Abstract

The leakage suppression problem is considered for a three-level ladder-type quantum system, in which the first two levels are the qubit system and the third is the leakage state weakly coupled to the qubit system. We show that two (three) phase- and amplitude-controlled pulses are sufficient for arbitrary qubit controls from the ground (an arbitrary) initial state, with leakage suppressed up to the first order of perturbation without additional pulse-area cost. A proof-of-principle experiment was performed with shaped ultrafast optical pulses and cold rubidium atoms, and the result shows a good agreement with the theory.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. A. Derevianko, P. Kómár, T. Topcu, R. M. Kroeze, and M. D. Lukin, “Effects of molecular resonances on Rydberg blockade,” Phys. Rev. A. 92, 063419 (2015).
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    [Crossref]
  4. F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, “Simple pulse for elimination of leakage in weakly nonlinear qubits,” Phys. Rev. Lett. 103, 110501 (2009).
    [Crossref]
  5. Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
    [Crossref]
  6. A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotation by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
    [Crossref]
  7. C. A. Ryan, C. Negrevergne, M. Laforest, E. Knill, and R. Laflamme, “Liquid-state nuclear magnetic resonance as a testbed for developing quantum control methods,” Phys. Rev. A 78, 012328 (2008).
    [Crossref]
  8. A. Spörl, T. Schulte-Herbrüggen, S. J. Glaser, V. Bergholm, M. J. Storcz, J. Ferber, and F. K. Wilhelm,” Optimal control of coupled Josephson qubits,” Phys. Rev. A 75, 012302 (2007).
    [Crossref]
  9. P. Rebentrost and F. K. Wilhelm, “Optimal control of a leaking qubit,” Phys. Rev. B 79, 060507(R) (2009).
    [Crossref]
  10. P. Doria, T. Calarco, and S. Montangero, “Optimal control technique for many-body quantum dynamics,” Phys. Rev. Lett. 106, 190501 (2011).
    [Crossref] [PubMed]
  11. L. S. Theis, F. Motzoi, F. K. Wilhelm, and M. Saffman, “High-fidelity Rydberg-blockade entangling gate using shaped, analytic pulses,” Phys. Rev. A 94, 032306 (2016).
    [Crossref]
  12. A. Kiely and A. Ruschhaupt, “Inhibiting unwanted transitions in population transfer in two- and three-level quantum systems,” J. Phys. B: At. Mol. Opt. Phys. 47, 115501 (2014).
    [Crossref]
  13. F. Motzoi and F. K. Wilhelm, “Improving frequency selection of driven pulses using derivative based transition suppression,” Phys. Rev. A 88, 062318 (2013).
    [Crossref]
  14. J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
    [Crossref]
  15. E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
    [Crossref]
  16. G. T. Genov and N. V. Vitanov, “Dynamical suppression of unwanted transitions in multistate quantum system,” Phys. Rev. Lett. 110, 133002 (2013).
    [Crossref]
  17. G. T. Genov, B. T. Torosov, and N. V. Vitanov, “Optimized control of multistate quantum systems by composite pulse sequences,” Phys. Rev. A,  84, 063413 (2011).
    [Crossref]
  18. J. Randall, A. M. Lawrence, S. C. Webster, S. Weidt, N. V. Vitanov, and W. K. Hensinger, “Generation of high-fidelity quantum control methods for multilevel systems,” Phys. Rev. A 98, 043414 (2018).
    [Crossref]
  19. D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (2008).
    [Crossref]
  20. K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
    [Crossref]
  21. Y. Song, H. Lee, H. Kim, H. Jo, and J. Ahn, “Subpicosecond X rotations of atomic clock states,” Phys. Rev. A 97, 052322 (2018).
    [Crossref]
  22. W. C. Campbell, J. Mizrahi, Q. Quraishi, C. Senko, D. Hayes, D. Hucul, D. N. Matsukevich, P. Maunz, and C. Monroe, “Ultrafast gates for single atomic qubits,” Phys. Rev. Lett. 105, 090502 (2010).
    [Crossref]
  23. J. Ghosh, S. N. Coppersmith, and M. Friesen, “Pulse sequences for suppressing leakage in single-qubit gate operations,” Phys. Rev. B 95, 241307 (2017).
    [Crossref]
  24. J. Lim, H. Lee, S. Lee, C. Y. Park, and J. Ahn, “Ultrafast Ramsey interferometry to implement cold atomic qubit gates,” Sci. Rep. 4, 5867 (2014).
    [Crossref]
  25. H. Lee, H. Kim, and J. Ahn, “Ultrafast laser-driven Rabi oscillations of a trapped atomic vapor,” Opt. Lett. 40, 510–513 (2015).
    [Crossref]
  26. H. Jo, H. G. Lee, S. Guérin, and J. Ahn, “Robust two-level system control by a detuned and chirped laser pulse,” Phys. Rev. A,  96, 033403 (2017).
    [Crossref]
  27. H. G. Lee, Y. Song, and J. Ahn, “Single-laser-pulse implementation of arbitrary ZYZ rotations of an atomic qubit,” Phys. Rev. A. 96, 012326 (2017).
    [Crossref]
  28. P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245–249 (1997).
    [Crossref]
  29. A. M. Weiner, “Ultrafast optical pulse shaping: a tutorial review,” Opt. Commun. 284, 3669–3692 (2011).
    [Crossref]
  30. B. W. Shore, “Two-state behavior in N-state quantum systems: The Morris shore transformation reviewed,” J. Mod. Opt. 61, 787–815 (2013).
    [Crossref]
  31. J. P. Provost and G. Vallee, “Riemannian structure on manifolds of quantum states,” Commun. Math. Phys. 76, 289–301 (1980).
    [Crossref]
  32. D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
    [Crossref]

2018 (2)

