Coherent and incoherent superposition of transition matrix elements of the squeezing operator

Abstract

We discuss the general matrix elements of the squeezing operator between number eigenstates of a harmonic oscillator (which may also represent a quantized mode of the electromagnetic radiation). These matrix elements have first been used by Popov and Perelomov (1969 Zh. Eksp. Teor. Fiz. 56 1375–90) long ago, in their thorough analysis of the parametric excitation of harmonic oscillators. They expressed the matrix elements in terms of transcendental functions, the associated Legendre functions. In the present paper we will show that these matrix elements can also be derived in a different form, expressed by the classical Gegenbauer polynomials. This new expression makes it possible to determine coherent and incoherent superpositions of these matrix elements in closed analytic forms. As an application, we describe multiphoton transitions in the system ‘charged particle + electromagnetic radiation’, induced by a (strong) coherent field or by a black-body radiation component (with a Planck–Bose photon number distribution). The exact results are compared with the semi-classical ones. We will show that in case of interaction with a thermal field, the semi-classical result (with a Gaussian stochastic field amplitude) yields an acceptable approximation only in the Rayleigh–Jeans limit, however, in the Wien limit it completely fails.

Diatomic molecule in a strong infrared laser field: level-shifts and bond-length change due to laser-dressed Morse potential

“…An emerging topic in this field of research is molecules in strong IR fields without ionization [17], having obvious relevance also to important experimental techniques of laser manipulation of molecules, like trapping [18], alignment [19], orientation [20]. Ultra-high intensity laser pulses (10 18 -10 20 W cm −2 ) have a pedestal [21] typically in the intensity range of 10 10 -10 14 W cm −2 (having also an interesting nontrivial photon statistics [22]) which raises questions and concerns about the true "initial" state of the target molecule when the actual ultra-high intensity pulse reaches it.…”

Diatomic molecule in a strong infrared laser field: level-shifts and bond-length change due to laser-dressed Morse potential

“…An emerging topic in this field of research is molecules in strong IR fields without ionization [15], having obvious relevance also to important experimental techniques of laser manipulation of molecules, like trapping [16], alignment [17], orientation [18]. Ultra-high intensity laser pulses (10 18 − 10 20 W/cm 2 ) have a pedestal [19] typically in the intensity range of 10 10 −10 14 W/cm 2 (having also an interesting nontrivial photon statistics [20]) which raises questions and concerns about the true "initial" state of the target molecule when the actual ultra-high intensity pulse reaches it.…”