In the last two decades there has been an enormous progress in the experimental investigation of single quantum systems. This progress covers fields such as quantum optics, quantum computation, quantum cryptography, and quantum metrology, which are sometimes summarized as `quantum technologies'. A key issue there is entanglement, which can be considered as the characteristic feature of quantum theory. As disparate as these various fields maybe, they all have to deal with a quantum mechanical treatment of the measurement process and, in particular, the control process. Quantum control is, according to the authors, `control for which the design requires knowledge of quantum mechanics'. Quantum control situations in which measurements occur at important steps are called feedback (or feedforward) control of quantum systems and play a central role here. This book presents a comprehensive and accessible treatment of the theoretical tools that are needed to cope with these situations. It also provides the reader with the necessary background information about the experimental developments. The authors are both experts in this field to which they have made significant contributions. After an introduction to quantum measurement theory and a chapter on quantum parameter estimation, the central topic of open quantum systems is treated at some length. This chapter includes a derivation of master equations, the discussion of the Lindblad form, and decoherence – the irreversible emergence of classical properties through interaction with the environment. A separate chapter is devoted to the description of open systems by the method of quantum trajectories. Two chapters then deal with the central topic of quantum feedback control, while the last chapter gives a concise introduction to one of the central applications – quantum information. All sections contain a bunch of exercises which serve as a useful tool in learning the material. Especially helpful are also various separate boxes presenting important background material on topics such as the block representation or the feedback gain-bandwidth relation. The two appendices on quantum mechanics and phase-space and on stochastic differential equations serve the same purpose. As the authors emphasize, the book is aimed at physicists as well as control engineers who are already familiar with quantum mechanics. It takes an operational approach and presents all the material that is needed to follow research on quantum technologies. On the other hand, conceptual issues such as the relevance of the measurement process for the interpretation of quantum theory are neglected. Readers interested in them may wish to consult instead a textbook such as Decoherence and the Quantum-to-Classical Transition by Maximilian Schlosshauer. Although the present book does not contain applications to gravity, part of its content might become relevant for the physics of gravitational-wave detection and quantum gravity phenomenology. In this respect it should be of interest also for the readers of this journal.

https://iopscience.iop.org/article/10.1088/0264-9381/27/24/249002/pdf

Quantum Measurement and Control

Optical resonance and two-level atoms

Many coherent optical experiments that were originally performed on atomic or molecular systems1 are now being performed in semiconductors.2 This has been made possible by the current ready availability of lasers with pulse widths on the order of the dephasing time in semiconductors (100 fs). Because coherent phenomena can be strongly modified by many-body interactions, these experiments provide insight into the many-body physics present in semiconductors. Optically induced transient nutation, also known as Rabi flopping,1,3 where strong resonant incident optical fields drive the excitation from the ground state to the excited state and back again, is a coherent experiment of particular interest. This interest arises due to the theoretical prediction that the flopping frequency can be strongly modified by many- body contributions.4

Rabi flopping in semiconductors

Optical Frequency Comb (OFC) generated by semiconductor lasers are currently widely used in the extremely timely field of high capacity optical interconnects and high precision spectroscopy. In the last decade, several experimental evidences of spontaneous OFC generation have been reported in single section Quantum Dot (QD) lasers. Here we provide a physical understanding of these self-organization phenomena by simulating the multi-mode dynamics of a single section Fabry-Perot (FP) QD laser using a Time-Domain Traveling-Wave (TDTW) model that properly accounts for coherent radiation-matter interaction in the semiconductor active medium and includes the carrier grating generated by the optical standing wave pattern in the laser cavity. We show that the latter is the fundamental physical effect at the origin of the multi-mode spectrum appearing just above threshold. A self-mode-locking regime associated with the emission of OFC is achieved for higher bias currents and ascribed to nonlinear phase sensitive effects as Four Wave Mixing (FWM). Our results explain in detail the behaviour observed experimentally by different research groups and in different QD and Quantum Dash (QDash) devices.

Self-generation of optical frequency comb in single section quantum dot Fabry-Perot lasers: a theoretical study.

