of the
total count rate by the position of the dynamical beat minima.
In order to implement the steep dispersion, we used a variety of the cavity featuring spontaneously generated coherences (see Sect. 3.7.3) optimized for the linear
dispersion. Both EIT (see Sect. 3.7.2) and SGC may feature transparency windows
and steep linear dispersion, and in fact are related [35, 37]. The advantage of the
SGC cavities is the simpler design, and that previous experiments [29] had already
demonstrated the possibility to reach almost perfect transparency, see Fig. 3.14.
Furthermore, the SGC cavities rely on the magnetic substructure of the nuclei in a
way which allows to rotate the polarization of the scattered light as required for the
polarimetry method to generate spectrally narrow x-ray pulses.
To analyze light propagation in the cavity setting, in analogy to the procedure leading to Eq. (3.55), we expand the cavity response R(ω) around the transparency resonance ω 0 in linear order. We find R(ω) ≈ R(ω 0 )e
i(ω−ω 0 )τ , where τ =
∂
∂ω
arg[R(ω 0 )].
The action of the cavity on an input pulse E in (t) with spectrum E in (ω) is therefore
given by
E out (t) ∝
E in (ω)R(ω)e
−iωt dω
≈ R(ω 0 )e
−iω 0 τ
E in (ω)e
−iω(t−τ ) dω
∝ E in (t − τ ) .
(3.57)
We thus find that the input pulse preserves its shape, but is delayed by the time τ ,
as desired for slow light. The expression of τ can be understood by noting that in a
cavity setting, the real and imaginary parts of the medium susceptibility are in fact