Quantum Optics for Experimentalists

Zheyu Jeff Ou

• Editorial: WSPC
• Año: 2017
• ISBN:
  9789813220225
• Categoría: Physical Sciences
• Categoría: Mathematical & Computational Physics

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This book on quantum optics is from the point of view of an experimentalist. It approaches the theory of quantum optics with the language of optical modes of classical wave theory, with which experimentalists are most familiar. This approach makes the transition easy from classical optics to quantum optics. The emphasis on the multimode description of an optical system is more realistic than in most quantum optics textbooks. After the theoretical part, the book goes directly to the two most basic experimental techniques in quantum optics and establishes the connection between the experiments and the theory. The applications include some key quantum optics experiments, and a few more current interests that deal with quantum correlation and entanglement, quantum noise in phase measurement and amplification, and quantum state measurement.

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--> Contents:

• Theoretical Foundations of Quantum Optics:
  • Historical Development of Quantum Optics and A Brief Introduction
  • Mode Theory of Optical Fields and Their Quantization
  • Quantum States of Single-Mode Fields
  • Quantum States of Multi-Mode Fields
  • Theory of Photo-detection and Quantum Theory of Coherence
  • Generation and Transformation of Quantum States
• Experimental Techniques in Quantum Optics and Their Applications:
  • Experimental Techniques of Quantum Optics I: Photon Counting Technique
  • Applications of Photon Counting Techniques: Multi-Photon Interference and Entanglement
  • Experimental Techniques of Quantum Optics II: Detection of Continuous Photo-Currents
  • Applications of Homodyne Detection Technique: Quantum Measurement of Continuous Variables
  • Quantum Noise in Phase Measurement
• Appendices:
  • Derivation of an Explicit Expression for Û of a Lossless Beam Splitter
  • Evaluation of the Two Sums in Eq. (8.100)

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--> Readership: Advanced undergraduates, graduate students and researchers in quantum optics. -->
Quantum Optics;Optical Fields;Quantum States;Photo-Currents;Quantum Theory of Coherence;Entangled States;Phase Measurement0

PART 1

Theoretical Foundations of Quantum Optics

Chapter 1

Historical Development of Quantum Optics and A Brief Introduction

1.1Historical Background

Light is the most commonly seen matter in the universe, it is also the simplest system in the universe. That is why understanding the behavior of light has played a pivotal role in the development of physics. Many ground breaking concepts in physics originated from optics. For example, Fermat’s least action principle was first developed in optics: light propagates between two points in a medium in the shortest time. Then it was extended to other physical systems. The first conceptual revolution in quantum mechanics stemmed from the study of blackbody radiation. Quantum information is the current hot topic in research, yet many of the protocols of quantum information were first realized in optical systems. The reason for all this is straightforward: the simplicity of optical systems makes them easier than others to implement otherwise complicated models in physics. So, understanding of light will help us study other physical systems. Quantum optics is the most complete theory of light. It can explain all the optical phenomena observed so far.

The development of classical optics has a history of a few hundred years. Its highest form is Maxwell’s electromagnetic theory of light. Although quantum optics was only developed in recent decades, its origin can be traced back to the start of quantum mechanics. Planck’s quantum theory of blackbody radiation [Planck (1900)] is about energy quantization in the atomic emission and absorption of light. It was assumed that the energy of atomic emission or absorption of light can only be integer multiples of some small quantity

. Then Einstein in 1905 introduced the concept of light quanta for the explanation of the photo-electric effect [Einstein (1905)]. This concept is about quantization of the optical fields and is totally independent of atoms. Therefore, it was generally believed that the blackbody radiation theory of Planck in 1900 was the start of the quantum theory whereas the concept of photon was born in 1905 for the start of quantum optics.

It is worth noting that after the introduction of photon, Einstein in 1909 studied the energy fluctuations in blackbody radiation and proposed for the first time the duality of wave and particle for light [Einstein (1909)]. This result is earlier than the duality theory of matter waves by de Broglie. Starting from Planck’s blackbody radiation energy spectrum formula, Einstein applied the general argument of thermodynamics to arrive at the following formula for the energy fluctuations:

where A is the average value of quantity A. hν is the energy of a photon and Z is some function related to frequency ν and thermal energy kT. In discussing the physical meaning of Eq. (1.1), Einstein first assumed that the field of blackbody radiation consists of independent particles as photons and obtained from the Poisson statistics of random particles the fluctuation of particle number N as:

. Then using the famous formula for energy quanta from his paper on photoelectric effect:

= hν and total energy formula E = N

, he obtained

, the first term in Eq. (1.1). For the second term, Einstein assumed that the field of blackbody radiation consi...