Free Download Quantum Physics An Introduction Based on Photons by A. I. Lvovsky

Undergraduate Lecture Notes in Physics

Authors of: Quantum Physics An Introduction Based on Photons by A. I. Lvovsky

A. I. Lvovsky

Series Editors

Neil Ashby

William Brantley

Matthew Deady

Michael Fowler

Morten Hjorth-Jensen

Michael Inglis

Heinz Klose

Helmy Sherif

Table of Contents in Quantum Physics An Introduction Based on Photons by A. I. Lvovsky

1 The quantum postulates

1.1 The scope of quantum mechanics

1.2 The Hilbert Space Postulate

1.3 Polarization of the photon

1.4 Quantum measurements

1.4.1 The Measurement Postulate

1.4.2 Polarization measurements

1.5 Quantum interference and complementarity

1.6 Quantum cryptography

1.6.1 The BB84 protocol

1.6.2 Practical matters in quantum cryptography

1.7 Operators in quantum mechanics

1.8 Projection operators and unnormalized states

1.9 Quantum observables

1.9.1 Observable operators

1.9.2 Mean value and uncertainty of an observable

1.9.3 The uncertainty principle

1.10 Quantum evolution

1.11 Problems

2 Entanglement

2.1 Tensor product spaces

2.1.1 Tensor product states and entangled states

2.1.2 Measurements in tensor product spaces

2.1.3 Tensor products of operators

2.1.4 Local operators

2.2 Local measurements of entangled states

2.2.1 Remote state preparation

2.2.2 Partial inner product

2.2.3 Local measurements and causality

2.2.4 Mixed states

2.3 Quantum nonlocality

2.3.1 Einstein–Podolsky–Rosen paradox

2.3.2 The Bell inequality

2.3.3 Violation of the Bell inequality

2.3.4 Greenberger–Horne–Zeilinger (GHZ) nonlocality

2.4 An insight into quantum measurements

2.4.1 Von Neumann measurements

2.4.2 Decoherence

2.4.3 Interpretations of quantum mechanics

2.4.4 The superposition tree

2.5 Quantum computation

2.6 Quantum teleportation and its applications

2.6.1 Quantum teleportation

2.6.2 Quantum repeater

2.7 Problems

3 One-dimensional motion

3.1 Continuous observables

3.2 De Broglie wave

3.3 Position and momentum bases

3.3.1 Conversion between position and momentum bases

3.3.2 Position–momentum uncertainty

3.3.3 The original Einstein–Podolsky–Rosen paradox

3.4 The free space potential

3.5 Time-independent Schr¨odinger equation

3.6 Bound states

3.7 Unbound states

3.7.1 The single-step potential

3.7.2 Quantum tunnelling

3.8 Harmonic oscillator

3.8.1 Annihilation and creation operators

3.8.2 Fock states

3.8.3 Coherent states

3.9 Heisenberg picture

3.9.1 Operator evolution

3.9.2 Displacement operator

3.9.3 Evolution of probability densities

3.10 Transformations of harmonic oscillator states

3.10.1 Coherent state as displaced vacuum

3.10.2 Phase shift

3.10.3 Squeezing

3.11 Problems

4 Angular momentum

4.1 3D motion

4.2 Rotationally symmetric potential

4.2.1 Spherical coordinates

4.2.2 Angular momentum

4.3 Angular momentum eigenstates

4.3.1 Matrix representation of the angular momentum

4.3.2 Wavefunctions of angular momentum eigenstates

4.3.3 Spin

4.4 The hydrogen atom

4.4.1 Radial wavefunctions

4.4.2 Energy spectrum and transitions

4.4.3 The periodic table

4.5 The Bloch sphere

4.6 Magnetic moment and magnetic field

4.6.1 Angular momentum and magnetic moment

4.6.2 Stern–Gerlach apparatus

4.6.3 Evolution of magnetic states

4.7 Magnetic resonance

4.7.1 Rotating basis

4.7.2 Evolution under the rotating-wave approximation

4.7.3 Pulse area

4.7.4 Applications of magnetic resonance

4.8 Problems

5 Quantum physics of complex systems

5.1 The density operator

5.2 Trace

5.3 Partial trace

5.4 Density matrix and Bloch vector

5.5 Density matrix and magnetic resonance

5.6 Generalized measurements

5.7 Quantum tomography

5.8 Problems

A Linear algebra basics

B Probabilities and distributions

C Optical polarization tutorial

D Dirac delta function and the Fourier transformation

Index

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