Heisenberg treatment of spontaneous emission

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Table of contents

I Introduction 
II Quantum control with trapped ions and optical cavities 
1 Trapped ions controlled by lasers and quantum information
1.1 Quantum Information in the adiabatic limit
1.1.1 Basic notions of quantum computing
1.1.2 Adiabatic theorem
1.1.3 Stimulated Raman adiabatic passage (STIRAP)
1.2 Ion trap as a model for quantum information
1.2.1 Linear Paul trap – trapping of a single ion
1.2.2 Quantization of the vibrational modes
1.2.3 Manipulating ions by laser – Lamb-Dicke regime
1.3 Building arbitrary gates by adiabatic passage
1.3.1 Householder reflections by adiabatic passage
1.3.2 Quantum Fourier transform on a quartit and energy study
1.A Derivation of the Householder reflection for a qubit
2 Quantum optics with atoms in cavities
2.1 Model for cavity quantum electrodynamics (cQED) with imperfect mirrors
2.1.1 Quantization of the electromagnetic field
2.1.2 The one-dimensional cavity field
2.1.3 Three-level atoms in a cavity
2.1.4 Cavity input-output relation and photon flux
2.1.5 Heisenberg treatment of spontaneous emission
2.1.6 Master equation
2.2 An alternative derivation of the cQED effective model
2.2.1 Atom-field interaction
2.2.2 Mode-selective quantum dynamics and effective Hamiltonian
2.3 Production of photon states with atoms in a cavity
2.3.1 Single photons with one atom in a cavity
2.3.2 Single and two-photon states with two atoms in a cavity
2.3.3 Characterization of the outgoing two-photon state
2.A Canonical quantization of the electromagnetic field in a dielectric medium
2.B Lorentzian structure of the cavity spectral response function
2.C Complex plane integration of the atom-field coupling
2.D Numerical solution of _~X (t) = M(t)~X (t) + ~Y (t)
III Quantum control of emitters coupled to plasmons 91
3 Mode-selective quantization procedure in a spherically layered medium
3.1 Light-emitter interactions and quantum plasmonics
3.1.1 Nano-optics and plasmonics
3.1.2 Nano-emitters near plasmonic structures
3.1.3 Localized plasmons and nanoparticles
3.2 Mode expansion in a spherically layered medium
3.2.1 Spherical vector harmonics and orthogonality relations
3.2.2 Green’s tensor expansion
3.3 Mode-selective quantization
3.3.1 Field quantization
3.3.2 Addressing harmonic excitations
3.3.3 Spherical mode-structured field and quantum emitters
3.A Green’s tensor in a spherically layered medium
4 Effective models for quantum plasmonics
4.1 Continuous model with multiple emitters
4.1.1 Single emitter – dark and bright operators
4.1.2 Multiple two-level emitters
4.2 Discrete model
4.2.1 Single emitter
4.2.2 Multiple emitters
4.3 Application: two emitters and a single metallic nanoparticle
4.3.1 Continuous model
4.3.2 Discrete effective model
4.A Single Lorentzian model – continuous and discrete Hamiltonian
4.A.1 Discretization
4.A.2 Dynamics
5 Quantum plasmonics with metallic nanoparticles 132
5.1 Quantum emitter coupled to a metallic nanoparticle
5.1.1 Local density of states
5.1.2 Dynamics and strong coupling regime
5.2 Adiabatic passage mediated by plasmons
5.2.1 Population transfer: STIRAP
5.2.2 Entanglement: fractional STIRAP
5.2.3 Simplified model and discussion
5.2.4 General model and perspectives
IV Conclusion