Abstract

A time-correlated single-photon counting method is used to measure the spontaneous emission lifetime of a single trapped barium ion, yielding a standard deviation of 0.5% for 8 min of integration time. The statistical power of this one-atom technique is comparable with that of other methods that use a macroscopic sample, but the technique has potentially lower systematic errors. The method depends on the use of an electro-optic phase modulator as an Nth-order nonlinear switch, which improves the response time by a factor of N and the on–off ratio by the Nth power.

© 1994 Optical Society of America

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  1. M. S. Kim, F. A. M. de Olivera, P. L. Knight, Opt. Commun. 70, 473 (1989).
    [Crossref]
  2. F. Diedrich, E. Peik, J. M. Chen, W. Quint, H. Walther, Phys. Rev. Lett. 59, 2931 (1987).
    [Crossref] [PubMed]
  3. D. J. Wineland, J. C. Bergquist, W. M Itano, J. J. Bollinger, C. J. Manning, Phys. Rev. Lett. 59, 2935 (1987).
    [Crossref] [PubMed]
  4. J. Hoffnagle, R. G. DeVoe, L. Reyna, R. G. Brewer, Phys. Rev. Lett. 61, 255 (1988).
    [Crossref] [PubMed]
  5. R. G. Brewer, R. G. DeVoe, R. Kallenbach, Phys. Rev A 46, R6781 (1992).
    [Crossref] [PubMed]
  6. G. Grynberg, B. Lounis, P. Verkerk, J. Y. Courtis, C. Salomon, Phys. Rev. Lett. 70, 2249 (1993).
    [Crossref] [PubMed]
  7. A. Hemmerich, R. W. Hänsch, Phys. Rev. Lett. 70, 410 (1993).
    [Crossref] [PubMed]
  8. C. Guet, W. R. JohnsonPhys. Rev. A 44, 1531 (1991).
    [Crossref] [PubMed]
  9. C. E. Tanner, A. E. Livingston, R. J. Rafac, F. G. Serpa, K. W. Kulka, H. G. Berry, L. Young, C. A. Kurz, Phys. Rev. Lett. 69, 2765 (1992).
    [Crossref] [PubMed]
  10. L. Young, W. T. Hill, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, S. R. Leone, Phys. Rev. A 50, 2174 (1994).
    [Crossref] [PubMed]
  11. D. V. O’Connor, D. Phillips, in Time Correlated Single Photon Counting (Academic, London, 1984), Chap. 2, p. 36.
  12. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 361.
  13. L. R. Brothers, D. Lee, N. C. Wong, Opt. Lett. 19, 245 (1994), and references therein.
    [Crossref] [PubMed]
  14. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1986), Chap. 14, p. 526.

1994 (2)

L. Young, W. T. Hill, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, S. R. Leone, Phys. Rev. A 50, 2174 (1994).
[Crossref] [PubMed]

L. R. Brothers, D. Lee, N. C. Wong, Opt. Lett. 19, 245 (1994), and references therein.
[Crossref] [PubMed]

1993 (2)

G. Grynberg, B. Lounis, P. Verkerk, J. Y. Courtis, C. Salomon, Phys. Rev. Lett. 70, 2249 (1993).
[Crossref] [PubMed]

A. Hemmerich, R. W. Hänsch, Phys. Rev. Lett. 70, 410 (1993).
[Crossref] [PubMed]

1992 (2)

R. G. Brewer, R. G. DeVoe, R. Kallenbach, Phys. Rev A 46, R6781 (1992).
[Crossref] [PubMed]

C. E. Tanner, A. E. Livingston, R. J. Rafac, F. G. Serpa, K. W. Kulka, H. G. Berry, L. Young, C. A. Kurz, Phys. Rev. Lett. 69, 2765 (1992).
[Crossref] [PubMed]

1991 (1)

C. Guet, W. R. JohnsonPhys. Rev. A 44, 1531 (1991).
[Crossref] [PubMed]

1989 (1)

M. S. Kim, F. A. M. de Olivera, P. L. Knight, Opt. Commun. 70, 473 (1989).
[Crossref]

1988 (1)

J. Hoffnagle, R. G. DeVoe, L. Reyna, R. G. Brewer, Phys. Rev. Lett. 61, 255 (1988).
[Crossref] [PubMed]

1987 (2)

F. Diedrich, E. Peik, J. M. Chen, W. Quint, H. Walther, Phys. Rev. Lett. 59, 2931 (1987).
[Crossref] [PubMed]

D. J. Wineland, J. C. Bergquist, W. M Itano, J. J. Bollinger, C. J. Manning, Phys. Rev. Lett. 59, 2935 (1987).
[Crossref] [PubMed]

Abramowitz, M.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 361.

