From Nonlinear Optics to Entanglement and Squeezing (PW)5 ECTS
(englische Bezeichnung: From Nonlinear Optics to Entanglement and Squeezing)
(Prüfungsordnungsmodul: Physics elective courses)

Lectures:

• • From Nonlinear Optics to Entanglement and Squeezing
    (Vorlesung, 2 SWS, Maria Chekhova, Wed, 15:30 - 17:00, SR 01.779)
  • From Nonlinear Optics to Entanglement and Squeezing (Exercise class)
    (Übung, 3 SWS, Maria Chekhova, Wed, 13:00 - 14:30, SR 01.566)

Inhalt:

Contents
The course will start from the consideration of nonlinear optical interactions (second and third harmonic generation, parametric down-conversion, four-wave mixing). Using field quantization, we will derive the Hamiltonians. We will then show how these Hamiltonians create, in the case of parametric down-conversion and four-wave mixing, quantum states. The second half of the course will be dedicated to the instruments for witnessing quantum behavior, from photon counting to homodyne detection. In a separate lecture, various typical quantum features will be considered: entanglement, anti-bunching, Sub-Poissonian statistics, squeezing. The course will have a strong experimental focus: on each subject, some experiments will be described.

There will be 10 lectures, 5 problem class sessions, and 1 lab tour.

• Lecture 1. Introduction: the motivation for this course. Brief history of nonlinear optics, and of quantum optics. Quantum optics without nonlinear optics: atoms and solid-state emitters. How the two subjects merged together.

• Lecture 2. Nonlinear interactions: harmonic generation, sum frequency generation, frequency up-conversion, parametric down-conversion, four-wave mixing and modulation instability. Efficiencies, phase matching conditions. Non-phase-matched processes.

• Lecture 3. From the energy of nonlinear interaction to Hamiltonians: parametric down-conversion, four-wave mixing/modulation instability.

• Lecture 4. From the Hamiltonian to a quantum state, at low and high efficiency of interaction.

• Lecture 5. Instruments of quantum optics: Glauber’s correlation functions, HBT experiment. Wigner function, quadratures, homodyne detection.

• Lecture 6. Nonclassicality: strict definition, experimental witnessing (anti-bunching and generalized versions, photon-number probability distribution, Cauchy-Schwarz inequality, sub-shot-noise statistics, Wigner function negativity).

• Lecture 7. Photon correlations obtained from nonlinear optical effects. Characterization with Glauber’s correlation functions. Calculation and experiments. Two-photon amplitude, methods of measurement.

• Lecture 8. Squeezing obtained from nonlinear optical effects. Squeezing as it follows from the Hamiltonian. Obtaining squeezed vacuum and squeezed coherent light. Review of experiments. Passing from quadrature to twin-beam squeezing.

• Lecture 9. Entanglement, including macroscopic entanglement.

• Lecture 10. Seeding of nonlinear processes and related effects like photon addition, stimulated emission tomography and brightness measurement.

Lernziele und Kompetenzen:

Learning goals and competences:
Students

• explain the relevant topics of the lecture
  

• apply the methods to specific examples

Studien-/Prüfungsleistungen:

From Nonlinear Optics to Entanglement and Squeezing (Prüfungsnummer: 403141)

(englischer Titel: From Nonlinear Optics to Entanglement and Squeezing)

Prüfungsleistung, mündliche Prüfung, Dauer (in Minuten): 30, benotet, 5 ECTS

Anteil an der Berechnung der Modulnote: 100.0 %

weitere Erläuterungen:
Masterstudierende mit Studienbeginn ab Sommersemester 2015 können Prüfungen in deutscher Sprache nur mit Genehmigung des Prüfungsausschussvorsitzenden ablegen.

Prüfungssprache: Englisch

Erstablegung: SS 2017, 1. Wdh.: SS 2017 (nur für Wiederholer)

1. Prüfer:

Maria Chekhova