Abstract

We report phase-coherent Doppler detection of optical dipole forces using large ion crystals in a Penning trap. The technique is based on laser Doppler velocimetry using a cycling transition in 9Be+ near 313 nm and the center-of-mass (COM) ion motional mode. The optical dipole force is tuned to excite the COM mode, and measurements of photon arrival times synchronized with the excitation potential show oscillations with a period commensurate with the COM motional frequency. Experimental results compare well with a quantitative model for a driven harmonic oscillator. This technique permits characterization of motional modes in ion crystals; the measurement of both frequency and phase information relative to the driving force is a key enabling capability – comparable to lockin detection – providing access to a parameter that is typically not available in time-averaged measurements. This additional information facilitates discrimination of nearly degenerate motional modes.

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  2. C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
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    [PubMed]
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  8. M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, “High-fidelity quantum control using ion crystals in a Penning trap,” Quantum Inf. Comput. 9, 920–949 (2009).
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    [PubMed]
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    [PubMed]
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    [PubMed]
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  16. D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
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    [PubMed]
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    [PubMed]
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  22. H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Ion strings for quantum gates,” Appl. Phys. B 66, 603–608 (1998).
  23. T. B. Mitchell, J. J. Bollinger, D. H. E. Dubin, X.-P. Huang, W. M. Itano, and R. H. Baughman, “Direct observations of structural phase transitions in planar crystallized ion plasmas,” Science 282, 1290–1293 (1998).
    [PubMed]
  24. J. J. Bollinger, T. B. Mitchell, X.-P. Huang, W. M. Itano, J. N. Tan, B. M. Jelenkovic, and D. J. Wineland, “Crystalline order in laser-cooled, nonneutral ion plasmas,” Phys. Plasmas 7, 7–13 (2000).
  25. T. B. Mitchell, J. J. Bollinger, X.-P. Huang, and W. M. Itano, “Doppler imaging of plasma modes in a Penning trap,” Opt. Express 2, 314–322 (1998).
    [PubMed]
  26. D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Minimization of ion micromotion in a Paul trap,” J. Appl. Phys. 83, 5025–5033 (1998).
  27. M. J. Biercuk, H. Uys, J. W. Britton, A. P. VanDevender, and J. J. Bollinger, “Ultrasensitive detection of force and displacement using trapped ions,” Nat. Nanotechnol. 5, 646–650 (2010).
    [PubMed]
  28. J. J. Bollinger and D. J. Wineland, “Strongly coupled nonneutral ion plasma,” Phys. Rev. Lett. 53, 348–351 (1984).
  29. L. R. Brewer, J. D. Prestage, J. J. Bollinger, W. M. Itano, D. J. Larson, and D. J. Wineland, “Static properties of a non-neutral 9Be+ ion plasma,” Phys. Rev. A 38, 859–873 (1988).
    [PubMed]
  30. M. J. Jensen, T. Hasegawa, and J. J. Bollinger, “Temperature and heating rate of ion crystals in Penning traps,” Phys. Rev. A 70, 033401 (2004).
  31. M. J. Jensen, T. Hasegawa, J. J. Bollinger, and D. H. E. Dubin, “Rapid heating of a strongly coupled plasma near the solid-liquid phase transition,” Phys. Rev. Lett. 94, 025001 (2005).
    [PubMed]
  32. W. M. Itano, J. J. Bollinger, J. N. Tan, B. Jelenković, X.-P. Huang, and D. J. Wineland, “Bragg diffraction from crystallized ion plasmas,” Science 279, 686–689 (1998).
    [PubMed]
  33. X.-P. Huang, J. J. Bollinger, T. B. Mitchell, and W. M. Itano, “Phase-locked rotation of crystallized non-neutral plasmas by rotating electric fields,” Phys. Rev. Lett. 80, 73–76 (1998).
  34. X.-P. Huang, J. J. Bollinger, T. B. Mitchell, W. M. Itano, and D. H. E. Dubin, “Precise control of the global rotation of strongly coupled ion plasmas in a Penning trap,” Phys. Plasmas 5, 1656–1663 (1998).
  35. J. J. Bollinger, D. J. Wineland, and D. H. E. Dubin, “Non-neutral ion plasmas and crystals, laser cooling, and atomic clocks,” Phys. Plasmas 1, 1403–1414 (1994).

2010 (4)

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

R. Gerritsma, G. Kirchmair, F. Zahringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[PubMed]

K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, “Quantum simulation of frustrated Ising spins with trapped ions,” Nature 465, 590–593 (2010).
[PubMed]

M. J. Biercuk, H. Uys, J. W. Britton, A. P. VanDevender, and J. J. Bollinger, “Ultrasensitive detection of force and displacement using trapped ions,” Nat. Nanotechnol. 5, 646–650 (2010).
[PubMed]

2009 (4)

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

S. Olmschenk, D. N. Matsukevich, P. Maunz, D. Hayes, L.-M. Duan, and C. Monroe, “Quantum teleportation between distant matter qubits,” Science 323, 486–489 (2009).
[PubMed]

M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, “High-fidelity quantum control using ion crystals in a Penning trap,” Quantum Inf. Comput. 9, 920–949 (2009).

2008 (2)

R. Blatt and D. J. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1014 (2008).
[PubMed]

D. Porras, D. Marquardt, J. von Delft, and J. J. Cirac, “Mesoscopic spin-boson models of trapped ions,” Phys. Rev. A 78, 010101 (2008).

2006 (1)

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[PubMed]

2005 (3)

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

P. O. Schmidt, T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, “Spectroscopy using quantum logic,” Science. 309, 749–752 (2005).
[PubMed]

M. J. Jensen, T. Hasegawa, J. J. Bollinger, and D. H. E. Dubin, “Rapid heating of a strongly coupled plasma near the solid-liquid phase transition,” Phys. Rev. Lett. 94, 025001 (2005).
[PubMed]

2004 (1)

M. J. Jensen, T. Hasegawa, and J. J. Bollinger, “Temperature and heating rate of ion crystals in Penning traps,” Phys. Rev. A 70, 033401 (2004).

