Spatial Characterization Of Two-Photon States - GAP-Optique

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4. OAM transfer in noncollinear configurations The different spatial shapes in figure 4.12 clearly show that the downconversion cone does not posses azimuthal symmetry. As was predicted by the theoretical calculations, the coincidence measurement for α = 90 ◦ , presents a nearly Gaussian shape, while the other cases are highly elliptical. The slight discrepancies between experimental data and theoretical predictions observed might be due to the small (but not negligible) bandwidth of the pump beam, and due to the fact that the resolution of our system is limited by the detection pinhole size. Conclusion The spdc parameters and the detection system determine the portion of the cone that is detected in a noncollinear configuration. This chapter explains how the pump beam waist and the Poynting vector walk-off affect the oam transfer. By tailoring both parameters it is possible to generate photons with specific spatial shapes. The walk-off affects especially those configurations where pairs of photons with different α are used. The next chapter extends the analysis of the spatial correlations to pairs of photons generated in Raman transitions. The chapter describes how the specific characteristics of that source are translated into the two-photon spatial state. 50
CHAPTER 5 <strong>Spatial</strong> correlations in Raman transitions <strong>Two</strong>-photon states can be generated in different nonlinear processes, and in every case the oam transfer will depend on the particular configuration. Raman transition is an alternative method for the generation of two-photon states. Several authors have proven the generation of correlated photons in polarization [59], frequency [60] and oam [23] via Raman transitions. Typical configurations involve the partial detection of the generated photons [61, 62, 63] in quasi-collinear configurations [64]. Just as in the case of spdc, the geometrical conditions determine the oam transfer. This chapter analyses the oam transfer in Raman transitions using the techniques of the previous chapters. This chapter is divided in three sections. Section 5.1 describes the generated two-photon state by introducing its mode function. Section 5.2 studies the oam content of one of the photons with the oam of the other photons fixed. Section 5.3 describes the effect of the geometry of the process on the spatial entanglement between the photons. Numerical calculations show the effect of the geometrical configuration on the oam transfer mechanism. The finite size of the nonlinear medium results in new effects that do not appear in spdc. 51
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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
Page 19: This thesis is based on the followi
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
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 118 and 119: 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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Spatial Characterization Of Two-Photon States - GAP-Optique

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