Book contents
- Frontmatter
- Contents
- Dedication
- Preface
- 1 Quantum theory of radiation
- 2 Coherent and squeezed states of the radiation field
- 3 Quantum distribution theory and partially coherent radiation
- 4 Field–field and photon–photon interferometry
- 5 Atom–field interaction – semiclassical theory
- 6 Atom–field interaction – quantum theory
- 7 Lasing without inversion and other effects of atomic coherence and interference
- 8 Quantum theory of damping – density operator and wave function approach
- 9 Quantum theory of damping – Heisenberg–Langevin approach
- 10 Resonance fluorescence
- 11 Quantum theory of the laser – density operator approach
- 12 Quantum theory of the laser – Heisenberg–Langevin approach
- 13 Theory of the micromaser
- 14 Correlated emission laser: concept, theory, and analysis
- 15 Phase sensitivity in quantum optical systems: applications
- 16 Squeezing via nonlinear optical processes
- 17 Atom optics
- 18 The EPR paradox, hidden variables, and Bell's theorem
- 19 Quantum nondemolition measurements
- 20 Quantum optical tests of complementarity
- 21 Two-photon interferometry, the quantum measurement problem, and more
- Index
2 - Coherent and squeezed states of the radiation field
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Dedication
- Preface
- 1 Quantum theory of radiation
- 2 Coherent and squeezed states of the radiation field
- 3 Quantum distribution theory and partially coherent radiation
- 4 Field–field and photon–photon interferometry
- 5 Atom–field interaction – semiclassical theory
- 6 Atom–field interaction – quantum theory
- 7 Lasing without inversion and other effects of atomic coherence and interference
- 8 Quantum theory of damping – density operator and wave function approach
- 9 Quantum theory of damping – Heisenberg–Langevin approach
- 10 Resonance fluorescence
- 11 Quantum theory of the laser – density operator approach
- 12 Quantum theory of the laser – Heisenberg–Langevin approach
- 13 Theory of the micromaser
- 14 Correlated emission laser: concept, theory, and analysis
- 15 Phase sensitivity in quantum optical systems: applications
- 16 Squeezing via nonlinear optical processes
- 17 Atom optics
- 18 The EPR paradox, hidden variables, and Bell's theorem
- 19 Quantum nondemolition measurements
- 20 Quantum optical tests of complementarity
- 21 Two-photon interferometry, the quantum measurement problem, and more
- Index
Summary
Following the development of the quantum theory of radiation and with the advent of the laser, the states of the field that most nearly describe a classical electromagnetic field were widely studied. In order to realize such ‘classical’ states, we will consider the field generated by a classical monochromatic current, and find that the quantum state thus generated has many interesting properties and deserves to be called a coherent state. An important consequence of the quantization of the radiation field is the associated uncertainty relation for the conjugate field variables. It therefore appears reasonable to propose that the wave function which corresponds most closely to the classical field must have minimum uncertainty for all times subject to the appropriate simple harmonic potential.
In this chapter we show that a displaced simple harmonic oscillator ground state wave function satisfies this property and the wave packet oscillates sinusoidally in the oscillator potential without changing shape as shown in Fig. 2.1. This coherent wave packet always has minimum uncertainty, and resembles the classical field as nearly as quantum mechanics permits. The corresponding state vector is the coherent state |α〉, which is the eigenstate of the positive frequency part of the electric field operator, or, equivalently, the eigenstate of the destruction operator of the field.
Classically an electromagnetic field consists of waves with welldefined amplitude and phase. Such is not the case when we treat the field quantum mechanically.
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- Information
- Quantum Optics , pp. 46 - 71Publisher: Cambridge University PressPrint publication year: 1997
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