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Journal of Contemporary Physics (Armenian Academy of Sciences)

Three-photon states in phase space

T. V. Gevorgyan

Published Jan 1, 2015• 2 citations
Publisher

Abstract

The cascade parametric down-conversion of photons in the optical resonator in pulsed regime is considered for production of three-photon states. Photon number distributions, as well as the Wigner functions are investigated for subharmonic mode in quantum approach. The three-photon structure of subharmonic mode and its three-phase localization in phase-space are shown.

DOI
10.3103/s1068337215010077

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The cascade parametric down-conversion of photons in the optical resonator in pulsed regime is considered for production of three-photon states. Photon number distributions, as well as the Wigner functions are investigated for subharmonic mode in quantum approach. The three-photon structure of subharmonic mode and its three-phase localization in phase-space are shown.
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We investigate production of three-photon states in cascaded parametric down-conversion (PDC). The analysis includes preparation of Greenberger-Horne-Zeilinger polarization-entangled states in cascaded type-II and type-I PDC in the framework of considering the dual-grid structure that involves two periodically poled crystals. Considering cascaded optical parametric oscillator (OPO) driven by a sequence of laser pulses with Gaussian time-dependent envelopes, we investigate quantum statistical properties of high intensity mode generated in intracavity three-photon splitting. Calculating the normalized third-order correlation function below-and at the generation threshold, we demonstrate that in the pulsed regime, depending on the duration of pulses and the time-interval separations between them, the degree of three-photon-number correlation essentially exceed the analogous one for the case of continuous pumping.
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The quantum dynamics of the mean number of photons and quantum entropy of interacting modes, as well as the Wigner function of the stationary state of the fundamental mode and the third subharmonic mode has been investigated for the intracavity third-subharmonic generation. It is shown that the quantum dynamics of the system depends strongly on the nonlinear coupling coefficient between the modes. It is also demonstrated that, in the steady-state limit, depending on the intermodal coupling coefficient, the fundamental mode can be either in a pure coherent state, or in a squeezed state, or in a pure vacuum state. The third subharmonic mode in the subthreshold regime of generation of this mode is in the vacuum state. The Wigner function is squeezed over three sides of an equilateral triangle (squeezed vacuum). The quantum entropy of this state is nonzero. It is also shown that the third subharmonic mode, depending on the nonlinear coupling coefficient in the steady-state limit, can be localized in the three-component state with the same probability of detecting a field in each coherent component of the state and with the presence of quantummechanical interference between the state components. The mean number of photons in this state is smaller than unity. Depending on the nonlinear coupling coefficient, the third subharmonic mode can also be localized in the three-component state, which is a statistical mixture of three squeezed states.