the two-photon state generated by spontaneous parametric...

The Two-Photon State Generated by Spontaneous Parametric Down-Conversion

The Two-Photon State Generated bySpontaneous Parametric Down-Conversion

C. H. Monkenand

A. G. da Costa Moura

Universidade Federal de Minas GeraisBrazil

Funding

Conselho Nacional de DesenvolvimentoCientífico e Tecnológico

Instituto do Milênio de Informação Quântica

C A P E S

Interest: • Fundamental• Quantum state engineering

Spontaneous Parametric Down-Conversion

down-convertedfields

nonlinearmedium

In first order, the interaction hamiltonian contains terms like

By energy conservation and phase matching,

optic axis

ordinaryextraordinary

The Refractive Index Surface

Type I Phase Matching

optic axis

Collinear

pump beam extraordinaryrefractive index surface(ellipsoid)

down-converted field ordinaryrefractive index surface (sphere)

dispersion

optic axis

noncollinear

pump beam extraordinaryrefractive index surface(ellipsoid)

down-converted field ordinaryrefractive index surface (sphere)

pump beam

crystal

down-convertedtwo-photon field

The Two-Photon State in the Paraxial Approximation

C. H. Monken, P. H. Souto Ribeiro, and S. Pádua, Phys. Rev. A 57, 3123 (1998)

C. K. Hong and L. Mandel, Phys. Rev. A 31, 2409 (1985)

The Two-Photon State in the Paraxial Approximation

1 photonplane wavemodes

two-photonplane wavespectrum

Paraxial Approximation in Uniaxial Media

Ordinary Polarization:

Paraxial Approximation in Uniaxial Media

Ordinary Polarization:

Extraordinary Polarization:

pump beamplane wavespectrum

BBO - Collinear type II SPDC

Lens f = 200 mm

U.V. mirror

B.S.P.

Counters

0 2 4 6 80

position

) D1 counts/10000in 10 s

1.6 -- 2.01.2 -- 1.60.8 -- 1.20.4 -- 0.80.0 -- 0.4

0 2 4 6 80

Coincidencesin 10 s

200 -- 250150 -- 200100 -- 150

50 -- 1000 -- 50

Image transfer experiment

D1 horizontal position (mm)

position

aperture

Laser Ar 351 nm

pump beamplane wavespectrum

D1 H-position (mm)

osition

Calculated Measured coincidences

0-2 21-1

D2 fixed atthe origin

Results I - No interferenceS. P. Walborn et al., Phys. Rev. A 69, 023811 (2004)

Results II - Interference Regime (Interferometer balanced)

D2 fixed atthe origin

D1 H-position (mm)

osition

Calculated Measured coincidences

0-2 21-1

S. P. Walborn et al., Phys. Rev. A 69, 023811 (2004)

pump laserwavenumber

collinear indexmismatch

walk-offvector*

* M. V. Fedorov et al., quant-ph/0612104v1 (2006)

walk-offvector

for 351nm –> 702nm in BBO

New Coordinates:

Monochromatic Approximation:

pump laserangularspectrum

displacementin x direction(walk-off)

For collinear 351nm 702nm in BBO

astigmatism*

*E. Abramochkin and V. Volostnikov, Opt. Commun. 83, 123 (1991)

astigmatism simplepropagation

collinear( )

noncollinear

Dependence on

Depends on

detectors in the far field scanned in opposite senses:

0 0 0 0

Dependence on (for ):

May “clip”

unless ( )

detectors in the far field scanned in the same sense:

-0.002 -0.001 0.001 0.002-0.002 -0.001 0.001 0.002-0.002 -0.001 0.001 0.002

Example: For collinear down-conversion in BBO

BBO - Collinear type II SPDC

Lens f = 200 mm

U.V. mirror

B.S.P.

Counters

0 2 4 6 80

position

) D1 counts/10000in 10 s

1.6 -- 2.01.2 -- 1.60.8 -- 1.20.4 -- 0.80.0 -- 0.4

0 2 4 6 80

Coincidencesin 10 s

200 -- 250150 -- 200100 -- 150

50 -- 1000 -- 50

Image transfer experiment

D1 horizontal position (mm)

position

aperture

Laser Ar 351 nm

optic axis

astigmatism*

Factors that affect the transfer of angular spectrum

clipping walk-off

* The basic phenomenon behind the mode converter

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)

All deviations from a constant in will affectthe transfer of angular spectrum.

Conclusions and Perspectives

The two-photon wave function carries the information containedin 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 phasematching must be used.

The transfer of longitudinal properties of the pump beam is stillunder investigation.

the two-photon state generated by spontaneous parametric...

Documents

two-photon absorption and two-photon-resonant

quantum enigma machine: experimentally demonstrating...

photon pair-state preparation with tailored spectral ......

spontaneous generation unit 3. what is spontaneous...

calibration of single-photon detectors from spontaneous...

spontaneous and non spontaneous reactions

nanophotonics class 4 density of states. outline spontaneous...

photon-photon colliders ( gg c )

entangled photon pair generation by spontaneous parametric...

registration of spontaneous photon emission from...

photon correlation in single-photon frequency upconversion

entangled photon pair generation by spontaneous parametric...

signatures of two-photon pulses from a quantum two-level...

photon strength function deduced from photon scattering

non-invasive visualization of physiological changes...

measurement of spontaneous photon emission from the human...

physics 200 class #1 outline - depaul university · web...

bolum4b -...

sq-st two photon absorption dynamics of organic dye...

cf-252 spontaneous fission prompt neutron and photon...