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Trapped Ion Spectroscopy

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Quantum-Enhanced Nonlinear Spectroscopy

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

So far, we have been concerned with the development of novel spectroscopic techniques to investigate the dynamics of complex quantum systems such as molecular aggregates. This final chapter will present novel protocols to obtain nonlinear spectroscopic signals in a very different setup - namely in linear chains of trapped ions. The goal in this chapter is to provide a versatile toolbox to probe and to characterize the emergent complexity in such well-controlled systems. In strong contrast to the spirit of tomographic methods in quantum information, these methods do not intend to characterize the full quantum state of the system, but instead to tailor custom-fit measurement protocols to investigate desired processes or properties of the system. The crucial ingredient in this undertaking is the use of ladder diagrams, which yield the intuition necessary to estimate the information content of the created signals beforehand.

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Notes

  1. 1.

    The results presented in this chapter were obtained in collaboration with Manuel Gessner, so a similar presentation thereof can be found in [Gessner15].

  2. 2.

    We trust that these protocols are equally applicable to similar synthetic quantum systems such as, e.g., cold atoms in optical lattices [Bloch08], or Rydberg atoms in optical tweezers [Saffman10, Fuhrmanek11].

  3. 3.

    Details can be found in the dissertation of M. Gessner [Gessner15].

  4. 4.

    The interaction term is clearly invariant under the simultaneous flip of all the spin in the x-direction, which changes \(\sigma ^{(k)}_x \rightarrow - \sigma ^{(k)}_x\).

  5. 5.

    In the present chapter, we only consider signals in the impulsive limit. Hence, to simplify our notation, we dropped the superscript “\(^{(0)}\)” for the time delays in Eq. (2.141).

  6. 6.

    In case a single excitation pulse interacts multiple times with the sample (e.g. when driving two consecutive excitations in the system), it is understood that the intermediate propagators are evaluated at \(t_i = 0\), and hence only yield the identity, \(\mathcal {G} (0) = \mathcal {I}\). Such a scenario will be discussed in the next section.

  7. 7.

    For the Liouville space notation, see Sect. 2.2.

  8. 8.

    Our following discussion may also be applied to systems in thermal equilibrium, for instance. One simply needs to take additional diagrams into account, just like in our discussion of multiple excitations in the previous Sect. 7.3.4.

  9. 9.

    In optical signals, GSB and ESE pathways show up as positive resonances and ESA as a negative contribution (compare Chap. 4). Here, the signs are reversed, but their relative signs remain the same. We employ the terminology for the pathways developed in Ref. [Lott11].

References

  1. M. Gessner, Dynamics and Characterization of Composite Quantum Systems. Ph.D. thesis, Albert-Ludwidgs Universität Freiburg (2015)

    Google Scholar 

  2. I. Bloch, J. Dalibard, W. Zwerger, Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008)

    Article  ADS  Google Scholar 

  3. M. Saffman, T.G. Walker, K. Mølmer, Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313–2363 (2010)

    Article  ADS  Google Scholar 

  4. A. Fuhrmanek, R. Bourgain, Y.R.P. Sortais, A. Browaeys, Free-space lossless state detection of a single trapped atom. Phys. Rev. Lett. 106, 133003 (2011)

    Article  ADS  Google Scholar 

  5. M. Ramm, T. Pruttivarasin, H. Häffner, Energy transport in trapped ion chains. New J. Phys. 16, 063062 (2014)

    Article  ADS  Google Scholar 

  6. J. Johansson, P. Nation, F. Nori, Qutip 2: a python framework for the dynamics of open quantum systems. Comp. Phys. Commun. 184, 1234–1240 (2013)

    Article  ADS  Google Scholar 

  7. D. Porras, J.I. Cirac, Bose–Einstein condensation and strong-correlation behavior of phonons in ion traps. Phys. Rev. Lett. 93, 263602 (2004)

    Article  ADS  Google Scholar 

  8. D. Leibfried, R. Blatt, C. Monroe, D. Wineland, Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281–324 (2003)

    Article  ADS  Google Scholar 

  9. D. James, Quantum dynamics of cold trapped ions with application to quantum computation. Appl. Phys. B 66, 181–190 (1998)