J. Randall, A. M. Lawrence, S. C. Webster, S. Weidt, N. V. Vitanov, and W. K. Hensinger, “Generation of high-fidelity quantum control methods for multilevel systems,” Phys. Rev. A 98, 043414 (2018).
[Crossref]

Y. Song, H. Lee, H. Kim, H. Jo, and J. Ahn, “Subpicosecond X rotations of atomic clock states,” Phys. Rev. A 97, 052322 (2018).
[Crossref]

2017 (3)

J. Ghosh, S. N. Coppersmith, and M. Friesen, “Pulse sequences for suppressing leakage in single-qubit gate operations,” Phys. Rev. B 95, 241307 (2017).
[Crossref]

H. Jo, H. G. Lee, S. Guérin, and J. Ahn, “Robust two-level system control by a detuned and chirped laser pulse,” Phys. Rev. A,  96, 033403 (2017).
[Crossref]

H. G. Lee, Y. Song, and J. Ahn, “Single-laser-pulse implementation of arbitrary ZYZ rotations of an atomic qubit,” Phys. Rev. A. 96, 012326 (2017).
[Crossref]

2016 (3)

M. Saffman, “Quantum computing with atomic qubits and rydberg interactions: progress and challenges,” J. Phys. B: At. Mol. Opt. Phys. 49, 202001 (2016).
[Crossref]

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

L. S. Theis, F. Motzoi, F. K. Wilhelm, and M. Saffman, “High-fidelity Rydberg-blockade entangling gate using shaped, analytic pulses,” Phys. Rev. A 94, 032306 (2016).
[Crossref]

2015 (2)

A. Derevianko, P. Kómár, T. Topcu, R. M. Kroeze, and M. D. Lukin, “Effects of molecular resonances on Rydberg blockade,” Phys. Rev. A. 92, 063419 (2015).
[Crossref]

H. Lee, H. Kim, and J. Ahn, “Ultrafast laser-driven Rabi oscillations of a trapped atomic vapor,” Opt. Lett. 40, 510–513 (2015).
[Crossref]

2014 (2)

J. Lim, H. Lee, S. Lee, C. Y. Park, and J. Ahn, “Ultrafast Ramsey interferometry to implement cold atomic qubit gates,” Sci. Rep. 4, 5867 (2014).
[Crossref]

A. Kiely and A. Ruschhaupt, “Inhibiting unwanted transitions in population transfer in two- and three-level quantum systems,” J. Phys. B: At. Mol. Opt. Phys. 47, 115501 (2014).
[Crossref]

2013 (4)

F. Motzoi and F. K. Wilhelm, “Improving frequency selection of driven pulses using derivative based transition suppression,” Phys. Rev. A 88, 062318 (2013).
[Crossref]

G. T. Genov and N. V. Vitanov, “Dynamical suppression of unwanted transitions in multistate quantum system,” Phys. Rev. Lett. 110, 133002 (2013).
[Crossref]

D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
[Crossref]

B. W. Shore, “Two-state behavior in N-state quantum systems: The Morris shore transformation reviewed,” J. Mod. Opt. 61, 787–815 (2013).
[Crossref]

2011 (5)

K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
[Crossref]

A. M. Weiner, “Ultrafast optical pulse shaping: a tutorial review,” Opt. Commun. 284, 3669–3692 (2011).
[Crossref]

G. T. Genov, B. T. Torosov, and N. V. Vitanov, “Optimized control of multistate quantum systems by composite pulse sequences,” Phys. Rev. A,  84, 063413 (2011).
[Crossref]

P. Doria, T. Calarco, and S. Montangero, “Optimal control technique for many-body quantum dynamics,” Phys. Rev. Lett. 106, 190501 (2011).
[Crossref] [PubMed]

J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
[Crossref]

2010 (3)

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotation by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
[Crossref]

W. C. Campbell, J. Mizrahi, Q. Quraishi, C. Senko, D. Hayes, D. Hucul, D. N. Matsukevich, P. Maunz, and C. Monroe, “Ultrafast gates for single atomic qubits,” Phys. Rev. Lett. 105, 090502 (2010).
[Crossref]

2009 (2)

F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, “Simple pulse for elimination of leakage in weakly nonlinear qubits,” Phys. Rev. Lett. 103, 110501 (2009).
[Crossref]

P. Rebentrost and F. K. Wilhelm, “Optimal control of a leaking qubit,” Phys. Rev. B 79, 060507(R) (2009).
[Crossref]

2008 (2)

C. A. Ryan, C. Negrevergne, M. Laforest, E. Knill, and R. Laflamme, “Liquid-state nuclear magnetic resonance as a testbed for developing quantum control methods,” Phys. Rev. A 78, 012328 (2008).
[Crossref]

D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (2008).
[Crossref]

2007 (1)

A. Spörl, T. Schulte-Herbrüggen, S. J. Glaser, V. Bergholm, M. J. Storcz, J. Ferber, and F. K. Wilhelm,” Optimal control of coupled Josephson qubits,” Phys. Rev. A 75, 012302 (2007).
[Crossref]

2000 (1)

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A 62, 042305 (2000).
[Crossref]

1997 (1)

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245–249 (1997).
[Crossref]

1980 (1)

J. P. Provost and G. Vallee, “Riemannian structure on manifolds of quantum states,” Commun. Math. Phys. 76, 289–301 (1980).
[Crossref]

Ahn, J.

