Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Often, the theoretical treatments are accompanied by the corresponding experiments. An exhaustive list of references provides a guide to the literature. Quantum Optics in Phase Space also serves advanced researchers as a comprehensive reference book.
Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect.
Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields.
Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.
- Träger des Max-Planck-Forschungspreises 2002
Autorentext
- Recipient of the Max Planck Research Award 2002
Leseprobe
1
What's Quantum Optics?
What is quantum optics? This is a rather personal question. A well-known scientist in this field once gave the following authoritative answer: "Whatever I do defines quantum optics!" On a more objective basis one is tempted to define this branch of physics by the pun: "Quantum optics is that branch of optics where the quantum features of light matter."
Which discovery in physics marks the birthday of quantum optics? Many phenomena come to our mind. Is it the discovery of the quantum, the development of QED, or the maser/laser? Or is it none of the above?
In this chapter we answer this question in a back handed way by summarizing some path breaking experiments that define quantum optics. Admittedly this list is not complete and chosen in a rather subjective way. The rapidly moving field of quantum optics demonstrates most clearly that even after 100 years of quantum physics there is still a lot to be learned from Planck's original discovery.
1.1 On the Road to Quantum Optics
More than hundred years ago M. Planck was struggling with the experimental data of black body radiation obtained at the Physikalisch-Technische Reichsanstalt in Berlin by H. Rubens and F. Kurlbaum. From todays point of view these experiments look rather academic. However, they were motivated by industrial applications. Indeed, standards had to be developed in order to describe light bulbs. This need triggered one of the most important problems in the physics of the 20 th century: Classical electromagnetic theory cannot explain the measured black body spectrum. In a desperate but courageous attempt Planck postulated that the oscillators in the walls of the cavity can only absorb and emit radiation in discrete units. This revolutionary idea of discreteness rather than a continuum provided the celebrated radiation formula and was the starting point of quantum mechanics.
Nowadays we associate the quantization with the field rather than with the mechanical oscillators in the wall. However, wave and matrix mechanics were first developed for massive particles and then, later, transferred to the electromagnetic field leading to quantized electrodynamics.
The field of quantum electrodynamics, QED, which deals with the interaction of quantized matter with quantized electromagnetic fields started with P.A.M. Dirac. He was the first to derive the Einstein A and B coefficients of spontaneous and induced emission. The field of QED culminated on the one hand with the experimental discovery of the level shift in the hydrogen atom by W.E. Lamb and R.C. Retherford and the measurement of the anomalous moment of the electron by H.M. Foley and P. Kusch. On the other hand the theoretical works of S. Tomonaga, J. Schwinger and R. Feynman showed how to avoid the infinities that had plagued the theory since the thirties. The incredible agreement between theory and experiment established nowadays in many QED systems confirms beyond any doubt the quantized nature of light.
The development of the ammonium maser by C.H. Townes, J. Gordon and H. Zeiger, and the laser by T. Maiman following the paper Optical Masers by A. Schawlow and Townes has opened the new field of quantum electronics. Motivated by the experiments on the maser and building on his own theoretical work on water-vapor absorption W.E. Lamb developed a theory of the maser during the years 1954-1956. Later he worked out a complete semi-classical theory of laser action. Independently the group of H. Haken in Stuttgart developed their own approach. In the semiclassical treatment of Lamb and Haken the electromagnetic field was described classically and the atom quantum mechanically.
Since then laser theory has come a long way from the early approaches using birth and death equations via the semiclassical theory of the laser to the fully quantized version. T
Inhalt
What is Quantum Optics?
Ante
The Wigner Function
Quantum States in Phase Space
Waves a la WKB
WKB Wave Functions and Berry's Phase
Interference in Phase Space
Applications of Interference in Phase Space
Wave Packet Dynamics
Quantization of the Radiation Field
Quantum States of the Radiation Field
Phase Space Functions
Optical Interferometry
Atom-Field Interaction
Dynamics of Jaynes-Cummings-Paul Model
State Preparation and Entanglement
The Paul Trap
Damping and Amplification
Atom Optics in Quantized Light Fields
Wigner Functions in Atom Optics
Appendix
Time Dependent Operators -
Derivation of Equations Determining the Moyal Function -
Energy Wave Functions of Harmonic Oscillator -
Method of Stationary Phase -
Radial Equation -
Airy Function -
Asymptotic Expansion of the Poisson Distribution -
Area of Overlap -
P-Distributions -
Homodyne Detection Kernel -
Effective Hamiltonian -
Spontaneous Emission -
A Model for the Square Root of a Delta Function -
Bessel …
Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect.
Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields.
Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.
- Träger des Max-Planck-Forschungspreises 2002
Dieses Lehrbuch behandelt moderne Entwicklungen der Quantenoptik aus dem Blickwinkel des Phasenraums. Dazu werden konkrete Bilder von Quantenzuständen in Form von Phasenraumverteilungen wie z.B. der Wignerfunktion vermittelt. Diese Bilder machen es leicht, die Dynamik von Wellenpaketen in Atomen und Molekülen zu verstehen. Insbesondere vereinfachen sie sich im semi-klassischen Grenzfall.
