The control of individual quantum systems promises a new technology for the 21st century – quantum technology. This book is the first comprehensive treatment of modern quantum measurement and measurement-based quantum control, which are vital elements for realizing quantum technology. Readers are introduced to key experiments and technologies through dozens of recent experiments in cavity QED, quantum optics, mesoscopic electronics, and trapped particles several of which are analyzed in detail. Nearly 300 exercises help build understanding, and prepare readers for research in these exciting areas. This important book will interest graduate students and researchers in quantum information, quantum metrology, quantum control and related fields. Novel topics covered include adaptive measurement; realistic detector models; mesoscopic current detection; Markovian, state-based and optimal feedback; and applications to quantum information processing.

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Quantum Measurement and Control

The topic of quantum noise has become extremely timely due to the rise of quantum information physics and the resulting interchange of ideas between the condensed matter and atomic, molecular, optical--quantum optics communities. This review gives a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification. After introducing quantum noise spectra and methods for their detection, the basics of weak continuous measurements are described. Particular attention is given to the treatment of the standard quantum limit on linear amplifiers and position detectors within a general linear-response framework. This approach is shown how it relates to the standard Haus-Caves quantum limit for a bosonic amplifier known in quantum optics and its application to the case of electrical circuits is illustrated, including mesoscopic detectors and resonant cavity detectors.

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Introduction to quantum noise, measurement, and amplification

Spintronics refers commonly to phenomena in which the spin of electrons in a solid state environment plays the determining role In a more narrow sense spintronics is an emerging research field of electronics: spintronics devices are based on a spin control of electronics, or on an electrical and optical control of spin or magnetism This review presents selected themes of semiconductor spintronics, introducing important concepts in spin transport, spin injection, Silsbee-Johnson spin-charge coupling, and spindependent tunneling, as well as spin relaxation and spin dynamics The most fundamental spin-dependent nteraction in nonmagnetic semiconductors is spin-orbit coupling Depending on the crystal symmetries of the material, as well as on the structural properties of semiconductor based heterostructures, the spin-orbit coupling takes on different functional forms, giving a nice playground of effective spin-orbit Hamiltonians The effective Hamiltonians for the most relevant classes of materials and heterostructures are derived here from realistic electronic band structure descriptions Most semiconductor device systems are still theoretical concepts, waiting for experimental demonstrations A review of selected proposed, and a few demonstrated devices is presented, with detailed description of two important classes: magnetic resonant tunnel structures and bipolar magnetic diodes and transistors In most cases the presentation is of tutorial style, introducing the essential theoretical formalism at an accessible level, with case-study-like illustrations of actual experimental results, as well as with brief reviews of relevant recent achievements in the field

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Semiconductor Spintronics

1. Semiconductor Laser Diodes 2. Basic Concepts 3. Free-Carrier Theory 4. Coulomb Effects 5. Many-Body Gain 6. Band Mixing and Strain in Quantum Wells 7. Semiclassical laser Theory 8. Multimode Operation 9. Quantum Theory of the Laser 10. Propagation Effects 11. Beyond Quasiequilibrium Theory, Appendices A-e, Index

Semiconductor-Laser Physics

We report on a general theory for analyzing quantum transport through devices in the metal-QD-metal configuration where QD is a quantum dot or the device-scattering region which contains Rashba spin-orbital and electron-electron interactions. The metal leads may or may not be ferromagnetic, and they are assumed to weakly couple to the QD region. Our theory is formulated by second quantizing the Rashba spin-orbital interaction in spectral space (instead of real space), and quantum transport is then analyzed within the Keldysh nonequilibrium Green's function formalism. The Rashba interaction causes two main effects to the Hamiltonian: (i) it gives rise to an extra spin-dependent phase factor in the coupling matrix elements between the leads and the QD, and (ii) it gives rise to an interlevel spin-flip term, but forbids any intralevel spin flips. Our formalism provides a starting point for analyzing many quantum transport issues where spin-orbital effects are important. As an example, we investigate the transport properties of a Aharnov-Bohm ring in which a QD having a Rashba spin-orbital and electron-electron interactions is located in one arm of the ring. A substantial spin-polarized conductance or current emerges in this device due to the combined effect of a magnetic flux and the Rashba interaction. The direction and strength of the spin polarization are shown to be controllable by both the magnetic flux and a gate voltage.