Y. Song, H. Lee, H. Kim, H. Jo, and J. Ahn, “Subpicosecond X rotations of atomic clock states,” Phys. Rev. A 97, 052322 (2018).
[Crossref]

H. Jo, H. G. Lee, S. Guérin, and J. Ahn, “Robust two-level system control by a detuned and chirped laser pulse,” Phys. Rev. A,  96, 033403 (2017).
[Crossref]

H. G. Lee, Y. Song, and J. Ahn, “Single-laser-pulse implementation of arbitrary ZYZ rotations of an atomic qubit,” Phys. Rev. A. 96, 012326 (2017).
[Crossref]

H. Lee, H. Kim, and J. Ahn, “Ultrafast laser-driven Rabi oscillations of a trapped atomic vapor,” Opt. Lett. 40, 510–513 (2015).
[Crossref]

J. Lim, H. Lee, S. Lee, C. Y. Park, and J. Ahn, “Ultrafast Ramsey interferometry to implement cold atomic qubit gates,” Sci. Rep. 4, 5867 (2014).
[Crossref]

Barends, R.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Bergholm, V.

A. Spörl, T. Schulte-Herbrüggen, S. J. Glaser, V. Bergholm, M. J. Storcz, J. Ferber, and F. K. Wilhelm,” Optimal control of coupled Josephson qubits,” Phys. Rev. A 75, 012302 (2007).
[Crossref]

Bialczak, R. C.

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

Bisping, D.

K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
[Crossref]

Blatt, R.

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A 62, 042305 (2000).
[Crossref]

Calarco, T.

P. Doria, T. Calarco, and S. Montangero, “Optimal control technique for many-body quantum dynamics,” Phys. Rev. Lett. 106, 190501 (2011).
[Crossref] [PubMed]

Campbell, B.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Campbell, W. C.

W. C. Campbell, J. Mizrahi, Q. Quraishi, C. Senko, D. Hayes, D. Hucul, D. N. Matsukevich, P. Maunz, and C. Monroe, “Ultrafast gates for single atomic qubits,” Phys. Rev. Lett. 105, 090502 (2010).
[Crossref]

Chen, Y.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Chen, Z.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Chiaro, B.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Cleland, A. N.

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

Coppersmith, S. N.

J. Ghosh, S. N. Coppersmith, and M. Friesen, “Pulse sequences for suppressing leakage in single-qubit gate operations,” Phys. Rev. B 95, 241307 (2017).
[Crossref]

Daems, D.

D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
[Crossref]

De Greve, K.

K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
[Crossref]

Derevianko, A.

A. Derevianko, P. Kómár, T. Topcu, R. M. Kroeze, and M. D. Lukin, “Effects of molecular resonances on Rydberg blockade,” Phys. Rev. A. 92, 063419 (2015).
[Crossref]

Doria, P.

P. Doria, T. Calarco, and S. Montangero, “Optimal control technique for many-body quantum dynamics,” Phys. Rev. Lett. 106, 190501 (2011).
[Crossref] [PubMed]

Dunsworth, A.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Ferber, J.

A. Spörl, T. Schulte-Herbrüggen, S. J. Glaser, V. Bergholm, M. J. Storcz, J. Ferber, and F. K. Wilhelm,” Optimal control of coupled Josephson qubits,” Phys. Rev. A 75, 012302 (2007).
[Crossref]

Forchel, A.

K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
[Crossref]

Fowler, A. G.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Fox, A. M.

A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotation by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
[Crossref]

Friesen, M.

J. Ghosh, S. N. Coppersmith, and M. Friesen, “Pulse sequences for suppressing leakage in single-qubit gate operations,” Phys. Rev. B 95, 241307 (2017).
[Crossref]

Gambetta, J. M.

J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
[Crossref]

F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, “Simple pulse for elimination of leakage in weakly nonlinear qubits,” Phys. Rev. Lett. 103, 110501 (2009).
[Crossref]

Gauger, E. M.

A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotation by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
[Crossref]

Genov, G. T.

G. T. Genov and N. V. Vitanov, “Dynamical suppression of unwanted transitions in multistate quantum system,” Phys. Rev. Lett. 110, 133002 (2013).
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G. T. Genov, B. T. Torosov, and N. V. Vitanov, “Optimized control of multistate quantum systems by composite pulse sequences,” Phys. Rev. A,  84, 063413 (2011).
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Ghosh, J.

J. Ghosh, S. N. Coppersmith, and M. Friesen, “Pulse sequences for suppressing leakage in single-qubit gate operations,” Phys. Rev. B 95, 241307 (2017).
[Crossref]

Glaser, S. J.

A. Spörl, T. Schulte-Herbrüggen, S. J. Glaser, V. Bergholm, M. J. Storcz, J. Ferber, and F. K. Wilhelm,” Optimal control of coupled Josephson qubits,” Phys. Rev. A 75, 012302 (2007).
[Crossref]

Gopal, A. V.

A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotation by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
[Crossref]

Guérin, S.

H. Jo, H. G. Lee, S. Guérin, and J. Ahn, “Robust two-level system control by a detuned and chirped laser pulse,” Phys. Rev. A,  96, 033403 (2017).
[Crossref]

D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
[Crossref]

Hayes, D.

W. C. Campbell, J. Mizrahi, Q. Quraishi, C. Senko, D. Hayes, D. Hucul, D. N. Matsukevich, P. Maunz, and C. Monroe, “Ultrafast gates for single atomic qubits,” Phys. Rev. Lett. 105, 090502 (2010).
[Crossref]

Hensinger, W. K.

J. Randall, A. M. Lawrence, S. C. Webster, S. Weidt, N. V. Vitanov, and W. K. Hensinger, “Generation of high-fidelity quantum control methods for multilevel systems,” Phys. Rev. A 98, 043414 (2018).
[Crossref]

Höfling, S.

K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
[Crossref]

Hucul, D.

W. C. Campbell, J. Mizrahi, Q. Quraishi, C. Senko, D. Hayes, D. Hucul, D. N. Matsukevich, P. Maunz, and C. Monroe, “Ultrafast gates for single atomic qubits,” Phys. Rev. Lett. 105, 090502 (2010).
[Crossref]

Jeffrey, E.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Jo, H.