2003 (2)

F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412–415 (2003).
[PubMed]

2002 (1)

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[PubMed]

2000 (2)

J. J. Bollinger, T. B. Mitchell, X.-P. Huang, W. M. Itano, J. N. Tan, B. M. Jelenkovic, and D. J. Wineland, “Crystalline order in laser-cooled, nonneutral ion plasmas,” Phys. Plasmas 7, 7–13 (2000).

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[PubMed]

1998 (11)

Q. A. Turchette, C. S. Wood, B. E. King, C. J. Myatt, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Deterministic entanglement of two ions,” Phys. Rev. Lett. 81, 3631–3634 (1998).

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol. 103, 259–328 (1998).

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, C. J. Myatt, and C. S. Wood, “Trapped-ion quantum simulator,” Phys. Scr. T76, 147–151 (1998).

T. B. Mitchell, J. J. Bollinger, X.-P. Huang, and W. M. Itano, “Doppler imaging of plasma modes in a Penning trap,” Opt. Express 2, 314–322 (1998).
[PubMed]

D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Minimization of ion micromotion in a Paul trap,” J. Appl. Phys. 83, 5025–5033 (1998).

B. King, C. Myatt, Q. A. Turchette, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Cooling the collective motion of trapped ions to initialize a quantum register,” Phys. Rev. Lett. 81, 1525–1528 (1998).

H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Ion strings for quantum gates,” Appl. Phys. B 66, 603–608 (1998).

T. B. Mitchell, J. J. Bollinger, D. H. E. Dubin, X.-P. Huang, W. M. Itano, and R. H. Baughman, “Direct observations of structural phase transitions in planar crystallized ion plasmas,” Science 282, 1290–1293 (1998).
[PubMed]

W. M. Itano, J. J. Bollinger, J. N. Tan, B. Jelenković, X.-P. Huang, and D. J. Wineland, “Bragg diffraction from crystallized ion plasmas,” Science 279, 686–689 (1998).
[PubMed]

X.-P. Huang, J. J. Bollinger, T. B. Mitchell, and W. M. Itano, “Phase-locked rotation of crystallized non-neutral plasmas by rotating electric fields,” Phys. Rev. Lett. 80, 73–76 (1998).

X.-P. Huang, J. J. Bollinger, T. B. Mitchell, W. M. Itano, and D. H. E. Dubin, “Precise control of the global rotation of strongly coupled ion plasmas in a Penning trap,” Phys. Plasmas 5, 1656–1663 (1998).

1995 (1)

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, “Demonstration of a fundamental quantum logic gate,” Phys. Rev. Lett. 75, 4714–4717 (1995).
[PubMed]

1994 (1)

J. J. Bollinger, D. J. Wineland, and D. H. E. Dubin, “Non-neutral ion plasmas and crystals, laser cooling, and atomic clocks,” Phys. Plasmas 1, 1403–1414 (1994).

1988 (1)

L. R. Brewer, J. D. Prestage, J. J. Bollinger, W. M. Itano, D. J. Larson, and D. J. Wineland, “Static properties of a non-neutral 9Be+ ion plasma,” Phys. Rev. A 38, 859–873 (1988).
[PubMed]

1984 (1)

J. J. Bollinger and D. J. Wineland, “Strongly coupled nonneutral ion plasma,” Phys. Rev. Lett. 53, 348–351 (1984).

Barrett, M.

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412–415 (2003).
[PubMed]

Baughman, R. H.

T. B. Mitchell, J. J. Bollinger, D. H. E. Dubin, X.-P. Huang, W. M. Itano, and R. H. Baughman, “Direct observations of structural phase transitions in planar crystallized ion plasmas,” Science 282, 1290–1293 (1998).
[PubMed]

Becher, C.

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[PubMed]

Bechter, W.

H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Ion strings for quantum gates,” Appl. Phys. B 66, 603–608 (1998).

Benhelm, J.

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

Ben-Kish, A.

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[PubMed]

Bergquist, J. C.

P. O. Schmidt, T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, “Spectroscopy using quantum logic,” Science. 309, 749–752 (2005).
[PubMed]

D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Minimization of ion micromotion in a Paul trap,” J. Appl. Phys. 83, 5025–5033 (1998).

Berkeland, D. J.

D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Minimization of ion micromotion in a Paul trap,” J. Appl. Phys. 83, 5025–5033 (1998).

Biercuk, M. J.

M. J. Biercuk, H. Uys, J. W. Britton, A. P. VanDevender, and J. J. Bollinger, “Ultrasensitive detection of force and displacement using trapped ions,” Nat. Nanotechnol. 5, 646–650 (2010).
[PubMed]

M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, “High-fidelity quantum control using ion crystals in a Penning trap,” Quantum Inf. Comput. 9, 920–949 (2009).

Blakestad, R. B.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[PubMed]

Blatt, R.

R. Gerritsma, G. Kirchmair, F. Zahringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[PubMed]

R. Blatt and D. J. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1014 (2008).
[PubMed]

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[PubMed]

H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Ion strings for quantum gates,” Appl. Phys. B 66, 603–608 (1998).

Bollinger, J. J.

M. J. Biercuk, H. Uys, J. W. Britton, A. P. VanDevender, and J. J. Bollinger, “Ultrasensitive detection of force and displacement using trapped ions,” Nat. Nanotechnol. 5, 646–650 (2010).
[PubMed]

M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, “High-fidelity quantum control using ion crystals in a Penning trap,” Quantum Inf. Comput. 9, 920–949 (2009).

M. J. Jensen, T. Hasegawa, J. J. Bollinger, and D. H. E. Dubin, “Rapid heating of a strongly coupled plasma near the solid-liquid phase transition,” Phys. Rev. Lett. 94, 025001 (2005).
[PubMed]

M. J. Jensen, T. Hasegawa, and J. J. Bollinger, “Temperature and heating rate of ion crystals in Penning traps,” Phys. Rev. A 70, 033401 (2004).

