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Journal of Contemporary Physics (Armenian Academy of Sciences)

Photon states and Wigner functions in parametric generation

N. H. Adamyan, Gagik Yu. Kryuchkyan

Published May 6, 2008• 1 citation
Publisher

Abstract

The problem of preparation of photon states from two correlated modes of subharmonics generated in pulsed regime of optical parametric oscillator is investigated. Because of quantum correlation, detecting of n -photon Fock states in one mode transfers the other mode into also an n -photon state. Conditional Wigner functions are calculated whose negative parts describe the prepared photon states in cases of one-, two-, and three-photon schemes of measurements.

DOI
10.3103/s1068337208030018

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The problem of preparation of photon states from two correlated modes of subharmonics generated in pulsed regime of optical parametric oscillator is investigated. Because of quantum correlation, detecting of n -photon Fock states in one mode transfers the other mode into also an n -photon state. Conditional Wigner functions are calculated whose negative parts describe the prepared photon states in cases of one-, two-, and three-photon schemes of measurements.
Generation of multi-photon states (such as for instance three- and four-photon states) is one of the most challenging problems of modern quantum optics. In many works the authors claim to have produced such states by means of overlapping photon pairs generated in spontaneous parametric down-conversion (SPDC). Moreover three- and four-photon states generated this way have been used for observing Greenberger-Horne-Zeilinger (GHZ) polarization states testing Bell's inequalities for spin-1 quantum systems preparing W-states and other applications. In this paper we show that the criterion for obtaining three- or four-photon states is the behavior of the corresponding normalized Glauber's correlation function. Calculations carried out for the case of SPDC or even PDC in the stimulated regime demonstrate that these processes are not capable of generating three- or four-photon states: photon statistics reveals typically two-photon behaviour. We suggest a method of measuring higher-order correlation functions in the pulsed regime which allows one to study multi-photon correlations for these and many other processes.
Conditional preparation of two-photon states from a continuous wave non-degenerate optical parametric oscillator is investigated. We derive the phase space Wigner function for the output state conditioned on two nearby photo detection events, and we maximize its overlap with a two-photon state by varying the temporal output state mode function. In the low intensity limit, we generalize to n-photon state production. We find a simple expression for the conditional output, and from this we determine the optimal output state mode function and n-photon state fidelity.
We have reconstructed the quantum state of optical pulses containing single photons using the method of phase-randomized pulsed optical homodyne tomography. The single-photon Fock state 1> was prepared using conditional measurements on photon pairs born in the process of parametric down-conversion. A probability distribution of the phase-averaged electric field amplitudes with a strongly non-Gaussian shape is obtained with the total detection efficiency of (55+/-1)%. The angle-averaged Wigner function reconstructed from this distribution shows a strong dip reaching classically impossible negative values around the origin of the phase space.
Conditional preparation of photon number states from a continuous-wave nondegenerate optical parametric oscillator is investigated. We derive the phase space Wigner function for the output state conditioned on photodetection events that are not necessarily simultaneous, and we maximize its overlap with the desired photon number state by choosing the optimal temporal output state mode function. We present a detailed numerical analysis for the case of two-photon state generation from a parametric oscillator driven with an arbitrary intensity below threshold, and in the low-intensity limit we present a formalism that yields the optimal output state mode function and fidelity for higher-photon-number states.