Bergquist, J. C.

D. J. Wineland, J. C. Bergquist, W. M Itano, J. J. Bollinger, C. J. Manning, Phys. Rev. Lett. 59, 2935 (1987).
[Crossref] [PubMed]

Berry, H. G.

C. E. Tanner, A. E. Livingston, R. J. Rafac, F. G. Serpa, K. W. Kulka, H. G. Berry, L. Young, C. A. Kurz, Phys. Rev. Lett. 69, 2765 (1992).
[Crossref] [PubMed]

Bollinger, J. J.

D. J. Wineland, J. C. Bergquist, W. M Itano, J. J. Bollinger, C. J. Manning, Phys. Rev. Lett. 59, 2935 (1987).
[Crossref] [PubMed]

Brewer, R. G.

R. G. Brewer, R. G. DeVoe, R. Kallenbach, Phys. Rev A 46, R6781 (1992).
[Crossref] [PubMed]

J. Hoffnagle, R. G. DeVoe, L. Reyna, R. G. Brewer, Phys. Rev. Lett. 61, 255 (1988).
[Crossref] [PubMed]

Brothers, L. R.

Chen, J. M.

F. Diedrich, E. Peik, J. M. Chen, W. Quint, H. Walther, Phys. Rev. Lett. 59, 2931 (1987).
[Crossref] [PubMed]

Courtis, J. Y.

G. Grynberg, B. Lounis, P. Verkerk, J. Y. Courtis, C. Salomon, Phys. Rev. Lett. 70, 2249 (1993).
[Crossref] [PubMed]

de Olivera, F. A. M.

M. S. Kim, F. A. M. de Olivera, P. L. Knight, Opt. Commun. 70, 473 (1989).
[Crossref]

DeVoe, R. G.

R. G. Brewer, R. G. DeVoe, R. Kallenbach, Phys. Rev A 46, R6781 (1992).
[Crossref] [PubMed]

J. Hoffnagle, R. G. DeVoe, L. Reyna, R. G. Brewer, Phys. Rev. Lett. 61, 255 (1988).
[Crossref] [PubMed]

Diedrich, F.

F. Diedrich, E. Peik, J. M. Chen, W. Quint, H. Walther, Phys. Rev. Lett. 59, 2931 (1987).
[Crossref] [PubMed]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1986), Chap. 14, p. 526.

Grynberg, G.

G. Grynberg, B. Lounis, P. Verkerk, J. Y. Courtis, C. Salomon, Phys. Rev. Lett. 70, 2249 (1993).
[Crossref] [PubMed]

Guet, C.

C. Guet, W. R. JohnsonPhys. Rev. A 44, 1531 (1991).
[Crossref] [PubMed]

Hänsch, R. W.

A. Hemmerich, R. W. Hänsch, Phys. Rev. Lett. 70, 410 (1993).
[Crossref] [PubMed]

Hemmerich, A.

A. Hemmerich, R. W. Hänsch, Phys. Rev. Lett. 70, 410 (1993).
[Crossref] [PubMed]

Hill, W. T.

L. Young, W. T. Hill, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, S. R. Leone, Phys. Rev. A 50, 2174 (1994).
[Crossref] [PubMed]

Hoffnagle, J.

J. Hoffnagle, R. G. DeVoe, L. Reyna, R. G. Brewer, Phys. Rev. Lett. 61, 255 (1988).
[Crossref] [PubMed]

Itano, W. M

D. J. Wineland, J. C. Bergquist, W. M Itano, J. J. Bollinger, C. J. Manning, Phys. Rev. Lett. 59, 2935 (1987).
[Crossref] [PubMed]

Johnson, W. R.

C. Guet, W. R. JohnsonPhys. Rev. A 44, 1531 (1991).
[Crossref] [PubMed]

Kallenbach, R.

R. G. Brewer, R. G. DeVoe, R. Kallenbach, Phys. Rev A 46, R6781 (1992).
[Crossref] [PubMed]

Kim, M. S.

M. S. Kim, F. A. M. de Olivera, P. L. Knight, Opt. Commun. 70, 473 (1989).
[Crossref]

Knight, P. L.

M. S. Kim, F. A. M. de Olivera, P. L. Knight, Opt. Commun. 70, 473 (1989).
[Crossref]

Kulka, K. W.

