Semiconductor Quantum Optics.

By: Kira, MackilloContributor(s): Koch, Stephan WPublisher: Cambridge : Cambridge University Press, 2011Copyright date: ©2011Description: 1 online resource (660 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781139185639Subject(s): Semiconductors.;Quantum optix.;Quantum electrodynamicsGenre/Form: Electronic books. Additional physical formats: Print version:: Semiconductor Quantum OpticsDDC classification: 621.38152 LOC classification: QC611.6.Q36 K57 2012Online resources: Click to View
Contents:
Cover -- SEMICONDUCTOR QUANTUM OPTICS -- Title -- Copyright -- Contents -- Preface -- 1 Central concepts in classical mechanics -- 1.1 Classical description -- 1.1.1 Conservation laws -- 1.1.2 Single-particle motion for simple potentials -- 1.2 Statistical description of particles -- 1.2.1 Liouville equation -- 1.2.2 Classical averaging of statistical distributions -- Exercises -- Further reading -- 2 Central concepts in classical electromagnetism -- 2.1 Classical description of electromagnetic fields -- 2.1.1 Wave equation -- 2.1.2 Superposition of waves -- 2.2 Particle aspects of electromagnetic waves -- 2.2.1 Eikonal equation -- 2.2.2 Classical trajectories within wave equation -- 2.3 Generalized wave and Helmholtz equations -- 2.3.1 Formal eigenvalue problem -- 2.3.2 Temporal properties of generalized waves -- 2.3.3 Generalized waves and particles -- Exercises -- Further reading -- 3 Central concepts in quantum mechanics -- 3.1 Schrödinger equation -- 3.1.1 Free quantum-mechanical propagation -- 3.1.2 Interpretation of the wave function -- 3.2 Expectation values in quantum mechanics -- 3.2.1 Particle momentum -- 3.2.2 Commutation relations -- 3.2.3 Canonical quantization -- 3.2.4 Representations of position and momentum operators -- Exercises -- Further reading -- 4 Central concepts in stationary quantum theory -- 4.1 Stationary Schrödinger equation -- 4.2 One-dimensional Schrödinger equation -- 4.3 Classification of stationary eigenstates -- 4.3.1 Propagating solutions -- 4.3.2 Tunneling solutions -- 4.3.3 Bound solutions -- 4.4 Generic classification of energy eigenstates -- Exercises -- Further reading -- 5 Central concepts in measurement theory -- 5.1 Hermitian operators -- 5.2 Eigenvalue problems -- 5.2.1 Dirac notation -- 5.2.2 Central eigenvalue problems -- 5.3 Born's theorem -- 5.3.1 Heisenberg uncertainty principle.
5.3.2 Schrödinger and Heisenberg picture -- Exercises -- Further reading -- 6 Wigner's phase-space representation -- 6.1 Wigner function -- 6.1.1 Averages in phase space -- 6.1.2 Quantum properties of the Wigner function -- 6.1.3 Negativity of the Wigner function -- 6.2 Wigner-function dynamics -- 6.3 Density matrix -- 6.4 Feasibility of quantum-dynamical computations -- Exercises -- Further reading -- 7 Hamiltonian formulation of classical electrodynamics -- 7.1 Basic concepts -- 7.2 Hamiltonian for classical electrodynamics -- 7.2.1 Functional derivative -- 7.2.2 Electromagnetic-field Hamiltonian -- 7.3 Hamilton equations for light-matter system -- 7.3.1 Classical particle equations -- 7.3.2 Classical equations for the electromagnetic field -- 7.4 Generalized system Hamiltonian -- Exercises -- Further reading -- 8 System Hamiltonian of classical electrodynamics -- 8.1 Elimination of the scalar potential -- 8.2 Coulomb and Lorentz gauge -- 8.2.1 Scalar-potential elimination in the Coulomb gauge -- 8.2.2 Scalar-potential elimination in the Lorentz gauge -- 8.3 Transversal and longitudinal fields -- 8.3.1 Poisson equation -- 8.3.2 Wave equation -- 8.4 Mode expansion of the electromagnetic field -- 8.4.1 Modes with periodic boundary conditions -- 8.4.2 Real-valued mode expansion -- 8.4.3 Particle aspects -- Exercises -- Further reading -- 9 System Hamiltonian in the generalized Coulomb gauge -- 9.1 Separation of electronic and ionic motion -- 9.2 Inclusion of the ionic polarizability -- 9.2.1 Generalized Coulomb gauge -- 9.2.2 System Hamiltonian -- 9.3 Generalized Coulomb potential -- 9.3.1 Image potentials -- 9.3.2 Generalized Coulomb potential -- 9.4 Generalized light-mode functions -- 9.4.1 Transmission and reflection of light modes -- 9.4.2 Boundary conditions -- 9.4.3 Fresnel coefficients for s- and p-polarized modes.
