Abstract

We describe a method to probe the spectral fluctuations of a transition over broad ranges of frequencies and timescales with the high spectral resolution of Fourier spectroscopy, and a temporal resolution as high as the excited state lifetime, even in the limit of very low photocounting rates. The method derives from a simple relation between the fluorescence spectral dynamics of a single radiating dipole and its fluorescence intensity correlations at the outputs of a continuously scanning Michelson interferometer. These findings define an approach to investigate the fast fluorescence spectral dynamics of single molecules and other faint light sources beyond the time-resolution capabilities of standard spectroscopy experiments.

© 2006 Optical Society of America

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References

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  1. D. Haarer and R.J. Silbey, “Hole burning spectroscopy of glasses,” Phys. Today, May, 58 (1990). L. Allen and J. Eberly, Optical Resonance and Two-Level Atoms (Dover, New-York, 1987).
  2. E. Geva and J.L. Skinner, “Theory of single-molecule optical line-shape distributions in low-temperature glasses,” J. Phys. Chem. B 101, 8920 (1997).
    [Crossref]
  3. K. Fritsch et al., “Spectral diffusion in proteins, “Europhys. Lett.41, 339 (1998). A.D. Stein and M.D. Fayer,”Spectral diffusion in liquids,” J. Chem. Phys.97, 2948 (1992).
    [Crossref]
  4. W.E. Moerner and M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670 (1999).
    [Crossref] [PubMed]
  5. S. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science 283, 1676 (1999).
    [Crossref] [PubMed]
  6. B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. 68, 1129 (2005).
    [Crossref]
  7. M. Lippitz, F. Kulzer, and M. Orrit, “Statistical evaluation of single nano-object fluorescence,”Chem. Phys. Chem. 6, 770 (2005).
    [Crossref] [PubMed]
  8. T. Plakhotnik and D. Walser, “Time resolved single molecule spectroscopy,” Phys. Rev. Lett. 80, 4064 (1998).
    [Crossref]
  9. T. Plakhotnik, “Time-dependent single molecule spectral lines,” Phys. Rev. B 59, 4658 (1999).
    [Crossref]
  10. The extension of this method to delays τ<T1 pertains to quantum electrodynamics - so as to account for photon antibunching and photon coalescence effects - and will be analyzed in a forthcoming paper entitled “Spectral diffusion and time-coherence of single photons”.
  11. R. Hanbury-Brown and R.Q. Twiss, “A Test of a New Type of Stellar Interferometer on Sirius,” Nature 178, 1046 (1956).
    [Crossref]
  12. R. Kubo, “A Stochastic Theory of Line Shape,” Adv. Chem. Phys. 15, 101 (1969).
    [Crossref]
  13. C. Kammerer et al., “Interferometric correlation spectroscopy in single quantum dots,” Appl. Phys. Lett. 81, 2737 (2002).
    [Crossref]
  14. M. Wahl, I. Gregor, M. Patting, and J. Enderlein, “Fast calculation of fluorescence correlation data with asynchronous time-correlated single-photon counting,” Opt. Express 11, 3583 (2003).
    [Crossref] [PubMed]

2005 (2)

B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. 68, 1129 (2005).
[Crossref]

M. Lippitz, F. Kulzer, and M. Orrit, “Statistical evaluation of single nano-object fluorescence,”Chem. Phys. Chem. 6, 770 (2005).
[Crossref] [PubMed]

2003 (1)

2002 (1)

C. Kammerer et al., “Interferometric correlation spectroscopy in single quantum dots,” Appl. Phys. Lett. 81, 2737 (2002).
[Crossref]

1999 (3)

W.E. Moerner and M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670 (1999).
[Crossref] [PubMed]

S. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science 283, 1676 (1999).
[Crossref] [PubMed]

T. Plakhotnik, “Time-dependent single molecule spectral lines,” Phys. Rev. B 59, 4658 (1999).
[Crossref]

1998 (1)

T. Plakhotnik and D. Walser, “Time resolved single molecule spectroscopy,” Phys. Rev. Lett. 80, 4064 (1998).
[Crossref]

1997 (1)

E. Geva and J.L. Skinner, “Theory of single-molecule optical line-shape distributions in low-temperature glasses,” J. Phys. Chem. B 101, 8920 (1997).
[Crossref]

1969 (1)

R. Kubo, “A Stochastic Theory of Line Shape,” Adv. Chem. Phys. 15, 101 (1969).
[Crossref]

1956 (1)

R. Hanbury-Brown and R.Q. Twiss, “A Test of a New Type of Stellar Interferometer on Sirius,” Nature 178, 1046 (1956).
[Crossref]

Allen, L.

D. Haarer and R.J. Silbey, “Hole burning spectroscopy of glasses,” Phys. Today, May, 58 (1990). L. Allen and J. Eberly, Optical Resonance and Two-Level Atoms (Dover, New-York, 1987).

Eberly, J.