    Article  ADS  Google Scholar 

  10. M. Gessner, F. Schlawin, H. Häffner, S. Mukamel, A. Buchleitner, Nonlinear spectroscopy of controllable many-body quantum systems. New J. Phys. 16, 092001 (2014)

    Article  ADS  Google Scholar 

  11. F. Schlawin, M. Gessner, S. Mukamel, A. Buchleitner, Nonlinear spectroscopy of trapped ions. Phys. Rev. A 90, 023603 (2014)

    Article  ADS  Google Scholar 

  12. H. Häffner, C. Roos, R. Blatt, Quantum computing with trapped ions. Phys. Rep. 469, 155–203 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  13. J.I. Cirac, P. Zoller, Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995)

    Article  ADS  Google Scholar 

  14. A. Sørensen, K. Mølmer, Quantum computation with ions in thermal motion. Phys. Rev. Lett. 82, 1971–1974 (1999)

    Article  ADS  Google Scholar 

  15. D. Porras, J.I. Cirac, Effective quantum spin systems with trapped ions. Phys. Rev. Lett. 92, 207901 (2004)

    Article  ADS  Google Scholar 

  16. L. Reichl, A Modern Course in Statistical Physics (Wiley, Weinheim, 2009)

    Google Scholar 

  17. P. Hamm, M. Zanni, Concepts and Methods of 2D Infrared Spectroscopy (Cambridge University Press, Cambridge, 2011)

    Book  Google Scholar 

  18. S. Mukamel, S. Rahav, Ultrafast nonlinear optical signals viewed from the molecule’s perspective: Kramers–Heisenberg transition-amplitudes versus susceptibilities, in Advances in Atomic, Molecular, and Optical Physics, vol. 59, Advances In Atomic, Molecular, and Optical Physics, ed. by P.B.E. Arimondo, C. Lin (Academic, Waltham, 2010), pp. 223–263

    Chapter  Google Scholar 

  19. T. Peifang, D. Keusters, Y. Suzaki, W.S. Warren, Femtosecond phase-coherent two-dimensional spectroscopy. Science 300, 1553–1555 (2003)

    Article  ADS  Google Scholar 

  20. P.F. Tekavec, G.A. Lott, A.H. Marcus, Fluorescence-detected two-dimensional electronic coherence spectroscopy by acousto-optic phase modulation. J. Chem. Phys. 127, 214307 (2007)

    Article  ADS  Google Scholar 

  21. J.F. Poyatos, J.I. Cirac, P. Zoller, Quantum reservoir engineering with laser cooled trapped ions. Phys. Rev. Lett. 77, 4728–4731 (1996)

    Article  ADS  Google Scholar 

  22. C.J. Myatt, B.E. King, Q.A. Turchette, C.A. Sackett, D. Kielpinski, W.M. Itano, C. Monroe, D.J. Wineland, Decoherence of quantum superpositions through coupling to engineered reservoirs. Nature 403, 269–273 (2000)

    Article  ADS  Google Scholar 

  23. J.T. Barreiro, M. Müller, P. Schindler, D. Nigg, T. Monz, M. Chwalla, M. Heinrich, C.F. Roos, P. Zoller, R. Blatt, An open-system quantum simulator with trapped ions. Nature 470, 486–491 (2011)

    Article  ADS  Google Scholar 

  24. H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)

    MATH  Google Scholar 

  25. S.L. Sondhi, S.M. Girvin, J.P. Carini, D. Shahar, Continuous quantum phase transitions. Rev. Mod. Phys. 69, 315–333 (1997)

    Article  ADS  Google Scholar 

  26. M. Gessner, M. Ramm, H. Häffner, A. Buchleitner, H.-P. Breuer, Observing a quantum phase transition by measuring a single spin. EPL 107, 40005 (2014)

    Article  ADS  Google Scholar 

  27. P. Jurcevic, B.P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, C.F. Roos, Quasiparticle engineering and entanglement propagation in a quantum many-body system. Nature 511, 202–205 (2014)

    Article  ADS  Google Scholar 

  28. M.A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, M. Rigol, One dimensional bosons: From condensed matter systems to ultracold gases. Rev. Mod. Phys. 83, 1405–1466 (2011)

