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IMPERIAL COLLEGE PRESS eBooks

The physics of quantum-optical devices

Crispin W. Gardiner, P. Zoller

Published Jan 1, 2015• 0 citations
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Abstract

Principles of Quantum Devices: A Quantum-Optical Perspective on Quantum Science and Technology From Atoms to Qubits Quantum Information Coherent Optical Manipulation of Atoms: The Two-Level System Approximation Coherent Manipulation of Two-Level Systems Coherent Manipulation of Multilevel Systems The Two-Level System Including Atomic Motion Modelling Real Atoms Atoms and Quantized Optical Fields: The Quantum Stochastic Schrodinger Equation The Master Equation Inputs, Outputs, and Quantum Langevin Equations Cascaded Quantum Systems Dissipative Dynamics of Driven Systems Dissipative Dynamics of Driven Atoms Multi-Atom Optical Bloch Equations Laser Cooling: Quantum Stochastic Equations for Laser Cooling of Atoms Laser Cooling of Untrapped Atoms Laser Cooling of a Trapped Ion Continuous Measurement and Quantum Trajectories: Continuous Measurement Quantum Trajectories Homodyne Measurement Squeezing and Quantum Correlations Two-Level Systems, Photons and Phonons: Cavity Quantum Electrodynamics Optical Manipulation of Trapped Ions The Ion Trap Quantum Computer Superconductors: Quantum Circuit Theory Superconducting Quantum Devices Quantum Networks: Cavity Quantum Electrodynamics Networks The Dark-State Ensemble Quantum Memory Spatially Extended Atomic Ensembles

