New research activities in quantum optics and quantum information

1. New research activities in quantum optics and quantum information

2. MIT, Cambridge, US Univ. Erlangen, Germany Experimental quantum information in optical fibers Friedrich König + … Theoretical quantum optics and practical quantum communication Natalia Korolkova + 2 year post-doc + ….. Other related activities at St. Andrews: Quantum optics, theory, Prof. U. Leonhardt (black holes) + numerous photonics, nonlinear optics, etc projects

3. Quantum information group in Erlangen • Prof. Gerd Leuchs QIT-Group: N. Lütkenhaus • S. Lorenz R. LoudonM. Curty • N. Korolkova P. van Loock • O. GlöcklT. RalphP. Raynal • Ch. MarquardtP. DrummondK. Tamaki • J. Heersink M. Reid • J. Schneider • A. Dolinska since April: U. Andersen • (C. Silberhorn Oxford) • (F. KönigMIT) “Telekom”: M. Meissner • (T. Gaber)K. Sponsel • A. KornR. HolzlöhnerK. Cevcek

4. Entanglement from OPO, Kimble group (Caltech) 1992 130 fs soliton pulses @ 1.5 m in a fiber Squeezing: Kerr nonlinearity of a fiber (Intensity dependent refractive index) Generation of entanglement Silberhorn, Lam, Weiss, Koenig, Korolkova, Leuchs, PRL 86, 4267 (2000), Leuchs, Ralph, Silberhorn, Korolkova, J. Mod. Opt. 46, 1927 (1999)

5. correlation matrix of the output two mode state: - nonseparability Characterization: Reid et al, PRL 60, 2731 (1988) Duan et al, PRL 84, 2722 (2000), Simon, ibid, 2726 Werner Giedke, Cirac Eisert, Scheel, Plenio Silberhorn, Lam, Weiss, Koenig, Korolkova, Leuchs, PRL 86, 4267 (2000)

6. Quantum interferometry Korolkova et al, Eur. Phys. J. D 18, 229 (2002) Quantum teleportation Gloeckl, Lorenz, Marquardt,Heersink, Silberhorn, Van Loock, Korolkova, Leuchs, Experiment towards CV entanglement swapping: highly correlated 4-partite quantum state, PR A, submitted see talk at QIPC Oxford, Tue For intense beams, direct detection only: Leuchs, Ralph, Silberhorn, Korolkova, J. Mod. Opt. 46, 1927 (1999)

7. Quantum communication with "classical" and non-classical continuous variable polarization states Natalia Korolkova University of Erlangen, Germany University of St. Andrews, Scotland – from 01.09.03 R. Loudon T. C. Ralph J. Heersink T. Gaber O. Glöckl S. Lorenz N. Lütkenhaus S. Lorenz J. Schneider O. Glöckl Ch. Marquardt (Ch. Silberhorn) Gerd Leuchs

8. Continuous polarization variables for quantum communication • Motivation: • Quantum interface • Quantum key distribution • (and ev.other q. comm. tasks)

9. Quantum Stokes operators quantum Poincaré sphere Squeezing: • nonseparability criterion, • entanglement & squeezing properties • operator-valued commutator Heisenberg un. rel. state-dependent Korolkova, Leuchs, Loudon, Ralph, Silberhorn, Phys. Rev. A 65, 052306 (2002); Korolkova, Loudon, submitted (2003)

10. Two orthogonal polarization modes spectrum S c + analyzer 1 - x' spectrum S analyzer x 0 PBS a y y' d b c - spectrum x' S l analyzer 2 / 2 a PBS x ix' y y' y' d 45° b c - spectrum x' S l 4 / analyzer l 3 2 / Only passive elements for direct PBS a ix measurement of all S-parameters y y' d without local oscillator b Continuous polarization variables Stokes operators Direct detection = homodyning with an built-in reference

11. operator-valued commutator: everything gets state-dependent (ent & sq boundaries; Poincare sphere, etc) minimum uncertainty state (coherent state) Construction of minimum uncertainty & coherent states for atomic and agular momentum states J. M. Radcliffe, J. Phys. A 4, 313 (1971). P. W. Atkins, J. C. Dobson, Proc. Roy. Soc. Lond A 321, 321 (1971). R. Jackiw, J. Math. Phys. 9, 339 (1968). F. T. Arecchi, E. Courtens, R. Gilmore, H. Thomas, Phys. Rev. A 6, 2211 (1972). Minimum uncertainty state for all 3 pairs of the Stokes operators number states (for strong 45 linear polarized beam)

