MESOSCOPIC QUANTUM OPTICS
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1 MESOSCOPIC QUANTUM OPTICS by Yoshihisa Yamamoto Ata Imamoglu A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York Chichester Weinheim Brisbane Toronto Singapore
2 Preface xi 1 Basic Concepts l 1.1 Probability Interpretation of Quantum Mechanics Heisenberg Uncertainty Principle Commutator Bracket and the Minimum Uncertainty State Quantum Interference and Wave-Particle Duality Time Evolution of a Minimum Uncertainty State Coherent State and Squeezed State von Neumann's Projection Postulate Measurement Error and Back Action Noise Pauli's First-Kind and Second-Kind Measurements Density Operator and LiouviUe-von Neumann Equation General Description of Indirect Quantum Measurements Quantum Nondemolition Measurement Simultaneous Measurement of Two Conjugate Observables 25 References 28 2 Canonical Quantization Minimum Action Principle and Lagrangian Formalism Quantization of the Electromagnetic Field Second Quantization of the Schrödinger Field 38 References 42 3 Quantum States of the Electromagnetic Fields Photon Number Eigenstates Properties of Photon Number Eigenstates Generation of Photon Number Eigenstates Coherent States Properties of Coherent States Generation of Coherent States 58
3 3.3 Squeezed States Properties of Quadrature Amplitude Squeezed States Generation of Quadrature Amplitude Squeezed States Properties of Number-Phase Squeezed States Generation of Number-Phase Squeezed States Correlated Twin Photons and Quantum Entanglement Generation of Arbitrary Quantum States by Projective Measurements Nonlocal Quantum Entanglement Probability Distribution Functions for a Density Operator 71 References 74 Coherence of the Electromagnetic Fields 4.1 Photodetection Young's Interference Experiment and First-Order Coherence Hanbury-Brown-Twiss Experiment and Second-Order Coherence Photon Counting Classical Theory of Photon Count Distribution Quantum Theory of Photon Count Distribution Phase Operator of the Quantized Electromagnetic Field Quantum Limits of Optical Interferometry Standard Quantum Limits of Optical Interferometry Squeezed State Interferometer Photon Number Eigenstate Interferometer Photonic de Broglie Wave Interferometer 97 References 100 Quantum States of Atoms 5.1 Angular Momentum Algebra Quantization of Angular Momentum Angular Momentum Operators and Eigenstates Assembly of Two-Level Atoms Pauli Spin Operators Collective Angular Momentum Operators Angular Momentum Eigenstates (Dicke States) Coherent Atomic States (Bloch States) 109 References 113
4 vii 6 Interaction between Atoms and Fields Atom-Field Interaction in the Length Gauge Jaynes-Cummings Hamiltonian Two-Level Atom and Single-Mode Photon Number State Vacuum Rabi Oscillation Normal Mode Splitting N Two-Level Atoms and a Single-Mode Photon Number State Collective Rabi Oscillation and Normal Mode Splitting Dressed Fermions and Dressed Bosons Atomic Cavity Quantum Electrodynamics (QED) Mollow's Triplet Radiation Trapped State Cummings Collapse and Revival Two-Level Atoms with a Continuum of Radiation Fields Superradiance 134 References Mathematical Methods for System-Reservoir Interaction Noise Operator Method Field Damping by Field Reservoirs Einstein Relation between Drift and Diffusion Coefficients Density Operator Method Derivation of the Master Equation Field Damping by Atomic Reservoirs Atom Damping by Field Reservoirs Field Damping by Field Reservoirs The Fokker-Planck Equation Glauber-Sudarshan P Representation Stochastic Differential Equations Quantum Regression Theorem 154 References Stochastic Wavefunction Methods Monte Carlo Wavefunction Approach Description and Equivalence to Master Equation Two-Time Correlation Functions Two-Level Atom Driven by a Laser Field Single-Mode Cavity Driven by a Thermal Field 168
5 viii CONTENTS 8.2 Quantum State Diffusion Model 171 References Quantum Nondemolition Measurements QND Measurement of Photon Number Heisenberg Picture Schrödinger Picture Experimental QND Measurements QND Measurement of Quadrature Amplitudes 182 References Semiconductor Bloch Equations Field Theory of Semiconductors Semiconductor Bloch Equations Semiconductor Bloch Equations in the Non-interacting Limit Semiconductor Bloch Equations with Interactions Excitons Nonlinear Response of Excitons 198 References Excitons and Polaritons Non-interacting Excitons Bulk Exciton Polaritons Quantum-Well Excitons and Cavity Polaritons Excitons as Bosons Bosonization Bose Condensation of Excitons Stimulated Scattering of Excitons Stimulated Scattering Experiment With Excitons 216 References Coulomb Blockade and Squeezing Coulomb Blockade of Tunneling Macroscopic Coulomb Blockade of Electron Injection AC-Voltage-Driven Mesoscopic p-i-n Junctions 228 References 234
6 ix 13 Current Noise in Mesoscopic and Macroscopic Conductors Suppression of Electrical Current Noise in Dissipative Conductors Equilibrium and Nonequilibnum Transport Noise in Mesoscopic Conductors Suppression of Nonequilibnum Partition Noise by Inelastic Scattering Microscopic Model for Suppression of Nonequilibrium Partition Noise and Loss of Electron Wave Coherence Quantum Interference in Electron Collision Negative Correlation in Electron Partition 250 References Nonequilibrium Green's Function Formalism Green's Function and Self-Energy Correlation and Scattering Functions Current Flow Noninteracting Transport Strongly Interacting Transport Conductance through a Single Site 262 References Quantum Statistical Properties of a Laser Density Operator Master Equation Derivation of the Master Equation Fast Dephasing Case Lifetime Broadened Laser System Threshold Characteristics Photon Statistics Spectral Linewidth Fokker-Planck Equation Langevin Equation Derivation of the Langevin Equation Linearization of the Langevin Equations Quantum Noise at Well Above Threshold Sub-Poissonian Lasers Standard Quantum Limit of the Output Field Photon Number Noise and Phase Noise of Pump-Noise-Suppressed Lasers Commutator Bracket Conservation 288
7 x CONTENTS Index 15.5 Squeezing in Semiconductor Lasers Observation of Mode Partition Noise 294 References 297
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Contents Preface 1. The structure of the space of the physical states 1 1.1 Introduction......................... 1 1.2 The space of the states of physical particles........ 2 1.3 The Weyl Heisenberg algebra
Molecular spectroscopy
Molecular spectroscopy Origin of spectral lines = absorption, emission and scattering of a photon when the energy of a molecule changes: rad( ) M M * rad( ' ) ' v' 0 0 absorption( ) emission ( ) scattering