J. J. Bollinger, T. B. Mitchell, X.-P. Huang, W. M. Itano, J. N. Tan, B. M. Jelenkovic, and D. J. Wineland, “Crystalline order in laser-cooled, nonneutral ion plasmas,” Phys. Plasmas 7, 7–13 (2000).

T. B. Mitchell, J. J. Bollinger, D. H. E. Dubin, X.-P. Huang, W. M. Itano, and R. H. Baughman, “Direct observations of structural phase transitions in planar crystallized ion plasmas,” Science 282, 1290–1293 (1998).
[PubMed]

T. B. Mitchell, J. J. Bollinger, X.-P. Huang, and W. M. Itano, “Doppler imaging of plasma modes in a Penning trap,” Opt. Express 2, 314–322 (1998).
[PubMed]

W. M. Itano, J. J. Bollinger, J. N. Tan, B. Jelenković, X.-P. Huang, and D. J. Wineland, “Bragg diffraction from crystallized ion plasmas,” Science 279, 686–689 (1998).
[PubMed]

X.-P. Huang, J. J. Bollinger, T. B. Mitchell, and W. M. Itano, “Phase-locked rotation of crystallized non-neutral plasmas by rotating electric fields,” Phys. Rev. Lett. 80, 73–76 (1998).

X.-P. Huang, J. J. Bollinger, T. B. Mitchell, W. M. Itano, and D. H. E. Dubin, “Precise control of the global rotation of strongly coupled ion plasmas in a Penning trap,” Phys. Plasmas 5, 1656–1663 (1998).

J. J. Bollinger, D. J. Wineland, and D. H. E. Dubin, “Non-neutral ion plasmas and crystals, laser cooling, and atomic clocks,” Phys. Plasmas 1, 1403–1414 (1994).

L. R. Brewer, J. D. Prestage, J. J. Bollinger, W. M. Itano, D. J. Larson, and D. J. Wineland, “Static properties of a non-neutral 9Be+ ion plasma,” Phys. Rev. A 38, 859–873 (1988).
[PubMed]

J. J. Bollinger and D. J. Wineland, “Strongly coupled nonneutral ion plasma,” Phys. Rev. Lett. 53, 348–351 (1984).

Brewer, L. R.

L. R. Brewer, J. D. Prestage, J. J. Bollinger, W. M. Itano, D. J. Larson, and D. J. Wineland, “Static properties of a non-neutral 9Be+ ion plasma,” Phys. Rev. A 38, 859–873 (1988).
[PubMed]

Britton, J.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412–415 (2003).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[PubMed]

Britton, J. W.

M. J. Biercuk, H. Uys, J. W. Britton, A. P. VanDevender, and J. J. Bollinger, “Ultrasensitive detection of force and displacement using trapped ions,” Nat. Nanotechnol. 5, 646–650 (2010).
[PubMed]

Campbell, W. C.

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

Chang, M.-S.

K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, “Quantum simulation of frustrated Ising spins with trapped ions,” Nature 465, 590–593 (2010).
[PubMed]

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

Chek-al-kar, D.

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

Chwalla, M.

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

Cirac, J. J.

D. Porras, D. Marquardt, J. von Delft, and J. J. Cirac, “Mesoscopic spin-boson models of trapped ions,” Phys. Rev. A 78, 010101 (2008).

DeMarco, B.

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412–415 (2003).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[PubMed]

Deuschle, T.

F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[PubMed]

Duan, L.-M.

K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, “Quantum simulation of frustrated Ising spins with trapped ions,” Nature 465, 590–593 (2010).
[PubMed]

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

S. Olmschenk, D. N. Matsukevich, P. Maunz, D. Hayes, L.-M. Duan, and C. Monroe, “Quantum teleportation between distant matter qubits,” Science 323, 486–489 (2009).
[PubMed]

Dubin, D. H. E.

M. J. Jensen, T. Hasegawa, J. J. Bollinger, and D. H. E. Dubin, “Rapid heating of a strongly coupled plasma near the solid-liquid phase transition,” Phys. Rev. Lett. 94, 025001 (2005).
[PubMed]

X.-P. Huang, J. J. Bollinger, T. B. Mitchell, W. M. Itano, and D. H. E. Dubin, “Precise control of the global rotation of strongly coupled ion plasmas in a Penning trap,” Phys. Plasmas 5, 1656–1663 (1998).

T. B. Mitchell, J. J. Bollinger, D. H. E. Dubin, X.-P. Huang, W. M. Itano, and R. H. Baughman, “Direct observations of structural phase transitions in planar crystallized ion plasmas,” Science 282, 1290–1293 (1998).
[PubMed]

J. J. Bollinger, D. J. Wineland, and D. H. E. Dubin, “Non-neutral ion plasmas and crystals, laser cooling, and atomic clocks,” Phys. Plasmas 1, 1403–1414 (1994).

Dur, W.

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

Edwards, E. E.

K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, “Quantum simulation of frustrated Ising spins with trapped ions,” Nature 465, 590–593 (2010).
[PubMed]

Eschner, J.

F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[PubMed]

H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Ion strings for quantum gates,” Appl. Phys. B 66, 603–608 (1998).

Freericks, J. K.

K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, “Quantum simulation of frustrated Ising spins with trapped ions,” Nature 465, 590–593 (2010).
[PubMed]

Gerritsma, R.

R. Gerritsma, G. Kirchmair, F. Zahringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[PubMed]

Guhne, O.

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

Gulde, S.

F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[PubMed]

Haffner, H.

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[PubMed]

Hansel, W.

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

Hasegawa, T.

M. J. Jensen, T. Hasegawa, J. J. Bollinger, and D. H. E. Dubin, “Rapid heating of a strongly coupled plasma near the solid-liquid phase transition,” Phys. Rev. Lett. 94, 025001 (2005).
[PubMed]

M. J. Jensen, T. Hasegawa, and J. J. Bollinger, “Temperature and heating rate of ion crystals in Penning traps,” Phys. Rev. A 70, 033401 (2004).

