Abstract

We report new techniques for driving high-fidelity stimulated Raman transitions in trapped-ion qubits. An electro-optic modulator induces sidebands on an optical source, and interference between the sidebands allows coherent Rabi transitions to be efficiently driven between hyperfine ground states separated by 14.53 GHz in a single trapped  111Cd+ ion.

© 2003 Optical Society of America

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  1. J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).
    [CrossRef] [PubMed]
  2. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, J. Res. Natl. Stand. Technol. 103, 259 (1998).
    [CrossRef]
  3. D. Kielpinski, C. Monroe, and D. J. Wineland, Nature 417, 709 (2002).
    [CrossRef] [PubMed]
  4. C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 75, 4714 (1995).
    [CrossRef] [PubMed]
  5. K. Mølmer and A. Sørensen, Phys. Rev. Lett. 82, 1835 (1999).
    [CrossRef]
  6. 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, Nature 404, 256 (2000).
    [CrossRef] [PubMed]
  7. J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
    [CrossRef]
  8. M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992).
    [CrossRef] [PubMed]
  9. C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, Phys. Rev. Lett. 75, 4011 (1995).
    [CrossRef] [PubMed]
  10. B. Blinov, I. Deslauriers, P. Lee, M. Madsen, R. Miller, and C. Monroe, Phys. Rev. A 65, 040304 (2002).
    [CrossRef]
  11. U. Tanaka, H. Imajo, K. Hayasaka, R. Ohmukai, M. Watanabe, and S. Urabe, Phys. Rev. A 53, 3982 (1996).
    [CrossRef] [PubMed]
  12. M. Kasevich and S. Chu, Appl. Phys. B 54, 321 (1992).
    [CrossRef]

2002 (2)

D. Kielpinski, C. Monroe, and D. J. Wineland, Nature 417, 709 (2002).
[CrossRef] [PubMed]

B. Blinov, I. Deslauriers, P. Lee, M. Madsen, R. Miller, and C. Monroe, Phys. Rev. A 65, 040304 (2002).
[CrossRef]

2000 (1)

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, Nature 404, 256 (2000).
[CrossRef] [PubMed]

1999 (1)

K. Mølmer and A. Sørensen, Phys. Rev. Lett. 82, 1835 (1999).
[CrossRef]

1998 (1)

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, J. Res. Natl. Stand. Technol. 103, 259 (1998).
[CrossRef]

1996 (1)

U. Tanaka, H. Imajo, K. Hayasaka, R. Ohmukai, M. Watanabe, and S. Urabe, Phys. Rev. A 53, 3982 (1996).
[CrossRef] [PubMed]

1995 (3)

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, Phys. Rev. Lett. 75, 4011 (1995).
[CrossRef] [PubMed]

J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 75, 4714 (1995).
[CrossRef] [PubMed]

1992 (2)

M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992).
[CrossRef] [PubMed]

M. Kasevich and S. Chu, Appl. Phys. B 54, 321 (1992).
[CrossRef]

1982 (1)

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

Blinov, B.

B. Blinov, I. Deslauriers, P. Lee, M. Madsen, R. Miller, and C. Monroe, Phys. Rev. A 65, 040304 (2002).
[CrossRef]

Chu, S.

M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992).
[CrossRef] [PubMed]

M. Kasevich and S. Chu, Appl. Phys. B 54, 321 (1992).
[CrossRef]

Cirac, J. I.

J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).
[CrossRef] [PubMed]

Deslauriers, I.

B. Blinov, I. Deslauriers, P. Lee, M. Madsen, R. Miller, and C. Monroe, Phys. Rev. A 65, 040304 (2002).
[CrossRef]

Ezekiel, S.

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

Gould, P.

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, Phys. Rev. Lett. 75, 4011 (1995).
[CrossRef] [PubMed]

Hayasaka, K.

U. Tanaka, H. Imajo, K. Hayasaka, R. Ohmukai, M. Watanabe, and S. Urabe, Phys. Rev. A 53, 3982 (1996).
[CrossRef] [PubMed]

Hemmer, P. R.

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

Imajo, H.

U. Tanaka, H. Imajo, K. Hayasaka, R. Ohmukai, M. Watanabe, and S. Urabe, Phys. Rev. A 53, 3982 (1996).
[CrossRef] [PubMed]

Itano, W. M.

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, Nature 404, 256 (2000).
[CrossRef] [PubMed]

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, J. Res. Natl. Stand. Technol. 103, 259 (1998).
[CrossRef]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 75, 4714 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, Phys. Rev. Lett. 75, 4011 (1995).
[CrossRef] [PubMed]

Jefferts, S. R.

