Spatial Characterization Of Two-Photon States - GAP-Optique

Contents
Contents vii
Acknowledgements ix
Abstract xi
Introduction xv
List of Publications xvii
1 General description of two-photon states 1
1.1 Spontaneous parametric down-conversion . . . . . . . . . . . . 2
1.2 Two-photon state . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Approximations and other considerations . . . . . . . . . . . . 5
1.4 The mode function in matrix form . . . . . . . . . . . . . . . . 12
2 Correlations and entanglement 15
2.1 The purity as a correlation indicator . . . . . . . . . . . . . . . 16
2.2 Correlations between space and frequency . . . . . . . . . . . . 18
2.3 Correlations between signal and idler . . . . . . . . . . . . . . . 23
3 Spatial correlations and OAM transfer 29
3.1 Laguerre-Gaussian modes and OAM content . . . . . . . . . . . 30
3.2 OAM transfer in general SPDC configurations . . . . . . . . . . 31
3.3 OAM transfer in collinear configurations . . . . . . . . . . . . . 34
4 OAM transfer in noncollinear configurations 37
4.1 Ellipticity in noncollinear configurations . . . . . . . . . . . . . 38
4.2 Effect of the pump beam waist on the OAM transfer . . . . . . 39
4.3 Effect of the Poynting vector walk-off on the OAM transfer . . 44
5 Spatial correlations in Raman transitions 51
5.1 The quantum state of Stokes and anti-Stokes photon pairs . . . 52
5.2 Orbital angular momentum correlations . . . . . . . . . . . . . 55
5.3 Spatial entanglement . . . . . . . . . . . . . . . . . . . . . . . . 57
6 Summary 61
A The matrix form of the mode function 63
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