Y. Song, H. Lee, H. Kim, H. Jo, and J. Ahn, “Subpicosecond X rotations of atomic clock states,” Phys. Rev. A 97, 052322 (2018).
[Crossref]

H. Jo, H. G. Lee, S. Guérin, and J. Ahn, “Robust two-level system control by a detuned and chirped laser pulse,” Phys. Rev. A,  96, 033403 (2017).
[Crossref]

Kamp, M.

K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
[Crossref]

Kelly, J.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

Kiely, A.

A. Kiely and A. Ruschhaupt, “Inhibiting unwanted transitions in population transfer in two- and three-level quantum systems,” J. Phys. B: At. Mol. Opt. Phys. 47, 115501 (2014).
[Crossref]

Kim, H.

Y. Song, H. Lee, H. Kim, H. Jo, and J. Ahn, “Subpicosecond X rotations of atomic clock states,” Phys. Rev. A 97, 052322 (2018).
[Crossref]

H. Lee, H. Kim, and J. Ahn, “Ultrafast laser-driven Rabi oscillations of a trapped atomic vapor,” Opt. Lett. 40, 510–513 (2015).
[Crossref]

Knill, E.

C. A. Ryan, C. Negrevergne, M. Laforest, E. Knill, and R. Laflamme, “Liquid-state nuclear magnetic resonance as a testbed for developing quantum control methods,” Phys. Rev. A 78, 012328 (2008).
[Crossref]

Kómár, P.

A. Derevianko, P. Kómár, T. Topcu, R. M. Kroeze, and M. D. Lukin, “Effects of molecular resonances on Rydberg blockade,” Phys. Rev. A. 92, 063419 (2015).
[Crossref]

Korotkov, A. N.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Kroeze, R. M.

A. Derevianko, P. Kómár, T. Topcu, R. M. Kroeze, and M. D. Lukin, “Effects of molecular resonances on Rydberg blockade,” Phys. Rev. A. 92, 063419 (2015).
[Crossref]

Ladd, T. D.

K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
[Crossref]

D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (2008).
[Crossref]

Laflamme, R.

C. A. Ryan, C. Negrevergne, M. Laforest, E. Knill, and R. Laflamme, “Liquid-state nuclear magnetic resonance as a testbed for developing quantum control methods,” Phys. Rev. A 78, 012328 (2008).
[Crossref]

Laforest, M.

C. A. Ryan, C. Negrevergne, M. Laforest, E. Knill, and R. Laflamme, “Liquid-state nuclear magnetic resonance as a testbed for developing quantum control methods,” Phys. Rev. A 78, 012328 (2008).
[Crossref]

Lawrence, A. M.

J. Randall, A. M. Lawrence, S. C. Webster, S. Weidt, N. V. Vitanov, and W. K. Hensinger, “Generation of high-fidelity quantum control methods for multilevel systems,” Phys. Rev. A 98, 043414 (2018).
[Crossref]

Lee, H.

Y. Song, H. Lee, H. Kim, H. Jo, and J. Ahn, “Subpicosecond X rotations of atomic clock states,” Phys. Rev. A 97, 052322 (2018).
[Crossref]

H. Lee, H. Kim, and J. Ahn, “Ultrafast laser-driven Rabi oscillations of a trapped atomic vapor,” Opt. Lett. 40, 510–513 (2015).
[Crossref]

J. Lim, H. Lee, S. Lee, C. Y. Park, and J. Ahn, “Ultrafast Ramsey interferometry to implement cold atomic qubit gates,” Sci. Rep. 4, 5867 (2014).
[Crossref]

Lee, H. G.

H. Jo, H. G. Lee, S. Guérin, and J. Ahn, “Robust two-level system control by a detuned and chirped laser pulse,” Phys. Rev. A,  96, 033403 (2017).
[Crossref]

H. G. Lee, Y. Song, and J. Ahn, “Single-laser-pulse implementation of arbitrary ZYZ rotations of an atomic qubit,” Phys. Rev. A. 96, 012326 (2017).
[Crossref]

Lee, S.

J. Lim, H. Lee, S. Lee, C. Y. Park, and J. Ahn, “Ultrafast Ramsey interferometry to implement cold atomic qubit gates,” Sci. Rep. 4, 5867 (2014).
[Crossref]

Leibfried, D.

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A 62, 042305 (2000).
[Crossref]

Lenander, M.

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

Lim, J.

J. Lim, H. Lee, S. Lee, C. Y. Park, and J. Ahn, “Ultrafast Ramsey interferometry to implement cold atomic qubit gates,” Sci. Rep. 4, 5867 (2014).
[Crossref]

Lovett, B. W.

A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotation by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
[Crossref]

Lucero, E.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

Lukin, M. D.

A. Derevianko, P. Kómár, T. Topcu, R. M. Kroeze, and M. D. Lukin, “Effects of molecular resonances on Rydberg blockade,” Phys. Rev. A. 92, 063419 (2015).
[Crossref]

Mariantoni, M.

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

Martinis, J. M.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

Matsukevich, D. N.

W. C. Campbell, J. Mizrahi, Q. Quraishi, C. Senko, D. Hayes, D. Hucul, D. N. Matsukevich, P. Maunz, and C. Monroe, “Ultrafast gates for single atomic qubits,” Phys. Rev. Lett. 105, 090502 (2010).
[Crossref]

Maunz, P.

W. C. Campbell, J. Mizrahi, Q. Quraishi, C. Senko, D. Hayes, D. Hucul, D. N. Matsukevich, P. Maunz, and C. Monroe, “Ultrafast gates for single atomic qubits,” Phys. Rev. Lett. 105, 090502 (2010).
[Crossref]

McMahon, P. L.

K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
[Crossref]

Megrant, A.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Merkel, S. T.

J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
[Crossref]

Mizrahi, J.