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Quantum transport theory for nanostructures with Rashba spin-orbital interaction

Spin precession due to Rashba spin-orbit coupling in a two-dimension electron gas is the basis for the spin field effect transistor, in which the overall perfect spin-polarized current modulation could be acquired. There is a prerequisite, however, that a strong transverse confinement potential should be imposed on the electron gas or the width of the confined quantum well must be narrow. We propose relieving this rather strict limitation by applying an external magnetic field perpendicular to the plane of the electron gas because the effect of the magnetic field on the conductance of the system is equivalent to the enhancement of the lateral confining potential. Our results show that the applied magnetic field has little effect on the spin precession length or period although in this case Rashba spin-orbit coupling could lead to a Zeeman-type spin splitting of the energy band.

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Rashba spin precession in a magnetic field

We consider charge qubit monitoring (continuous-in-time weak measurement) by a single-electron transistor (SET) operating in the sequential-tunneling regime. We show that commonly used master equations for this regime are not of the Lindblad form that is necessary and sufficient for guaranteeing valid physical states. In this paper we derive a Lindblad-form master equation and a corresponding quantum trajectory model for continuous measurement of the charge qubit by a SET. Our approach requires that the SET-qubit coupling be strong compared to the SET tunneling rates. We present an analysis of the quality of the qubit measurement in this model (sensitivity versus back action). Typically, the strong coupling when the SET island is occupied causes back action on the qubit beyond the quantum back action necessary for its sensitivity, and hence the conditioned qubit state is mixed. However, in one strongly coupled, asymmetric regime, the SET can approach the limit of an ideal detector with an almost pure conditioned state. We also quantify the quality of the SET using more traditional concepts such as the measurement time and decoherence time, which we have generalized so as to treat the strongly responding regime.

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Sensitivity and back action in charge qubit measurements by a strongly coupled single-electron transistor

We present a new model for the continuous measurement of a coupled quantum dot charge qubit. We model the effects of a realistic measurement, namely adding noise to, and filtering, the current through the detector. This is achieved by embedding the detector in an equivalent circuit for measurement. Our aim is to describe the evolution of the qubit state conditioned on the macroscopic output of the external circuit. We achieve this by generalizing a recently developed quantum trajectory theory for realistic photodetectors [P. Warszawski, H. M. Wiseman, and H. Mabuchi, Phys. Rev. A 65, 023802 (2002)] to treat solid-state detectors. This yields stochastic equations whose (numerical) solutions are the realistic quantum trajectories of the conditioned qubit state. We derive our general theory in the context of a low transparency quantum point contact. Areas of application for our theory and its relation to previous work are discussed.

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Quantum trajectories for the realistic measurement of a solid-state charge qubit

We propose a model for non-ideal monitoring of the state of a coupled quantum dot qubit by a quantum tunnelling device. The non-ideality is modelled using an equivalent measurement circuit. This allows realistically available measurement results to be related to the state of the quantum system (qubit). We present a quantum trajectory that describes the stochastic evolution of the qubit state conditioned by tunnelling events (i.e. current) through the device. We calculate and compare the noise power spectra of the current in an ideal and a non-ideal measurement. The results show that when the two qubit dots are strongly coupled the non-ideal measurement cannot detect the qubit state precisely. The limitation of the ideal model for describing a realistic system may be estimated from the noise spectra.

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Non-ideal monitoring of a qubit state using a quantum tunnelling device

We propose an absorptive measurement scheme via coupled quantum dots based on studies of the quantum dynamics of coherently coupled dots. The system is described through a Markov master equation that is related to a measurable quantity, the current. We analyse the measurement configuration and calculate the correlations and noise spectra beyond the adiabatic approximation.

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He-Bi Sun

Papers

Rashba spin precession in a magnetic field

Sensitivity and back action in charge qubit measurements by a strongly coupled single-electron transistor

Quantum trajectories for the realistic measurement of a solid-state charge qubit

Non-ideal monitoring of a qubit state using a quantum tunnelling device

Absorptive Quantum Measurements via Coherently Coupled Quantum Dots