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
Page 1: DOCTORAL THESIS IN PHOTONICS ICFO B
Page 5: Spatial Characterization Of Two-Pho
Page 9 and 10: Contents Contents vii Acknowledgeme
Page 11 and 12: Acknowledgements This thesis compil
Page 13 and 14: Abstract In the same way that elect
Page 15 and 16: Resumen De la misma manera que la e
Page 17: Introduction The role of photons in
Page 22 and 23: 1. General description of two-photo
Page 35 and 36: CHAPTER 2 Correlations and entangle
Page 37 and 38: 2.1. The purity as a correlation in
Page 39 and 40: 2.2. Correlations between space and
Page 41 and 42: 2.2. Correlations between space and
Page 43 and 44: 2.3. Correlations between signal an
Page 45 and 46: 2.3. Correlations between signal an
Page 47 and 48: Signal purity 1 0 (a) 0.1 3 2.3. Co
Page 49 and 50: CHAPTER 3 Spatial correlations and
Page 51 and 52: 3.2. OAM transfer in general SPDC c
Page 53 and 54: 3.2. OAM transfer in general SPDC c
Page 55: Phase front 3.3. OAM transfer in co
Page 58 and 59: 4. OAM transfer in noncollinear con
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4. OAM transfer in noncollinear con
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4. OAM transfer in noncollinear con
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5. Spatial correlations in Raman tr
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CHAPTER 6 Summary This thesis chara
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APPENDIX A The matrix form of the m
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v =γ 2 L 2 Np sin ϕi − γ 2 L 2
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The matrix C is given by C = 1 ⎛
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B. Integrals of the matrix mode fun
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C. Methods for OAM measurements Inp
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Bibliography [13] M. Barbieri, C. C
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Bibliography [41] C. I. Osorio, A.
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Bibliography [68] S. Chen, Y.-A. Ch
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Spatial Characterization Of Two-Pho
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A Luz Stella y Luis Alfonso, mis pa
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Contents B Integrals of the matrix
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When he [Kepler] found that his lon
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Abstract The matrix notation, intro
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Abstract La notación matricial int
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Introduction the transfer of oam fr
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CHAPTER 1 General description of Tw
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y y x z z pump s i (a) signal idle
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1.3. Approximations and other consi
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x 1.3. Approximations and other con
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x Wave fronts 1.3. Approximations a
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1 0 -0.2 1.3. Approximations and ot
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1.4. The mode function in matrix fo
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2. Correlations and entanglement (a
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2. Correlations and entanglement ch
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2. Correlations and entanglement th
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2. Correlations and entanglement Fi
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2. Correlations and entanglement q
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2. Correlations and entanglement Si
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2. Correlations and entanglement ri
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3. Spatial correlations and OAM tra
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CHAPTER 4 OAM transfer in noncollin
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4.2. Effect of the pump beam waist
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1.0 0.0 4.2. Effect of the pump bea
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Coincidences 800 0 -4 4.2. Effect o
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Weight 1 0 4.3. Effect of the Poynt
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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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