C. E. Tanner, A. E. Livingston, R. J. Rafac, F. G. Serpa, K. W. Kulka, H. G. Berry, L. Young, C. A. Kurz, Phys. Rev. Lett. 69, 2765 (1992).
[Crossref] [PubMed]

Kurz, C. A.

C. E. Tanner, A. E. Livingston, R. J. Rafac, F. G. Serpa, K. W. Kulka, H. G. Berry, L. Young, C. A. Kurz, Phys. Rev. Lett. 69, 2765 (1992).
[Crossref] [PubMed]

Lee, D.

Leone, S. R.

L. Young, W. T. Hill, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, S. R. Leone, Phys. Rev. A 50, 2174 (1994).
[Crossref] [PubMed]

Livingston, A. E.

C. E. Tanner, A. E. Livingston, R. J. Rafac, F. G. Serpa, K. W. Kulka, H. G. Berry, L. Young, C. A. Kurz, Phys. Rev. Lett. 69, 2765 (1992).
[Crossref] [PubMed]

Lounis, B.

G. Grynberg, B. Lounis, P. Verkerk, J. Y. Courtis, C. Salomon, Phys. Rev. Lett. 70, 2249 (1993).
[Crossref] [PubMed]

Manning, C. J.

D. J. Wineland, J. C. Bergquist, W. M Itano, J. J. Bollinger, C. J. Manning, Phys. Rev. Lett. 59, 2935 (1987).
[Crossref] [PubMed]

O’Connor, D. V.

D. V. O’Connor, D. Phillips, in Time Correlated Single Photon Counting (Academic, London, 1984), Chap. 2, p. 36.

Peik, E.

F. Diedrich, E. Peik, J. M. Chen, W. Quint, H. Walther, Phys. Rev. Lett. 59, 2931 (1987).
[Crossref] [PubMed]

Phillips, D.

D. V. O’Connor, D. Phillips, in Time Correlated Single Photon Counting (Academic, London, 1984), Chap. 2, p. 36.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1986), Chap. 14, p. 526.

Price, S. D.

L. Young, W. T. Hill, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, S. R. Leone, Phys. Rev. A 50, 2174 (1994).
[Crossref] [PubMed]

Quint, W.

F. Diedrich, E. Peik, J. M. Chen, W. Quint, H. Walther, Phys. Rev. Lett. 59, 2931 (1987).
[Crossref] [PubMed]

Rafac, R. J.

C. E. Tanner, A. E. Livingston, R. J. Rafac, F. G. Serpa, K. W. Kulka, H. G. Berry, L. Young, C. A. Kurz, Phys. Rev. Lett. 69, 2765 (1992).
[Crossref] [PubMed]

Reyna, L.

J. Hoffnagle, R. G. DeVoe, L. Reyna, R. G. Brewer, Phys. Rev. Lett. 61, 255 (1988).
[Crossref] [PubMed]

Salomon, C.

G. Grynberg, B. Lounis, P. Verkerk, J. Y. Courtis, C. Salomon, Phys. Rev. Lett. 70, 2249 (1993).
[Crossref] [PubMed]

Serpa, F. G.

C. E. Tanner, A. E. Livingston, R. J. Rafac, F. G. Serpa, K. W. Kulka, H. G. Berry, L. Young, C. A. Kurz, Phys. Rev. Lett. 69, 2765 (1992).
[Crossref] [PubMed]

Sibener, S. J.

L. Young, W. T. Hill, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, S. R. Leone, Phys. Rev. A 50, 2174 (1994).
[Crossref] [PubMed]

Stegun, I.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 361.

Tanner, C. E.

L. Young, W. T. Hill, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, S. R. Leone, Phys. Rev. A 50, 2174 (1994).
[Crossref] [PubMed]

C. E. Tanner, A. E. Livingston, R. J. Rafac, F. G. Serpa, K. W. Kulka, H. G. Berry, L. Young, C. A. Kurz, Phys. Rev. Lett. 69, 2765 (1992).
[Crossref] [PubMed]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1986), Chap. 14, p. 526.

Verkerk, P.

G. Grynberg, B. Lounis, P. Verkerk, J. Y. Courtis, C. Salomon, Phys. Rev. Lett. 70, 2249 (1993).
[Crossref] [PubMed]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1986), Chap. 14, p. 526.

Walther, H.

F. Diedrich, E. Peik, J. M. Chen, W. Quint, H. Walther, Phys. Rev. Lett. 59, 2931 (1987).
[Crossref] [PubMed]

Wieman, C. E.