W. C. Campbell, J. Mizrahi, Q. Quraishi, C. Senko, D. Hayes, D. Hucul, D. N. Matsukevich, P. Maunz, and C. Monroe, “Ultrafast gates for single atomic qubits,” Phys. Rev. Lett. 105, 090502 (2010).
[Crossref]

Monroe, C.

W. C. Campbell, J. Mizrahi, Q. Quraishi, C. Senko, D. Hayes, D. Hucul, D. N. Matsukevich, P. Maunz, and C. Monroe, “Ultrafast gates for single atomic qubits,” Phys. Rev. Lett. 105, 090502 (2010).
[Crossref]

Montangero, S.

P. Doria, T. Calarco, and S. Montangero, “Optimal control technique for many-body quantum dynamics,” Phys. Rev. Lett. 106, 190501 (2011).
[Crossref] [PubMed]

Motzoi, F.

L. S. Theis, F. Motzoi, F. K. Wilhelm, and M. Saffman, “High-fidelity Rydberg-blockade entangling gate using shaped, analytic pulses,” Phys. Rev. A 94, 032306 (2016).
[Crossref]

F. Motzoi and F. K. Wilhelm, “Improving frequency selection of driven pulses using derivative based transition suppression,” Phys. Rev. A 88, 062318 (2013).
[Crossref]

J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
[Crossref]

F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, “Simple pulse for elimination of leakage in weakly nonlinear qubits,” Phys. Rev. Lett. 103, 110501 (2009).
[Crossref]

Mundt, A.

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A 62, 042305 (2000).
[Crossref]

Mutus, J.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Nazir, A.

A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotation by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
[Crossref]

Neeley, M.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

Negrevergne, C.

C. A. Ryan, C. Negrevergne, M. Laforest, E. Knill, and R. Laflamme, “Liquid-state nuclear magnetic resonance as a testbed for developing quantum control methods,” Phys. Rev. A 78, 012328 (2008).
[Crossref]

Neill, C.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

O’Connell, A. D.

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

O’Malley, P. J. J.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Park, C. Y.

J. Lim, H. Lee, S. Lee, C. Y. Park, and J. Ahn, “Ultrafast Ramsey interferometry to implement cold atomic qubit gates,” Sci. Rep. 4, 5867 (2014).
[Crossref]

Press, D.

K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
[Crossref]

D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (2008).
[Crossref]

Provost, J. P.

J. P. Provost and G. Vallee, “Riemannian structure on manifolds of quantum states,” Commun. Math. Phys. 76, 289–301 (1980).
[Crossref]

Quintana, C.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Quraishi, Q.

W. C. Campbell, J. Mizrahi, Q. Quraishi, C. Senko, D. Hayes, D. Hucul, D. N. Matsukevich, P. Maunz, and C. Monroe, “Ultrafast gates for single atomic qubits,” Phys. Rev. Lett. 105, 090502 (2010).
[Crossref]

Ramsay, A. J.

A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotation by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
[Crossref]

Randall, J.

J. Randall, A. M. Lawrence, S. C. Webster, S. Weidt, N. V. Vitanov, and W. K. Hensinger, “Generation of high-fidelity quantum control methods for multilevel systems,” Phys. Rev. A 98, 043414 (2018).
[Crossref]

Rebentrost, P.

F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, “Simple pulse for elimination of leakage in weakly nonlinear qubits,” Phys. Rev. Lett. 103, 110501 (2009).
[Crossref]

P. Rebentrost and F. K. Wilhelm, “Optimal control of a leaking qubit,” Phys. Rev. B 79, 060507(R) (2009).
[Crossref]

Roos, C. F.

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A 62, 042305 (2000).
[Crossref]

Roushan, P.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Ruschhaupt, A.

A. Kiely and A. Ruschhaupt, “Inhibiting unwanted transitions in population transfer in two- and three-level quantum systems,” J. Phys. B: At. Mol. Opt. Phys. 47, 115501 (2014).
[Crossref]

D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
[Crossref]

Ryan, C. A.

C. A. Ryan, C. Negrevergne, M. Laforest, E. Knill, and R. Laflamme, “Liquid-state nuclear magnetic resonance as a testbed for developing quantum control methods,” Phys. Rev. A 78, 012328 (2008).
[Crossref]

Saffman, M.

L. S. Theis, F. Motzoi, F. K. Wilhelm, and M. Saffman, “High-fidelity Rydberg-blockade entangling gate using shaped, analytic pulses,” Phys. Rev. A 94, 032306 (2016).
[Crossref]

M. Saffman, “Quantum computing with atomic qubits and rydberg interactions: progress and challenges,” J. Phys. B: At. Mol. Opt. Phys. 49, 202001 (2016).
[Crossref]

Sank, D.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

Schmidt-Kaler, F.

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A 62, 042305 (2000).
[Crossref]

Schneider, C.

K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
[Crossref]

Schulte-Herbrüggen, T.

A. Spörl, T. Schulte-Herbrüggen, S. J. Glaser, V. Bergholm, M. J. Storcz, J. Ferber, and F. K. Wilhelm,” Optimal control of coupled Josephson qubits,” Phys. Rev. A 75, 012302 (2007).
[Crossref]

Senko, C.

W. C. Campbell, J. Mizrahi, Q. Quraishi, C. Senko, D. Hayes, D. Hucul, D. N. Matsukevich, P. Maunz, and C. Monroe, “Ultrafast gates for single atomic qubits,” Phys. Rev. Lett. 105, 090502 (2010).
[Crossref]

Shore, B. W.

B. W. Shore, “Two-state behavior in N-state quantum systems: The Morris shore transformation reviewed,” J. Mod. Opt. 61, 787–815 (2013).
[Crossref]

Skolnick, M. S.

A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotation by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
[Crossref]

Song, Y.