12. Overlap two orthogonally polarized amplitude squeezed beams Feedback loop for phase lock Generation of amplitude squeezing: Kerr nonlinearity in optical fibre + Sagnac interferometer

13. S S 0 1 -3,4dB -3,4dB only S1 polarization squeezed S S 2 3 -2,8dB +23,5dB x and y modes amplitude- squeezed beams Heersink,Gaber, Lorenz, Glöckl, Korolkova, Leuchs, quant-ph 2003

14. Which new physics continuous polarization states contain? Let us first look at equivalences: how you can look at polarization states in “old” terms?

15. Polarization states & weak signal with a strong reference  appropriate change of the Stokes basis Polarization squeezing & quadrature entanglement cf. Josse, Dantan, Bramati, Pinard, Giacobino, quant-ph/0302142; Bowen, Treps, Schnabel, Lam, PRL 89, 253601 (02) - “pol”.sq

16. Continuous variable polarization entanglement Korolkova et al, Phys. Rev. A 65, 052306 (2002)

17. Continuous variable polarization entanglement quantum uncertainties of Stokes operators non-locally correlated Non-separability criterion for continuous variables: Duan,Giedke, Cirac, Zoller, PRL 84, 2726 (2000): Simon, ibid: 2722 (For canonical commutator); Korolkova et al PRA (2000); Bowen et al PRL 89, 253601 (02); Korolkova, Loudon, quant-ph 03 Demonstration of the EPR paradox Reid, Drummond, PRL (1988): Reid, PRA (1989) (For canonical commutator)

18. generalized Heisenberg • uncertainty relation cf. Bowen et al PRL 89, 253601 (02) - operator-valued Korolkova, Loudon, quant-ph 03 - sufficient non-separability criterion

19. Continuous variable polarization entanglement Korolkova et al, Phys. Rev. A 65, 052306 (2002) Exp: Bowen, Treps, Schnabel, Lam, Phys. Rev. Lett. (2002) Gloeckl, Heersink, Korolkova, Leuchs, Lorenz, quant-ph (2003)

20. Quantum cryptography

21. 0 Alice Bob 01001 10111 10010 0100... 01001 10111 10010 0100... Eve 1 0,1  H,V QM does not allow Eve to be unrevealed: Eve’s manipulations on quantum states introduce errors in the raw key NEW: protocols with a coherent laser beam: no squeezing! no entanglement! nonorthogonal quantum states  BB84 B92 protocol BB84 protocol Ekert protocol Photonic continuous variables Homodyne detection just two nonorthogonal states Implementations: single photons (weak coherent pulses) single photon detection Efficient sources, detectors High data rates Entangled photon pairs Nonlocality test (Bell inequality) Ralph 2000 (EPR), Hillery (Squeezing), Reid 2000 (EPR), Silberhorn et al 2000 (EPR), Cerf et al, 2001 (Squeezing)….. First implementation of CV crypto: Grangier et al, Nature 421, 238 (2003) Review: Gisin et al, Rev. Mod. Phys.74, 145 (2002) Bennett 1992 Bennett, Brassard 1984 Ekert 1992 nonorthogonal quantum states cannot be discriminated deterministically unknown quantum state cannot be cloned perfectly

22. Continuous variable quantum cryptography using entanglement Silberhorn, Korolkova, Leuchs, IQEC 2000 Nice & Phys.Rev.Lett. 88, 167902 (2002)

23. 4 nonorthogonal state protocol Overlap: Distinguishability between two nonorthogonal states: The smallest possible error probability Pe in a decision about the signal‘s identity The maximum accessible mutual information: Security for quadratures: Ch. Silberhorn, T.C. Ralph, N. Lütkenhaus, G. Leuchs, PRL 89, 167901 (2002) For Stokes operators: N. Korolkova, N. Lütkenhaus, S. Lorenz, G. Leuchs, in preparation

