Arbitrary superpositions of quantum operators by single-photon interference

Transcription

1 Bri, 29 settembre 2009 Società Itlin di Fisic XCV Congresso Nzionle Seoul Ntionl University Arbitrry superpositions of quntum opertors by single-photon interference Alessndro Zvtt CNR-INOA (Firenze) Vlentin Prigi LENS (Firenze) M.S. Kim Queen s University (Belfst) H. Jeong Seoul University (Seoul) Mrco Bellini CNR-INOA (Firenze) 1

2 Outline 1. Experimentl implementtion of photon cretion nd nnihiltion opertors 2. Appliction to completely clssicl light field 3. Direct probing of fundmentl quntum rules 2

3 Implementing single-photon ddition nd subtrction Use photon cretion nd nnihiltion opertors Photon-dded stte Photon-subtrcted stte Conditionl genertion schemes 3

4 Adding single photon to light field Use prmetric mplifiction in nonliner crystl Sty in the low-gin regime (elimintes higher-order excittions) Inject seed pure stte in the signl mode 2ω ω 1 ψ s + s ψ s 1 ω 1 i i χ (2) Stimulted emission regime Emission probbility increses with <n> whenever n idler photon is detected, the signl is prepred in single-photon-excited version of the initil stte 4 A. Zvtt, S. Vicini, M. Bellini, Science 306, 660 (2004)

5 (Pseudo-)therml light source Single-mode fiber Rotting ground glss disk Diffuses the input coherent bem nd dds rndom mplitude nd phse fluctutions 5

6 Experimentl single-photon ddition 6

7 Ultrfst homodyne detection Gted time-domin cquisition Ultr-high bndwidth (~100 MHz) Low electronic noise (S/N >12 db) High subtrction efficiency (~60 82 MHz) A. Zvtt, M. Bellini, P.L. Rmzz, F. Mrin, F.T. Arecchi, J. Opt. Soc. Am. B 19, 1189 (2001). P θ (x θ ) Complete set of qudrture mesurements x θ Mximum likelihood estimtion K. Bnszek, G. M. D Arino, M. G. A. Pris nd M. F. Scchi, PRA 61, (R) (1999) Z. Hrdil, D. Mogilevtsev, J. Rehcek, PRL 96, (2006) Density mtrix elements nm Wigner function 7

8 Experimentl tomogrphic reconstruction _ n=0.1 _ n=1.15 No correction for the finite homodyne detection efficiency Therml sttes A. Zvtt, V. Prigi, M. Bellini, PRA 75, (2007) Single-photon-dded therml sttes 8

9 How to subtrct single photon? On/off detection Input stte Fithful implementtion of the nnihiltion opertor for: - Low BS reflectivity - Low photon numbers 9 J. Wenger, R. Tulle-Brouri, nd P. Grngier, Phys. Rev. Lett. 92, (2004)

10 Experimentl single-photon subtrction 10

11 Less is more _ n=0.36 _ n sub =0.69 Therml stte Photon-subtrcted therml stte 11

12 Combining quntum opertors 12

13 Experimentl sequences of single-photon ddition nd subtrction 13

14 Homodyne dt nd reconstructions Reconstructions corrected for the finite detection efficiency (η=64%) Limited preprtion efficiency (ξ=92%) in the photon-ddition stge dds smll contmintions Clerly different finl sttes V. Prigi, A. Zvtt, M.S. Kim, nd M. Bellini Science 317, 1890 (2007) 14

15 Superpositions of quntum opertors Opticl conditioning signl ( herld light mode) Erses the informtion bout the origin of click Arbitrry superpositions of opertors cn be implemented Apply to ny stte Arbitrry stte superposition 15

16 Complete test of commuttion reltions φ = π Anti-commuttor φ = 0 16 M. S. Kim, H. Jeong, A. Zvtt, V. Prigi, nd M. Bellini Phys. Rev. Lett. 101, (2008) Theoreticl proposl

17 Experimentl opertor superpositions Rw qudrture distributions vs. superposition phse The finl stte strongly depends on the phse of the opertor superposition 17

18 Testing commuttion rules After commuttor Initil therml stte After nti-commuttor Experimentlly reconstructed Wigner functions The stte does not chnge in the commuttor setup 18

19 Quntittive test of commuttion rules Becuse of quntum stte normliztion K=2 K=3 then the nti-commuttor would correspond to K=0 The finl stte strongly depends on the exct vlue of K nd cn be experimentlly tested Rw qudrture histogrms for the nti-commuttor setup Bosonic commuttion reltion is quntittively verified 19 A. Zvtt, V. Prigi, M. S. Kim, H. Jeong, nd M. Bellini Phys. Rev. Lett. 103, (2009)

20 Conclusions First implementtion of bsic quntum opertor sequences nd superpositions Direct test of fundmentl quntum rules Initil steps towrds full quntum stte engineering. quntum light sttes for pplictions? 20

21 Florence Quntum Optics Group Thnk you for your ttention Emil: 21

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23 The photon subtrction Subtrcting single photon from stte my increse the resulting men photon number if the initil stte ws super-poissonin. where n sub = n 1+ F F ( n) n 2 Fno prmeter n sub = n 1 for Fock stte n sub = n n sub = 2n for coherent stte for therml stte!!! Photon cretion nd nnihiltion opertors do not perform deterministic photon ddition nd subtrction! 23 M. Ued, N. Imoto, T. Ogw, Phys. Rev. A 41, 3891 (1990)

24 24 How to subtrct single photon? ( ) )) ( exp( ; 0 0 (0) ) ( b b U U M U Tr b b b dd = λ 0 0 M = 1 PDC opertor ( ) )) ( exp( ; 0 0 (0) ) ( b b B B B M Tr b b b sub = θ ) ( R = sin 2 θ BS opertor BS reflectivity R~1% + 2 (0) 2 4 (0) (0) 4 (0) 4 2 ) ( sub θ θ θ θ θ (0) 2 4 (0) (0) 4 (0) 4 2 ) ( dd λ λ λ λ λ, << 1 θ λ On/off detection F > 98%

25 Subtrcting photons from specil light sttes Therml _ stte n=0.36 Photon-subtrcted therml stte _ n sub =0.69 _ Subtrct one more photon n subsub =1.03 Single-photon Fock stte Vcuum stte 0> 1> 0> 25

26 Testing the invrince of coherent sttes under photon nnihiltion A coherent stte is defined s the eigenstte of the nnihiltion opertor The ction of the nnihiltion opertor leves coherent stte unchnged 26 A. Zvtt, V. Prigi, M.S. Kim, nd M. Bellini, New J. Phys. 10, (2008)