Hayes, D.

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

S. Olmschenk, D. N. Matsukevich, P. Maunz, D. Hayes, L.-M. Duan, and C. Monroe, “Quantum teleportation between distant matter qubits,” Science 323, 486–489 (2009).
[PubMed]

Huang, X.-P.

J. J. Bollinger, T. B. Mitchell, X.-P. Huang, W. M. Itano, J. N. Tan, B. M. Jelenkovic, and D. J. Wineland, “Crystalline order in laser-cooled, nonneutral ion plasmas,” Phys. Plasmas 7, 7–13 (2000).

T. B. Mitchell, J. J. Bollinger, D. H. E. Dubin, X.-P. Huang, W. M. Itano, and R. H. Baughman, “Direct observations of structural phase transitions in planar crystallized ion plasmas,” Science 282, 1290–1293 (1998).
[PubMed]

T. B. Mitchell, J. J. Bollinger, X.-P. Huang, and W. M. Itano, “Doppler imaging of plasma modes in a Penning trap,” Opt. Express 2, 314–322 (1998).
[PubMed]

W. M. Itano, J. J. Bollinger, J. N. Tan, B. Jelenković, X.-P. Huang, and D. J. Wineland, “Bragg diffraction from crystallized ion plasmas,” Science 279, 686–689 (1998).
[PubMed]

X.-P. Huang, J. J. Bollinger, T. B. Mitchell, W. M. Itano, and D. H. E. Dubin, “Precise control of the global rotation of strongly coupled ion plasmas in a Penning trap,” Phys. Plasmas 5, 1656–1663 (1998).

X.-P. Huang, J. J. Bollinger, T. B. Mitchell, and W. M. Itano, “Phase-locked rotation of crystallized non-neutral plasmas by rotating electric fields,” Phys. Rev. Lett. 80, 73–76 (1998).

Islam, R.

K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, “Quantum simulation of frustrated Ising spins with trapped ions,” Nature 465, 590–593 (2010).
[PubMed]

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

Itano, W. M.

M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, “High-fidelity quantum control using ion crystals in a Penning trap,” Quantum Inf. Comput. 9, 920–949 (2009).

P. O. Schmidt, T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, “Spectroscopy using quantum logic,” Science. 309, 749–752 (2005).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412–415 (2003).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[PubMed]

J. J. Bollinger, T. B. Mitchell, X.-P. Huang, W. M. Itano, J. N. Tan, B. M. Jelenkovic, and D. J. Wineland, “Crystalline order in laser-cooled, nonneutral ion plasmas,” Phys. Plasmas 7, 7–13 (2000).

T. B. Mitchell, J. J. Bollinger, D. H. E. Dubin, X.-P. Huang, W. M. Itano, and R. H. Baughman, “Direct observations of structural phase transitions in planar crystallized ion plasmas,” Science 282, 1290–1293 (1998).
[PubMed]

T. B. Mitchell, J. J. Bollinger, X.-P. Huang, and W. M. Itano, “Doppler imaging of plasma modes in a Penning trap,” Opt. Express 2, 314–322 (1998).
[PubMed]

D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Minimization of ion micromotion in a Paul trap,” J. Appl. Phys. 83, 5025–5033 (1998).

X.-P. Huang, J. J. Bollinger, T. B. Mitchell, and W. M. Itano, “Phase-locked rotation of crystallized non-neutral plasmas by rotating electric fields,” Phys. Rev. Lett. 80, 73–76 (1998).

X.-P. Huang, J. J. Bollinger, T. B. Mitchell, W. M. Itano, and D. H. E. Dubin, “Precise control of the global rotation of strongly coupled ion plasmas in a Penning trap,” Phys. Plasmas 5, 1656–1663 (1998).

W. M. Itano, J. J. Bollinger, J. N. Tan, B. Jelenković, X.-P. Huang, and D. J. Wineland, “Bragg diffraction from crystallized ion plasmas,” Science 279, 686–689 (1998).
[PubMed]

Q. A. Turchette, C. S. Wood, B. E. King, C. J. Myatt, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Deterministic entanglement of two ions,” Phys. Rev. Lett. 81, 3631–3634 (1998).

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol. 103, 259–328 (1998).

B. King, C. Myatt, Q. A. Turchette, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Cooling the collective motion of trapped ions to initialize a quantum register,” Phys. Rev. Lett. 81, 1525–1528 (1998).

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, C. J. Myatt, and C. S. Wood, “Trapped-ion quantum simulator,” Phys. Scr. T76, 147–151 (1998).

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, “Demonstration of a fundamental quantum logic gate,” Phys. Rev. Lett. 75, 4714–4717 (1995).
[PubMed]

L. R. Brewer, J. D. Prestage, J. J. Bollinger, W. M. Itano, D. J. Larson, and D. J. Wineland, “Static properties of a non-neutral 9Be+ ion plasma,” Phys. Rev. A 38, 859–873 (1988).
[PubMed]

Jelenkovic, B.

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412–415 (2003).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[PubMed]

W. M. Itano, J. J. Bollinger, J. N. Tan, B. Jelenković, X.-P. Huang, and D. J. Wineland, “Bragg diffraction from crystallized ion plasmas,” Science 279, 686–689 (1998).
[PubMed]

Jelenkovic, B. M.

J. J. Bollinger, T. B. Mitchell, X.-P. Huang, W. M. Itano, J. N. Tan, B. M. Jelenkovic, and D. J. Wineland, “Crystalline order in laser-cooled, nonneutral ion plasmas,” Phys. Plasmas 7, 7–13 (2000).

Jensen, M. J.

M. J. Jensen, T. Hasegawa, J. J. Bollinger, and D. H. E. Dubin, “Rapid heating of a strongly coupled plasma near the solid-liquid phase transition,” Phys. Rev. Lett. 94, 025001 (2005).
[PubMed]

M. J. Jensen, T. Hasegawa, and J. J. Bollinger, “Temperature and heating rate of ion crystals in Penning traps,” Phys. Rev. A 70, 033401 (2004).

