Spatial Characterization Of Two-Photon States - GAP-Optique

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Introduction the transfer of oam from the generating pump beam to the down-converted photons. Several studies have reported a compleate transfer of the oam of the pump [7, 8, 22, 27, 28, 29], while other studies have reported a partial transfer [30, 31, 32, 33]. The elucidation of the oam spectra of down-converted photons, and their relation with the spectra of the pump, is a key step for developing new applications based on this degree of freedom. This thesis addresses the mentioned oam controversy, as well as the characterization of the different correlations present in two-photon states. For both processes, spdc and Raman transitions in cold atoms, this thesis describes the generated two-photon state, the correlations between different degrees of freedom and between photons, and the oam transfer. A general goal of the thesis is to contribute to the characterization of the two-photon sources, making it possible to exploit a bigger portion of the total quantum state of the light in future applications. xvi
This thesis is based on the following papers: List of Publications Orbital angular momentum correlations of entangled paired photons. C. I. Osorio, G. Molina-Terriza, J. P. Torres. J. Opt. A: Pure Appl. Opt. 11, 094013 (2009). Chapters 3 and 5 <strong>Spatial</strong> entanglement of paired photons generated in cold atomic ensembles C. I. Osorio, S. Barreiro, M. W. Mitchell, and J. P. Torres. Phys. Rev. A 78, 052301 (2008). arXiv:0804.3257v2 [quant-ph]. Chapter 5 Spatiotemporal correlations in entangled photons generated by spontaneous parametric down conversion. C. I. Osorio, A. Valencia, and J. P. Torres. New J. Phys. 10, 113012 (2008). arXiv:0804.2425v2 [quant-ph]. Chapters 1 and 2 Correlations in orbital angular momentum of spatially entangled paired photons generated in parametric downconversion. C. I. Osorio, G. Molina-Terriza, and J. P. Torres. Phys. Rev. A 77, 015810 (2008). arXiv:0711.4500v1 [quant-ph]. Chapters 3 Azimuthal distinguishability of entangled photons generated in spontaneous parametric down-conversion. C. I. Osorio, G. Molina-Terriza, B. Font, and J. P. Torres. Opt. Express 15, 14636 (2007). arXiv:0709.3437v1 [quant-ph]. Chapter 4 Control of the shape of the spatial mode function of photons generated in noncollinear spontaneous parametric down-conversion. G. Molina-Terriza, S. Minardi, Y. Deyanova, C. I. Osorio, M. Hendrych, and J. P. Torres. Phys. Rev. A 72, 065802 (2005). arXiv:quant-ph/0508058v1. Chapter 4 Orbital angular momentum of entangled counterpropagating photons. J. P. Torres, C. I. Osorio, and L. Torner. Opt. Lett. 29, 1939 (2004). Chapters 3 and 4 xvii
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DOCTORAL THESIS IN PHOTONICS ICFO B
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Spatial Characterization Of Two-Pho
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Contents Contents vii Acknowledgeme
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Acknowledgements This thesis compil
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Abstract In the same way that elect
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Resumen De la misma manera que la e
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Introduction The role of photons in
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This thesis is based on the followi
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1. General description of two-photo
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CHAPTER 2 Correlations and entangle
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2.1. The purity as a correlation in
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2.2. Correlations between space and
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2.2. Correlations between space and
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2.3. Correlations between signal an
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2.3. Correlations between signal an
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Signal purity 1 0 (a) 0.1 3 2.3. Co
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CHAPTER 3 Spatial correlations and
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3.2. OAM transfer in general SPDC c
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3.2. OAM transfer in general SPDC c
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Phase front 3.3. OAM transfer in co
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4. OAM transfer in noncollinear con
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Page 68 and 69: 4. OAM transfer in noncollinear con
Page 70 and 71: 4. OAM transfer in noncollinear con
Page 72 and 73: 5. Spatial correlations in Raman tr
Page 81 and 82: CHAPTER 6 Summary This thesis chara
Page 83 and 84: APPENDIX A The matrix form of the m
Page 85 and 86: v =γ 2 L 2 Np sin ϕi − γ 2 L 2
Page 87: The matrix C is given by C = 1 ⎛
Page 90 and 91: B. Integrals of the matrix mode fun
Page 92 and 93: C. Methods for OAM measurements Inp
Page 94 and 95: Bibliography [13] M. Barbieri, C. C
Page 96 and 97: Bibliography [41] C. I. Osorio, A.
Page 98: Bibliography [68] S. Chen, Y.-A. Ch
Page 103: Spatial Characterization Of Two-Pho
Page 107: A Luz Stella y Luis Alfonso, mis pa
Page 110 and 111: Contents B Integrals of the matrix
Page 112 and 113: When he [Kepler] found that his lon
Page 114 and 115: Abstract The matrix notation, intro
Page 116 and 117: Abstract La notación matricial int
Page 121 and 122: CHAPTER 1 General description of Tw
Page 123 and 124: y y x z z pump s i (a) signal idle
Page 125 and 126: 1.3. Approximations and other consi
Page 127 and 128: x 1.3. Approximations and other con
Page 129 and 130: x Wave fronts 1.3. Approximations a
Page 131 and 132: 1 0 -0.2 1.3. Approximations and ot
Page 133: 1.4. The mode function in matrix fo
Page 136 and 137: 2. Correlations and entanglement (a
Page 138 and 139: 2. Correlations and entanglement ch
Page 140 and 141: 2. Correlations and entanglement th
Page 142 and 143: 2. Correlations and entanglement Fi
Page 144 and 145: 2. Correlations and entanglement q
Page 146 and 147: 2. Correlations and entanglement Si
Page 148 and 149: 2. Correlations and entanglement ri
Page 150 and 151: 3. Spatial correlations and OAM tra
Page 157 and 158: CHAPTER 4 OAM transfer in noncollin
Page 159 and 160: 4.2. Effect of the pump beam waist
Page 161 and 162: 1.0 0.0 4.2. Effect of the pump bea
Page 163 and 164: Coincidences 800 0 -4 4.2. Effect o
Page 165 and 166: Weight 1 0 4.3. Effect of the Poynt
Page 167 and 168: 4.3. Effect of the Poynting vector
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Before the crystal 4.3. Effect of t
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CHAPTER 5 Spatial correlations in R
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x y z 5.1. The quantum state of Sto
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where 5.2. Orbital angular momentum
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weight 1 0.6 -180º -90º 0º 90º
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5.3. Spatial entanglement 5.20 is s
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6. Summary Experiments that explain
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A. The matrix form of the mode func
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A. The matrix form of the mode func
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APPENDIX B Integrals of the matrix
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APPENDIX C Methods for OAM measurem
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Bibliography [1] M. A. Nielsen and
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Bibliography [27] J. P. Torres, A.
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Bibliography [55] M. C. Booth, M. A
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