Spatial Characterization Of Two-Photon States - GAP-Optique

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2. Correlations and entanglement rity as correlation indicator it is possible to determine the conditions in which the specific correlations are suppressed, without requiring the use of infinitely narrow filters. The next chapter continues with the description of the correlations between photons, in the case where only their spatial state is relevant. The chapter describes the spatial correlations in terms of orbital angular momentum transfer. 28
CHAPTER 3 <strong>Spatial</strong> correlations and orbital angular momentum transfer The previous chapter describes the correlations between the signal and idler photons considering space and frequency, as well as the correlations between those degrees of freedom. This chapter focuses on the cases where the degrees of freedom are not correlated, and the only relevant correlations are those between the photons in the spatial degree of freedom. To characterize those correlations I use the orbital angular momentum (oam) content of the generated photons, which is directly associated to their spatial distribution. The spatial correlations between the photons determine the mechanism of oam transfer from the pump to the signal and idler. Most studies of the oam correlations in spdc can be divided in two categories: those reporting a full transference of the pump’s oam [7, 8, 22, 27, 28, 29], and those reporting a partial transference [30, 31, 32, 33]. This chapter describes the oam transfer mechanism, and shows the difference between both regimes. The chapter is divided in three sections. Section 3.1 introduces the eigenstates of the oam operator: the Laguerre-Gaussian modes. This section shows how to calculate and measure the oam content of the photons. Section 3.2 describes how the oam is transferred in spdc. As an example, section 3.3 shows how this transfer happens in the collinear case, where all the emitted photons propagate in the same direction. The main result of this chapter is a selection rule that summarizes the oam transfer mechanism: the oam carried by the pump is completely transferred to all the signal and idler photons emitted over the cone. 29
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 and 18: 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: Signal purity 1 0 (a) 0.1 3 2.3. Co
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.
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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
Page 110 and 111:
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.
Page 197 and 198:
Bibliography [55] M. C. Booth, M. A
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Spatial Characterization Of Two-Photon States - GAP-Optique

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