In the previous chapters, we have seen that quantum-optical correlations can produce effects that have no classical explanation. In particular, the matter excitations can depend strongly on the specific form of the quantum fluctuations, i.e., the quantum statistics of the light source. For example, Fock-state sources can produce quantum Rabi flopping with discrete frequencies while coherent-state sources generate a sequence of collapses and revivals in atomic excitations. Hence, not only the intensity or the classical amplitude of the field is relevant but also the quantum statistics of the exciting light influences the matter response. Even if we take sources with identical intensities, the resulting atomic excitations are fully periodic for a Fock-state excitation while a coherentstate excitation produces a chaotic Bloch-vector trajectory with multiple collapses and revivals. In this chapter, we use this fundamental observation as the basis to develop the concept of quantum-optical spectroscopy. We show in Chapter 30 that this method yields a particularly intriguing scheme to characterize and control the quantum dynamics in solids. Since one cannot imagine how to exactly compute the many-body wave function or the density matrix, we also study how principal quantum-optical effects can be described with the help of the cluster-expansion scheme. Quantum-optical spectroscopy Historically, the continued refinement of optical spectroscopy and its use to manipulate the states of matter has followed a very distinct path where one simultaneously tries to control and characterize light with increased accuracy.
In the previous chapters, we have seen that quantum-optical correlations can produce effects that have no classical explanation. In particular, the matter excitations can depend strongly on the specific form of the quantum fluctuations, i.e., the quantum statistics of the light source. For example, Fock-state sources can produce quantum Rabi flopping with discrete frequencies while coherent-state sources generate a sequence of collapses and revivals in atomic excitations. Hence, not only the intensity or the classical amplitude of the field is relevant but also the quantum statistics of the exciting light influences the matter response. Even if we take sources with identical intensities, the resulting atomic excitations are fully periodic for a Fock-state excitation while a coherentstate excitation produces a chaotic Bloch-vector trajectory with multiple collapses and revivals. In this chapter, we use this fundamental observation as the basis to develop the concept of quantum-optical spectroscopy. We show in Chapter 30 that this method yields a particularly intriguing scheme to characterize and control the quantum dynamics in solids. Since one cannot imagine how to exactly compute the many-body wave function or the density matrix, we also study how principal quantum-optical effects can be described with the help of the cluster-expansion scheme. Quantum-optical spectroscopy Historically, the continued refinement of optical spectroscopy and its use to manipulate the states of matter has followed a very distinct path where one simultaneously tries to control and characterize light with increased accuracy.
The optically generated excitations in semiconductors constitute a genuine many-body system. To describe its quantum-optical features, we have to expand significantly the theoretical models used so far. However, the important insights of Chapters 16–23 are already presented in a form in which most of them can directly be used and generalized to analyze central properties of the optical excitations in solids. As for atoms, the optical transitions in semiconductors are induced via dipole interaction between photons and electrons. We can thus efficiently construct a systematic quantum-optical theory for semiconductors by following the cluster-expansion approach. One of the main differences from atoms is that the electronic excitations in semiconductors form a strongly interacting many-body system. Thus, we must systematically treat the arising Coulomb-induced hierarchy problem together with the quantum-optical one. Moreover, the coupling of electrons to lattice vibrations, i.e., the phonons, produces yet another hierarchy problem. In addition, in solid-state spectroscopy one often uses multimode light fields such that one cannot rely on the single-mode simplifications to study semiconductor quantum optics. As shown in Chapter 15, the Coulomb-, phonon-, and photon-induced hierarchy problems have formally an identical structure. Thus, we start the analysis by investigating how semiconductor quantum optics emerges from the dynamics of correlated clusters. We first focus on the basic properties of the optical transitions in the classical regime. This means investigating the fundamental optical phenomena resulting from the singlets. The full singlet–doublet approach is presented in Chapters 28–30.
Chapter 6 begins by transforming the optical wave itself into a quantized form, and the full implications of the wave‐particle duality of Chapter 2 become clear. The electric field may be pictured as an infinite ladder of discrete states and this structure allows optical interactions to be described photon by photon. The origin of spontaneous emission emerges from this treatment as a transition process that is stimulated by electric field fluctuations of the vacuum, and Weisskopf–Wigner theory explains why it is irreversible. The subject of coherent states is introduced and intriguing possibilities outlined regarding the noise properties of components of these states that form different quadratures in terms of the optical phase. Next, statistical analysis of light fields is considered to serve as a basis for more quantitative comparisons of fields and their noise properties. Methods of calculating the first and second degrees of coherence are presented, and the ranges of values corresponding to “classical” versus “quantum” light sources are discussed. The reduced density matrix is developed to justify analysis that focuses on only certain aspects of optical dynamics while ignoring others, as an important tool for simplifying complex problems. Finally, in view of its historical importance, the problem of calculating the fluorescence spectrum of resonantly excited two‐level atoms is considered using both a method of moments and dressed atom theory.