9.4.4 Transfer-matrix solutions for generalized modes -- Exercises -- Further reading -- 10 Quantization of light and matter -- 10.1 Canonical quantization -- 10.1.1 Toward semiconductor quantum optics -- 10.1.2 Real vs. auxiliary quantization space -- 10.2 Second quantization of light -- 10.2.1 Unitary transformations -- 10.2.2 Complex-valued modes -- 10.3 Eigenstates of quantized modes -- 10.3.1 Explicit representation of operators -- 10.3.2 Properties of creation and annihilation operators -- 10.3.3 Fock states -- 10.3.4 Fock states in x space -- 10.4 Elementary properties of Fock states -- 10.4.1 Quantum statistics in terms of Fock states -- 10.4.2 Vacuum-field fluctuations -- Exercises -- Further reading -- 11 Quasiparticles in semiconductors -- 11.1 Second-quantization formalism -- 11.1.1 Fermion many-body states -- 11.1.2 Fermion creation and annihilation operators -- 11.1.3 Fermions in second quantization -- 11.1.4 Pragmatic formulation of second quantization -- 11.2 System Hamiltonian of solids -- 11.2.1 Second quantization of system Hamiltonian -- 11.2.2 Second quantization of lattice vibrations -- Exercises -- Further reading -- 12 Band structure of solids -- 12.1 Electrons in the periodic lattice potential -- 12.1.1 k.p theory -- 12.1.2 Two-band approximation -- 12.2 Systems with reduced effective dimensionality -- 12.2.1 Quasi two-, one-, and zero-dimensional systems -- 12.2.2 Electron density of states -- Exercises -- Further reading -- 13 Interactions in semiconductors -- 13.1 Many-body Hamiltonian -- 13.2 Light-matter interaction -- 13.2.1 Separation of length scales -- 13.2.2 Light-matter-coupling integrals -- 13.2.3 Inner products within k · p theory -- 13.2.4 Light-matter interaction in k · p theory -- 13.3 Phonon-carrier interaction -- 13.4 Coulomb interaction -- 13.5 Complete system Hamiltonian in different dimensions.
13.5.1 Quantum-well system Hamiltonian -- 13.5.2 Quantum-wire system Hamiltonian -- 13.5.3 Quantum-dot system Hamiltonian -- Exercises -- Further reading -- 14 Generic quantum dynamics -- 14.1 Dynamics of elementary operators -- 14.1.1 Evaluation strategy -- 14.1.2 Quantum dynamics of free quasiparticles -- 14.1.3 Photon-operator dynamics -- 14.1.4 Macroscopic matter-response operators -- 14.1.5 Phonon and carrier dynamics -- 14.2 Formal properties of light -- 14.2.1 Quantized wave equation -- 14.2.2 Plasmon response -- 14.3 Formal properties of general operators -- 14.3.1 Operator hierarchy problem -- 14.3.2 BBGKY hierarchy problem -- Exercises -- Further reading -- 15 Cluster-expansion representation of the quantum dynamics -- 15.1 Singlet factorization -- 15.1.1 Expectation values of a Slater-determinant state -- 15.1.2 Hartree-Fock approximation and singlet factorization -- 15.2 Cluster expansion -- 15.2.1 Boson and Fermion factorizations -- 15.2.2 Most relevant singlet-doublet factorizations -- 15.3 Quantum dynamics of expectation values -- 15.4 Quantum dynamics of correlations -- 15.5 Scattering in terms of correlations -- Exercises -- Further reading -- 16 Simple many-body systems -- 16.1 Single pair state -- 16.1.1 Electron-hole system -- 16.1.2 Separation of relative and center-of-mass motion -- 16.2 Hydrogen-like eigenstates -- 16.2.1 Low-dimensional systems -- 16.2.2 Numerical solutions of bound and unbound states -- 16.3 Optical dipole -- 16.3.1 Momentum-matrix elements -- 16.3.2 Long-wave-length limit for the  · p̂ interaction -- Exercises -- Further reading -- 17 Hierarchy problem for dipole systems -- 17.1 Quantum dynamics in the  · p̂ picture -- 17.1.1 Lorentz force -- 17.1.2 Time scale for the center-of-mass motion -- 17.2 Light-matter coupling -- 17.3 Dipole emission -- 17.3.1 Dipole-emission dynamics.
