"*
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 term photon (ref. 17) 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, including experimental data of one-photon states, by the group of Alexander Lvovsky (ref 15 and the link below).

1. E. Schroedinger,
"Der stetige Übergang von der Mikro- zur Makromechanik"
, Die Naturwiss. **28**, 665 (1926);

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;

4. U. Leonhardt, *Measuring the quantum state of light*, Cambridge University
Press, Cambridge 1997;

5. W.P. Schleich, E. Mayr, D. Kraehmer, *Quantum Optics in Phase Space*, Wiley,
Weinheim 1999;

6. D.F. Walls and G.J. Milburn, *Quantum Optics*, Springer Berlin 1994;

7. R.E. Slusher, L.W. Hollberg, B. Yurke, J.C. Mertz, and J.F. Valley,
"Observation of squeezing by four wave mixing in a cavity" Phys. Rev. Lett. **50**,
2409 (1985);

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);

9. D.T. Smithey, M. Beck, M.G. Raymer, A. Faridani, "Measurement of the Wigner
distribution and the density matrix of a light mode using optical homodyne tomography:
Application to squeezed states and the vacuum", Phys. Rev. Lett. **70**, 1244
(1993);

10. H.P. Yuen and V.W.S. Chan, "Noise in homodyne and heterodyne detection",
Opt. Lett. **8**, 177 (1983);

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 Quantenzustände", 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);
I. Tittonen, G. Breitenbach, T. Kalkbrenner, T. Müller, R. Conradt,
S. Schiller, J. Mlynek, E. Steinsland, N. Blanc, and N.F. Rooij,
"Interferometric measurements of the position of a macroscopic body: towards the standard quantum limit"
,
Phys. Rev. A, **59**, 1038 (1999)

17. Special issue Optics and Photonic News, "The nature of light: What is a photon?" ,OPN, (2003), see also "A Nine Point Argument on: What is a Photon" by Mike Raymer, "Experiments with single Photons" by Philippe Grangier, and "Wie gross ist ein Photon?" by H.D.Zeh

18.A. Lvovsky, M. Raymer, Review article "Continuous-variable optical quantum-state tomography" , Rev. Mod. Phys., 81, (2009)

19. S. Machida and Y. Yamamoto, "Observation of amplitude squeezing in a constant-current driven semiconductor laser" , Phys. Rev. Lett. 58, 1000-1003 (1987)

20. T. Coudreau, L. Vernac, A.Z. Khoury, G. Breitenbach, and E. Giacobino, "Quantum tomography of a laser beam interacting with cold atoms", Europhys. Lett. 46, (1999)

21.
G.Breitenbach, S. Schiller, and J. Mlynek,
"81% Conversion Efficiency in Frequency-stable Continuous-Wave Parametric Oscillation",
J. Opt. Soc. Am. B, **12**, 2095 (1995)

22. T. P. Purdy, R. W. Peterson, and C. A. Regal, "Observation of radiation pressure shot noise on a macroscopic object", Science, 339:801, 2013; T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, "Strong Optomechanical Squeezing of Light", prx.aps.org/abstract/PRX/v3/i3/e031012 (2013)

23. M. Mehmet, S. Ast, T. Eberle, S. Steinlechner, H. Vahlbruch and R. Schnabel, "Squeezed light at 1550nm with a quantum noise reduction of 12.3 dB", arxiv.org/abs/1110.3737 (2013)

Tutorial quantum physics, ecole polytechnique, Paris

Group of Mike Raymer, Eugene, Oregon

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 S. Schiller, Düsseldorf, Quantum Optics and Relativity

Group of Antoine Heidmann, Quantum Optics and movable mirrors

Gravitational waves and quantum noise control, GEO600 Hannover

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:

Last modified: Dec. 2013