Y. Song, H. Lee, H. Kim, H. Jo, and J. Ahn, “Subpicosecond X rotations of atomic clock states,” Phys. Rev. A 97, 052322 (2018).
[Crossref]

H. G. Lee, Y. Song, and J. Ahn, “Single-laser-pulse implementation of arbitrary ZYZ rotations of an atomic qubit,” Phys. Rev. A. 96, 012326 (2017).
[Crossref]

Spörl, A.

A. Spörl, T. Schulte-Herbrüggen, S. J. Glaser, V. Bergholm, M. J. Storcz, J. Ferber, and F. K. Wilhelm,” Optimal control of coupled Josephson qubits,” Phys. Rev. A 75, 012302 (2007).
[Crossref]

Steane, A.

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A 62, 042305 (2000).
[Crossref]

Stevens, D.

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A 62, 042305 (2000).
[Crossref]

Storcz, M. J.

A. Spörl, T. Schulte-Herbrüggen, S. J. Glaser, V. Bergholm, M. J. Storcz, J. Ferber, and F. K. Wilhelm,” Optimal control of coupled Josephson qubits,” Phys. Rev. A 75, 012302 (2007).
[Crossref]

Sugny, D.

D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
[Crossref]

Theis, L. S.

L. S. Theis, F. Motzoi, F. K. Wilhelm, and M. Saffman, “High-fidelity Rydberg-blockade entangling gate using shaped, analytic pulses,” Phys. Rev. A 94, 032306 (2016).
[Crossref]

Topcu, T.

A. Derevianko, P. Kómár, T. Topcu, R. M. Kroeze, and M. D. Lukin, “Effects of molecular resonances on Rydberg blockade,” Phys. Rev. A. 92, 063419 (2015).
[Crossref]

Torosov, B. T.

G. T. Genov, B. T. Torosov, and N. V. Vitanov, “Optimized control of multistate quantum systems by composite pulse sequences,” Phys. Rev. A,  84, 063413 (2011).
[Crossref]

Tournois, P.

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245–249 (1997).
[Crossref]

Vainsencher, A.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Vallee, G.

J. P. Provost and G. Vallee, “Riemannian structure on manifolds of quantum states,” Commun. Math. Phys. 76, 289–301 (1980).
[Crossref]

Vitanov, N. V.

J. Randall, A. M. Lawrence, S. C. Webster, S. Weidt, N. V. Vitanov, and W. K. Hensinger, “Generation of high-fidelity quantum control methods for multilevel systems,” Phys. Rev. A 98, 043414 (2018).
[Crossref]

G. T. Genov and N. V. Vitanov, “Dynamical suppression of unwanted transitions in multistate quantum system,” Phys. Rev. Lett. 110, 133002 (2013).
[Crossref]

G. T. Genov, B. T. Torosov, and N. V. Vitanov, “Optimized control of multistate quantum systems by composite pulse sequences,” Phys. Rev. A,  84, 063413 (2011).
[Crossref]

Wang, H.

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

Webster, S. C.

J. Randall, A. M. Lawrence, S. C. Webster, S. Weidt, N. V. Vitanov, and W. K. Hensinger, “Generation of high-fidelity quantum control methods for multilevel systems,” Phys. Rev. A 98, 043414 (2018).
[Crossref]

Weides, M.

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

Weidt, S.

J. Randall, A. M. Lawrence, S. C. Webster, S. Weidt, N. V. Vitanov, and W. K. Hensinger, “Generation of high-fidelity quantum control methods for multilevel systems,” Phys. Rev. A 98, 043414 (2018).
[Crossref]

Weiner, A. M.

A. M. Weiner, “Ultrafast optical pulse shaping: a tutorial review,” Opt. Commun. 284, 3669–3692 (2011).
[Crossref]

Wenner, J.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

White, T. C.

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

Wilhelm, F. K.

L. S. Theis, F. Motzoi, F. K. Wilhelm, and M. Saffman, “High-fidelity Rydberg-blockade entangling gate using shaped, analytic pulses,” Phys. Rev. A 94, 032306 (2016).
[Crossref]

F. Motzoi and F. K. Wilhelm, “Improving frequency selection of driven pulses using derivative based transition suppression,” Phys. Rev. A 88, 062318 (2013).
[Crossref]

J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
[Crossref]

P. Rebentrost and F. K. Wilhelm, “Optimal control of a leaking qubit,” Phys. Rev. B 79, 060507(R) (2009).
[Crossref]

F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, “Simple pulse for elimination of leakage in weakly nonlinear qubits,” Phys. Rev. Lett. 103, 110501 (2009).
[Crossref]

A. Spörl, T. Schulte-Herbrüggen, S. J. Glaser, V. Bergholm, M. J. Storcz, J. Ferber, and F. K. Wilhelm,” Optimal control of coupled Josephson qubits,” Phys. Rev. A 75, 012302 (2007).
[Crossref]

Worschech, L.

K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
[Crossref]

Yamamoto, T.

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

Yamamoto, Y.

K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
[Crossref]

D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (2008).
[Crossref]

Zhang, B.

