3 Quantum Optical Phenomena in Nuclear Resonant Scattering
133
3.7.2 Electromagnetically Induced Transparency
As shown in Sect. 3.6, an ensemble of nuclei in a cavity can be effectively considered
as an artificial atom with an enhanced decay width and a self-energy correction of
its resonance energy given by the collective Lamb shift. The strong spatial variation
of the photonic density of states inside the cavity opens the possibility to tune these
properties via placement of the atoms within the wavefield of the cavity. An ensemble
in an antinode of the cavity field displays a strong superradiant enhancement, which
defines a new evolution time scale which is much faster than the usual single-nucleus
single decay. Relative to this accelerated time scale, ensembles in a node will remain
subradiant, since their dynamics is not accelerated. Thus, a cavity with two atomic
ensembles at positions with such markedly different photonic densities of states can
be considered as an artificial atom with three levels: one belonging the common
ground state and two excited state levels that correspond to the superradient and
subradiant ensembles, respectively. Effectively, the subradiant ensemble represents
a metastable level because its radiative lifetime is much longer than that of the
superradiant ensemble. In this three-level system, all levels are radiatively coupled
through the vacuum field of the cavity. Such a coupling gives rise to a key phenomenon
of quantum optics, electromagnetically induced transparency (EIT) [72].
The EIT effect arises from the cancellation of resonant absorption due to quantum
interference between atomic levels with significantly different radiative lifetimes. In
the original version of EIT, the quantum interference is induced by an external laser
field tuned to the transition between a metastable level and a shortlived excited state
in a three-level system. The basic ingredients for EIT are illustrated in Fig. 3.11a,
where a three-level system is shown, represented by the ground state, |1, and two
upper states, |2 and |3 with respective energies E 2 and E 3 . A strong laser field with
Rabi frequency C induces an atomic coherence between states |2 and |3. Tuning
a (weak) probe laser field across the resonant transition 1 → 3 leads to a Fano-type
quantum interference [80] that renders the medium almost transparent in a narrow
window around the exact resonance frequency. The transparency arises since due
to the coherent superposition of the two states |1 and |2, the two excitation pathways |1 → |3 and |2 → |3 interfere destructively, such that no excitation takes
place. The degree of transparency is limited by the dephasing of the atomic coherence resulting from the decay of state |2 or external perturbations. Thus, maximum
transparency is observed if |2 can be considered metastable, i.e., if it has a decay
width, γ 2 , that is negligibly small relative to the radiative decay width, γ 3 , of the
state |3.
To investigate the possibility of EIT in the
57 Fe containing cavity, we replace the
spatially extended
57 Fe layer in Fig. 3.8 by two layers with a separation of half the
period of the standing wave in the cavity, as shown in Fig. 3.10. Energy spectra of the
cavity reflectivity are calculated via the transfer matrix formalism already employed
in Sect. 3.4.2. Quite remarkably, the appearance of the dip in the reflectivity very
sensitively depends on the location of this pair of layers in the cavity. The dip is
most pronounced (Fig. 3.10a) if the first of the resonant layers (seen from the top) is
133
3.7.2 Electromagnetically Induced Transparency
As shown in Sect. 3.6, an ensemble of nuclei in a cavity can be effectively considered
as an artificial atom with an enhanced decay width and a self-energy correction of
its resonance energy given by the collective Lamb shift. The strong spatial variation
of the photonic density of states inside the cavity opens the possibility to tune these
properties via placement of the atoms within the wavefield of the cavity. An ensemble
in an antinode of the cavity field displays a strong superradiant enhancement, which
defines a new evolution time scale which is much faster than the usual single-nucleus
single decay. Relative to this accelerated time scale, ensembles in a node will remain
subradiant, since their dynamics is not accelerated. Thus, a cavity with two atomic
ensembles at positions with such markedly different photonic densities of states can
be considered as an artificial atom with three levels: one belonging the common
ground state and two excited state levels that correspond to the superradient and
subradiant ensembles, respectively. Effectively, the subradiant ensemble represents
a metastable level because its radiative lifetime is much longer than that of the
superradiant ensemble. In this three-level system, all levels are radiatively coupled
through the vacuum field of the cavity. Such a coupling gives rise to a key phenomenon
of quantum optics, electromagnetically induced transparency (EIT) [72].
The EIT effect arises from the cancellation of resonant absorption due to quantum
interference between atomic levels with significantly different radiative lifetimes. In
the original version of EIT, the quantum interference is induced by an external laser
field tuned to the transition between a metastable level and a shortlived excited state
in a three-level system. The basic ingredients for EIT are illustrated in Fig. 3.11a,
where a three-level system is shown, represented by the ground state, |1, and two
upper states, |2 and |3 with respective energies E 2 and E 3 . A strong laser field with
Rabi frequency C induces an atomic coherence between states |2 and |3. Tuning
a (weak) probe laser field across the resonant transition 1 → 3 leads to a Fano-type
quantum interference [80] that renders the medium almost transparent in a narrow
window around the exact resonance frequency. The transparency arises since due
to the coherent superposition of the two states |1 and |2, the two excitation pathways |1 → |3 and |2 → |3 interfere destructively, such that no excitation takes
place. The degree of transparency is limited by the dephasing of the atomic coherence resulting from the decay of state |2 or external perturbations. Thus, maximum
transparency is observed if |2 can be considered metastable, i.e., if it has a decay
width, γ 2 , that is negligibly small relative to the radiative decay width, γ 3 , of the
state |3.
To investigate the possibility of EIT in the
57 Fe containing cavity, we replace the
spatially extended
57 Fe layer in Fig. 3.8 by two layers with a separation of half the
period of the standing wave in the cavity, as shown in Fig. 3.10. Energy spectra of the
cavity reflectivity are calculated via the transfer matrix formalism already employed
in Sect. 3.4.2. Quite remarkably, the appearance of the dip in the reflectivity very
sensitively depends on the location of this pair of layers in the cavity. The dip is
most pronounced (Fig. 3.10a) if the first of the resonant layers (seen from the top) is