17.3.2 Emission of planar dipoles -- 17.4 Quantum dynamics in the Ê · x̂ picture -- 17.4.1 Göppert-Mayer transformation -- 17.4.2 Dipole self-energy -- 17.4.3 System Hamiltonian -- 17.4.4 Quantum dynamics -- Exercises -- Further reading -- 18 Two-level approximation for optical transitions -- 18.1 Classical optics in atomic systems -- 18.1.1 Separation of relative and center-of-mass motion -- 18.1.2 Formal aspects of the optical excitation -- 18.1.3 Two-level approximation -- 18.1.4 Rotating-wave approximation (RWA) -- 18.2 Two-level system solutions -- 18.2.1 Analytic solution of the two-level system -- 18.2.2 Bloch-vector representation -- 18.2.3 Rabi oscillations -- 18.2.4 Pulse area and Rabi flopping -- 18.2.5 Square-pulse excitation -- Exercises -- Further reading -- 19 Self-consistent extension of the two-level approach -- 19.1 Spatial coupling between light and two-level system -- 19.1.1 Center-of-mass distribution in optical coupling -- 19.1.2 Optical Bloch equations -- 19.1.3 Angle parametrization of Bloch vector -- 19.2 Maxwell-optical Bloch equations -- 19.2.1 Radiative decay of the atomic dipole -- 19.2.2 Radiative decay of planar dipoles -- 19.3 Optical Bloch equations with radiative coupling -- Exercises -- Further reading -- 20 Dissipative extension of the two-level approach -- 20.1 Spin representation of optical excitations -- 20.2 Dynamics of Pauli spin matrices -- 20.3 Phenomenological dephasing -- 20.3.1 Dephasing-induced effects -- 20.3.2 Dephasing and radiative decay -- 20.4 Coupling between reservoir and two-level system -- 20.4.1 Master-equation description of dephasing -- 20.4.2 Master-equation for two-level system -- Exercises -- Further reading -- 21 Quantum-optical extension of the two-level approach -- 21.1 Quantum-optical system Hamiltonian -- 21.1.1 Reduction to two-level system -- 21.1.2 Rotating-wave approximation.
21.1.3 Operator dynamics.
Summary: Combining methods from quantum optics and solid-state physics to give researchers and graduate students a deeper understanding of the subject.
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Cover -- SEMICONDUCTOR QUANTUM OPTICS -- Title -- Copyright -- Contents -- Preface -- 1 Central concepts in classical mechanics -- 1.1 Classical description -- 1.1.1 Conservation laws -- 1.1.2 Single-particle motion for simple potentials -- 1.2 Statistical description of particles -- 1.2.1 Liouville equation -- 1.2.2 Classical averaging of statistical distributions -- Exercises -- Further reading -- 2 Central concepts in classical electromagnetism -- 2.1 Classical description of electromagnetic fields -- 2.1.1 Wave equation -- 2.1.2 Superposition of waves -- 2.2 Particle aspects of electromagnetic waves -- 2.2.1 Eikonal equation -- 2.2.2 Classical trajectories within wave equation -- 2.3 Generalized wave and Helmholtz equations -- 2.3.1 Formal eigenvalue problem -- 2.3.2 Temporal properties of generalized waves -- 2.3.3 Generalized waves and particles -- Exercises -- Further reading -- 3 Central concepts in quantum mechanics -- 3.1 Schrödinger equation -- 3.1.1 Free quantum-mechanical propagation -- 3.1.2 Interpretation of the wave function -- 3.2 Expectation values in quantum mechanics -- 3.2.1 Particle momentum -- 3.2.2 Commutation relations -- 3.2.3 Canonical quantization -- 3.2.4 Representations of position and momentum operators -- Exercises -- Further reading -- 4 Central concepts in stationary quantum theory -- 4.1 Stationary Schrödinger equation -- 4.2 One-dimensional Schrödinger equation -- 4.3 Classification of stationary eigenstates -- 4.3.1 Propagating solutions -- 4.3.2 Tunneling solutions -- 4.3.3 Bound solutions -- 4.4 Generic classification of energy eigenstates -- Exercises -- Further reading -- 5 Central concepts in measurement theory -- 5.1 Hermitian operators -- 5.2 Eigenvalue problems -- 5.2.1 Dirac notation -- 5.2.2 Central eigenvalue problems -- 5.3 Born's theorem -- 5.3.1 Heisenberg uncertainty principle.