Jost, J.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[PubMed]

Kielpinski, D.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[PubMed]

Kim, K.

K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, “Quantum simulation of frustrated Ising spins with trapped ions,” Nature 465, 590–593 (2010).
[PubMed]

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

King, B.

B. King, C. Myatt, Q. A. Turchette, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Cooling the collective motion of trapped ions to initialize a quantum register,” Phys. Rev. Lett. 81, 1525–1528 (1998).

King, B. E.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[PubMed]

Q. A. Turchette, C. S. Wood, B. E. King, C. J. Myatt, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Deterministic entanglement of two ions,” Phys. Rev. Lett. 81, 3631–3634 (1998).

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol. 103, 259–328 (1998).

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, C. J. Myatt, and C. S. Wood, “Trapped-ion quantum simulator,” Phys. Scr. T76, 147–151 (1998).

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, “Demonstration of a fundamental quantum logic gate,” Phys. Rev. Lett. 75, 4714–4717 (1995).
[PubMed]

Kirchmair, G.

R. Gerritsma, G. Kirchmair, F. Zahringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[PubMed]

Knill, E.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[PubMed]

Korber, T.

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

Korenblit, S.

K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, “Quantum simulation of frustrated Ising spins with trapped ions,” Nature 465, 590–593 (2010).
[PubMed]

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

Lancaster, G. P. T.

F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[PubMed]

Langer, C.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[PubMed]

P. O. Schmidt, T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, “Spectroscopy using quantum logic,” Science. 309, 749–752 (2005).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412–415 (2003).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[PubMed]

Larson, D. J.

L. R. Brewer, J. D. Prestage, J. J. Bollinger, W. M. Itano, D. J. Larson, and D. J. Wineland, “Static properties of a non-neutral 9Be+ ion plasma,” Phys. Rev. A 38, 859–873 (1988).
[PubMed]

Leibfried, D.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412–415 (2003).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[PubMed]

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, C. J. Myatt, and C. S. Wood, “Trapped-ion quantum simulator,” Phys. Scr. T76, 147–151 (1998).

B. King, C. Myatt, Q. A. Turchette, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Cooling the collective motion of trapped ions to initialize a quantum register,” Phys. Rev. Lett. 81, 1525–1528 (1998).

Q. A. Turchette, C. S. Wood, B. E. King, C. J. Myatt, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Deterministic entanglement of two ions,” Phys. Rev. Lett. 81, 3631–3634 (1998).

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol. 103, 259–328 (1998).

Lin, G.-D.

K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, “Quantum simulation of frustrated Ising spins with trapped ions,” Nature 465, 590–593 (2010).
[PubMed]

Lucas, D.

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412–415 (2003).
[PubMed]

Marquardt, D.

D. Porras, D. Marquardt, J. von Delft, and J. J. Cirac, “Mesoscopic spin-boson models of trapped ions,” Phys. Rev. A 78, 010101 (2008).

Matsukevich, D. N.

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

S. Olmschenk, D. N. Matsukevich, P. Maunz, D. Hayes, L.-M. Duan, and C. Monroe, “Quantum teleportation between distant matter qubits,” Science 323, 486–489 (2009).
[PubMed]

Maunz, P.

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

S. Olmschenk, D. N. Matsukevich, P. Maunz, D. Hayes, L.-M. Duan, and C. Monroe, “Quantum teleportation between distant matter qubits,” Science 323, 486–489 (2009).
[PubMed]

Meekhof, D.

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol. 103, 259–328 (1998).

Meekhof, D. M.

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, “Demonstration of a fundamental quantum logic gate,” Phys. Rev. Lett. 75, 4714–4717 (1995).
[PubMed]

Meyer, V.

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412–415 (2003).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[PubMed]

Miller, J. D.

D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Minimization of ion micromotion in a Paul trap,” J. Appl. Phys. 83, 5025–5033 (1998).

Mitchell, T. B.

J. J. Bollinger, T. B. Mitchell, X.-P. Huang, W. M. Itano, J. N. Tan, B. M. Jelenkovic, and D. J. Wineland, “Crystalline order in laser-cooled, nonneutral ion plasmas,” Phys. Plasmas 7, 7–13 (2000).

T. B. Mitchell, J. J. Bollinger, X.-P. Huang, and W. M. Itano, “Doppler imaging of plasma modes in a Penning trap,” Opt. Express 2, 314–322 (1998).
[PubMed]

T. B. Mitchell, J. J. Bollinger, D. H. E. Dubin, X.-P. Huang, W. M. Itano, and R. H. Baughman, “Direct observations of structural phase transitions in planar crystallized ion plasmas,” Science 282, 1290–1293 (1998).
[PubMed]

X.-P. Huang, J. J. Bollinger, T. B. Mitchell, and W. M. Itano, “Phase-locked rotation of crystallized non-neutral plasmas by rotating electric fields,” Phys. Rev. Lett. 80, 73–76 (1998).

X.-P. Huang, J. J. Bollinger, T. B. Mitchell, W. M. Itano, and D. H. E. Dubin, “Precise control of the global rotation of strongly coupled ion plasmas in a Penning trap,” Phys. Plasmas 5, 1656–1663 (1998).

Mizrahi, J.

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

Monroe, C.

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

K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, “Quantum simulation of frustrated Ising spins with trapped ions,” Nature 465, 590–593 (2010).
[PubMed]

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
[PubMed]

S. Olmschenk, D. N. Matsukevich, P. Maunz, D. Hayes, L.-M. Duan, and C. Monroe, “Quantum teleportation between distant matter qubits,” Science 323, 486–489 (2009).
[PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[PubMed]

Q. A. Turchette, C. S. Wood, B. E. King, C. J. Myatt, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Deterministic entanglement of two ions,” Phys. Rev. Lett. 81, 3631–3634 (1998).

