66
3 Light–Matter Interactions for Photonic Applications
e
h
f
Reversible periodic energy exchange
Probability oscillation for hybridised system
Energy stored in field
Energy stored in emitter
a
b
Fig. 3.3 The temporal evolution of an undamped hybrid light–matter system, here representing
an exciton–polariton in a semiconductor, is depicted as the probability to find the energy stored in
the field or emitter (a) and in a diagrammatic representation (b). a The dotted line represents the
average. b Its photonic state is indicated as a wavy line and the electronic particles electron and
hole in the semiconductor crystal lattice, of which the exciton is comprised, as solid (curved) lines.
From left to right: An incident photon creates an electron–hole pair. This dipolar pair, which is
bound by Coulomb interactions and exists as an exciton, consecutively recombines under emission
of a photon, which can again excite the electronic system and be afterwards re-emitted and so forth.
Here, Coulomb interaction is represented by a virtual exchange of photons between the electron
and hole indicated by the vertical double line. b Freely drawn after [87]. To obtain such hybrid, the
dipole oscillator strength of the exciton must be sufficiently large. Note that such coupling regime
results in a (periodic) coherent energy exchange and that the initial photon and re-emitted photon
are in phase with each other and quantum-mechanically coupled to the matter excitation. Therefore,
a polariton can act as a good quantum bit (qubit) within the dephasing time of the coupled system,
or can for instance be used in entanglement schemes with single photons
polarisation in bulk with an irradiated electromagnetic wave. A diagrammatic representation of such a hybrid light–matter system, referred to as exciton–polariton, is
presented in Fig. 3.3.
3
3 This seemingly simple diagram is of very fundamental nature and invites to a deeper consideration
of quantum electrodynamics (see double lines connecting the “pathways” of electrons and holes in
Fig. 3.3). It deserves more attention than being the content of a footnote, but this would be easily out
of the scope for this work, which has a different focus. With photons the fundamental excitations
of the electromagnetic vacuum field, the virtual photons are understood as the mediator of force
between charged particles (e.g. electrons and positrons, protons, or holes in solid state crystals,
the defect electrons). Thus, processes such as charge-carrier scattering processes can be depicted
as quantum-mechanical processes involving the exchange of photons (momentum transfer). Note
that while hardly anyone knows with certainty what the fermionic (spin-half) electrons “really
look like” (the same true for the bosonic photons), based on their behaviour and properties one is
tempted to make presumptions about these entities. Interestingly, while in classical electrodynamics
field lines are drawn from positive to negative charge (indicating force), speaking of springs (in
German: ‘Quellen’) and drainages (‘Senken’) of the electric field, respectively, for the quantum
electrodynamical picture one could literally understand charged particles as such (emitting and
absorbing sheer endless numbers of virtual photons), with the density of field lines indicating the
density of virtual photons across the path from negative to positive charge. At this point, the attention
3 Light–Matter Interactions for Photonic Applications
e
h
f
Reversible periodic energy exchange
Probability oscillation for hybridised system
Energy stored in field
Energy stored in emitter
a
b
Fig. 3.3 The temporal evolution of an undamped hybrid light–matter system, here representing
an exciton–polariton in a semiconductor, is depicted as the probability to find the energy stored in
the field or emitter (a) and in a diagrammatic representation (b). a The dotted line represents the
average. b Its photonic state is indicated as a wavy line and the electronic particles electron and
hole in the semiconductor crystal lattice, of which the exciton is comprised, as solid (curved) lines.
From left to right: An incident photon creates an electron–hole pair. This dipolar pair, which is
bound by Coulomb interactions and exists as an exciton, consecutively recombines under emission
of a photon, which can again excite the electronic system and be afterwards re-emitted and so forth.
Here, Coulomb interaction is represented by a virtual exchange of photons between the electron
and hole indicated by the vertical double line. b Freely drawn after [87]. To obtain such hybrid, the
dipole oscillator strength of the exciton must be sufficiently large. Note that such coupling regime
results in a (periodic) coherent energy exchange and that the initial photon and re-emitted photon
are in phase with each other and quantum-mechanically coupled to the matter excitation. Therefore,
a polariton can act as a good quantum bit (qubit) within the dephasing time of the coupled system,
or can for instance be used in entanglement schemes with single photons
polarisation in bulk with an irradiated electromagnetic wave. A diagrammatic representation of such a hybrid light–matter system, referred to as exciton–polariton, is
presented in Fig. 3.3.
3
3 This seemingly simple diagram is of very fundamental nature and invites to a deeper consideration
of quantum electrodynamics (see double lines connecting the “pathways” of electrons and holes in
Fig. 3.3). It deserves more attention than being the content of a footnote, but this would be easily out
of the scope for this work, which has a different focus. With photons the fundamental excitations
of the electromagnetic vacuum field, the virtual photons are understood as the mediator of force
between charged particles (e.g. electrons and positrons, protons, or holes in solid state crystals,
the defect electrons). Thus, processes such as charge-carrier scattering processes can be depicted
as quantum-mechanical processes involving the exchange of photons (momentum transfer). Note
that while hardly anyone knows with certainty what the fermionic (spin-half) electrons “really
look like” (the same true for the bosonic photons), based on their behaviour and properties one is
tempted to make presumptions about these entities. Interestingly, while in classical electrodynamics
field lines are drawn from positive to negative charge (indicating force), speaking of springs (in
German: ‘Quellen’) and drainages (‘Senken’) of the electric field, respectively, for the quantum
electrodynamical picture one could literally understand charged particles as such (emitting and
absorbing sheer endless numbers of virtual photons), with the density of field lines indicating the
density of virtual photons across the path from negative to positive charge. At this point, the attention