5.3.2 Schrödinger and Heisenberg picture -- Exercises -- Further reading -- 6 Wigner's phase-space representation -- 6.1 Wigner function -- 6.1.1 Averages in phase space -- 6.1.2 Quantum properties of the Wigner function -- 6.1.3 Negativity of the Wigner function -- 6.2 Wigner-function dynamics -- 6.3 Density matrix -- 6.4 Feasibility of quantum-dynamical computations -- Exercises -- Further reading -- 7 Hamiltonian formulation of classical electrodynamics -- 7.1 Basic concepts -- 7.2 Hamiltonian for classical electrodynamics -- 7.2.1 Functional derivative -- 7.2.2 Electromagnetic-field Hamiltonian -- 7.3 Hamilton equations for light-matter system -- 7.3.1 Classical particle equations -- 7.3.2 Classical equations for the electromagnetic field -- 7.4 Generalized system Hamiltonian -- Exercises -- Further reading -- 8 System Hamiltonian of classical electrodynamics -- 8.1 Elimination of the scalar potential -- 8.2 Coulomb and Lorentz gauge -- 8.2.1 Scalar-potential elimination in the Coulomb gauge -- 8.2.2 Scalar-potential elimination in the Lorentz gauge -- 8.3 Transversal and longitudinal fields -- 8.3.1 Poisson equation -- 8.3.2 Wave equation -- 8.4 Mode expansion of the electromagnetic field -- 8.4.1 Modes with periodic boundary conditions -- 8.4.2 Real-valued mode expansion -- 8.4.3 Particle aspects -- Exercises -- Further reading -- 9 System Hamiltonian in the generalized Coulomb gauge -- 9.1 Separation of electronic and ionic motion -- 9.2 Inclusion of the ionic polarizability -- 9.2.1 Generalized Coulomb gauge -- 9.2.2 System Hamiltonian -- 9.3 Generalized Coulomb potential -- 9.3.1 Image potentials -- 9.3.2 Generalized Coulomb potential -- 9.4 Generalized light-mode functions -- 9.4.1 Transmission and reflection of light modes -- 9.4.2 Boundary conditions -- 9.4.3 Fresnel coefficients for s- and p-polarized modes.

9.4.4 Transfer-matrix solutions for generalized modes -- Exercises -- Further reading -- 10 Quantization of light and matter -- 10.1 Canonical quantization -- 10.1.1 Toward semiconductor quantum optics -- 10.1.2 Real vs. auxiliary quantization space -- 10.2 Second quantization of light -- 10.2.1 Unitary transformations -- 10.2.2 Complex-valued modes -- 10.3 Eigenstates of quantized modes -- 10.3.1 Explicit representation of operators -- 10.3.2 Properties of creation and annihilation operators -- 10.3.3 Fock states -- 10.3.4 Fock states in x space -- 10.4 Elementary properties of Fock states -- 10.4.1 Quantum statistics in terms of Fock states -- 10.4.2 Vacuum-field fluctuations -- Exercises -- Further reading -- 11 Quasiparticles in semiconductors -- 11.1 Second-quantization formalism -- 11.1.1 Fermion many-body states -- 11.1.2 Fermion creation and annihilation operators -- 11.1.3 Fermions in second quantization -- 11.1.4 Pragmatic formulation of second quantization -- 11.2 System Hamiltonian of solids -- 11.2.1 Second quantization of system Hamiltonian -- 11.2.2 Second quantization of lattice vibrations -- Exercises -- Further reading -- 12 Band structure of solids -- 12.1 Electrons in the periodic lattice potential -- 12.1.1 k.p theory -- 12.1.2 Two-band approximation -- 12.2 Systems with reduced effective dimensionality -- 12.2.1 Quasi two-, one-, and zero-dimensional systems -- 12.2.2 Electron density of states -- Exercises -- Further reading -- 13 Interactions in semiconductors -- 13.1 Many-body Hamiltonian -- 13.2 Light-matter interaction -- 13.2.1 Separation of length scales -- 13.2.2 Light-matter-coupling integrals -- 13.2.3 Inner products within k · p theory -- 13.2.4 Light-matter interaction in k · p theory -- 13.3 Phonon-carrier interaction -- 13.4 Coulomb interaction -- 13.5 Complete system Hamiltonian in different dimensions.