D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (2008).
[Crossref]

Commun. Math. Phys. (1)

J. P. Provost and G. Vallee, “Riemannian structure on manifolds of quantum states,” Commun. Math. Phys. 76, 289–301 (1980).
[Crossref]

J. Mod. Opt. (1)

B. W. Shore, “Two-state behavior in N-state quantum systems: The Morris shore transformation reviewed,” J. Mod. Opt. 61, 787–815 (2013).
[Crossref]

J. Phys. B: At. Mol. Opt. Phys. (2)

M. Saffman, “Quantum computing with atomic qubits and rydberg interactions: progress and challenges,” J. Phys. B: At. Mol. Opt. Phys. 49, 202001 (2016).
[Crossref]

A. Kiely and A. Ruschhaupt, “Inhibiting unwanted transitions in population transfer in two- and three-level quantum systems,” J. Phys. B: At. Mol. Opt. Phys. 47, 115501 (2014).
[Crossref]

Nat. Phys. (1)

K. De Greve, P. L. McMahon, D. Press, T. D. Ladd, D. Bisping, C. Schneider, M. Kamp, L. Worschech, S. Höfling, A. Forchel, and Y. Yamamoto, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878 (2011).
[Crossref]

Nature (1)

D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, “Complete quantum control of a single quantum dot spin using ultrafast optical pulses,” Nature 456, 218–221 (2008).
[Crossref]

Opt. Commun. (2)

P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245–249 (1997).
[Crossref]

A. M. Weiner, “Ultrafast optical pulse shaping: a tutorial review,” Opt. Commun. 284, 3669–3692 (2011).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (11)

H. Jo, H. G. Lee, S. Guérin, and J. Ahn, “Robust two-level system control by a detuned and chirped laser pulse,” Phys. Rev. A,  96, 033403 (2017).
[Crossref]

Y. Song, H. Lee, H. Kim, H. Jo, and J. Ahn, “Subpicosecond X rotations of atomic clock states,” Phys. Rev. A 97, 052322 (2018).
[Crossref]

F. Motzoi and F. K. Wilhelm, “Improving frequency selection of driven pulses using derivative based transition suppression,” Phys. Rev. A 88, 062318 (2013).
[Crossref]

J. M. Gambetta, F. Motzoi, S. T. Merkel, and F. K. Wilhelm, “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator,” Phys. Rev. A 83, 012308 (2011).
[Crossref]

E. Lucero, J. Kelly, R. C. Bialczak, M. Lenander, M. Mariantoni, M. Neeley, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Reduced phase error through optimized control of a superconducting qubit,” Phys. Rev. A 82, 042339 (2010).
[Crossref]

L. S. Theis, F. Motzoi, F. K. Wilhelm, and M. Saffman, “High-fidelity Rydberg-blockade entangling gate using shaped, analytic pulses,” Phys. Rev. A 94, 032306 (2016).
[Crossref]

G. T. Genov, B. T. Torosov, and N. V. Vitanov, “Optimized control of multistate quantum systems by composite pulse sequences,” Phys. Rev. A,  84, 063413 (2011).
[Crossref]

J. Randall, A. M. Lawrence, S. C. Webster, S. Weidt, N. V. Vitanov, and W. K. Hensinger, “Generation of high-fidelity quantum control methods for multilevel systems,” Phys. Rev. A 98, 043414 (2018).
[Crossref]

A. Steane, C. F. Roos, D. Stevens, A. Mundt, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, “Speed of ion-trap quantum-information processors,” Phys. Rev. A 62, 042305 (2000).
[Crossref]

C. A. Ryan, C. Negrevergne, M. Laforest, E. Knill, and R. Laflamme, “Liquid-state nuclear magnetic resonance as a testbed for developing quantum control methods,” Phys. Rev. A 78, 012328 (2008).
[Crossref]

A. Spörl, T. Schulte-Herbrüggen, S. J. Glaser, V. Bergholm, M. J. Storcz, J. Ferber, and F. K. Wilhelm,” Optimal control of coupled Josephson qubits,” Phys. Rev. A 75, 012302 (2007).
[Crossref]

Phys. Rev. A. (2)

A. Derevianko, P. Kómár, T. Topcu, R. M. Kroeze, and M. D. Lukin, “Effects of molecular resonances on Rydberg blockade,” Phys. Rev. A. 92, 063419 (2015).
[Crossref]

H. G. Lee, Y. Song, and J. Ahn, “Single-laser-pulse implementation of arbitrary ZYZ rotations of an atomic qubit,” Phys. Rev. A. 96, 012326 (2017).
[Crossref]

Phys. Rev. B (2)

J. Ghosh, S. N. Coppersmith, and M. Friesen, “Pulse sequences for suppressing leakage in single-qubit gate operations,” Phys. Rev. B 95, 241307 (2017).
[Crossref]

P. Rebentrost and F. K. Wilhelm, “Optimal control of a leaking qubit,” Phys. Rev. B 79, 060507(R) (2009).
[Crossref]

Phys. Rev. Lett. (7)

P. Doria, T. Calarco, and S. Montangero, “Optimal control technique for many-body quantum dynamics,” Phys. Rev. Lett. 106, 190501 (2011).
[Crossref] [PubMed]

F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, “Simple pulse for elimination of leakage in weakly nonlinear qubits,” Phys. Rev. Lett. 103, 110501 (2009).
[Crossref]

Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, “Measuring and suppressing quantum state leakage in a superconducting qubit,” Phys. Rev. Lett. 116, 020501 (2016).
[Crossref]

A. J. Ramsay, A. V. Gopal, E. M. Gauger, A. Nazir, B. W. Lovett, A. M. Fox, and M. S. Skolnick, “Damping of exciton Rabi rotation by acoustic phonons in optically excited InGaAs/GaAs quantum dots,” Phys. Rev. Lett. 104, 017402 (2010).
[Crossref]

G. T. Genov and N. V. Vitanov, “Dynamical suppression of unwanted transitions in multistate quantum system,” Phys. Rev. Lett. 110, 133002 (2013).
[Crossref]

W. C. Campbell, J. Mizrahi, Q. Quraishi, C. Senko, D. Hayes, D. Hucul, D. N. Matsukevich, P. Maunz, and C. Monroe, “Ultrafast gates for single atomic qubits,” Phys. Rev. Lett. 105, 090502 (2010).
[Crossref]

D. Daems, A. Ruschhaupt, D. Sugny, and S. Guérin, “Robust quantum control by a single-shot shaped pulse,” Phys. Rev. Lett. 111, 050404 (2013).
[Crossref]

Sci. Rep. (1)