D. Haarer and R.J. Silbey, “Hole burning spectroscopy of glasses,” Phys. Today, May, 58 (1990). L. Allen and J. Eberly, Optical Resonance and Two-Level Atoms (Dover, New-York, 1987).

Enderlein, J.

Fayer, M.D.

K. Fritsch et al., “Spectral diffusion in proteins, “Europhys. Lett.41, 339 (1998). A.D. Stein and M.D. Fayer,”Spectral diffusion in liquids,” J. Chem. Phys.97, 2948 (1992).
[Crossref]

Fritsch, K.

K. Fritsch et al., “Spectral diffusion in proteins, “Europhys. Lett.41, 339 (1998). A.D. Stein and M.D. Fayer,”Spectral diffusion in liquids,” J. Chem. Phys.97, 2948 (1992).
[Crossref]

Geva, E.

E. Geva and J.L. Skinner, “Theory of single-molecule optical line-shape distributions in low-temperature glasses,” J. Phys. Chem. B 101, 8920 (1997).
[Crossref]

Gregor, I.

Haarer, D.

D. Haarer and R.J. Silbey, “Hole burning spectroscopy of glasses,” Phys. Today, May, 58 (1990). L. Allen and J. Eberly, Optical Resonance and Two-Level Atoms (Dover, New-York, 1987).

Hanbury-Brown, R.

R. Hanbury-Brown and R.Q. Twiss, “A Test of a New Type of Stellar Interferometer on Sirius,” Nature 178, 1046 (1956).
[Crossref]

Kammerer, C.

C. Kammerer et al., “Interferometric correlation spectroscopy in single quantum dots,” Appl. Phys. Lett. 81, 2737 (2002).
[Crossref]

Kubo, R.

R. Kubo, “A Stochastic Theory of Line Shape,” Adv. Chem. Phys. 15, 101 (1969).
[Crossref]

Kulzer, F.

M. Lippitz, F. Kulzer, and M. Orrit, “Statistical evaluation of single nano-object fluorescence,”Chem. Phys. Chem. 6, 770 (2005).
[Crossref] [PubMed]

Lippitz, M.

M. Lippitz, F. Kulzer, and M. Orrit, “Statistical evaluation of single nano-object fluorescence,”Chem. Phys. Chem. 6, 770 (2005).
[Crossref] [PubMed]

Lounis, B.

B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. 68, 1129 (2005).
[Crossref]

Moerner, W.E.

W.E. Moerner and M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670 (1999).
[Crossref] [PubMed]

Orrit, M.

M. Lippitz, F. Kulzer, and M. Orrit, “Statistical evaluation of single nano-object fluorescence,”Chem. Phys. Chem. 6, 770 (2005).
[Crossref] [PubMed]

B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. 68, 1129 (2005).
[Crossref]

W.E. Moerner and M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670 (1999).
[Crossref] [PubMed]

Patting, M.

Plakhotnik, T.

T. Plakhotnik, “Time-dependent single molecule spectral lines,” Phys. Rev. B 59, 4658 (1999).
[Crossref]

T. Plakhotnik and D. Walser, “Time resolved single molecule spectroscopy,” Phys. Rev. Lett. 80, 4064 (1998).
[Crossref]

Silbey, R.J.

D. Haarer and R.J. Silbey, “Hole burning spectroscopy of glasses,” Phys. Today, May, 58 (1990). L. Allen and J. Eberly, Optical Resonance and Two-Level Atoms (Dover, New-York, 1987).

Skinner, J.L.

E. Geva and J.L. Skinner, “Theory of single-molecule optical line-shape distributions in low-temperature glasses,” J. Phys. Chem. B 101, 8920 (1997).
[Crossref]

Stein, A.D.

K. Fritsch et al., “Spectral diffusion in proteins, “Europhys. Lett.41, 339 (1998). A.D. Stein and M.D. Fayer,”Spectral diffusion in liquids,” J. Chem. Phys.97, 2948 (1992).
[Crossref]

Twiss, R.Q.

R. Hanbury-Brown and R.Q. Twiss, “A Test of a New Type of Stellar Interferometer on Sirius,” Nature 178, 1046 (1956).
[Crossref]

Wahl, M.

Walser, D.

T. Plakhotnik and D. Walser, “Time resolved single molecule spectroscopy,” Phys. Rev. Lett. 80, 4064 (1998).
[Crossref]

Weiss, S.

S. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science 283, 1676 (1999).
[Crossref] [PubMed]

Adv. Chem. Phys. (1)

R. Kubo, “A Stochastic Theory of Line Shape,” Adv. Chem. Phys. 15, 101 (1969).
[Crossref]

Appl. Phys. Lett. (1)

C. Kammerer et al., “Interferometric correlation spectroscopy in single quantum dots,” Appl. Phys. Lett. 81, 2737 (2002).
[Crossref]

Chem. Phys. Chem. (1)

M. Lippitz, F. Kulzer, and M. Orrit, “Statistical evaluation of single nano-object fluorescence,”Chem. Phys. Chem. 6, 770 (2005).
[Crossref] [PubMed]

J. Phys. Chem. B (1)

E. Geva and J.L. Skinner, “Theory of single-molecule optical line-shape distributions in low-temperature glasses,” J. Phys. Chem. B 101, 8920 (1997).
[Crossref]

Nature (1)

R. Hanbury-Brown and R.Q. Twiss, “A Test of a New Type of Stellar Interferometer on Sirius,” Nature 178, 1046 (1956).
[Crossref]

Opt. Express (1)

Phys. Rev. B (1)

T. Plakhotnik, “Time-dependent single molecule spectral lines,” Phys. Rev. B 59, 4658 (1999).
[Crossref]

Phys. Rev. Lett. (1)

T. Plakhotnik and D. Walser, “Time resolved single molecule spectroscopy,” Phys. Rev. Lett. 80, 4064 (1998).
[Crossref]

Rep. Prog. Phys. (1)

B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. 68, 1129 (2005).
[Crossref]

Science (2)

W.E. Moerner and M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670 (1999).
[Crossref] [PubMed]

S. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science 283, 1676 (1999).
[Crossref] [PubMed]

Other (3)

K. Fritsch et al., “Spectral diffusion in proteins, “Europhys. Lett.41, 339 (1998). A.D. Stein and M.D. Fayer,”Spectral diffusion in liquids,” J. Chem. Phys.97, 2948 (1992).
[Crossref]

D. Haarer and R.J. Silbey, “Hole burning spectroscopy of glasses,” Phys. Today, May, 58 (1990). L. Allen and J. Eberly, Optical Resonance and Two-Level Atoms (Dover, New-York, 1987).

The extension of this method to delays τ<T1 pertains to quantum electrodynamics - so as to account for photon antibunching and photon coalescence effects - and will be analyzed in a forthcoming paper entitled “Spectral diffusion and time-coherence of single photons”.

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Figures (3)

Fig. 1.
Fig. 1.

Single molecule photon-correlation Fourier spectroscopy setup. Starting from an initial optical path difference δ i , the intensity correlation function g(τ) of the output intensities I a(t) and I b(t) is measured during a continuous scan of the interferometer at a velocity V. Repeating this procedure for various values of δ i provides the time-resolved frequency fluctuation spectrum p τ(ζ) of the emitter.

Fig. 2.
Fig. 2.

Photon correlation spectroscopy of a single static (left) or switching doublet (right). (a) Intensity correlation function at various delays δ i . The scatter plots are numerical simulations for an emitter detected with an intensity I=50 kHz. (b) Evolution of g(τ) with δ i for τ=4 ns (∘), 2.5 µs (□), 10 µs (◄), 160 µs (⋆), depending of the optical delay δ i where the measurement was performed. (c) Corresponding fluctuation distribution p τ(ζ) (∘). (d,e,f) Same as in (a,b,c) for the switching doublet. Solid continuous lines are the theoretical expectations corresponding to the simulation parameters (see Table 1).

Fig. 3.
Fig. 3.

Photon correlation spectroscopy of a doublet of separation Ω undergoing Gaussian stationnary fluctuations of correlation time τ c =5µs, over a spectral range σ=5Ω (corresponding to δλ=1nm). (a) Intensity correlation function at various delays δi obtained from numerical simulations when the emitter is detected with an intensity I=50 kHz. (b) Evolution of g(τ) with δ i for τ=2 ns (□), 40 ns (×), 640 ns (∘) as observed from the measurement of g(τ), depending of the optical delay δi where the measurement was made. At short timescales (τ<10 ns), oscillations of periodicity 2πc/Ω are observed, as the doublet becomes resolved. (c) Corresponding fluctuation distribution p τ(ζ). At short timescales, a triplet appear, i.e. the doublet is resolved. Solid lines are the theoretical expectations corresponding to the simulation parameters (see Table 1).

Tables (1)

Tables Icon

Table 1. Theoretical expression of the intensity correlation function g(τ) measured in PCFS for discrete and continuous spectral fluctuations. p i=1,2 denote the fraction of time spent by the transition in states 1 and 2 respectively.

Equations (7)

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{ I a ( t ) 1 + cos [ ( 2 V t + δ i ) ω ( t ) c ] I b ( t ) 1 cos [ ( 2 V t + δ i ) ω ( t ) c ] .
g ( τ ) = I a ( t ) I b ( t + τ ) ¯ I a ( t ) ¯ I b ( t + τ ) ¯ ,
g ( τ ) = 1 1 2 T 0 T cos ( 2 ω o V τ c + α ( t ) δ i c ) d t
g ( τ ) = 1 1 2 cos ( 2 ω o V τ c ) F T [ p τ ( ζ ) ] δ i c
p τ ( ζ ) = + s t ( ω ) s t + τ ( ω + ζ ) d ω ,
s t ( ω ) = 1 π 0 + e t 2 T 1 [ e i ω o t e i 0 t δ ω ( t + u ) du ] dt
p τ ( ζ ) = 2 FT 1 [ 1 g ( τ ) ] ζ = 2 π c δ i .

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