Integrated optical circuits for classical and quantum light. Part 2: Integrated quantum optics. Alexander Szameit

Transcription

1 Integrated optical circuits for classical and quantum light Part 2: Integrated quantum optics Alexander Szameit Alexander Szameit +49(0) (0)

2 Outline Introduction Implementation of integrated wave plates Realisation of high-order single-photon W-states Integrated discrete fractional Fourier transforms Summary

3 Rapid growth of global transmitted data

4 Computer power for data processing reaches limit

5 Different platforms for quantum computation ions spins in solids qubits in super conductors Photons

6 Photons as qubits NATURE VOL JANUARY 2001 =

7 Problem: settings are usually large and complex Source: Vienna University

8 How would a photonic quantum computer look like? Source:

9 Size of our photonic quantum computer chips

10 Our (current) setting

11 The integrated beam splitter bulk optics waveguides aout T irain b ir T b out in Jones, J. Opt. Soc. Am. 155, 261 (1965). C coupling constant C Generalized beam splitter: R. Heilmann et al., Appl. Phys. Lett. 105, (2014).

12 Integrated quantum-photonics devices

13 Outline Introduction Implementation of integrated wave plates Realisation of high-order single-photon W-states Integrated discrete fractional Fourier transforms Summary

14 Herstellung Fabrication using mittels ultrashort ultrakurzer laser Laserpulse pulses

15 Polarization dependency index raise and mode profile depend on polarisation polarization dependent coupling additional degree of freedom

16 Polarization dependent coupling

17 Polarizing beam splitters polarization dependent transmission in a directional coupler PPBS C coupling constant C

18 General phase gate general phase gate PBSs and geometrical length shift G phase 1 0 e 0 i polarization dependent transmission in a directional coupler PPBS

19 Arbitrary wave plate: fundamentals polarized light Jones formalism wave plate: fast axis orientation α phase shifts φ o, φ e retardation Δφ = φ e φ o M waveplate J E E out in x x M out J in E y E y io 2 ie 2 io i e e cos e sin e e sin cos io ie io 2 ie 2 e e sin cos e sin e cos 2 i 2 i cos e sin 1 e sin cos io e i 2 i 2 1 e sin cos sin e cos

20 Particular wave plates polarized light Jones formalism wave plate: fast axis orientation α phase shifts φ o, φ e retardation Δφ = φ e φ o HWP: Δφ = π Pauli-X: α = 45 Hadamard: α = 22.5 E E out in x x M out J in E y E y waveplate M J M J M J 2 2 cos sin 2sin cos 2sin cos sin cos 2 2 cos2 sin 2 2sin cos2 HWP HWP

21 Birefringence in waveguides Fernandes et al., Opt. Express 20, (2012).

22 Tunable birefringence in laser-written waveguides fast axis cross section Fernandes et al., Opt. Express 20, (2012). index ellipsoid

23 Tunable birefringence in laser-written waveguides fast axis cross section Heilmann et al., Scientific Reports 4, 4118 (2014) index ellipsoid

24 Classical light measurements =45 Pauli-X Pauli-X Hadamard =22.5 Hadamard Heilmann et al., Scientific Reports 4, 4118 (2014)

25 Quantum light measurements F H, V X 0.992(7) F H, V Had 0.999(5)

26 Outline Introduction Implementation of integrated wave plates Realisation of high-order single-photon W-states Integrated discrete fractional Fourier transforms Summary

27 Multipartite entangled W-states coherent superposition of eigenstates robust against loss [Dür et al., Phys. Rev. A 62, (2000)] secure communication [Yuan et al., Int. J. Quantum Inform. 9, 607 (2011)] teleportation [Shi & Tomita Phys. Lett. A 296, 161 (2002); Joo et al., New J. Phys. 5, 136 (2005)] quantum cloning machines [Bruß et al., Phys. Rev. A 57, 2368 (1998)] genuine random number generation

28 Generation of even-order W-states

29 W-states via waveguide arrays ĈC C C ĈC prob. Engineered coupling coefficients Perez-Leija et al., PRA 87, (2013).

30 Generation of odd-order W-states

31 Experimental results WR in optics WR in ultra cold atoms Gräfe et al., Nature Photon. 8, 791 (2014).

32 Coherence test Gräfe et al., Nature Photon. 8, 791 (2014).

33 Entanglement verification Entanglement verification due to fidelity criterion: number of modes Inspired by Lougovski et al., New J. Phys. 11, (2009)

34 Quantum Random Number Generation using W-states eigenstates have equal probability amplitude no post processing required (e.g. Hash function) in practice: output 1 to 8 numbers 0 to 7 photon time steps range of QRNG statistical tests by NIST N 0 8 N 1 for M output channels: 0 M N 1 generation of QRNG on demand & on chip limitation in speed only by single-photon source & detector efficiency

35 Outline Introduction Implementation of integrated wave plates Realisation of high-order single-photon W-states Integrated discrete fractional Fourier transforms Summary

36 The Fourier transform: Useful everywhere Optics Electrodynamics Quantum Mechanics Image and Signal Processing Statististics & Finance Theory Economics

37 The fractional Fourier transform 2 1 tan e e e d 0 V. Namias, J.Inst.Maths. Applics 25,241 (1980).

38 Applications of the discrete Fourier transform Beam synthesis and shaping Joint frequency-time analysis Quantum wavefield reconstruction FrFT Differential equations Phase estimation Encryption theory H. A. Ozaktas, The fractional Fourier transform and its applications, Wiley (2003).

39 Fractional Fourier transform J x operator harmonic oscillator Fourier operator: fractional Fourier transform Namias, J. Inst. Appl. Math. 25, 241 (1980)

40 The fractional Fourier transform J x operator fractional Fourier transform

41 Discrete fractional Fourier transform J x operator harmonic oscillator discrete fractional Fourier transform Atakishiyev & Wolf, J. Opt. Soc. am. A 14, 1467 (1997)

42 Transferring the Hamiltonian to photonics with parabolic coupling distribution coupling J n J x photonic lattices 1 N n 1 n 2 n 1 n n+1 n+2 J n 1 J n J n+1 J n 2 Perez Leija et al., Phys. Rev. A 87, (2013). Perez Leija et al., Phys. Rev. A 87, (2013). N

43 The discrete fractional Fourier transform on chip

44 Classical experiments Weimann et al., Nature Commun. 7, (2015). Arrays with 21 elements and L= 7.5 cm

45 Classical experiments output: sinc like function 21 waveguides 7.5 cm long Z Z input: top hat function + phase ramp!

46 J x lattice & eigenstates element of the unitary propagation operator: transition probability amplitude from site to Weimann et al., Nature Commun. 7, (2015). eigenfunction of the J x lattice

47 2-photon quantum interferometry separable N00N Brobov et al., Phys. Rev. A 89, (2014).

48 Photon correlations in our FT device N 2 N 1 N Weimann et al., Nature Commun. 7, (2015). Fourier Suppression Law: Tichy et al., Phys. Rev Lett. 113, (2014).

49 Conclusions fs-laser written waveguides for integrated quantum circuits realization of integrated PPBS arbitrary wave plates in optical integrated devices using induced birefringence generation of W-states with 16 modes discrete fractional Fourier transform