An introduction to Quantum Optics. T. Coudreau Laboratoire Kastler Brossel, UMR CNRS 8552 et Université Pierre et Marie Curie, PARIS, France also with Pôle Matériaux et Phénomènes Quantiques, Fédération de Recherche CNRS 2437 et Université Denis Diderot , PARIS, France.
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An introduction to Quantum Optics
Laboratoire Kastler Brossel, UMR CNRS 8552 et Université Pierre et Marie Curie, PARIS, France
also withPôle Matériaux et Phénomènes Quantiques, Fédération de Recherche CNRS 2437 et Université Denis Diderot , PARIS, France
Does light consist in waves or particles ?
Everything is understood but...
Planck : energy exchange occur with multiples of
Bohr : atomic energy levels
This was later checked by Millikan
The particle (“photon”) possesses a given momentum
light can be seen as a photon current
Taylor (1909) : Young's slits with an attenuated source
("a candle burning at a distance slightly exceeding a mile”)
"each photon then interferes only with itself”, Dirac
Classical electromagnetic waveQuantum atom
« Semi classical theory :
same for the photographic plate in Taylor ’s experiment
Light remains a classical electromagnetic wave
(Vacuum, absence of radiation, fundamental state of the system)
(for a monochromatic wave)
The field is null only on average : existence of vacuum fluctuations
1) Problem of interpretation
2) Problem of formalism : many diverging quantities
e.g. Vacuum energy :
3) Problem of "concurrence" : the more simple semiclassical theory gives (generally) the same results
QED serves as a base and model for all modern theoretical physics (elementary particles…)
A crucial experiment : the semitransparent plate
The plate does not cut the photon in two !
But a very faint source does not produce a true one photon state :
the beam is a superposition of different states, e.g.
A faint source does not give a clear result
A single dipole (atom, ion…) emits a single photon at a time
Kimble, Dagenais and Mandel, Phys. Rev. Lett. 39 691 (1977)
First experimental proof of the particle nature of light
Grangier et al., Europhys. Lett 1 173(1986)
There is a perfect correlation between the two channels
the resulting light cannot be described by two classical waves emitted by a crystal described quantically
Hong, Ou and Mandel,
Phys. Rev. Lett. 59 2044 (1987)
No interference fringes : the crystal does not produce classical beams but
Value predicted by
Perfect anticorrelations at zero phase shift
(2) and (4) give which is not verified experimentally
the crystal does not produce classical particles
(1) (2) (3) (4)
A and B measure the spin of particles 1 and 2 along a given axis.
If the two observers choose the same axis, they get an opposite result but if they choose different axis, can they measure simultaneously orthogonal directions ?
is there a “supertheory” (hidden variables) ?
1965 (J. S. Bell, Physics 1, 195 (1965). ) : J.S Bell proposes a way to discriminate between a local hidden variables theory and quantum theory.
One assumes that the experimental result depends on a “hidden variable” and on the magnets orientations but not on the other measurement :
The classical probability to obtain a given result is given by
While the quantum theory prediction is written
Classical, hidden variable theory predicts
P(SaSb)+P(Sb Sc)+P(ScSa) = 1 + 2(P1+P8) 1
while Quantum Mechanics predicts :
P(SiSj) = cos2(60°) = 1/4 so that
P(SaSb)+P(Sb Sc)+P(ScSa) = 3/4 < 1!
“Bell inequalities” enable us to discriminate
Among the first experiments :
A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett. 49, 91 (1982).
Weihs et al. performed an experiment using parametric down conversion and detectors 400 m apart
Weihs et al., Phys. Rev. Lett 81, 5039(1998)
Experimental result :
Non local correlations exist !
They do not allow superluminous transfer of information
At the output of an OPO, the signal and idler beams have quantum
Heidmann et al., Phys. Rev. Lett. 59, 2555 (1987)
Result : 30 % noise reduction
(now : over 85 %)
QED explains without ambiguity all phenomena
but still "strange" behaviours