L. Young, W. T. Hill, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, S. R. Leone, Phys. Rev. A 50, 2174 (1994).
[Crossref] [PubMed]

Wineland, D. J.

D. J. Wineland, J. C. Bergquist, W. M Itano, J. J. Bollinger, C. J. Manning, Phys. Rev. Lett. 59, 2935 (1987).
[Crossref] [PubMed]

Wong, N. C.

Young, L.

L. Young, W. T. Hill, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, S. R. Leone, Phys. Rev. A 50, 2174 (1994).
[Crossref] [PubMed]

C. E. Tanner, A. E. Livingston, R. J. Rafac, F. G. Serpa, K. W. Kulka, H. G. Berry, L. Young, C. A. Kurz, Phys. Rev. Lett. 69, 2765 (1992).
[Crossref] [PubMed]

Opt. Commun. (1)

M. S. Kim, F. A. M. de Olivera, P. L. Knight, Opt. Commun. 70, 473 (1989).
[Crossref]

Opt. Lett. (1)

Phys. Rev A (1)

R. G. Brewer, R. G. DeVoe, R. Kallenbach, Phys. Rev A 46, R6781 (1992).
[Crossref] [PubMed]

Phys. Rev. A (2)

C. Guet, W. R. JohnsonPhys. Rev. A 44, 1531 (1991).
[Crossref] [PubMed]

L. Young, W. T. Hill, S. J. Sibener, S. D. Price, C. E. Tanner, C. E. Wieman, S. R. Leone, Phys. Rev. A 50, 2174 (1994).
[Crossref] [PubMed]

Phys. Rev. Lett. (6)

C. E. Tanner, A. E. Livingston, R. J. Rafac, F. G. Serpa, K. W. Kulka, H. G. Berry, L. Young, C. A. Kurz, Phys. Rev. Lett. 69, 2765 (1992).
[Crossref] [PubMed]

G. Grynberg, B. Lounis, P. Verkerk, J. Y. Courtis, C. Salomon, Phys. Rev. Lett. 70, 2249 (1993).
[Crossref] [PubMed]

A. Hemmerich, R. W. Hänsch, Phys. Rev. Lett. 70, 410 (1993).
[Crossref] [PubMed]

F. Diedrich, E. Peik, J. M. Chen, W. Quint, H. Walther, Phys. Rev. Lett. 59, 2931 (1987).
[Crossref] [PubMed]

D. J. Wineland, J. C. Bergquist, W. M Itano, J. J. Bollinger, C. J. Manning, Phys. Rev. Lett. 59, 2935 (1987).
[Crossref] [PubMed]

J. Hoffnagle, R. G. DeVoe, L. Reyna, R. G. Brewer, Phys. Rev. Lett. 61, 255 (1988).
[Crossref] [PubMed]

Other (3)

D. V. O’Connor, D. Phillips, in Time Correlated Single Photon Counting (Academic, London, 1984), Chap. 2, p. 36.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 9, p. 361.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1986), Chap. 14, p. 526.

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Figures (4)

Fig. 1
Fig. 1

Approximate power-law behavior of the Bessel functions J1(x) through J4(x) for xN/2. The first sideband is therefore linear in modulating voltage, the second is quadratic, the third cubic, and so on.

Fig. 2
Fig. 2

Block diagram of the experiment. A cw dye laser is phase modulated by a traveling-wave electro-optic modulator (TWEO) driven by a pulsed of source. The Nth sideband is selected by the Fabry–Perot cavity and excites the single trapped ion. The time of arrival of spontaneous photons is recorded on the time-to-digital converter (TDC) triggered by an imaging photomultiplier (PM) operated in the single-photon-counting mode. Similar systems are used for both red and blue lasers.

Fig. 3
Fig. 3

Experimental data measuring the fall times of the N = 1 through N = 4 sidebands generated by a narrow-band resonant cavity modulator. The exponential decay times of 38.5, 19.8, 13.2, and 9.5 ns for the N = 1, 2, 3, and 4 sidebands confirm the 1/N relation predicted in the text. Note that the first and second sidebands initially increase in amplitude because of the large modulation index of 3.6 (see Fig. 1).

Fig. 4
Fig. 4

Decay of the spontaneous emission of the 6p2P1/2 state of a single trapped barium ion excited by the N = 2 sideband for an integration time of 8 min (dots). The three-parameter fit (solid curve) yields a standard deviation for the lifetime of 0.5% and a χ2 = 65 for 60 degrees of freedom.

Equations (1)

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exp [ i β sin ( Ω t ) ] = N J N ( β ) exp ( i N Ω t ) .

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