Abstract

We stabilize a chosen radio frequency beat note between two optical fields derived from the same mode-locked laser pulse train in order to coherently manipulate quantum information. This scheme does not require access or active stabilization of the laser repetition rate. We implement and characterize this external lock, in the context of two-photon stimulated Raman transitions between the hyperfine ground states of trapped Yb+171 quantum bits.

© 2014 Optical Society of America

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  1. M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).
  2. R. Feynman, Int. J. Theor. Phys. 21, 467 (1982).
    [CrossRef]
  3. D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, C. Monroe, Phys. Rev. Lett. 104, 140501 (2010).
    [CrossRef]
  4. A. Pe’er, E. A. Shapiro, M. C. Stowe, M. Shapiro, J. Ye, Phys. Rev. Lett. 98, 113004 (2007).
    [CrossRef]
  5. K. D. Greve, D. Press, P. L. McMahon, Y. Yamamoto, Rep. Prog. Phys. 76, 092501 (2013).
    [CrossRef]
  6. T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J. L. O’Brien, Nature 464, 45 (2010).
    [CrossRef]
  7. P. J. Lee, K.-A. Brickman, L. Deslauriers, P. C. Haljan, L.-M. Duan, C. Monroe, J. Opt. B 7, S371 (2005).
    [CrossRef]
  8. Y. Wu, Phys. Rev. A 54, 1586 (1996).
    [CrossRef]
  9. J. E. Thomas, P. R. Hemmer, S. Ezekiel, C. C. Leiby, R. H. Picard, C. R. Willis, Phys. Rev. Lett. 48, 867 (1982).
    [CrossRef]
  10. P. J. Lee, B. Blinov, K.-A. Brickman, L. Deslauriers, M. Madsen, R. Miller, D. Moehring, D. Stick, C. Monroe, Opt. Lett. 28, 1582 (2003).
    [CrossRef]
  11. S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, G. Steinmeyer, Nat. Photonics 4, 462 (2010).
    [CrossRef]
  12. S. Olmschenk, K. C. Younge, D. L. Moehring, D. N. Matsukevich, P. Maunz, C. Monroe, Phys. Rev. A 76, 052314 (2007).
    [CrossRef]

2013 (1)

K. D. Greve, D. Press, P. L. McMahon, Y. Yamamoto, Rep. Prog. Phys. 76, 092501 (2013).
[CrossRef]

2010 (3)

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J. L. O’Brien, Nature 464, 45 (2010).
[CrossRef]

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, C. Monroe, Phys. Rev. Lett. 104, 140501 (2010).
[CrossRef]

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, G. Steinmeyer, Nat. Photonics 4, 462 (2010).
[CrossRef]

2007 (2)

S. Olmschenk, K. C. Younge, D. L. Moehring, D. N. Matsukevich, P. Maunz, C. Monroe, Phys. Rev. A 76, 052314 (2007).
[CrossRef]

A. Pe’er, E. A. Shapiro, M. C. Stowe, M. Shapiro, J. Ye, Phys. Rev. Lett. 98, 113004 (2007).
[CrossRef]

2005 (1)

P. J. Lee, K.-A. Brickman, L. Deslauriers, P. C. Haljan, L.-M. Duan, C. Monroe, J. Opt. B 7, S371 (2005).
[CrossRef]

2003 (1)

1996 (1)

Y. Wu, Phys. Rev. A 54, 1586 (1996).
[CrossRef]

1982 (2)

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

R. Feynman, Int. J. Theor. Phys. 21, 467 (1982).
[CrossRef]

Anderson, A.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, G. Steinmeyer, Nat. Photonics 4, 462 (2010).
[CrossRef]

Assion, A.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, G. Steinmeyer, Nat. Photonics 4, 462 (2010).
[CrossRef]

Blinov, B.

Brickman, K.-A.

P. J. Lee, K.-A. Brickman, L. Deslauriers, P. C. Haljan, L.-M. Duan, C. Monroe, J. Opt. B 7, S371 (2005).
[CrossRef]

P. J. Lee, B. Blinov, K.-A. Brickman, L. Deslauriers, M. Madsen, R. Miller, D. Moehring, D. Stick, C. Monroe, Opt. Lett. 28, 1582 (2003).
[CrossRef]

Campbell, W.

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, C. Monroe, Phys. Rev. Lett. 104, 140501 (2010).
[CrossRef]

Chuang, I. L.

M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

Deslauriers, L.