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol. 103, 259–328 (1998).

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, C. J. Myatt, and C. S. Wood, “Trapped-ion quantum simulator,” Phys. Scr. T76, 147–151 (1998).

B. King, C. Myatt, Q. A. Turchette, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Cooling the collective motion of trapped ions to initialize a quantum register,” Phys. Rev. Lett. 81, 1525–1528 (1998).

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, “Demonstration of a fundamental quantum logic gate,” Phys. Rev. Lett. 75, 4714–4717 (1995).
[PubMed]

Myatt, C.

B. King, C. Myatt, Q. A. Turchette, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Cooling the collective motion of trapped ions to initialize a quantum register,” Phys. Rev. Lett. 81, 1525–1528 (1998).

Myatt, C. J.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[PubMed]

Q. A. Turchette, C. S. Wood, B. E. King, C. J. Myatt, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Deterministic entanglement of two ions,” Phys. Rev. Lett. 81, 3631–3634 (1998).

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, C. J. Myatt, and C. S. Wood, “Trapped-ion quantum simulator,” Phys. Scr. T76, 147–151 (1998).

Nagerl, H. C.

H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Ion strings for quantum gates,” Appl. Phys. B 66, 603–608 (1998).

Olmschenk, S.

S. Olmschenk, D. N. Matsukevich, P. Maunz, D. Hayes, L.-M. Duan, and C. Monroe, “Quantum teleportation between distant matter qubits,” Science 323, 486–489 (2009).
[PubMed]

Ozeri, R.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[PubMed]

Porras, D.

D. Porras, D. Marquardt, J. von Delft, and J. J. Cirac, “Mesoscopic spin-boson models of trapped ions,” Phys. Rev. A 78, 010101 (2008).

Prestage, J. D.

L. R. Brewer, J. D. Prestage, J. J. Bollinger, W. M. Itano, D. J. Larson, and D. J. Wineland, “Static properties of a non-neutral 9Be+ ion plasma,” Phys. Rev. A 38, 859–873 (1988).
[PubMed]

Quraihi, Q.

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

Rapol, U. D.

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

Reichle, R.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[PubMed]

Riebe, M.

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[PubMed]

Roos, C. F.

R. Gerritsma, G. Kirchmair, F. Zahringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[PubMed]

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[PubMed]

Rosenband, T.

P. O. Schmidt, T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, “Spectroscopy using quantum logic,” Science. 309, 749–752 (2005).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412–415 (2003).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[PubMed]

Rowe, M.

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[PubMed]

Sackett, C. A.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[PubMed]

Schmidt, P. O.

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

P. O. Schmidt, T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, “Spectroscopy using quantum logic,” Science. 309, 749–752 (2005).
[PubMed]

Schmidt-Kaler, F.

F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[PubMed]

H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Ion strings for quantum gates,” Appl. Phys. B 66, 603–608 (1998).

Seidelin, S.

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[PubMed]

Senko, C.

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

Shiga, N.

M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, “High-fidelity quantum control using ion crystals in a Penning trap,” Quantum Inf. Comput. 9, 920–949 (2009).

Solano, E.

R. Gerritsma, G. Kirchmair, F. Zahringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[PubMed]

Tan, J. N.

J. J. Bollinger, T. B. Mitchell, X.-P. Huang, W. M. Itano, J. N. Tan, B. M. Jelenkovic, and D. J. Wineland, “Crystalline order in laser-cooled, nonneutral ion plasmas,” Phys. Plasmas 7, 7–13 (2000).

W. M. Itano, J. J. Bollinger, J. N. Tan, B. Jelenković, X.-P. Huang, and D. J. Wineland, “Bragg diffraction from crystallized ion plasmas,” Science 279, 686–689 (1998).
[PubMed]

Turchette, Q. A.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[PubMed]

Q. A. Turchette, C. S. Wood, B. E. King, C. J. Myatt, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Deterministic entanglement of two ions,” Phys. Rev. Lett. 81, 3631–3634 (1998).

B. King, C. Myatt, Q. A. Turchette, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Cooling the collective motion of trapped ions to initialize a quantum register,” Phys. Rev. Lett. 81, 1525–1528 (1998).

Uys, H.

M. J. Biercuk, H. Uys, J. W. Britton, A. P. VanDevender, and J. J. Bollinger, “Ultrasensitive detection of force and displacement using trapped ions,” Nat. Nanotechnol. 5, 646–650 (2010).
[PubMed]

M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, “High-fidelity quantum control using ion crystals in a Penning trap,” Quantum Inf. Comput. 9, 920–949 (2009).

VanDevender, A. P.

M. J. Biercuk, H. Uys, J. W. Britton, A. P. VanDevender, and J. J. Bollinger, “Ultrasensitive detection of force and displacement using trapped ions,” Nat. Nanotechnol. 5, 646–650 (2010).
[PubMed]

M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, “High-fidelity quantum control using ion crystals in a Penning trap,” Quantum Inf. Comput. 9, 920–949 (2009).

von Delft, J.

D. Porras, D. Marquardt, J. von Delft, and J. J. Cirac, “Mesoscopic spin-boson models of trapped ions,” Phys. Rev. A 78, 010101 (2008).

Wineland, D. J.

R. Blatt and D. J. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1014 (2008).
[PubMed]

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[PubMed]

P. O. Schmidt, T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, “Spectroscopy using quantum logic,” Science. 309, 749–752 (2005).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412–415 (2003).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
[PubMed]

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[PubMed]

J. J. Bollinger, T. B. Mitchell, X.-P. Huang, W. M. Itano, J. N. Tan, B. M. Jelenkovic, and D. J. Wineland, “Crystalline order in laser-cooled, nonneutral ion plasmas,” Phys. Plasmas 7, 7–13 (2000).

D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Minimization of ion micromotion in a Paul trap,” J. Appl. Phys. 83, 5025–5033 (1998).

