Quantum theory of synchronously pumped type I optical parametric oscillators: characterization of the squeezed supermodes

Abstract

Quantum models for synchronously pumped type I optical parametric oscillators (SPOPO) are presented. The study of the dynamics of SPOPOs, which typically involves millions of coupled signal longitudinal modes, is significantly simplified when one considers the "supermodes", which are independent linear superpositions of all the signal modes diagonalizing the parametric interaction. In terms of these supermodes the SPOPO dynamics becomes that of about a hundred of independent, single mode degenerate OPOs, each of them being a squeezer. One derives a general expression for the squeezing spectrum measured in a balanced homodyne detection experiment, valid for any temporal shape of the local oscillator. Realistic cases are then studied using both analytical and numerical methods: the oscillation threshold is derived, and the spectral and temporal shapes of the squeezed supermodes are characterized.

Pulsed-squeezed-light generation in a waveguide with second-subharmonic generation and periodic corrugation

“…Also the relation between the Bloch-Messiah reduction and Schmidt decomposition of a two-photon spectral amplitude characterizing spontaneous parametric down-conversion has been found. The results obtained in single-pass geometry have been generalized to the nonlinear interaction in a cavity [51]. Mode structure of nonclassical states arising from squeezed states after post-selection done with on/off detectors has been analyzed in [52].…”

Noncritical generation of nonclassical frequency combs via spontaneous rotational symmetry breaking

“…In this case a single frequency comb around the subharmonic frequency ω 0 is generated and the distinction between signal and idler photons is completely superfluous; hence we will refer to any subharmonic photon as a signal photon for brevity. In order to understand why such SPOPOs have so remarkable quantum properties, let us analyze their interaction Hamilto- nian which can be written as [18,19] …”

“…h is the phasemismatch factor, and we assumed a common value for the coupling constant χ for any PDC channel, which is an excellent approximation [18,19]. Note that (1) is just the sum of infinite PDC Hamiltonians, each corresponding to the generic PDC channel…”

“…This has enormous consequences: on one hand classical correlations appear (all signal modes get phase-locked, giving rise to well-defined trains of identical pulses separated by t cav ), and on the other hand strong quantum correlations are built up, leading to highly multimode squeezing [18,19] and multipartite entanglement [20,21]. Indeed, recent experiments have proven SPOPOs to be highly versatile sources of nonclassical light [22][23][24][25], with foreseen applications in quantum computation [21,25] and communication [25].…”

“…−iωs,mt +H.c., (2) where E s is the single photon field amplitude [19], taken equal for all signal modes to an excellent approximation, s m,l are the (interaction picture) annihilation operators for photons of frequency ω s,m and transverse profile…”