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Principles of Quantum Devices: A Quantum-Optical Perspective on Quantum Science and Technology From Atoms to Qubits Quantum Information Coherent Optical Manipulation of Atoms: The Two-Level System Approximation Coherent Manipulation of Two-Level Systems Coherent Manipulation of Multilevel Systems The Two-Level System Including Atomic Motion Modelling Real Atoms Atoms and Quantized Optical Fields: The Quantum Stochastic Schrodinger Equation The Master Equation Inputs, Outputs, and Quantum Langevin Equations Cascaded Quantum Systems Dissipative Dynamics of Driven Systems Dissipative Dynamics of Driven Atoms Multi-Atom Optical Bloch Equations Laser Cooling: Quantum Stochastic Equations for Laser Cooling of Atoms Laser Cooling of Untrapped Atoms Laser Cooling of a Trapped Ion Continuous Measurement and Quantum Trajectories: Continuous Measurement Quantum Trajectories Homodyne Measurement Squeezing and Quantum Correlations Two-Level Systems, Photons and Phonons: Cavity Quantum Electrodynamics Optical Manipulation of Trapped Ions The Ion Trap Quantum Computer Superconductors: Quantum Circuit Theory Superconducting Quantum Devices Quantum Networks: Cavity Quantum Electrodynamics Networks The Dark-State Ensemble Quantum Memory Spatially Extended Atomic Ensembles
This century has seen the development of technologies for manipulating and controlling matter and light at the level of individual photons and atoms, a realm in which physics is fully quantum-mechanical. The dominant experimental technology is the laser, and the theoretical paradigm is quantum optics. The Quantum World of Ultra-Cold Atoms and Light is a trilogy, which presents the quantum optics way of thinking and its applications to quantum devices. This book The Physics of Quantum-Optical Devices provides a comprehensive treatment of theoretical quantum optics. It covers applications to the optical manipulation of the quantum states of atoms, laser cooling, continuous measurement, quantum computers and quantum processors, superconducting systems and quantum networks. The subject is consistently formulated in terms of quantum stochastic techniques, and a systematic and thorough development of these techniques is a central part of the book. There is also a compact overview of the ideas of quantum information theory. The main aim of the book is to present the theoretical techniques necessary for the understanding of quantum optical devices, with special attention to those devices used in quantum information processing and quantum simulation. Although these techniques were developed originally for the optical regime, they are also applicable to electromagnetic radiation from the microwave realm to the ultra-violet, and for atomic systems, Josephson junction systems, quantum dots and nano-mechanical systems.
Preface FOUNDATIONS OF QUANTUM INFORMATICS Spins: The Stern-Gerlach experiment and spin filter EPR, Bell's inequalities, and hidden variables The Landauer principle QUANTUM COMPUTATION AND QUANTUM SYSTEMS Turing machines and binary logic gates Quantum mechanical systems Hilbert spaces Complex finite dimensional Hilbert Spaces Quantum Turing machines Universality of elementary quantum gates Quantum algorithms Quantum adder and multiplier Quantum error correction codes Lasers: a heuristic introduction Quantum computing devices and requirements TWO-LEVEL ATOMS AND CAVITY QED Two-level atoms Quantization of the electromagnetic field Cavity QED Cavity QED for the quantum phase gate Quantum eraser Quantum disentanglement eraser IMPERFECT QUANTUM OPERATIONS Fidelity Density matrices Time evolution of density matrices Examples of master equations Fidelity calculations ION TRAPS Introduction Ion qubits Summary of ion preparation Coherence Quantum gates Large scale confined-ion quantum computer Trap architecture and performance Teleportation of coherent information Experimental DFS logic gates Quantum error correction by ion traps Summary of ion quantum computation QUANTUM LOGIC USING COLD, CONFINED ATOMS Introduction Atom trapping and detection Atom interactions with external fields Atom trapping Qubits and gates Controlled two-qubit gates Coherence properties of atom gates Assessment QUANTUM DOTS QUANTUM COMPUTING GATES Introduction Electrons in quantum dots microcavity Coupled electron spins Biexciton in a single quantum dot Conclusions LINEAR OPTICS COMPUTERS Classical electrodynamics - Classical computers Quantum electrodynamics - Quantum computers Teleportation Summary and outlook SUPERCONDUCTING QUANTUM COMPUTING DEVICES Introduction Superconductivity More on Cooper pairs and Josephson junctions Superconducting circuits: classical Superconducting circuits: quantum Quantum gates Measurement NMR QUANTUM COMPUTING Nuclear magnetic resonance Basic technology with NMR Solid state NMR Shor's algorithm and its experimental realization Quantum algorithm for lattice-gas systems Conclusion Appendix A: The Fock-Darwin States Appendix B: Evaluation of the exchange energy Appendix C: Transformation of quantum states: SU(2) and SO(3) Appendix D: The Homeomorphism from SU(2) to SO(3)
Theory of the interaction between atom and radiation field: three pictures in quantum mechanics description two-level atom and the optical Bloch equation quantized description of the radiation field Dicke Hamiltonian and Jaynes - Cummings model quantum theory of a small system coupling to a reservoir. The quantum properties of light: coherence of light squeezed states of light resonance fluorescence superfluorescence optical bistability effects of virtual photon processes. Quantum properties of the atomic behaviour under the interaction of the radiation field: collapses and revivals of the atomic populations squeezing effects of the atomic operators coherent trapping of the atomic population quantum characteristics of a two-atom system under the interaction of radiation field autoionization of the atom in a laser field motion of the atom in a laser field laser cooling.
Preface. 1. Atomic motion in laser light (C. Cohen-Tannoudji). 2. Laser cooling, optical traps and optical molasses (W.D. Phillips). 3. Phase transitions of stored laser-cooled ions (H. Walther). 4. Laser cooling of trapped ions (R. Blatt). 5. Propagation of laser beams and of atomic systems (Ch. J. Borde). 6. Chaos in atomic systems (D. Delande). 7. Experimental studies of chaos in an atomic system (D. Kleppner). 8. Atomic physics tests of the electroweak theory: parity violation experiments (Ph. Jacquier). 9. Atomic hydrogen and liquid helium surfaces (J.T.M. Walraven). 10. Quantum fluctuations in quantum optics squeezing and related phenomena (H.J. Kimble). 11. Quantum noise in optical systems: a semi classical approach (C. Fabre and S. Reynaud). 12. More on interference in phase space (K. Vogel and W. Schleich). 13. Cavity quantum electrodynamics (S. Haroche). 14. Multistability, chaos and spatio-temporal dynamics (L.A. Lugiato and L.M. Narducci). 15. Surface nonlinear optics and applications (Y.R. Shen).
A Monte Carlo simulation of the atomic master equation for spontaneous emission in terms of atomic wave functions is developed. Realizations of the time evolution of atomic wave functions are constructed that correspond to an ensemble of atoms driven by laser light undergoing a sequence of spontaneous emissions. The atomic decay times are drawn according to the photon count distribution of the driven atom. Each quantum jump of the atomic electron projects the atomic wave function to the ground state of the atom. Our theory is based on a stochastic interpretation and generalization of Mollow's pure-state analysis of resonant light scattering, and the Srinivas-Davies theory of continuous measurements in photodetection. An extension of the theory to include mechanical light effects and a generalization to atomic systems with Zeeman substructure are given. We illustrate the method by simulating the solutions of the optical Bloch equations for two-level systems, and laser cooling of a two-level atom in an ion trap where the center-of-mass motion of the atom is described quantum mechanically.
The Dicke model describes the coherent interaction of a laser-driven ensemble of two-level atoms with a quantized light field. It is realized within cavity QED experiments, which in addition to the coherent Dicke dynamics feature dissipation due to, e.g., atomic spontaneous emission and cavity photon loss. Spontaneous emission supports the uncorrelated decay of individual atomic excitations as well as the enhanced collective decay of an excitation that is shared by NNN atoms and whose strength is determined by the cavity geometry. We derive a many-body master equation for the dissipative Dicke model including both spontaneous emission channels and analyze its dynamics on the basis of Heisenberg-Langevin and stochastic Bloch equations. We find that the collective loss channel leads to a region of bistability between the empty and the superradiant state. Transitions between these states are driven by nonthermal Markovian noise. The interplay between dissipative and coherent elements leads to a genuine nonequilibrium dynamics in the bistable regime, which is expressed via a nonconservative force and a multiplicative noise kernel appearing in the stochastic Bloch equations. We present a semiclassical approach, based on stochastic nonlinear optical Bloch equations, which for the infinite-range Dicke model become exact in the large-NNN-limit. The absence of an effective free-energy functional, however, necessitates the inclusion of fluctuation corrections with O(1/N)O(1/N)O(1/N) for finite $N<\ensuremath{\infty}$ to locate the nonthermal first-order phase transition between the superradiant and the empty cavity.