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, Phys. Rev. Lett. 75, 4011 (1995).
[CrossRef] [PubMed]

Kasevich, M.

M. Kasevich and S. Chu, Appl. Phys. B 54, 321 (1992).
[CrossRef]

M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992).
[CrossRef] [PubMed]

Kielpinski, D.

D. Kielpinski, C. Monroe, and D. J. Wineland, Nature 417, 709 (2002).
[CrossRef] [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, Nature 404, 256 (2000).
[CrossRef] [PubMed]

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, Nature 404, 256 (2000).
[CrossRef] [PubMed]

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, J. Res. Natl. Stand. Technol. 103, 259 (1998).
[CrossRef]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 75, 4714 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, Phys. Rev. Lett. 75, 4011 (1995).
[CrossRef] [PubMed]

Langer, C.

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, Nature 404, 256 (2000).
[CrossRef] [PubMed]

Lee, P.

B. Blinov, I. Deslauriers, P. Lee, M. Madsen, R. Miller, and C. Monroe, Phys. Rev. A 65, 040304 (2002).
[CrossRef]

Leibfried, D.

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, J. Res. Natl. Stand. Technol. 103, 259 (1998).
[CrossRef]

Leiby, Jr., C. C.

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

Madsen, M.

B. Blinov, I. Deslauriers, P. Lee, M. Madsen, R. Miller, and C. Monroe, Phys. Rev. A 65, 040304 (2002).
[CrossRef]

Meekhof, D. M.

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, J. Res. Natl. Stand. Technol. 103, 259 (1998).
[CrossRef]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 75, 4714 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, Phys. Rev. Lett. 75, 4011 (1995).
[CrossRef] [PubMed]

Meyer, V.

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, Nature 404, 256 (2000).
[CrossRef] [PubMed]

Miller, R.

B. Blinov, I. Deslauriers, P. Lee, M. Madsen, R. Miller, and C. Monroe, Phys. Rev. A 65, 040304 (2002).
[CrossRef]

Mølmer, K.

K. Mølmer and A. Sørensen, Phys. Rev. Lett. 82, 1835 (1999).
[CrossRef]

Monroe, C.

D. Kielpinski, C. Monroe, and D. J. Wineland, Nature 417, 709 (2002).
[CrossRef] [PubMed]

B. Blinov, I. Deslauriers, P. Lee, M. Madsen, R. Miller, and C. Monroe, Phys. Rev. A 65, 040304 (2002).
[CrossRef]

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, Nature 404, 256 (2000).
[CrossRef] [PubMed]

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, J. Res. Natl. Stand. Technol. 103, 259 (1998).
[CrossRef]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 75, 4714 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, Phys. Rev. Lett. 75, 4011 (1995).
[CrossRef] [PubMed]

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, Nature 404, 256 (2000).
[CrossRef] [PubMed]

Ohmukai, R.

U. Tanaka, H. Imajo, K. Hayasaka, R. Ohmukai, M. Watanabe, and S. Urabe, Phys. Rev. A 53, 3982 (1996).
[CrossRef] [PubMed]

Picard, R. H.

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

Rowe, M.

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, Nature 404, 256 (2000).
[CrossRef] [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, Nature 404, 256 (2000).
[CrossRef] [PubMed]

Sørensen, A.

K. Mølmer and A. Sørensen, Phys. Rev. Lett. 82, 1835 (1999).
[CrossRef]

Tanaka, U.

U. Tanaka, H. Imajo, K. Hayasaka, R. Ohmukai, M. Watanabe, and S. Urabe, Phys. Rev. A 53, 3982 (1996).
[CrossRef] [PubMed]

Thomas, J. E.

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

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, Nature 404, 256 (2000).
[CrossRef] [PubMed]

Urabe, S.

U. Tanaka, H. Imajo, K. Hayasaka, R. Ohmukai, M. Watanabe, and S. Urabe, Phys. Rev. A 53, 3982 (1996).
[CrossRef] [PubMed]

Watanabe, M.

U. Tanaka, H. Imajo, K. Hayasaka, R. Ohmukai, M. Watanabe, and S. Urabe, Phys. Rev. A 53, 3982 (1996).
[CrossRef] [PubMed]

Willis, C. R.

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

Wineland, D. J.

D. Kielpinski, C. Monroe, and D. J. Wineland, Nature 417, 709 (2002).
[CrossRef] [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, Nature 404, 256 (2000).
[CrossRef] [PubMed]

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, J. Res. Natl. Stand. Technol. 103, 259 (1998).
[CrossRef]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 75, 4714 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, Phys. Rev. Lett. 75, 4011 (1995).
[CrossRef] [PubMed]

Zoller, P.