Due to their intuitiveness, flexibility and relative numerical efficiency, the macroscopic Maxwell-Bloch (MB) equations are a widely used semiclassical and semi-phenomenological model to describe optical propagation and coherent light-matter interaction in media consisting of discrete-level quantum systems. This review focuses on the application of this model to advanced optoelectronic devices, such as quantum cascade and quantum dot lasers. The Bloch equations are here treated as a density matrix model for driven quantum systems with two or multiple discrete energy levels, where dissipation is included by Lindblad terms. Furthermore, the one-dimensional MB equations for semiconductor waveguide structures and optical fibers are rigorously derived. Special analytical solutions and suitable numerical methods are presented. Due to the importance of the MB equations in computational electrodynamics, an emphasis is placed on the comparison of different numerical schemes, both with and without the rotating wave approximation. The implementation of additional effects which can become relevant in semiconductor structures, such as spatial hole burning, inhomogeneous broadening and local-field corrections, is discussed. Finally, links to microscopic models and suitable extensions of the Lindblad formalism are briefly addressed.

Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations

Coherence in light-matter interaction is a necessary ingredient if light is used to control the quantum state of a material system. Coherent effects are firmly associated with isolated systems kept at low temperature. The exceedingly fast dephasing in condensed matter environments, in particular at elevated temperatures, may well erase all coherent information in the material at timescales shorter than a laser excitation pulse. Here we show for an ensemble of semiconductor quantum dots that even in the presence of ultrafast dephasing, for suitably designed condensed matter systems quantum-coherent effects are robust enough to be observable at room temperature. Our conclusions are based on an analysis of the reshaping an ultrafast laser pulse undergoes on propagation through a semiconductor quantum dot amplifier. We show that this pulse modification contains the signature of coherent light-matter interaction and can be controlled by adjusting the population of the quantum dots via electrical injection.

/pdf/quantum-coherence-induces-pulse-shape-modification-in-a-3yxc99bcbl.pdf

Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature

We use a semiconductor optical Bloch equation approach combined with a traveling wave equation for the electric field to explore the effect of noise on the signal quality of a quantum-dot(QD) semiconductor optical amplifier. Using a stochastic white noise source for the spontaneous emission inside the QDs, we can show that there is a tradeoff between amplification performance and signal quality. Nevertheless, optimized operation conditions exist and are discussed for various input signals.

Influence of Noise on the Signal Quality of Quantum-Dot Semiconductor Optical Amplifiers

We study experimentally and numerically the changes in pulse shape a Gaussian laser pulse undergoes when propagating through an electrically pumped quantum dot semiconductor optical amplifier (QD-SOA). The pulse energy is set to be resonant to the quantum dot ground state transition, and the pulse shape is analyzed in phase and amplitude in a heterodyne cross-correlation experiment. For the case of an inverted system, we observe the appearance of a periodic modulation of the temporal pulse profile above a critical pulse power. Similar signatures of pulse break-up have been observed at low temperature in quantum dot ensembles without electrical pumping and were linked to optically induced Rabi oscillations imprinting the coherent switching between absorption and stimulated emission of photons by the material system.

Evidence of macroscopic coherence at room temperature: Rabi oscillation induced pulse break-up in a quantum dot amplifier

Rabi oscillations imprint an intensity modulation on the electric field of the laser pulse creating them. We experimentally observe this signature in a quantum dot ensemble at room temperature for arbitrary degrees of inversion.

Pulse shape analysis resolves room temperature coherent light-matter interaction in quantum dots

We show the occurrence of Rabi oscillation induced pulse shaping and break-up in a 1.3μm wavelength semiconductor quantum-dot optical amplifiers at room temperature in numerical simulations and experimental results.

Julian Korn

Papers

Quantum coherence induces pulse shape modification in a semiconductor optical amplifier at room temperature

Influence of Noise on the Signal Quality of Quantum-Dot Semiconductor Optical Amplifiers

Evidence of macroscopic coherence at room temperature: Rabi oscillation induced pulse break-up in a quantum dot amplifier

Pulse shape analysis resolves room temperature coherent light-matter interaction in quantum dots

Pulse shaping and break-up by quantum-coherent effects in quantum-dot amplifiers at room temperature