The Two-Photon State Generated by Spontaneous Parametric Down-Conversion. C. H. Monken and A. G. da Costa Moura

Transcription

1 The Two-Photon State Generated by C. H. Monken and A. G. da Costa Moura Universidade Federal de Minas Gerais Brazil

2 Funding C A P E S Conselho Nacional de Desenvolvimento Científico e Tecnológico Instituto do Milênio de Informação Quântica

3 Interest: Fundamental Quantum state engineering

4 laser down-converted fields nonlinear medium In first order, the interaction hamiltonian contains terms like By energy conservation and phase matching,

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6 The Refractive Index Surface optic axis extraordinary ordinary

7 Type I Phase Matching pump beam extraordinary refractive index surface (ellipsoid) dispersion Collinear optic axis down-converted field ordinary refractive index surface (sphere)

8 Type I Phase Matching pump beam extraordinary refractive index surface (ellipsoid) noncollinear optic axis down-converted field ordinary refractive index surface (sphere)

9 pump beam down-converted two-photon field crystal

10 The Two-Photon State in the Paraxial Approximation C. K. Hong and L. Mandel, Phys. Rev. A 31, 2409 (1985) C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, Phys. Rev. A 57, 3123 (1998)

11 The Two-Photon State in the Paraxial Approximation two-photon plane wave spectrum 1 photon plane wave modes

12 Paraxial Approximation in Uniaxial Media Ordinary Polarization:

13 Paraxial Approximation in Uniaxial Media Ordinary Polarization: Extraordinary Polarization:

14 Type I Phase Matching

15 Type I Phase Matching pump beam plane wave spectrum

16 Image transfer experiment D1 Lens f = 200 mm BBO - Collinear type II SPDC U.V. mirror B.S.P. D2 Laser Ar 351 nm aperture c Counters D1 vertical position (mm) D1 horizontal position (mm) D1 horizontal position (mm) C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, Phys. Rev. A 57, 3123 (1998) D1 vertical position (mm) D1 counts/10000 in 10 s (a) Coincidences in 10 s (b)

17 Type I Phase Matching pump beam plane wave spectrum

18 Results I - No interference S. P. Walborn et al., Phys. Rev. A 69, (2004) Calculated Measured coincidences D1 V-position (mm) LG BS D2 fixed at the origin D D1 H-position (mm)

19 Results II - Interference Regime (Interferometer balanced) S. P. Walborn et al., Phys. Rev. A 69, (2004) Calculated D1 V-position (mm) Measured coincidences D1 H-position (mm) LG BS D2 fixed at the origin D

20 pump laser wavenumber Type I Phase Matching

21 pump laser wavenumber collinear index mismatch

22 pump laser wavenumber collinear index mismatch walk-off vector* * M. V. Fedorov et al., quant-ph/ v1 (2006)

23 pump laser wavenumber collinear index mismatch for 351nm > 702nm in BBO walk-off vector

24 Type I Phase Matching

25 New Coordinates: Monochromatic Approximation:

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30 pump laser angular spectrum

31 pump laser angular spectrum displacement in x direction (walk-off) For collinear 351nm 702nm in BBO

32 pump laser angular spectrum displacement in x direction (walk-off) astigmatism* For collinear 351nm 702nm in BBO *E. Abramochkin and V. Volostnikov, Opt. Commun. 83, 123 (1991)

33 pump laser angular spectrum displacement in x direction (walk-off) astigmatism simple propagation For collinear 351nm 702nm in BBO

34 Dependence on Depends on collinear ( ) noncollinear detectors in the far field scanned in opposite senses:

35 Dependence on (for ): detectors in the far field scanned in the same sense: May clip unless ( )

36 Example: For collinear down-conversion in BBO optic axis

37 Image transfer experiment D1 Lens f = 200 mm BBO - Collinear type II SPDC U.V. mirror B.S.P. D2 Laser Ar 351 nm aperture c Counters optic axis D1 vertical position (mm) D1 horizontal position (mm) D1 horizontal position (mm) C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, Phys. Rev. A 57, 3123 (1998) D1 vertical position (mm) D1 counts/10000 in 10 s (a) Coincidences in 10 s (b)

38 Factors that affect the transfer of angular spectrum pump laser angular spectrum clipping walk-off astigmatism* For collinear 351nm 702nm in BBO * The basic phenomenon behind the mode converter

39 Factors that affect the transfer of angular spectrum Mode Converter E. Abramochkin and V. Volostnikov, Opt. Commun. 83, 123 (1991) M. W. Beijersbergen et al., Optics Commun. 96, 123 (1993) M. Padgett, J. Arlt, N. Simpson, and L. Allen, Am. J. Phys. 64, 77 (1996)

40 Factors that affect the transfer of angular spectrum

41 Factors that affect the transfer of angular spectrum All deviations from a constant in the transfer of angular spectrum. will affect

42 Conclusions and Perspectives The two-photon wave function carries the information contained in the pump beam angular spectrum: transverse profile, parity, orbital angular momentum, (Gouy phase?), etc. The crystal anisotropy may affect this transfer of information. For a good transfer, very thin crystals or noncritical phase matching must be used. The transfer of longitudinal properties of the pump beam is still under investigation.