P. J. Lee, K.-A. Brickman, L. Deslauriers, P. C. Haljan, L.-M. Duan, C. Monroe, J. Opt. B 7, S371 (2005).
[CrossRef]

P. J. Lee, B. Blinov, K.-A. Brickman, L. Deslauriers, M. Madsen, R. Miller, D. Moehring, D. Stick, C. Monroe, Opt. Lett. 28, 1582 (2003).
[CrossRef]

Duan, L.-M.

P. J. Lee, K.-A. Brickman, L. Deslauriers, P. C. Haljan, L.-M. Duan, C. Monroe, J. Opt. B 7, S371 (2005).
[CrossRef]

Ezekiel, S.

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

Feynman, R.

R. Feynman, Int. J. Theor. Phys. 21, 467 (1982).
[CrossRef]

Frei, H.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, G. Steinmeyer, Nat. Photonics 4, 462 (2010).
[CrossRef]

Grebing, C.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, G. Steinmeyer, Nat. Photonics 4, 462 (2010).
[CrossRef]

Greve, K. D.

K. D. Greve, D. Press, P. L. McMahon, Y. Yamamoto, Rep. Prog. Phys. 76, 092501 (2013).
[CrossRef]

Haljan, P. C.

P. J. Lee, K.-A. Brickman, L. Deslauriers, P. C. Haljan, L.-M. Duan, C. Monroe, J. Opt. B 7, S371 (2005).
[CrossRef]

Hayes, D.

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, C. Monroe, Phys. Rev. Lett. 104, 140501 (2010).
[CrossRef]

Hemmer, P. R.

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

Hucul, D.

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, C. Monroe, Phys. Rev. Lett. 104, 140501 (2010).
[CrossRef]

Jelezko, F.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J. L. O’Brien, Nature 464, 45 (2010).
[CrossRef]

Koke, S.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, G. Steinmeyer, Nat. Photonics 4, 462 (2010).
[CrossRef]

Ladd, T. D.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J. L. O’Brien, Nature 464, 45 (2010).
[CrossRef]

Laflamme, R.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J. L. O’Brien, Nature 464, 45 (2010).
[CrossRef]

Lee, P. J.

P. J. Lee, K.-A. Brickman, L. Deslauriers, P. C. Haljan, L.-M. Duan, C. Monroe, J. Opt. B 7, S371 (2005).
[CrossRef]

P. J. Lee, B. Blinov, K.-A. Brickman, L. Deslauriers, M. Madsen, R. Miller, D. Moehring, D. Stick, C. Monroe, Opt. Lett. 28, 1582 (2003).
[CrossRef]

Leiby, C. C.

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

Madsen, M.

Matsukevich, D. N.

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, C. Monroe, Phys. Rev. Lett. 104, 140501 (2010).
[CrossRef]

S. Olmschenk, K. C. Younge, D. L. Moehring, D. N. Matsukevich, P. Maunz, C. Monroe, Phys. Rev. A 76, 052314 (2007).
[CrossRef]

Maunz, P.

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, C. Monroe, Phys. Rev. Lett. 104, 140501 (2010).
[CrossRef]

S. Olmschenk, K. C. Younge, D. L. Moehring, D. N. Matsukevich, P. Maunz, C. Monroe, Phys. Rev. A 76, 052314 (2007).
[CrossRef]

McMahon, P. L.

K. D. Greve, D. Press, P. L. McMahon, Y. Yamamoto, Rep. Prog. Phys. 76, 092501 (2013).
[CrossRef]

Miller, R.

Mizrahi, J.

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, C. Monroe, Phys. Rev. Lett. 104, 140501 (2010).
[CrossRef]

Moehring, D.

Moehring, D. L.

S. Olmschenk, K. C. Younge, D. L. Moehring, D. N. Matsukevich, P. Maunz, C. Monroe, Phys. Rev. A 76, 052314 (2007).
[CrossRef]

Monroe, C.

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, C. Monroe, Phys. Rev. Lett. 104, 140501 (2010).
[CrossRef]

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J. L. O’Brien, Nature 464, 45 (2010).
[CrossRef]

S. Olmschenk, K. C. Younge, D. L. Moehring, D. N. Matsukevich, P. Maunz, C. Monroe, Phys. Rev. A 76, 052314 (2007).
[CrossRef]

P. J. Lee, K.-A. Brickman, L. Deslauriers, P. C. Haljan, L.-M. Duan, C. Monroe, J. Opt. B 7, S371 (2005).
[CrossRef]

P. J. Lee, B. Blinov, K.-A. Brickman, L. Deslauriers, M. Madsen, R. Miller, D. Moehring, D. Stick, C. Monroe, Opt. Lett. 28, 1582 (2003).
[CrossRef]

Nakamura, Y.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J. L. O’Brien, Nature 464, 45 (2010).
[CrossRef]

Nielsen, M. A.

