xii
Preface
system, similar to photons occupying an electromagnetic mode of the vacuum field.
Occupation of a mode means energy is stored in that mode in integer numbers of the
resonance energy based on the occupation number, i.e. an excitation is present. That
excitation propagates like a wave but interacts with its environment like a discrete
entity, all according to quantum physics, discretely swapping from one mode to
another in what we refer to as energy transfer,
2 or partially being reduced in energy
in what can be seen in scattering processes, provided that the proper final states are
there. Amazingly, under certain conditions even virtual particles can be involved, and
the role of virtual states becomes prominent in processes such as Raman scattering,
two-photon absorption, spontaneous parametric down conversion, and so forth (here
using examples from optics). We often think about stimulated emission as an effect
of quantum physics, where optical feedback (the presence of an occupied mode)
literally causes a cloning of existing photons (bosons obey Bose–Einstein statistics
and therefore the so-called bunching effect occurs) when stimulated emission is
more likely than absorption for a given transition. But, we seldom regard spontaneous
emission as stimulated emission driven by fluctuations of the electromagnetic vacuum
field (virtual photons). In fact, the mere presence of 3D photonic modes governs the
radiation behaviour of electric dipoles in free space. And since quantum structures
allow one to tailor the (e.g. photonic) density of states, one can achieve a modification
of excitation lifetimes (e.g. radiative recombination times).
So, one can easily consider oneself playing with energy exchanges between
different modes of different types in a world full of resonances. The wave nature
can easily be used to tailor confinement conditions for particles and to obtain quantised energy levels from previously seemingly continuous (i.e. quasi-continuous)
3
states, based on constructive and destructive interference effects towards standing
waves
4 and the fulfilment of boundary conditions for them. Quantum potential wells
and low-dimensional structures provide us incredible means to alter the properties
of all kind of systems—most commonly optical/photonic or electronic ones, but can
also be vibrational/phononic or what have you. On the one hand, optical quantum
boxes can even be used to modify the photonic density of states to that extent that
radiative decay of electronic excitations can be suppressed or enhanced (see Purcell
effect in the literature), or that the empty cavity field can couple to a single exciton
(see vacuum Rabi splitting in the literature). On the other hand, superlattices, be it
vertical or in-plane, are nowadays frequently used to induce minibands for electronic
or optical states. Naturally, neither the concept of quantum boxes nor superlattices
is confined to one particle type, as 1D/2D/3D artificial photonic crystals, electron
or polariton traps/wires, or phonon tunnelling barriers and so forth demonstrate.
Remarkably, often the standard 2D quantum-well double-heterostructure is behind
2 Note that probability distributions describing a measurement outcome change continuously, as far
as a continuous flow of time is concerned, whereas a performed measurement causes a discrete
result as a consequence of the interactions with the applied probe system.
3 Quasi-continuity refers to the fact that very densely packed discrete states mimic a band of
seemingly continuous states.
4 Standing waves are nothing other than time-independent solutions of a confinement condition that
are else known as the (steady-state) modes of a resonator.
Preface
system, similar to photons occupying an electromagnetic mode of the vacuum field.
Occupation of a mode means energy is stored in that mode in integer numbers of the
resonance energy based on the occupation number, i.e. an excitation is present. That
excitation propagates like a wave but interacts with its environment like a discrete
entity, all according to quantum physics, discretely swapping from one mode to
another in what we refer to as energy transfer,
2 or partially being reduced in energy
in what can be seen in scattering processes, provided that the proper final states are
there. Amazingly, under certain conditions even virtual particles can be involved, and
the role of virtual states becomes prominent in processes such as Raman scattering,
two-photon absorption, spontaneous parametric down conversion, and so forth (here
using examples from optics). We often think about stimulated emission as an effect
of quantum physics, where optical feedback (the presence of an occupied mode)
literally causes a cloning of existing photons (bosons obey Bose–Einstein statistics
and therefore the so-called bunching effect occurs) when stimulated emission is
more likely than absorption for a given transition. But, we seldom regard spontaneous
emission as stimulated emission driven by fluctuations of the electromagnetic vacuum
field (virtual photons). In fact, the mere presence of 3D photonic modes governs the
radiation behaviour of electric dipoles in free space. And since quantum structures
allow one to tailor the (e.g. photonic) density of states, one can achieve a modification
of excitation lifetimes (e.g. radiative recombination times).
So, one can easily consider oneself playing with energy exchanges between
different modes of different types in a world full of resonances. The wave nature
can easily be used to tailor confinement conditions for particles and to obtain quantised energy levels from previously seemingly continuous (i.e. quasi-continuous)
3
states, based on constructive and destructive interference effects towards standing
waves
4 and the fulfilment of boundary conditions for them. Quantum potential wells
and low-dimensional structures provide us incredible means to alter the properties
of all kind of systems—most commonly optical/photonic or electronic ones, but can
also be vibrational/phononic or what have you. On the one hand, optical quantum
boxes can even be used to modify the photonic density of states to that extent that
radiative decay of electronic excitations can be suppressed or enhanced (see Purcell
effect in the literature), or that the empty cavity field can couple to a single exciton
(see vacuum Rabi splitting in the literature). On the other hand, superlattices, be it
vertical or in-plane, are nowadays frequently used to induce minibands for electronic
or optical states. Naturally, neither the concept of quantum boxes nor superlattices
is confined to one particle type, as 1D/2D/3D artificial photonic crystals, electron
or polariton traps/wires, or phonon tunnelling barriers and so forth demonstrate.
Remarkably, often the standard 2D quantum-well double-heterostructure is behind
2 Note that probability distributions describing a measurement outcome change continuously, as far
as a continuous flow of time is concerned, whereas a performed measurement causes a discrete
result as a consequence of the interactions with the applied probe system.
3 Quasi-continuity refers to the fact that very densely packed discrete states mimic a band of
seemingly continuous states.
4 Standing waves are nothing other than time-independent solutions of a confinement condition that
are else known as the (steady-state) modes of a resonator.