    Article  ADS  Google Scholar 

  29. J. Madroñero, A. Ponomarev, A.R. Carvalho, S. Wimberger, C. Viviescas, A. Kolovsky, K. Hornberger, P. Schlagheck, A. Krug, A. Buchleitner, G. Rempe, M.O. Scully, Quantum Chaos, Transport, and Control—in Quantum Optics (Academic Press, Waltham, 2006), pp. 33–73

    Google Scholar 

  30. A.R. Kolovsky, A. Buchleitner, Quantum chaos in the Bose–Hubbard model. EPL 68, 632 (2004)

    Article  ADS  MATH  Google Scholar 

  31. H. Venzl, A.J. Daley, F. Mintert, A. Buchleitner, Statistics of Schmidt coefficients and the simulability of complex quantum systems. Phys. Rev. E 79, 056223 (2009)

    Article  ADS  Google Scholar 

  32. Z. Li, D. Abramavičius, S. Mukamel, Probing electron correlations in molecules by two-dimensional coherent optical spectroscopy. J. Am. Chem. Soc. 130, 3509–3515 (2008)

    Article  Google Scholar 

  33. J. Kim, S. Mukamel, G.D. Scholes, Two-dimensional electronic double-quantum coherence spectroscopy. Acc. Chem. Res. 42, 1375–1384 (2009)

    Article  Google Scholar 

  34. S. Mukamel, Principles of Nonlinear Optical Spectroscopy, Oxford Series on Optical Sciences (Oxford University Press, Oxford, 1999)

    Google Scholar 

  35. G.A. Lott, A. Perdomo-Ortiz, J.K. Utterback, J.R. Widom, A. Aspuru-Guzik, A.H. Marcus, Conformation of self-assembled porphyrin dimers in liposome vesicles by phase-modulation 2d fluorescence spectroscopy. Proc. Nat. Acad. Sci. 108, 16521–16526 (2011)

    Article  ADS  Google Scholar 

  36. R. Hildner, D. Brinks, N.F. van Hulst, Femtosecond coherence and quantum control of single molecules at room temperature. Nature Phys. 7, 172–177 (2011)

    Article  ADS  Google Scholar 

  37. R. Hildner, D. Brinks, J.B. Nieder, R.J. Cogdell, N.F. van Hulst, Quantum coherent energy transfer over varying pathways in single light-harvesting complexes. Science 340, 1448–1451 (2013)

    Article  ADS  Google Scholar 

  38. S. Mukamel, Communications: signatures of quasiparticle entanglement in multidimensional nonlinear optical spectroscopy of aggregates. J. Chem. Phys. 132, 241105 (2010)

    Article  ADS  Google Scholar 

  39. M. Walschaers, A. Buchleitner, M. Fannes, On optimal currents of indistinguishable particles (2016). To be published

    Google Scholar 

  40. R. Ernst, G. Bodenhausen, A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, International Series of Monographs on Chemistry (Clarendon Press, Oxford, 1990)

    Google Scholar 

  41. D.A. Lidar, I.L. Chuang, K.B. Whaley, Decoherence-free subspaces for quantum computation. Phys. Rev. Lett. 81, 2594–2597 (1998)

    Article  ADS  Google Scholar 

  42. J. Benhelm, G. Kirchmair, C.F. Roos, R. Blatt, Towards fault-tolerant quantum computing with trapped ions. Nature Phys. 4, 463–466 (2008)

    Article  ADS  Google Scholar 

  43. C. Monroe, D.M. Meekhof, B.E. King, D.J. Wineland, A “schrödinger cat” superposition state of an atom. Science 272, 1131–1136 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  44. M.A. Nielsen, I.L. Chuang, Quantum computation and quantum information (Cambridge University Press, Cambridge, 2010)

    Google Scholar 

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  1. Clarendon Laboratory, University of Oxford, Oxford, UK

    Frank Schlawin

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  1. Frank Schlawin
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Schlawin, F. (2017). Trapped Ion Spectroscopy. In: Quantum-Enhanced Nonlinear Spectroscopy. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-44397-3_7

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