W. M. Itano, J. J. Bollinger, J. N. Tan, B. Jelenković, X.-P. Huang, and D. J. Wineland, “Bragg diffraction from crystallized ion plasmas,” Science 279, 686–689 (1998).
[PubMed]

Q. A. Turchette, C. S. Wood, B. E. King, C. J. Myatt, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Deterministic entanglement of two ions,” Phys. Rev. Lett. 81, 3631–3634 (1998).

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol. 103, 259–328 (1998).

B. King, C. Myatt, Q. A. Turchette, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Cooling the collective motion of trapped ions to initialize a quantum register,” Phys. Rev. Lett. 81, 1525–1528 (1998).

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, C. J. Myatt, and C. S. Wood, “Trapped-ion quantum simulator,” Phys. Scr. T76, 147–151 (1998).

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, “Demonstration of a fundamental quantum logic gate,” Phys. Rev. Lett. 75, 4714–4717 (1995).
[PubMed]

J. J. Bollinger, D. J. Wineland, and D. H. E. Dubin, “Non-neutral ion plasmas and crystals, laser cooling, and atomic clocks,” Phys. Plasmas 1, 1403–1414 (1994).

L. R. Brewer, J. D. Prestage, J. J. Bollinger, W. M. Itano, D. J. Larson, and D. J. Wineland, “Static properties of a non-neutral 9Be+ ion plasma,” Phys. Rev. A 38, 859–873 (1988).
[PubMed]

J. J. Bollinger and D. J. Wineland, “Strongly coupled nonneutral ion plasma,” Phys. Rev. Lett. 53, 348–351 (1984).

Wood, C. S.

Q. A. Turchette, C. S. Wood, B. E. King, C. J. Myatt, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Deterministic entanglement of two ions,” Phys. Rev. Lett. 81, 3631–3634 (1998).

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, C. J. Myatt, and C. S. Wood, “Trapped-ion quantum simulator,” Phys. Scr. T76, 147–151 (1998).

Zahringer, F.

R. Gerritsma, G. Kirchmair, F. Zahringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
[PubMed]

Appl. Phys. B (1)

H. C. Nagerl, W. Bechter, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Ion strings for quantum gates,” Appl. Phys. B 66, 603–608 (1998).

J. Appl. Phys. (1)

D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Minimization of ion micromotion in a Paul trap,” J. Appl. Phys. 83, 5025–5033 (1998).

J. Res. Natl. Inst. Stand. Technol. (1)

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol. 103, 259–328 (1998).

Nat. Nanotechnol. (1)

M. J. Biercuk, H. Uys, J. W. Britton, A. P. VanDevender, and J. J. Bollinger, “Ultrasensitive detection of force and displacement using trapped ions,” Nat. Nanotechnol. 5, 646–650 (2010).
[PubMed]

Nature (8)

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature 404, 256–259 (2000).
[PubMed]

H. Haffner, W. Hansel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Korber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Guhne, W. Dur, and R. Blatt, “Scalable multiparticle entanglement of trapped ions,” Nature 438, 643–646 (2005).
[PubMed]

R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature 443, 838–841 (2006).
[PubMed]

R. Blatt and D. J. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1014 (2008).
[PubMed]

F. Schmidt-Kaler, H. Haffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac–Zoller controlled-NOT quantum gate,” Nature 422, 408–411 (2003).
[PubMed]

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust high-fidelity geometric two ion-qubit phase gate,” Nature 422, 412–415 (2003).
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R. Gerritsma, G. Kirchmair, F. Zahringer, E. Solano, R. Blatt, and C. F. Roos, “Quantum simulation of the Dirac equation,” Nature 463, 68–71 (2010).
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K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, “Quantum simulation of frustrated Ising spins with trapped ions,” Nature 465, 590–593 (2010).
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Opt. Express (1)

Phys. Plasmas (3)

X.-P. Huang, J. J. Bollinger, T. B. Mitchell, W. M. Itano, and D. H. E. Dubin, “Precise control of the global rotation of strongly coupled ion plasmas in a Penning trap,” Phys. Plasmas 5, 1656–1663 (1998).

J. J. Bollinger, D. J. Wineland, and D. H. E. Dubin, “Non-neutral ion plasmas and crystals, laser cooling, and atomic clocks,” Phys. Plasmas 1, 1403–1414 (1994).

J. J. Bollinger, T. B. Mitchell, X.-P. Huang, W. M. Itano, J. N. Tan, B. M. Jelenkovic, and D. J. Wineland, “Crystalline order in laser-cooled, nonneutral ion plasmas,” Phys. Plasmas 7, 7–13 (2000).

Phys. Rev. A (3)

L. R. Brewer, J. D. Prestage, J. J. Bollinger, W. M. Itano, D. J. Larson, and D. J. Wineland, “Static properties of a non-neutral 9Be+ ion plasma,” Phys. Rev. A 38, 859–873 (1988).
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M. J. Jensen, T. Hasegawa, and J. J. Bollinger, “Temperature and heating rate of ion crystals in Penning traps,” Phys. Rev. A 70, 033401 (2004).

D. Porras, D. Marquardt, J. von Delft, and J. J. Cirac, “Mesoscopic spin-boson models of trapped ions,” Phys. Rev. A 78, 010101 (2008).

Phys. Rev. Lett. (10)

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
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B. King, C. Myatt, Q. A. Turchette, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Cooling the collective motion of trapped ions to initialize a quantum register,” Phys. Rev. Lett. 81, 1525–1528 (1998).

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, “Entanglement and tunable spin-spin couplings between trapped ions using multiple transverse modes,” Phys. Rev. Lett. 103, 120502 (2009).
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W. C. Campbell, J. Mizrahi, Q. Quraihi, C. Senko, D. Hayes, D. N. Matsukevich, P. Maunz, and C. Monroe, “Ultrafast gates for single atomic qubits,” Phys. Rev. Lett. 105, 090502 (2010).
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M. J. Jensen, T. Hasegawa, J. J. Bollinger, and D. H. E. Dubin, “Rapid heating of a strongly coupled plasma near the solid-liquid phase transition,” Phys. Rev. Lett. 94, 025001 (2005).
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X.-P. Huang, J. J. Bollinger, T. B. Mitchell, and W. M. Itano, “Phase-locked rotation of crystallized non-neutral plasmas by rotating electric fields,” Phys. Rev. Lett. 80, 73–76 (1998).