J. Lim, H. Lee, S. Lee, C. Y. Park, and J. Ahn, “Ultrafast Ramsey interferometry to implement cold atomic qubit gates,” Sci. Rep. 4, 5867 (2014).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1 (a) Leakage-state population (|cl|2) with and without the two-pulse leakage suppression scheme in Eq. (8) is compared for various laser bandwidths (ΔωFWHM). Numerical calculations performed with λ = 0.34 (scaled dipole moment for atomic rubidium) corresponds to the experiment in Sec. V. (b) Leakage suppression condition (cl = 0) of the two-pulse scheme for various laser bandwidths. The short-pulse approximation (SPA) solution in Eq. (9) (thick solid line) is shown in comparison with Eq. (8) for pulses with various bandwidths (ΔωFWHM2 = 2.5, 3.4, · · · , 15).
Fig. 2
Fig. 2 (a) Experimental result for the leakage state (5D) population measured as a function of total pulse area Θ and relative amplitude γ. The white dashed line represents the leakage suppression condition under the short-pulse approximation from Eq. (9). (b) Corresponding numerical calculation. (c) Comparison between the experiment (diamonds) and theory (solid lines) for Θ = π and 2π, extracted along the white dotted lines in Fig. 2(a) and 2(b).
Fig. 3
Fig. 3 (a–c) The leakage population map Pl(α, β) for X(π)-rotations initiated from three characteristic states: (a) the ground state (ai = 1, bi = 0), (b) the superposition state ( a i = 1 / 2, b i = 1 / 2), and (c) the excited state (ai = 0, bi = 1). TDSE calculations for the regions of small leakages are respectively plotted, where white stars indicate the Eq. (12) solution points (α = 0.27, β = 0.46 in each figure) for X(π)-rotation. (d) The solutions of Eq. (12) for (α, β). TDSE calculations are performed with λ = 0.34 (scaled dipole moment for atomic rubidium) and ΔωFWHM = 15Δ2 (near the SPA condition).

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

H = m = 0 2 Δ m Π m + m , n = 0 i < j 2 λ m n 2 ( Ω x σ m n ( x ) Ω y σ m n ( y ) ) ,
H q = m = 0 2 Δ m Π m + λ 01 2 ( Ω x σ 01 ( x ) Ω y σ 01 ( y ) ) ,
H l = λ 12 2 ( Ω x σ 12 ( x ) Ω y σ 12 ( y ) ) .
i d U ( q ) d t = H q U ( q ) ,
i d U ( l ) d t = U ( q ) H l U ( q ) U ( l ) H l U ( l ) .
H I = λ 2 ( Ω * U 10 ( q ) e i Δ 2 t σ 02 + Ω U 10 ( q ) e i Δ 2 t σ 02 + ) + λ 2 ( Ω * U 11 ( q ) e i Δ 2 t σ 12 + Ω U 11 ( q ) e i Δ 2 t σ 12 + ) ,
c l = i λ 2 Ω * ( a i U 10 ( q ) + b i U 11 ( q ) ) e i Δ 2 t d t .
E 1 ( t ) + E 2 ( t ) = E 0 e t 2 τ 2 cos ( ω L t ) + γ E 0 e ( t t d ) 2 τ 2 cos [ ω L ( t t d ) + ϕ ]
U 10 ( q ) ( t ) = i cos A ( t ) 2 ( 1 + γ ) sin γ A ( t t d ) 2 ( 1 + γ ) i sin A ( t ) 2 ( 1 + γ ) cos γ A ( t t d ) 2 ( 1 + γ )
λ Ω 1 ( t ) 2 sin A ( t ) 2 ( 1 + γ ) e i Δ 2 t d t + λ Ω 2 ( t t d ) 2 cos A ( ) 2 ( 1 + γ ) sin γ A ( t t d ) 2 ( 1 + γ ) e i Δ 2 ( t ) d t + λ Ω 2 ( t t d ) 2 sin A ( ) 2 ( 1 + γ ) cos γ A ( t t d ) 2 ( 1 + γ ) e i Δ 2 ( t ) d t = 0 .
γ = ( 1 2 Θ cos 1 1 + cos Θ 2 2 ) ( 2 Θ cos 1 1 + cos Θ 2 2 ) 1 .
γ ( V ) = ( 1 2 Θ sin 1 sin Θ 2 2 ) ( 2 Θ sin 1 sin Θ 2 2 ) 1 .
( 1 e i ϕ d 1 ) cos α Θ 2 + ( e i ϕ d 1 e i ϕ d 2 ) cos ( α + β ) Θ 2 + e i ϕ d 2 cos Θ 2 = 1 ,
( 1 e i ϕ d 1 ) sin α Θ 2 + ( e i ϕ d 1 e i ϕ d 2 ) sin ( α + β ) Θ 2 + e i ϕ d 2 sin Θ 2 = 0 ,
2 cos α Θ 2 2 cos ( α + β ) Θ 2 + cos Θ 2 = 1 ,
2 sin α Θ 2 2 sin ( α + β ) Θ 2 + sin Θ 2 = 0 .
= | ψ ( 0 ) | ψ ( η ) | ,
| ψ ( η ) = | ψ ( 0 ) + η | ψ | η = 0 η + 1 2 η 2 | ψ | η = 0 η 2 + .
= ψ ( η ) | ψ ( 0 ) ψ ( 0 ) | ψ ( η ) [ 1 + η ψ | ψ ψ | η ψ η 2 Re ( η ψ | η ψ η 2 ) ] 1 + 1 2 [ η ψ | ψ ψ | η ψ Re ( η ψ | η ψ ) ] η 2 .
λ | ψ | λ = 0 λ i H I d t | ψ i .
1 1 2 ( ψ i | i H I d t | 2 2 | i H I d t | ψ i ) 1 1 2 | c l | 2 ,

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