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Q: Quantenoptik und Photonik
Q 47: Quanteneffekte IV
Q 47.5: Vortrag
Freitag, 26. März 2004, 12:00–12:15, HS 218
Quantum optics of interferences in terms of the group SO(1,2) — •Hans Kastrup — DESY, Theorie Gruppe, Notkestr. 85, 22603 Hamburg
The interference pattern of two superposed optical amplitudes Aj = |Aj|exp(i ϕj), j=1,2, is esentially determined by the 3 quantities h0=I(1,2) = |A1||A2|, h1 = I(1,2) cosϕ, h2=−I(1,2) sinϕ, ϕ = ϕ1−ϕ2 which parametrize the associated optical phase space S2 ={φ mod 2π, I(1,2) >0}. The Poisson brackets {hi,hj}ϕ,I(1,2) constitute the Lie algebra of the group SO(1,2). This implies that the quantum theory of the system can be implemented in terms of (“positive discrete series”) irreducible unitary representations of that group, where the 3 classical functions hj are replaced by self-adjoint operators Kj which are the basic quantum mechanical “observables” here. K1 and K2 “measure” the phase content of appropriate states, e.g. coherent ones (there are 3 different types of coherent states in the framework of the group SO(1,2) !) One important prediction is that the classical Pythagorean relation h12+h22 = h02 generally will be violated in the quantum theory. It should be possible to test the theory in multiport quantum optical experiments. Ref.: quant-ph/0307069; Fortschr. Phys. 51(2003), 975.