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Quantum Simulation of the Haldane Phase

Quantum Simulation of the Haldane Phase. 19.12.2013 HUJI Alex Retzker Sussex Quantum Simulations with Trapped Ions, 2013 Itsik Cohen Accepted to PRL. MAGIC - Magnetic Gradient Induced Coupling. V. z. F. Mintert and C Wunderlich, PRL 87 , 257904 (2001); .

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Quantum Simulation of the Haldane Phase

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  1. Quantum Simulation of the Haldane Phase 19.12.2013 HUJI Alex Retzker Sussex Quantum Simulations with Trapped Ions, 2013 Itsik Cohen Accepted to PRL

  2. MAGIC - Magnetic Gradient Induced Coupling V z F. Mintertand C Wunderlich, PRL 87, 257904 (2001);

  3. MAGIC - Magnetic Gradient Induced Coupling MAGIC F. Mintertand C Wunderlich, PRL 87, 257904 (2001); δ z |1 Use microwave instead of laser light |0

  4. Short Qubit coherence time Ramsey experiment T ≈ 5 ms mF=+1 mF=0 mF=-1 F=1 F=0 mF=0

  5. Hahn Echo: SussexI 19.12.2013 I Folie: 5

  6. Background Carr Purcell – CP Spin echo decay A sequence of echos, i.e., of π pulses focuses the polarization for a long time z y x SussexI 19.12.2013 I Folie: 6

  7. Carr Purcell – CP: Spin echo decay A sequence of echos, i.e., of π pulses focuses the polarization for a long time z z y y 2 δΦ x π+δΦ x SussexI 19.12.2013 I Folie: 7

  8. Composite pulses Goal: z Real pulse: but: y • Torosov & Vitanov, PRA 87, 043418 (2013). Kyoseva & Vitanov arxiv:1310.7145. • Wang et al., arxiv: 1312.4523 And nowwecanusethe Suzuki Trotterdecomposition x The optimizationis on operationsnot on memorybut theoreticallythedifferenceisverysmall. • Kenneth R. Brown, Aram W. Harrow, and Isaac L. Chuang, PRA 70, 052318 (2004) SussexI 19.12.2013 I Folie: 8

  9. Coherentcontrol Timoney et, al., 2007 • Montangero et,. Al. PRL 99, 170501 (2007) SussexI 19.12.2013 I Folie: 9

  10. Search for a stablequbit Can we somehow construct two ‘good’ qubit levels? No dephasing but no coupling Coupled but strongly dephased SussexI 19.12.2013 I Folie: 10

  11. DynamicalDecoupling: take I Flipping(T1) Rate: Dephasing(T2) Rate: Dephasing(T2) Rate: +second order B effects SussexI 19.12.2013 I Folie: 11

  12. Dynamical Decoupling: take II Flipping(T1) Rate: + Relative phase fluctuations Dephasing(T2) Rate: +second order B effects SussexI 19.12.2013 I Folie: 12

  13. Ramsey measurementresults N. Timoney, I. Baumgart, M. Johanning, A. F. Varon, M. B. Plenio, A. Retzker & Ch. Wunderlich. Nature 476 (2011) SussexI 19.12.2013 I Folie: 13

  14. Rabi Oscillationofthe Sussex group S. C. Webster, S. Weidt, K. Lake, J. J. McLoughlin, and W. K. Hensinger. PRL 111, 140501 (2013) SussexI 19.12.2013 I Folie: 14

  15. Robustnesstoexternalnoise Generalisation to N levels General conditions: foreachi,j Robustnesstocontrolnoise foreach i Level structureofthecalciumion. N. Aharon, M. Drewsen, and A. Retzker, PRL 111, 230507 (2013) SussexI 19.12.2013 I Folie: 15

  16. Generalisation to N levels N. Aharon, M. Drewsen, and A. Retzker, PRL 111, 230507 (2013) SussexI 19.12.2013 I Folie: 16

  17. TheBoulderScheme C. Ospelkaus, et. al., PRL 101, 090502 (2008) C. Ospelkaus, et. al., Nature 476, 181 (2011)

  18. Oxford group D.P.L AudeCraik, et al., arxiv: 1308.2078

  19. Magnetometry locking the signal to the frequency of the pulses(Rabi frequency) Kotler et al., Nature, 473 (2011)

  20. Magnetometry locking to the frequency and not the Rabi frequency I. Baumgart, J.-M. Cai, A. Retzker, M. Plenio, andCh. Wunderlich, In preparation

  21. Magnetometry I. Baumgart, J.-M. Cai, A. Retzker, M. Plenio, andCh. Wunderlich, In preparation

  22. The Haldane Phase in the S=1 XXZ Antiferromagnetic chain Flip flops Neel Order Invariant under global rotations around z and global spin flips

  23. The Haldane Phase in the S=1 XXZ Antiferromagnetic chain Finite energy gap, short range correlations. (Haldane, 1983) Nonlocal string order parameter (Tasaki and Kennedy, 1987) Symmetry protected double-degeneracy of the entanglement spectrum (Pollmann et at., 2010)

  24. Spin degreesoffreedom This setup only kills external magnetic noise, but is not robust to power fluctuations We have to work in a decoherence free subspace The decoherence free subspace: SussexI 19.12.2013 I Folie: 24

  25. term The Analogousto a red/bluesidbandinteraction Flip flops will happend automaticallyifwestart in the DFS SussexI 19.12.2013 I Folie: 25

  26. Two-qubitgate almost: Gets into a fully entangled state in the middle; Schmidt number 3

  27. The effectiveHamiltonian – singlequbit Forzerotemperature Hasnoeffect For a thermal state Hasnoeffect SussexI 19.12.2013 I Folie: 27

  28. The effectiveHamiltonian – twoqubit Virtual phonon SussexI 19.12.2013 I Folie: 28

  29. The effectiveHamiltonian – the D term

  30. The effectiveHamiltonian – theλterm Byadding a termofthe form:

  31. The effectiveHamiltonian – theλterm Byadding a termofthe form: z y x

  32. The effectiveHamiltonian – theλterm In theinteractionpicture

  33. Reachingthe Haldane phase All thetransitionsaresecondorderandthushardtocross To break thesymmetriesweaddtheterm:

  34. Detectingthe Haldane phase 1) String order: 2) Double degenrate entanglementspectrum 3) Gap andexponentialydecayingcorrelationfunction

  35. Open postdoc and PhD positions Thanks a lot for your attention! ISF CIG Career integration grant

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