24. and For example: Stokes vector rotated by q: Overlap:  time slots & laser intensity  modulation depth One can achieve desired overlap f0by changing well accessible experimental parameters N. Korolkova, N. Lütkenhaus, S. Lorenz, G. Leuchs, in preparation

25. single photon detection? homodyne detection? else ?? Continuous polarization variables • a set of (nonorthogonal) pure quantum states Modification of the CV protocol for coherent states: Grosshans, Grangier, Phys.Rev.Lett. 88, 057902 (2002) particularly simple detection Q. crypto using coherent states and single photon detection Huttner, Imoto, Gisin, Mor, Phys.Rev. A 51, 1863 (1995) BB84  4 state protocol B92  2 state protocol needs strong reference pulse 4+2 protocol: 4 nonorthogonal states, inbuilt reference on orthogonal polarization  better security performance! Grosshans, Grangier BB84 with many bases and homodyne detection Our protocol  4+2 + homodyning with quantum correlations? (squeezing, entanglement) without?

26. see poster S. Lorenz at QIPC Oxford Proposed set-up U p-pol air or fiber Detector Laser Pol. Rotation S2 , S3/ S0 S1 S2 S3 U CW Laser, either solid state or diode. For air: diode laser  = 810nm; 100 W – 20 mW Electro optic modulator (/4 on/off) Electro optic modulator Balanced detection in two different bases Small modulation depth required => Fast modulation easy Generation of non-orthogonal states with several MHz Measurement with ~1MHz Vision for raw bit rates: @810 nm: Several 100MHz, limited by modulation and detection bandwidth @1550 nm: Several GHz, limited by modulation and detection bandwidth Technical question: is it easier to keep the Stokes vector preserved (over long distances) rather than deal with a LO?

27. Quantum information in St. Andrews (see also outlook in the next talk) Quantum cryptography with and without entanglement CoVa entanglement (concentration, nonlocality, protocols,…) Itrapulse entanglement; Nonlinear coupling: soliton collisions Continuous polarization variables for QIP Squeezing – EIT/SIT

28. Quantum intensity spectral correlations due to Kerr nonlinearity First experimental observation: Spaelter, Korolkova, Koenig, Sizmann, Leuchs, PRL 81, 786 (1998)

29. Intra-entanglement of a macroscopic “particle” travelling down a fiber? q.info SIT medium + Kerr medium Soliton pulses @ 1.5 m X1→ ~ ; Y1 → ~ n X2 → ~ x; Y2 → ~ p How to utilize the internal quantum structure most efficiently? Opatrny, Korolkova, Leuchs, PRA (2002) Partitioning of solitons yielding two entangled macroscopic objects Schmidt, Knoell, Welsch, Opt. Comm. 194, 393 (2001) 4 soliton parametersx, p; n,  Kozlov, Freyberger, Opt. Comm. 206, 287 (2002)

30. Nonlinear coupling Koenig, Zielonka, Sizmann, Transient quantum correlations of colliding solitons, Phys. Rev. A 66, 013812 (2002); Koenig, Buchler, Rechtenwald, Leuchs, Sizmann, ibid, 043810

31. Thank you

32. Efficient generation of polarization-entangled photon pairs at 795 and 1610 Friedrich König, Elliott. J. Mason, Franco N. C. Wong, and Marius A. Albota Funded by: Army Research Office (MURI), National Reconnaissance Office

33. Singlet - state distribution over long distances Local quantum memory: trapped-Rb in cavity Remote quantum memory: trapped-Rb in cavity Alice Bob ~10 km Photon upconverter 795 nm 795nm ~1600 nm Polarization entangled photon pair source Shapiro, New J. Phys. 4 (2002) 47.1 – 47.18 Photon entanglement is transferred to local and remote Rb quantum memories

34. Pump BBO Entangled pairs Photon pair sources Type II parametric downconversion in BBO: • Entanglement in one wavelength and one direction • Filtering required Requirements for teleportation scheme: • Wavelength selection quasi-phase matching: photons at 795nm and 1610nm • Long crystal: Efficient and narrowband source for coupling to Rb • Coupling the output into single mode fibers (TEM00) desired for coupling to Rb cavity or optical fiber delivery

