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