D. Leibfried, B. DeMarco, V. Meyer, M. Rowe, A. Ben-Kish, J. Britton, W. M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, and D. J. Wineland, “Trapped-ion quantum simulator: experimental application to nonlinear interferometers,” Phys. Rev. Lett. 89, 247901 (2002).
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J. J. Bollinger and D. J. Wineland, “Strongly coupled nonneutral ion plasma,” Phys. Rev. Lett. 53, 348–351 (1984).

Q. A. Turchette, C. S. Wood, B. E. King, C. J. Myatt, D. Leibfried, W. M. Itano, C. Monroe, and D. J. Wineland, “Deterministic entanglement of two ions,” Phys. Rev. Lett. 81, 3631–3634 (1998).

Phys. Scr. (1)

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, C. J. Myatt, and C. S. Wood, “Trapped-ion quantum simulator,” Phys. Scr. T76, 147–151 (1998).

Quantum Inf. Comput. (1)

M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, “High-fidelity quantum control using ion crystals in a Penning trap,” Quantum Inf. Comput. 9, 920–949 (2009).

Science (3)

S. Olmschenk, D. N. Matsukevich, P. Maunz, D. Hayes, L.-M. Duan, and C. Monroe, “Quantum teleportation between distant matter qubits,” Science 323, 486–489 (2009).
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T. B. Mitchell, J. J. Bollinger, D. H. E. Dubin, X.-P. Huang, W. M. Itano, and R. H. Baughman, “Direct observations of structural phase transitions in planar crystallized ion plasmas,” Science 282, 1290–1293 (1998).
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W. M. Itano, J. J. Bollinger, J. N. Tan, B. Jelenković, X.-P. Huang, and D. J. Wineland, “Bragg diffraction from crystallized ion plasmas,” Science 279, 686–689 (1998).
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Science. (1)

P. O. Schmidt, T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, “Spectroscopy using quantum logic,” Science. 309, 749–752 (2005).
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Figures (4)

Fig. 2
Fig. 2

Laser excitation setup. (a) Schematic diagram of laser beamline. (b) Schematic of lens system used for creation of oblate beams with independent control of wavefront tilts. Double-headed arrows indicate translation stages. In experimental setup beams are stacked vertically, and converge with crossing angle of 1.5°. (c) Schematic side-view of laser excitation beamline showing trap electrodes, ion cloud, and orientation of axial magnetic field. (d) Side-view image of fluorescence from the excitation lasers when tuned to be degenerate (Δω = 0) and on-resonance with cycling transition used for Doppler detection. The stationary interference pattern arising from lasers used to excite the optical dipole force is clearly visible. Here, the ions are heated above the liquid-solid phase transition and do now show crystalline order.

Fig. 3
Fig. 3

Direct detection of the optical dipole force in a two-dimensional ion crystal. (a,c,e) Experimental measurements of phase-coherent Doppler velocimetry as a function of excitation-laser difference frequency (vertical) and time delay for arrival of first detected photon. Times shorter than ∼4.5 μs are discarded due to hardware delays. Color scale indicates deviation from a fit to a simple exponential accounting for photon arrival statistics. (b,d,f) Theoretical calculations using equations 4 and 5, and a fit to the magnitude of the oscillation amplitude. Theory replicates salient experimental features including the resonance-linewidth scaling with drive time, and phase evolution with drive frequency. (g) Optical dipole force excitation of a mode nearly degenerate with the COM. In this measurement the phase evolution across resonance changes abruptly indicating the presence of multiple motional resonances. (h) Integrated root-mean-squared velocity of the resonance, using coherent excitation and detection, but averaging over phase information.

Fig. 1
Fig. 1

Schematic of excitation and detection scheme. (a) Details of pulse-timing used in phase-coherent excitation and detection of motional drive. (b) Schematic of experimental measurement apparatus. Dashed lines represent optical signals, solid lines represent electrical signals. Switches controlled via TTL signals shown schematically in panel (a).

Fig. 4
Fig. 4

Comparison of calculated phase-coherent Doppler velocimetry to energy-absorption measurments in the presence of closely spaced motional modes. (a–e) Integrated RMS velocity and absorbed energy for motional modes with spacings, Δ, designated by the column headers, and parameterized by t d 1 . (f–j) Two-dimensional doppler velocimetry signal as a function of drive detuning (horizontal) and photon arrival time (vertical). Phase information in both the central resonances and sidebands due to interference between closely spaced motional modes permits distinguishability relative to energy absorption approaches. (k–o) One-dimensional phase-trace demonstrating information contained in the phase-degree of freedom for t = 0. (p–s) Demonstration of interference between closely spaced motional modes due to the inclusion of a delay (”Offset”) between conclusion of the drive and commencement of Doppler detection, presented in units of the inverse peak spacing Δ−1. For a fixed value of Δ, accumulation of a time-dependent phase shift between motional modes improves resolving power.

Equations (6)

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m ( z ¨ + ω z 2 z ) = F d sin ( ω d t + ψ ) ,
z ( t ) 2 F d m ( ω z 2 ω d 2 ) sin [ 1 2 ( ω d ω z ) t ] cos [ ω z t + 1 2 ( ω d ω z ) t ] .
z ˙ ( t ) = v sin [ ω z t + ϕ ] ,
v = 2 F d ω d m ( ω z 2 ω d 2 ) sin [ ( ω z ω d ) t d 2 ] ,
ϕ = ( ω d ω z ) t d 2 .
η = h ¯ 2 m B e ω Z 2 k sin ( θ ) n ¯ + 1 0.07 ,

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