M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

O’Brien, J. L.

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J. L. O’Brien, Nature 464, 45 (2010).
[CrossRef]

Olmschenk, S.

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, C. Monroe, Phys. Rev. Lett. 104, 140501 (2010).
[CrossRef]

S. Olmschenk, K. C. Younge, D. L. Moehring, D. N. Matsukevich, P. Maunz, C. Monroe, Phys. Rev. A 76, 052314 (2007).
[CrossRef]

Pe’er, A.

A. Pe’er, E. A. Shapiro, M. C. Stowe, M. Shapiro, J. Ye, Phys. Rev. Lett. 98, 113004 (2007).
[CrossRef]

Picard, R. H.

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

Press, D.

K. D. Greve, D. Press, P. L. McMahon, Y. Yamamoto, Rep. Prog. Phys. 76, 092501 (2013).
[CrossRef]

Quraishi, Q.

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, C. Monroe, Phys. Rev. Lett. 104, 140501 (2010).
[CrossRef]

Senko, C.

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, C. Monroe, Phys. Rev. Lett. 104, 140501 (2010).
[CrossRef]

Shapiro, E. A.

A. Pe’er, E. A. Shapiro, M. C. Stowe, M. Shapiro, J. Ye, Phys. Rev. Lett. 98, 113004 (2007).
[CrossRef]

Shapiro, M.

A. Pe’er, E. A. Shapiro, M. C. Stowe, M. Shapiro, J. Ye, Phys. Rev. Lett. 98, 113004 (2007).
[CrossRef]

Steinmeyer, G.

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, G. Steinmeyer, Nat. Photonics 4, 462 (2010).
[CrossRef]

Stick, D.

Stowe, M. C.

A. Pe’er, E. A. Shapiro, M. C. Stowe, M. Shapiro, J. Ye, Phys. Rev. Lett. 98, 113004 (2007).
[CrossRef]

Thomas, J. E.

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

Willis, C. R.

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

Wu, Y.

Y. Wu, Phys. Rev. A 54, 1586 (1996).
[CrossRef]

Yamamoto, Y.

K. D. Greve, D. Press, P. L. McMahon, Y. Yamamoto, Rep. Prog. Phys. 76, 092501 (2013).
[CrossRef]

Ye, J.

A. Pe’er, E. A. Shapiro, M. C. Stowe, M. Shapiro, J. Ye, Phys. Rev. Lett. 98, 113004 (2007).
[CrossRef]

Younge, K. C.

S. Olmschenk, K. C. Younge, D. L. Moehring, D. N. Matsukevich, P. Maunz, C. Monroe, Phys. Rev. A 76, 052314 (2007).
[CrossRef]

Int. J. Theor. Phys. (1)

R. Feynman, Int. J. Theor. Phys. 21, 467 (1982).
[CrossRef]

J. Opt. B (1)

P. J. Lee, K.-A. Brickman, L. Deslauriers, P. C. Haljan, L.-M. Duan, C. Monroe, J. Opt. B 7, S371 (2005).
[CrossRef]

Nat. Photonics (1)

S. Koke, C. Grebing, H. Frei, A. Anderson, A. Assion, G. Steinmeyer, Nat. Photonics 4, 462 (2010).
[CrossRef]

Nature (1)

T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J. L. O’Brien, Nature 464, 45 (2010).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

S. Olmschenk, K. C. Younge, D. L. Moehring, D. N. Matsukevich, P. Maunz, C. Monroe, Phys. Rev. A 76, 052314 (2007).
[CrossRef]

Y. Wu, Phys. Rev. A 54, 1586 (1996).
[CrossRef]

Phys. Rev. Lett. (3)

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

D. Hayes, D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, C. Monroe, Phys. Rev. Lett. 104, 140501 (2010).
[CrossRef]

A. Pe’er, E. A. Shapiro, M. C. Stowe, M. Shapiro, J. Ye, Phys. Rev. Lett. 98, 113004 (2007).
[CrossRef]

Rep. Prog. Phys. (1)

K. D. Greve, D. Press, P. L. McMahon, Y. Yamamoto, Rep. Prog. Phys. 76, 092501 (2013).
[CrossRef]

Other (1)

M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

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Figures (5)

Fig. 1.
Fig. 1.