Quantum spectroscopy utilizes the quantum fluctuations of the light source to characterize and control matter. More specifically, desired many-body states can be directly excited to the semiconductor by adjusting light source's quantum fluctuations. The method is experimentally realizable by projecting an extensive set of classical measurements into a quantum-optical response resulting from any possible quantum source. In this work, quantum spectroscopy is used to identify new classes of many-body states and quantum processes in semiconductor nanostructures. In the first part of this Thesis, the optical properties of semiconductor quantum wells are analyzed with quantum spectroscopy by projecting high-precision optical measurements into quantum-optical responses. It is shown that quantum spectroscopy can characterize the properties of specific stable electron-hole cluster – called quasiparticles – much more sensitively than traditional ultrafast laser spectroscopy. In particular, unambiguous evidence is demonstrated for the identification of a new highly correlated quasiparticle in direct-gap Galliumarsenide quantum wells, the dropleton, that is a quantum droplet consisting of four-to-seven electron-hole pairs. To determine the detectable excitation energetics of such correlated quasiparticles in optically excited semiconductor quantum wells, a new theoretical framework is presented which allows for the computation of the excitation spectrum based on a pair-correlation function formulation of the quasiparticle state. Another study in this Thesis deals with the emission properties of optically pumped quantum-dot microcavities. Experimental and theoretical evidence is shown for a new intriguing quantum-memory effect that is controllable by adjusting pump source's quantum fluctuations. The last part of this Thesis presents a fundamental study about the general applicability of quantum spectroscopy in dissipative systems.
In Chapter 3 the interaction Hamiltonian which determines the way light interacts with matter is derived. Simple perturbative analysis is applied to see if basic dynamics of atoms can be explained. The partial successes of perturbation theory are compared with predictions of an “exact” method of calculating the occupation probabilities of various atomic states. Even the “exact” method is shown to fail, establishing the need for improved approaches that yield correct results in later chapters. Some elementary results for the transition rates, including Fermi's golden rule are covered. Then the density matrix is introduced as a tool for describing not only the populations of atomic energy levels but coherence that can be created and lost during the dynamic evolution of atoms in time. A vector model based on the Bloch vector is presented as a useful way of picturing coherent atom–field interactions in an optical “spin” space, particularly multiple‐pulse interactions. Mechanisms are described that cause line‐broadening in optical spectroscopy, such as the Doppler effect. The chapter closes by showing that it is usually possible to reduce the complexity of real atoms on an experimental basis to facilitate direct comparisons with theoretical calculations based on simple models with only two or three energy levels.
The discussions in the previous chapters show that already the spontaneous emission, i.e., the simplest manifestation of the quantum-optical fluctuations, exhibits highly nontrivial features as soon as the quantum light is coupled to interacting many-body systems. We have seen, for example, that pronounced resonances in the semiconductor luminescence originate from a nontrivial mixture of exciton and plasma contributions in contrast to the simple transitions between the eigenstates of isolated atomic systems. As a consequence of the conservation laws inherent to the light–matter coupling, the photon emission induces rearrangements in the entire many-body system leading, e.g., to pronounced hole burning in the exciton distribution. As discussed in Chapter 29, this depletion of the optically active excitons leads to a reduction of the total radiative recombination and the appearance of nonthermal luminescence even when the electron–hole system is in quasiequilibrium. Already these observations show that the coupled quantum-optical and many-body interactions induce new intriguing phenomena that are not explainable by the concepts of traditional quantum optics or classical semiconductor physics alone. The foundations of quantum optics are based on systematic investigations of simple systems interacting with few quantized light modes. In this context, one can evaluate and even measure the exact eigenstates or the density matrix with respect to both the photonic and the atomic degrees of freedom. In semiconductor systems, currently the investigations using one or a few quantum dots (QD) are closest to the atomic studies because, due to their discrete eigenstates, one can treat strongly confined quantum dots to some extent like artificial atoms.
It is critical to understand the nature of the propagation medium in terms of the available resonances which couple to the electromagnetic field. The detailed specification of the complex index of refraction as a function of frequency is the subject of spectroscopy. Since propagation media cover all phases of matter, the spectroscopy of gases, solids, and liquids is introduced in this chapter. Topics are not exhaustively covered, but rather with sufficient depth to support the practical applications that will come later. The chapter begins with a formal review of topics covered in stationary-state quantum mechanics necessary for the development of spectroscopy. The next section develops models to calculate spectral line positions, which are necessary to characterize a spectral line. The full development of spectral line parameters is not only the goal of this chapter but the next two as well. The remaining sections address the essential elements of the spectroscopy of gases, solids and liquids. Both classical and quantum models are used. Time-independent quantum mechanics allows the description of the quantized energy level structure of matter. This is the central topic of this chapter. Time-dependent quantum mechanics is necessary for the development of a theory covering transitions between stationary-state energy levels and is the topic of Chapter 5. The classical concept of light is that of an oscillating continuous wave field, as presented in the first two chapters. This is consistent with the classical electrodynamics based on Maxwell’s equations. However, the work by Planck on blackbody radiation and Einstein on the photoelectric effect showed that optical fields also have a quantized or particle-like nature. Planck, in 1900, suggested that the energy of light, E, be quantized according to . . . E = h f [J] (3.1) . . . where f is frequency (sec−1) and h is Planck’s constant (h = 6.6260755(40) × 10−34 J-sec). This allowed a theoretical description of blackbody radiation for the first time. However, it was Einstein, who, a few years later, made Eq. 3.1 more credible by applying it to explain the photoelectric effect.