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 43,58-65 (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, A. Eicker, J. Friedrich, B. M. Kharlamov,and J. M. Vanderkooi, "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, G. Cassabois, C. Voisin, M. Perrin, C, Delalande, Ph. Roussignol, and J. M. Gérard, "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

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

2002

C. Kammerer, G. Cassabois, C. Voisin, M. Perrin, C, Delalande, Ph. Roussignol, and J. M. Gérard, "Interferometric correlation spectroscopy in single quantum dots," Appl. Phys. Lett. 81, 2737 (2002).
[CrossRef]

1999

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

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]

1998

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

K. Fritsch, A. Eicker, J. Friedrich, B. M. Kharlamov,and J. M. Vanderkooi, "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]

1997

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]

1990

D. Haarer, and R. J. Silbey, "Hole burning spectroscopy of glasses," Phys. Today 43,58-65 (1990). L. Allen, and J. Eberly, Optical Resonance and Two-Level Atoms (Dover, New-York, 1987).

1969

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

1956

R. Hanbury-Brown, and R. Q. Twiss, "A test of a new type of Stellar interferometer on Sirius," Nature 178, 1046 (1956).
[CrossRef]

Cassabois, G.

C. Kammerer, G. Cassabois, C. Voisin, M. Perrin, C, Delalande, Ph. Roussignol, and J. M. Gérard, "Interferometric correlation spectroscopy in single quantum dots," Appl. Phys. Lett. 81, 2737 (2002).
[CrossRef]

Eicker, A.

K. Fritsch, A. Eicker, J. Friedrich, B. M. Kharlamov,and J. M. Vanderkooi, "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]

Enderlein, J.

Friedrich, J.

K. Fritsch, A. Eicker, J. Friedrich, B. M. Kharlamov,and J. M. Vanderkooi, "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, A. Eicker, J. Friedrich, B. M. Kharlamov,and J. M. Vanderkooi, "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 43,58-65 (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, G. Cassabois, C. Voisin, M. Perrin, C, Delalande, Ph. Roussignol, and J. M. Gérard, "Interferometric correlation spectroscopy in single quantum dots," Appl. Phys. Lett. 81, 2737 (2002).
[CrossRef]

Kharlamov, B. M.

K. Fritsch, A. Eicker, J. Friedrich, B. M. Kharlamov,and J. M. Vanderkooi, "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]

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.

Perrin, M.

C. Kammerer, G. Cassabois, C. Voisin, M. Perrin, C, Delalande, Ph. Roussignol, and J. M. Gérard, "Interferometric correlation spectroscopy in single quantum dots," Appl. Phys. Lett. 81, 2737 (2002).
[CrossRef]

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 43,58-65 (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]

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]

Vanderkooi, J. M.

K. Fritsch, A. Eicker, J. Friedrich, B. M. Kharlamov,and J. M. Vanderkooi, "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]

Voisin, C.

C. Kammerer, G. Cassabois, C. Voisin, M. Perrin, C, Delalande, Ph. Roussignol, and J. M. Gérard, "Interferometric correlation spectroscopy in single quantum dots," Appl. Phys. Lett. 81, 2737 (2002).
[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.

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

Appl. Phys. Lett.

C. Kammerer, G. Cassabois, C. Voisin, M. Perrin, C, Delalande, Ph. Roussignol, and J. M. Gérard, "Interferometric correlation spectroscopy in single quantum dots," Appl. Phys. Lett. 81, 2737 (2002).
[CrossRef]

Chem. Phys. Chem.

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

Europhys. Lett.

K. Fritsch, A. Eicker, J. Friedrich, B. M. Kharlamov,and J. M. Vanderkooi, "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]

J. Phys. Chem. B

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

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

Phys. Rev. B

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

Phys. Rev. Lett.

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

Phys. Today

D. Haarer, and R. J. Silbey, "Hole burning spectroscopy of glasses," Phys. Today 43,58-65 (1990). L. Allen, and J. Eberly, Optical Resonance and Two-Level Atoms (Dover, New-York, 1987).

Rep. Prog. Phys.

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

Science

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

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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