Energy level diagram in a three-level Λ system. Two laser beams with frequencies νaL and νbL off-resonantly couple the states |a and |b to the excited state |e. When the detunings νaνaL and νbνbL are larger than the strength of the couplings, the excited state may be adiabatically eliminated and the system behaves like an effective two-level qubit with states |a and |b.

Fig. 2.
Fig. 2.

(a) Optical comb teeth for the two Raman beams. The dotted arrow shows a pair of comb teeth that drive the desired two-photon Raman transition. (b)–(d) Measured rf comb teeth from a mode-locked laser pulse train striking a fast photodiode. The light is split with a beam splitter into two arms having separate AOMs, and recombined at the second beam splitter with the photodiode behind one of the ports. (a) Partial spectrum with the beam from AOM2 blocked, showing lines spaced by the laser repetition frequency νrep80MHz. (b) Spectrum with the beam from AOM1 blocked. (c) Spectrum with both beams, having sidebands at ±|ΔνM| due to interference of the beams. When a qubit replaces the beam splitter, these rf beat notes can drive transitions between the qubit states.

Fig. 3.
Fig. 3.

Repetition rate of a free-running Nd:YVO4 mode-locked laser at 355 nm (Vanguard from Spectra Physics), measured with a digital frequency counter in regular 2 min intervals. The drift of 1Hz/min appears to be correlated with ambient temperature drifts. Raman transitions between Yb+171 qubit states use the 157th comb tooth, which therefore drifts by 157Hz/min.

Fig. 4.
Fig. 4.

Schematics of the beat note frequency lock. (a) The output of a fast photodiode is mixed with a local oscillator (LO) signal, which is sent to a phase-locked loop (PLL) after rejecting the high-frequency beat note by using a low-pass filter (LPF). The output of the PLL drives the AOM. (b) Details of the repetition rate lock circuit used in our experiment. The second-harmonic light (at 532 nm) from a mode-locked YAG laser (Vanguard from Spectra Physics, repetition rate νrep80.6MHz) is incident on a fast photodiode, which generates an rf comb with comb teeth at frequencies mνrep (m is a positive integer). This signal is amplified and passed though a bandpass filter (BPF), which transmits the n=157th comb tooth at nνrep12.655GHz. This is then mixed with an rf signal at νLO=12.438GHz generated by an HP8672A oven-stabilized synthesizer, passed through the low-pass filter LPF1 with a corner frequency of 250 MHz and the lower frequency beat note (at 217MHz) is sent to the PLL, where an HP8640B function generator is frequency modulated by a proportional-integrator (PI) controller to produce a signal that is phase locked with the beat note. The bandwidth of the output signal depends on the bandwidth of the low-pass filter LPF2 (variable, from 3 Hz to 3 kHz) used in the PLL. The frequency spectra of the signals at monitoring points MP1 and MP2 are shown in Fig. 5.

Fig. 5.
Fig. 5.

(a) Frequency spectra of the error beat note that drives a modulator in one of the arms (AOM1) at points MP1 and MP2 in Fig. 4, with resolution bandwidth (RBW) of 110 Hz. The PLL eliminates the (white) noise outside the bandwidth of the low-pass filter, resulting in a fractional noise figure of α120dB/Hz. (b) Probability of Raman excitation of a single trapped Yb+171 ion qubit versus AOM2 frequency with and without the PLL. Here the system is initialized in the hyperfine state S1/22|F=0,mF=0. The Raman beams (perpendicular to each other) are applied for 40 μs, and the probability of finding the ion in the excited-state manifold (S1/22|F=1 states) is measured. This procedure is repeated at different frequencies of the Raman beat notes in order to obtain the spectrum. If the error signal at point MP1 is used to directly drive modulator AOM1, the noise excites unwanted transitions at all AOM2 frequencies, as seen in the constant background in the Raman spectrum. The output of the PLL does not have this noise beyond the bandwidth of the low-pass filter used, and hence the Raman frequency spectrum is cleaner. Here we show the “carrier” transition between the hyperfine Yb+171 “clock” states appearing at a frequency of 205MHz, and trapped ion vibrational upper and lower sidebands near 200MHz and 215MHz.

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