" If things of sight such heavens be, what heavens are those we cannot see? " Andrew Marvell
The discovery or maybe better to say the invention of the photon at the turn of the twentieth century marks the starting point of the development of quantum theory. At that time many experiments designed to test the new theory remained in the realm of thought experiments. Due to the fast development of laser optics it is now possible to carry out experiments that enable us to actually visualize this strange quantum world. This site intends to give a non-technical, intuitive introduction to quantum optics of the light field.
Recent measurements are employed to illuminate abstract quantum mechanical concepts such as the uncertainty relation, the wave packet, quantum noise, Wigner functions, density matrices, etc. using the concrete example of the freely propagating light field. For an animated version of some of the most common quantum states of the light field, showing their experimentally measured quantum noise distribution and the corresponding motion of their wave packet, see the Java animation at the end. Now including new experimental data of one-photon states, by the group of Alexander Lvovsky (see ref 15 and the link below).
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2. P. Carruthers, M.M. Nieto, "Coherent states and the forced quantum oscillator", Am. J. Phys. 7, 537 (1965);
3. M. Freyberger, P. Bardroff, C. Leichtle, G. Schrade, and W.P. Schleich, "The art of measuring quantum states", Phys. World, Nov. 1997;
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8. L.A. Wu, H.J. Kimble, J.L. Hall and H. Wu,"Generation of squeezed states by parametric down conversion", Phys. Rev. Lett. 57, 691 (1986);
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11. G. Breitenbach, S. Schiller, and J. Mlynek, "Measurement of the quantum states of squeezed light" , Nature, 387, 471 (1997);
12. G. Breitenbach and S. Schiller, "Homodyne tomography of classical and non-classical light", J. Mod. Opt. 44, 2207 (1997); G. Breitenbach, F. Illuminati, S. Schiller, and J. Mlynek, "Broadband quantum state reconstruction: A spectrum of quantum states", Europhys. Lett.. 44, 192 (1998); S. Schiller, G. Breitenbach, Die Vermessung optischer Quantenzustaende, Physikalische Blaetter, Mai 1999
13. T. Felbinger, S. Schiller, and J. Mlynek, "Oscillation in 3-photon downconversion and generation of non-classical light", Phys. Rev. Lett. 80, 492 (1998);
14. D. Leibfried et al., "Quantum state of the motion of a trapped ion", Phys. Rev. Lett. 77, 4281 (1996);
15. A.I. Lvovsky, H. Hansen, T. Aichele, O. Benson, J. Mlynek, and S. Schiller, "Quantum state reconstruction of the single-photon Fock state", Phys. Rev. Lett. 87, (2002); A.I. Lvovsky, and S.A. Babichev, " Synthesis and tomographic characterization of the displaced Fock state of light", Phys. Rev. A 66, (2002); A.I. Lvovsky, and J. Mlynek, "Quantum-optical catalysis: Generating nonclassical states of light by means of linear optics", Phys. Rev. Lett. 88, (2002);
16. T. Briant, P.F. Cohadon, M. Pinard & A. Heidmann, "Optical phase-space reconstruction of mirror motion at the attometer level", Eur. Phys. Journal D 22, 131 (2003),
17. Special issue Optics and Photonic News, "The nature of light: What is a photon?" , OPN, (2003),
18. Review article "Continuous-variable optical quantum-state tomography", A. Lvovsky, M. Raymer, Rev. Mod. Phys., 81, (2009)
Wikipedia article about quantum optics
Group of Alexander Lvovsky, Calgary, tutorial quantum opticsTutorial quantum physics, ecole polytechnique, Paris
Group of Prof. Jürgen Mlynek (now president Humboldt University Berlin)
Group of Mike Raymer, Eugene, Oregon
Group of Ian Walmsley, Rochester, New York
V. Buzek, Quantum State Reconstruction
Quantum state of the motion of a trapped ion, Dietrich Leibfried, NIST, Boulder, Colorado
Group of S. Haroche, M. Brune, ENS, Paris, Measurement of a cavity field Wigner function
Group of Andrew G. White at Univ. of Queensland, Quantum Optics and Quantum Computing
Group of Prof. Schiller, Düsseldorf, Quantum Optics and Relativity
Quantum Noise Control and Squeezed States in Condensed Matter, U. Michigan
Group of Antoine Heidmann, Quantum Optics and movable mirrors
my dissertation (full text), my homepage
Vibrating strings and Lissajous curves. The classical treatment of harmonic oscillation.
Crystals and Interference. This site gives a short introduction to optics in non-isotropic media. The reader can experiment with a virtual polarization microscope, generating various kinds of interference patterns
Contact: higobreitenbach@arcor.de
Last modified: Jan. 2005
