Spatial Characterization Of Two-Photon States - GAP-Optique

More documents

Recommendations

Info

6. Summary Experiments that explain oam transfer in noncollinear spdc. In noncollinear configurations only a subset of emission directions is detected. The transfer of oam to the detected photons is strongly affected by the change in geometry imposed by the detection system, and depends on the angle of detection, the pump-beam waist and the Poynting-vector walk-off. The thesis shows that, by tailoring these parameters, it is possible to design noncollinear sources that naturally generate spatially-separated photons with specific desired spatial shapes, as shown in chapter 4 and references [39, 33, 32]. An analysis of the spatial correlations generated by Raman transitions in cold atomic ensembles. Like for spdc, the spatial correlations between the Stokes and anti-Stokes photons depend on the geometrical configuration of the pump beam, the control beam, and the Stokes and anti-Stokes photons. This thesis shows how the size and shape of the atom cloud define the emission angles for which the correlations are maximum and minimum, as shown in chapter 5 and reference [73]. 62
APPENDIX A The matrix form of the mode function According to section 1.3, the normalized two-photon mode function, after some approximations, reads Φ(qs, Ωs, qi, Ωi) ∝ exp − w2 p 4 ∆2 0 − w2 p 4 ∆21 × exp − (γL)2 4 ∆2k − T 2 0 4 (Ωs + Ωi) 2 × exp − w2 s 2 |qs| 2 − w2 i 2 |qi| 2 − 1 2B2 Ω s 2 s − 1 2B2 Ω i 2 i . (A.1) The argument of the exponential function is a second order polynomial. Each term is the product of at most two variables (qx s , qy s , qx i , qy i , Ωs, Ωi) and a coefficient f = a 4 qx2 s + b 4 qy2 s + c 4 qx2 i + d 4 qy2 h i + . . . + 2 qx s q y s + . . . + z 2 ΩsΩi. (A.2) Such a polynomial can be written as the product of a matrix A with the coefficients as elements, and a vector x of the variables f = 1 x qs 4 qy s qx i q y i Ωs Ωs ⎛ ⎜ ⎜ ⎝ a h i j k h b m n p i m c s t j n s d v k p t v f l r u w z ⎞ ⎛ q ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎠ ⎝ l r u w z g x s qy s qx i q y i Ωs ⎞ ⎟ , ⎟ ⎠ Ωi (A.3) therefore, the mode function can be written using matrix notation as Φ(qs, Ωs, qi, Ωi) ∝ exp − 1 2 xt Ax . (A.4) 63
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 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33: 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: CHAPTER 6 Summary This thesis chara
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
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 152 and 153:
Page 154 and 155:
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
Page 169 and 170:
Before the crystal 4.3. Effect of t
Page 171 and 172:
CHAPTER 5 Spatial correlations in R
Page 173 and 174:
x y z 5.1. The quantum state of Sto
Page 175 and 176:
where 5.2. Orbital angular momentum
Page 177 and 178:
weight 1 0.6 -180º -90º 0º 90º
Page 179:
5.3. Spatial entanglement 5.20 is s
Page 182 and 183:
6. Summary Experiments that explain
Page 184 and 185:
A. The matrix form of the mode func
Page 186 and 187:
A. The matrix form of the mode func
Page 189 and 190:
APPENDIX B Integrals of the matrix
Page 191 and 192:
APPENDIX C Methods for OAM measurem
Page 193 and 194:
Bibliography [1] M. A. Nielsen and
Page 195 and 196:
Bibliography [27] J. P. Torres, A.
Page 197 and 198:
Bibliography [55] M. C. Booth, M. A
show all

Spatial Characterization Of Two-Photon States - GAP-Optique

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?