J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).
[CrossRef] [PubMed]

Appl. Phys. B (1)

M. Kasevich and S. Chu, Appl. Phys. B 54, 321 (1992).
[CrossRef]

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

D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, J. Res. Natl. Stand. Technol. 103, 259 (1998).
[CrossRef]

Nature (2)

D. Kielpinski, C. Monroe, and D. J. Wineland, Nature 417, 709 (2002).
[CrossRef] [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, Nature 404, 256 (2000).
[CrossRef] [PubMed]

Phys. Rev. A (1)

U. Tanaka, H. Imajo, K. Hayasaka, R. Ohmukai, M. Watanabe, and S. Urabe, Phys. Rev. A 53, 3982 (1996).
[CrossRef] [PubMed]

Phys. Rev. A (1)

B. Blinov, I. Deslauriers, P. Lee, M. Madsen, R. Miller, and C. Monroe, Phys. Rev. A 65, 040304 (2002).
[CrossRef]

Phys. Rev. Lett. (6)

J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).
[CrossRef] [PubMed]

J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, Jr., R. H. Picard, and C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
[CrossRef]

M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, Phys. Rev. Lett. 75, 4011 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 75, 4714 (1995).
[CrossRef] [PubMed]

K. Mølmer and A. Sørensen, Phys. Rev. Lett. 82, 1835 (1999).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Relevant energy levels of a  111Cd+ ion, with resonant detection (σ--polarized) and optical pumping (π-polarized) transitions indicated. (b) Coupling scheme for driving a SRT simultaneously with both ΔmF=±1 couplings. (c) Schematic of the optical source for driving the SRT, including a Mach–Zehnder interferometer and acousto-optic modulator (AOM) shifters to create the frequency shift Δω discussed in the text. The λ/2 plate and the external magnetic field provide constructive interference between the two paths in (b). Alternatively, the beams could be circularly polarized, with only one of the paths in (b) utilized.

Fig. 2
Fig. 2

Rabi flopping on a single ion by use of a SRT with 14-THz detuning. We prepare the ion in the S21/2 |F=0,mF=0 state and then pulse the Raman beams. The probability of the ion’s being in the S21/2 |F=1,mF=0 state versus Raman pulse time τ is plotted, with the Rabi frequency of Ω2π×2 kHz, consistent with the 5 mW of power focused to a 20µm waist. The decaying envelope is consistent with laser amplitude noise, and the slight upward trend is caused by residual light leakage from the resonant measuring beam, causing optical pumping. Each point represents an average of 100 experiments.

Fig. 3
Fig. 3

Rabi frequency versus MZ path-length difference for two values of EOM modulation index ϕ. The curves are theory, and the data are fitted to Eq. (4) by use of the y-axis scale and modulation index as parameters. The fits agree with independent measurements of the modulation index with a Fabry–Perot cavity.

Fig. 4
Fig. 4

Rabi frequency versus EOM modulation index for two different detunings δ of the β-barium borate buildup cavity FSR with respect to the EOM modulation frequency, scaled to the cavity linewidth (see text). The curves are theory, and the data are fitted to Eq. (5) with the y-axis scale and detuning as parameters. The fits agree with independent measurements of the cavity FSR and EOM modulation frequency.

Equations (7)

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

E1=E02expikx-ωtn=-Jnϕ×expinδkx-ωHFt/2+c.c.,
E2=ηE024exp2ikx-ωtn=-Jn2ϕ×expinδkx-ωHFt/2+c.c.,
Ω=μ1μ2E2E2* expiωHFt2Δ=Ω0 expiδk2x+Δxn=-Jn2ϕJn-22ϕ×cos2k+n-1δkΔx,
Ω=Ω0 exp-ikΔxexp-2iδkΔxn=-Jn2ϕ×Jn-22ϕexpinδkΔx,
Ω=2Ω0 exp2iδkxn=-m=-l=-Jn-mϕ1-i2n-mδ×Jmϕ1-i2mδJn+2-lϕ1+i2n+2-lδJlϕ1+i2lδ,
Ωeven=Ω0 exp-2iδkxn=-m=-l=-J2n-mϕ×J2mϕJ2n+1-lϕJ2lϕ,
Ωodd=Ω0 exp-2iδkxn=-m=-l=-J2n-m+1ϕ×J2m+1ϕJ2n+1-l+1ϕJ2l+1ϕ.

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