Quantum Walks and Phase Transitions in Quadratic Nonlinear Waveguide Arrays
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1 Quatum Walks ad Phase Trasitios i Quadratic Noliear Waveguide Arrays Adrey A. Sukhorukov joit work with Alexader S. Soltsev, Dragomir N. Neshev, Yuri S. Kivshar Noliear Physics Cetre, Australia Natioal Uiversity Frak Setzpfadt, Rolad Schiek, Thomas Pertsch Friedrich-Schiller-Uiversity Jea, Germay Outlie Waveguide arrays i material with quadratic oliearity Secod-harmoic geeratio: Phase trasitio through parametric iteractios; theory ad experimet Spotaeous parametric dowcoversio: Combied photo-pair geeratio ad quatum walks i arrays
2 z Optical arrays de dz - + E + E 0 i +C + = Light tuels betwee s E amplitude at umber C couplig coefficiet Review: Christodoulides, et al., Nature 424, 87 (2003) Periodically poled s i Lithium Niobate Parametric oliear iteractios Liear couplig betwee s Noliear couplig betwee FW ad SH through quadratic oliearity c FW + - period c FW c NL c NL c NL idex profile SH 02 ~750 m FW 00 ~500 m c SH c SH 2
3 Localizatio i quadratic layered structures Statioary (solito) solutios 0exp 0exp2 A z A i z B z B i z Small propagatio costat wide FW drivig force cotrols SH FW ad SH are i phase o staggered SH propagatio costat Large propagatio costat arrow FW drivig FW ad SH are out of phase staggered SH A c A A A B * FW (2) 2 B csh B B A (field) [a.u.] Localizatio & sychroizatio amplitude phase spatial spectrum umber trasverse waveumber =; c FW = c SH = umber (field) [a.u.] umber First theory: Sukhorukov, Kivshar, Bag, Soukoulis, PRE 63, 0665 (200) Experimet: Setzpfadt, Sukhorukov, Neshev, Schiek, Kivshar, Pertsch, PRL 05, (200) FW SH 3
4 Mismatch cotrolled by FW wavelegth Spectral peak aroud i spatial Fourier domai key feature of staggered phase profile Experimetal results 0 s 5 µm period 7 mm log 550 m laser 5.2 ps pulses Experimet: Setzpfadt, Sukhorukov, Neshev, Schiek, Kivshar, Pertsch, PRL 05, (200) Spotaeous Parametric Dow-Coversio Spotaeous Parametric Dow- Coversio (SPDC) is a commo source of etagled photo pairs s i,, k s k i p s i k k k p s i 4
5 Quatum walks of photo pairs sigal detector BBO idler detector array couplig iterface Correlatios of photo pairs at the output of the array coicidece measuremet idler umber Correlated photo pairs a - a 0 at a iput lead to output with o classical aalogy sigal umber Buchig & ati-buchig: sigal & idler photos primarily propagate i the same or opposite directios A. Peruzzo, M. Lobio, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahii, N. Ismail, K. Worhoff, et al., Sciece 329, 500 (200). Our work Simultaeous photo-pair geeratio ad quatum walks i array with quadratic oliearity Quatum statistics govered by: quatum walks - couplig to the right ad left photo correlatios i a pair probabilities to geerate the photo pairs at differet spatial locatios Pump stays i iput Degeerate type-i SPDC Soltsev, Sukhorukov, Neshev, Kivshar (20) submitted Itegrated device for ovel classically cotrollable quatum states 5
6 Photo pair correlatios for pump i oe Pump i oe =0 Phase-mismatch is equal to 0 whe for 0 i s idler detector sigal detector coicidece measuremet i real space K-space Real space I real space buchig ad ati-buchig are archieved Phase mismatch ca be cotrolled by pump wavelegth or temperature 2 With icrease of 4 sigle phase mismatch real-space output becomes classical Soltsev, Sukhorukov, Neshev, Kivshar (20) submitted Photo pair correlatios for pump i two s Pump i two eighbourig s with phase shift P I real space buchig ad ati-buchig switchig ca be cotrolled by phase shift P betwee pump waves I s = (0,) =0 = P = 0 P = π i s idler detector sigal detector K-space coicidece measuremet i real space Real space Soltsev, Sukhorukov, Neshev, Kivshar (20) submitted 6
7 Summary Fudametal effects ad future applicatios of quadratic oliear arrays New type of phase trasitio associated with secod-harmoic geeratio due to a iterplay of localizatio ad sychroisatio Theory: Sukhorukov, Kivshar, Bag, Soukoulis, PRE 63, 0665 (200); Experimet i LiNbO 3 : Setzpfadt et al., PRL 05, (200) Novel itegrated device icorporatig spotaeous parametric dow-coversio ad quatum walks photo pair source with strogly oclassical correlatios with simple classical cotrol of photo statistics by shapig the iput pump Soltsev, Sukhorukov, Neshev, Kivshar (20) submitted 7
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