Eine geschlossene Darstellung, detailliert abgeleitete Ergebnisse und eine große Auswahl an Übungsaufgaben charakterisieren dieses Buch, das nur elementare Kenntnisse der Quantenmechanik und Elektrodynamik voraussetzt. Eine Vielzahl kommentierter Literaturhinweise erlauben einen schnellen Einstieg in die aktuelle Forschung.
Autorentext
- Recipient of the Max Planck Research Award 2002
Leseprobe
1
What's Quantum Optics?
What is quantum optics? This is a rather personal question. A well-known scientist in this field once gave the following authoritative answer: "Whatever I do defines quantum optics!" On a more objective basis one is tempted to define this branch of physics by the pun: "Quantum optics is that branch of optics where the quantum features of light matter."
Which discovery in physics marks the birthday of quantum optics? Many phenomena come to our mind. Is it the discovery of the quantum, the development of QED, or the maser/laser? Or is it none of the above?
In this chapter we answer this question in a back handed way by summarizing some path breaking experiments that define quantum optics. Admittedly this list is not complete and chosen in a rather subjective way. The rapidly moving field of quantum optics demonstrates most clearly that even after 100 years of quantum physics there is still a lot to be learned from Planck's original discovery.
1.1 On the Road to Quantum Optics
More than hundred years ago M. Planck was struggling with the experimental data of black body radiation obtained at the Physikalisch-Technische Reichsanstalt in Berlin by H. Rubens and F. Kurlbaum. From todays point of view these experiments look rather academic. However, they were motivated by industrial applications. Indeed, standards had to be developed in order to describe light bulbs. This need triggered one of the most important problems in the physics of the 20 th century: Classical electromagnetic theory cannot explain the measured black body spectrum. In a desperate but courageous attempt Planck postulated that the oscillators in the walls of the cavity can only absorb and emit radiation in discrete units. This revolutionary idea of discreteness rather than a continuum provided the celebrated radiation formula and was the starting point of quantum mechanics.
Nowadays we associate the quantization with the field rather than with the mechanical oscillators in the wall. However, wave and matrix mechanics were first developed for massive particles and then, later, transferred to the electromagnetic field leading to quantized electrodynamics.
The field of quantum electrodynamics, QED, which deals with the interaction of quantized matter with quantized electromagnetic fields started with P.A.M. Dirac. He was the first to derive the Einstein A and B coefficients of spontaneous and induced emission. The field of QED culminated on the one hand with the experimental discovery of the level shift in the hydrogen atom by W.E. Lamb and R.C. Retherford and the measurement of the anomalous moment of the electron by H.M. Foley and P. Kusch. On the other hand the theoretical works of S. Tomonaga, J. Schwinger and R. Feynman showed how to avoid the infinities that had plagued the theory since the thirties. The incredible agreement between theory and experiment established nowadays in many QED systems confirms beyond any doubt the quantized nature of light.
The development of the ammonium maser by C.H. Townes, J. Gordon and H. Zeiger, and the laser by T. Maiman following the paper Optical Masers by A. Schawlow and Townes has opened the new field of quantum electronics. Motivated by the experiments on the maser and building on his own theoretical work on water-vapor absorption W.E. Lamb developed a theory of the maser during the years 1954-1956. Later he worked out a complete semi-classical theory of laser action. Independently the group of H. Haken in Stuttgart developed their own approach. In the semiclassical treatment of Lamb and Haken the electromagnetic field was described classically and the atom quantum mechanically.
Since then laser theory has come a long way from the early approaches using birth and death equations via the semiclassical theory of the laser to the fully quantized version. T
Inhalt
What is Quantum Optics?
Ante
The Wigner Function
Quantum States in Phase Space
Waves a la WKB
WKB Wave Functions and Berry's Phase
Interference in Phase Space
Applications of Interference in Phase Space
Wave Packet Dynamics
Quantization of the Radiation Field
Quantum States of the Radiation Field
Phase Space Functions
Optical Interferometry
Atom-Field Interaction
Dynamics of Jaynes-Cummings-Paul Model
State Preparation and Entanglement
The Paul Trap
Damping and Amplification
Atom Optics in Quantized Light Fields
Wigner Functions in Atom Optics
Appendix
Time Dependent Operators -
Derivation of Equations Determining the Moyal Function -
Energy Wave Functions of Harmonic Oscillator -
Method of Stationary Phase -
Radial Equation -
Airy Function -
Asymptotic Expansion of the Poisson Distribution -
Area of Overlap -
P-Distributions -
Homodyne Detection Kernel -
Effective Hamiltonian -
Spontaneous Emission -
A Model for the Square Root of a Delta Function -
Bessel …
Titel
Quantum Optics in Phase Space
Untertitel
Unterstützte Lesegerätegruppen: PC/MAC/eReader/Tablet
Autor
EAN
9783527802555
ISBN
978-3-527-80255-5
Format
E-Book (epub)
Hersteller
Herausgeber
Veröffentlichung
11.12.2015
Digitaler Kopierschutz
Adobe-DRM
Dateigrösse
31.8 MB
Anzahl Seiten
716
Jahr
2015
Untertitel
Englisch
Unerwartete Verzögerung
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