By Prof. Dr. Werner Vogel, Prof. Dr. Dirk?Gunnar Welsch(auth.)
This is often the 3rd, revised and prolonged variation of the
stated "Lectures on Quantum Optics" via W. Vogel and D.-G. Welsch. It deals theoretical recommendations of quantum optics, with detailed emphasis on present examine traits. A unified notion of measurement-based nonclassicality and entanglement standards and a unified method of medium-assisted electromagnetic vacuum results together with Van der Waals and Casimir Forces are the most new themes which are incorporated within the revised variation. The rigorous improvement of quantum optics within the context of quantum box concept and the eye to information makes the booklet helpful to graduate scholars in addition to to researchers.Content:
Chapter 1 advent (pages 1–13):
Chapter 2 parts of quantum electrodynamics (pages 15–72):
Chapter three Quantum states of bosonic structures (pages 73–112):
Chapter four Bosonic structures in section area (pages 113–134):
Chapter five Quantum thought of Damping (pages 135–172):
Chapter 6 Photoelectric Detection of sunshine (pages 173–235):
Chapter 7 Quantum?State Reconstruction (pages 237–264):
Chapter eight Nonclassicality and Entanglement of Bosonic platforms (pages 265–298):
Chapter nine Leaky Optical Cavities (pages 299–336):
Chapter 10 Medium?Assisted Electromagnetic Vacuum results (pages 337–366):
Chapter eleven Resonance Fluorescence (pages 367–406):
Chapter 12 A unmarried Atom in a High?Q hollow space (pages 407–441):
Chapter thirteen Laser?Driven Quantized movement of a Trapped Atom (pages 443–480):
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Additional resources for Quantum Optics, Third, revised and extended edition
Example text
Expanding in Eq. 61), respectively, after some lengthy but straightforward calculation we may express the Hamiltonian of the electromagnetic field in terms of the mode operators qˆλ and pˆ λ : Hˆ = 1 2 ∑( pˆ λ pˆ †λ + ωλ2 qˆλ qˆ†λ ). 66) λ As expected, Hˆ takes the familiar form of the Hamiltonian of an infinite set of uncoupled harmonic oscillators, whose excitation quanta of energy h¯ ωλ are called photons (of type λ). 68) are preferred to the (coordinate and momentum) operators qˆλ and pˆ λ . 68) reduce to the equations qˆλ = h¯ /(2ωλ ) ( aˆ λ + aˆ †λ ) and √ pˆ λ = i h¯ ωλ /2 ( aˆ †λ − aˆ λ ).
Note that the scalar potential VˆM (r) or, equivalently, Eˆ M (r) must also be thought of as being expressed in terms of the dynamical variables fˆ (r, ω ) and fˆ † (r, ω ). 213) with the (from the left) one-sided longitudinal Green tensor G in place of G. 3 The multipolar-coupling Hamiltonian In order to perform the transition from the minimal-coupling Hamiltonian to the multipolar-coupling Hamiltonian, we transform the variables by applicaˆ defined by Eq. 155). 227) are valid, and it is not difficult to prove that ˆ fˆ (r, ω )U ˆ† fˆ (r, ω ) = U i = fˆ (r, ω ) − h¯ h¯ ω πε 0 c2 Im ε(r, ω ) d3 r Pˆ A (r ) G ⊥∗ (r , r, ω ).
After some algebra we derive29 Hˆ = d3 r +∑ a + 1 ε0 ∞ 0 1 2m a dω h¯ ω fˆ † (r, ω )fˆ (r, ω ) pˆ a + Q a 1 0 ds s(rˆ a − r A ) × [∇ × A [r A + s(rˆ a − r A )]] ˆ ( r) + 1 d3 r Pˆ A (r)Π 2ε 0 2 ˆ d3 r Pˆ ⊥ A (r) + WCoul . 229) ˆ ˆ ˆ ˆ ˆ [Eq. 156)],30 W ˆ ˆ ˆ =A Note that A Coul = WCoul (VM = VM , PM = PM ) and ⊥ ˆ ˆ ˆ Π = Π − P A [Eq. 158)]. In particular for a neutral atom, we may write 29) Here the position r A of the (neutral) atomic system is again assumed to be a given parameter. For an extension of the multipolar-coupling scheme to moving systems where r A is also a dynamical variable (r A → rˆ A ), which plays the role of the center-of-mass coordinate, see Buhmann, Knöll, Welsch and Ho (2004).