35. Single pass parametric downconversion in 2-cm-PPLN • Inferred generation rate ~2x107 pairs/s/mW of pump power • Tunable outputs centered at 795 nm and 1600 nm • Phasematching bandwidth: 150 GHz E. J. Mason et al., Opt. Lett. 27, 2115 (2002) The signal photon is detected by the Si counter, whose electrical output pulse is used to trigger the gate for the InGaAs detector

36. Modeling the spontaneous output mode T = 183.6°C T = 180.6°C T = 177.6°C Observed divergence angles and Sellmeier equations prediction (s & p-pol.):

37. Single mode coincidence rate before det.: 4074 /s/mWConditional probability: 9.4% (Dl = 0.11nm filter) Single mode coincidence rate before det.: 16430 /s/mW Conditional probability: 5.2% (no filter) Coupling signal and idler into fibers Insertion of an ultra-narrow interference filter: Dl = 0.11nm Signal beam coupling efficiency ~ 18% Without interference filter: Signal beam coupling efficiency: ~ 2%

38. Polarization entangled photon pairs Shapiro and Wong, J. Opt. B 2 (2000) Polarization-entangled state:

39. Polarization entanglement – experimental setup

40. Polarization entanglement – quantum interference 795 nm ~1600nm source 45° variable f -45° + Coincidences Coincidence rate depends on the relative orientation of the analyzers produced state: Triplet Singlet Singlet passive stability: drift << p/4 over 5 min

41. Bell inequality violation Singlet (f = 0) Triplet (f = p) Horizontal Vertical Pump power 2.2 mW per side Visibility: Singlet / Triplet: 94.5 % / 93.7 % Horizontal / Vertical: 99.8 % / 98.0 % Bell violation: S = 2.606 ± 0.010 (Tcounting = 160 s)

42. Bandwidth of collected photons With the quantum interference the length of the interfering photons can be measured and the bandwidth can be estimated Interference visibility reduces by 50% if the paths of the two idlers differ by 2.3 mm • Collected pairs: • 2.3 mm long • 7.5 ps long • 60 GHz bandwidth

43. Summary • Demonstration of efficient downconversion for nondegenerate photon pairs at 795nm and 1600nm • Inferred production rate of 2x107 pairs/s/mW • Characterization and modeling of spatial mode • Coupling in fibers with 9.4% observed coincidence probability • Observation of polarization entanglement via quantum interference, visibility ~94% • Small 60 GHz bandwidth of photons in fiber; ~10 pairs/s/mW in 30 MHz bandwidth for atomic excitation(corrected for Si and InGaAs quantum efficiencies)

44. Experimental quantum information in optical fibers Friedrich König

45. Future research topics QI with qbits CV QI Efficient, bright sources Applications Teleportation Ent. distillation Qu. communication QND Tapping Using fiber optics

46. Content • Why fiber optics? • Fiber-optical photon pair source for quantum communication • CV entanglement generation • Applications…

47. Optical fibers: long nonlinear media

48. 7 h = 2*10 photon-pairs/s/mW of pump power (2) c (3) c (2) c (3) c spontaneous downconversion in Fiber optics + long interaction length + high nonlinearity + quadratic power dependence - poor output mode + generation into the fiber eigenmode + low bandwidth for long fibers because of phase matching - small nonlinear coefficient n 2 Efficient single photon sources Kwiat et al. postdeadline paper 2003 CLEO Conference in Baltimore Pump Crystal König, Mason, Wong, Albota, paper QTuB, 2003 CLEO Conference in Baltimore Mason, Albota, König, and Wong, Opt. Lett. 27, 2115 (2002).

49. Fiber-optic photon pair sources Phasematching in four-wave mixing : Phasematching types: Near zero dispersion wavelength Nonlinear due to In birefringent fibers due to Fiorentino et al., IEEE Ph. Tech. Lett. 14, 983 (2002) Wang et al., J. Opt. B 3,346 (2001) output pump1 pump2 x/y photon pair Pump FWM y x w Coupled-mode equations (classical parametric process): : slowly varying envelope :fiber nonlinearity

50. Cross-polarized fiber pair source • Narrow spectrum with long fibers: bandwidth(b2: dispersion, L: fiber length) • eliminate effects of Polarization mode dispersion • coupling to a resonant system • flexible wavelength choice, degenerate outputs • near perfect mode matching in fundamental mode • compact and stable