ELFT HÍRADÓ

[Janos Asboth <asboth.janos AT wigner.mta.hu>]

WIGNER SZFI SZEMINÁRIUM VARRÓ SÁNDOR

(MTA Wigner FK SZFI)
"New quantum phase operator and projectors based on SU(1,1) coherent states"

Időpont: 2014. október 07. (kedd) 10:00
Hely: MTA Wigner FK SZFI, I. épület 1. emeleti Tanácsterem
Összefoglaló:

In the present talk we offer a new solution to the long–standing problem of
quantum phase of an oscillator (which may represent for instance a
quantized mode of the radiation field). Recently we have shown that the
eigenstates of the simple new ‘exponential phase operator’ F, defined by
the ‘polar decomposition’ A=F*Sqrt[N+*g*]  of the quantized amplitude of a
linear oscillator, are SU(1,1) coherent states [1] with Bargmann index *k*
=(1+*g*)/2. In terms of powers of  F  we have defined in the original
Hilbert space an analogon of the quantum saw-tooth  phase operator [2],
originally introduced by Garrison and Wong [3] in the corresponding
Hardy-Lebesgue space. In the frame of the present approach a generalized
spectral decomposition of the phase operator can be derived in a natural
way, where the phase projectors also have a simple analytic form. The
parameter ‘*g*’ turns out to be the Golden Ratio *g*=(1+Sqrt[5])/2, by
keeping an analogy with the usual coherent states expansion of the number
operator N.

The present method developed by us, which leads to the generalized spectral
decomposition of the phase operator may for example be useful in describing
the quantum phase properties of extreme radiation fields, like few–cycle or
attosecond light pulses.


[1] Perelomov A, Generalized Coherent States and Their Applications (1986).
Sec. 5.2
[2] Varró S,  Talk 7.3.1., LPHYS’14: Quantum information and quantum
computation
[3] Garrison J C and Wong J, J. Math. Phys. 11, 2242-2249 (1970)

*Részletes információ:* http://www.szfki.hu/seminar
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Asbóth János
szfi-seminar AT wigner.mta.hu