13.5.1 Quantum-well system Hamiltonian -- 13.5.2 Quantum-wire system Hamiltonian -- 13.5.3 Quantum-dot system Hamiltonian -- Exercises -- Further reading -- 14 Generic quantum dynamics -- 14.1 Dynamics of elementary operators -- 14.1.1 Evaluation strategy -- 14.1.2 Quantum dynamics of free quasiparticles -- 14.1.3 Photon-operator dynamics -- 14.1.4 Macroscopic matter-response operators -- 14.1.5 Phonon and carrier dynamics -- 14.2 Formal properties of light -- 14.2.1 Quantized wave equation -- 14.2.2 Plasmon response -- 14.3 Formal properties of general operators -- 14.3.1 Operator hierarchy problem -- 14.3.2 BBGKY hierarchy problem -- Exercises -- Further reading -- 15 Cluster-expansion representation of the quantum dynamics -- 15.1 Singlet factorization -- 15.1.1 Expectation values of a Slater-determinant state -- 15.1.2 Hartree-Fock approximation and singlet factorization -- 15.2 Cluster expansion -- 15.2.1 Boson and Fermion factorizations -- 15.2.2 Most relevant singlet-doublet factorizations -- 15.3 Quantum dynamics of expectation values -- 15.4 Quantum dynamics of correlations -- 15.5 Scattering in terms of correlations -- Exercises -- Further reading -- 16 Simple many-body systems -- 16.1 Single pair state -- 16.1.1 Electron-hole system -- 16.1.2 Separation of relative and center-of-mass motion -- 16.2 Hydrogen-like eigenstates -- 16.2.1 Low-dimensional systems -- 16.2.2 Numerical solutions of bound and unbound states -- 16.3 Optical dipole -- 16.3.1 Momentum-matrix elements -- 16.3.2 Long-wave-length limit for the  · p̂ interaction -- Exercises -- Further reading -- 17 Hierarchy problem for dipole systems -- 17.1 Quantum dynamics in the  · p̂ picture -- 17.1.1 Lorentz force -- 17.1.2 Time scale for the center-of-mass motion -- 17.2 Light-matter coupling -- 17.3 Dipole emission -- 17.3.1 Dipole-emission dynamics.

17.3.2 Emission of planar dipoles -- 17.4 Quantum dynamics in the Ê · x̂ picture -- 17.4.1 Göppert-Mayer transformation -- 17.4.2 Dipole self-energy -- 17.4.3 System Hamiltonian -- 17.4.4 Quantum dynamics -- Exercises -- Further reading -- 18 Two-level approximation for optical transitions -- 18.1 Classical optics in atomic systems -- 18.1.1 Separation of relative and center-of-mass motion -- 18.1.2 Formal aspects of the optical excitation -- 18.1.3 Two-level approximation -- 18.1.4 Rotating-wave approximation (RWA) -- 18.2 Two-level system solutions -- 18.2.1 Analytic solution of the two-level system -- 18.2.2 Bloch-vector representation -- 18.2.3 Rabi oscillations -- 18.2.4 Pulse area and Rabi flopping -- 18.2.5 Square-pulse excitation -- Exercises -- Further reading -- 19 Self-consistent extension of the two-level approach -- 19.1 Spatial coupling between light and two-level system -- 19.1.1 Center-of-mass distribution in optical coupling -- 19.1.2 Optical Bloch equations -- 19.1.3 Angle parametrization of Bloch vector -- 19.2 Maxwell-optical Bloch equations -- 19.2.1 Radiative decay of the atomic dipole -- 19.2.2 Radiative decay of planar dipoles -- 19.3 Optical Bloch equations with radiative coupling -- Exercises -- Further reading -- 20 Dissipative extension of the two-level approach -- 20.1 Spin representation of optical excitations -- 20.2 Dynamics of Pauli spin matrices -- 20.3 Phenomenological dephasing -- 20.3.1 Dephasing-induced effects -- 20.3.2 Dephasing and radiative decay -- 20.4 Coupling between reservoir and two-level system -- 20.4.1 Master-equation description of dephasing -- 20.4.2 Master-equation for two-level system -- Exercises -- Further reading -- 21 Quantum-optical extension of the two-level approach -- 21.1 Quantum-optical system Hamiltonian -- 21.1.1 Reduction to two-level system -- 21.1.2 Rotating-wave approximation.

21.1.3 Operator dynamics.

Combining methods from quantum optics and solid-state physics to give researchers and graduate students a deeper understanding of the subject.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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