Abstract

We show that the single emitter linewidth underlying a broadened ensemble emission spectrum can be extracted from correlations among the stochastic intensity fluctuations in the ensemble spectrum. Spectral correlations can be observed at high temporal and spectral resolutions with a cross-correlated pair of avalanche photodiodes placed at the outputs of a scanning Michelson interferometer. As illustrated with simulations in conjunction with Fluorescence Correlation Spectroscopy, our approach overcomes ensemble and temporal inhomogeneous broadening to provide single emitter linewidths, even for emitters under weak, continuous, broadband excitation.

© 2009 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univeristy Press, 1995).
  2. V. S. Zapasskii and G. G. Kozlov, "Correlation analysis of spectral fluctuations in inhomogeneously broadened spectra," Opt. Express 8, 509-516 (2001).
    [CrossRef] [PubMed]
  3. F. Intonti, V. Emiliani, C. Lienau, Th. Elsaesser, V. Savona, E. Runge, R. Zimmermann, R. Notzel, and K. H. Ploog, "Quantum mechanical repulsion of exciton levels in a disordered quantum well," Phys. Rev. Lett. 27, 0768011-4 (2001).
  4. G. von Freymann, U. Neuberth, M. Deubel, M. Wegener, G. Khitrova, and H. M. Gibbs, "Level repulsion in nanophotoluminescence spectra from single GaAs quantum wells," Phys. Rev. B 65, 2053271-9 (2002).
  5. X. Brokmann, M. G. Bawendi, L. Coolen, and J. P. Hermier, "Photon-correlation Fourier spectroscopy," Opt. Express 14, 6333-6341 (2006).
    [CrossRef] [PubMed]
  6. D. Magde, E. L. Elson, and W. W. Webb, "Fluorescence Correlation Spectroscopy 2. Experimental Realization," Biopolymers 33, 29-61 (1974).
    [CrossRef]

2006 (1)

2002 (1)

G. von Freymann, U. Neuberth, M. Deubel, M. Wegener, G. Khitrova, and H. M. Gibbs, "Level repulsion in nanophotoluminescence spectra from single GaAs quantum wells," Phys. Rev. B 65, 2053271-9 (2002).

2001 (2)

F. Intonti, V. Emiliani, C. Lienau, Th. Elsaesser, V. Savona, E. Runge, R. Zimmermann, R. Notzel, and K. H. Ploog, "Quantum mechanical repulsion of exciton levels in a disordered quantum well," Phys. Rev. Lett. 27, 0768011-4 (2001).

V. S. Zapasskii and G. G. Kozlov, "Correlation analysis of spectral fluctuations in inhomogeneously broadened spectra," Opt. Express 8, 509-516 (2001).
[CrossRef] [PubMed]

1974 (1)

D. Magde, E. L. Elson, and W. W. Webb, "Fluorescence Correlation Spectroscopy 2. Experimental Realization," Biopolymers 33, 29-61 (1974).
[CrossRef]

Bawendi, M. G.

Brokmann, X.

Coolen, L.

Deubel, M.

G. von Freymann, U. Neuberth, M. Deubel, M. Wegener, G. Khitrova, and H. M. Gibbs, "Level repulsion in nanophotoluminescence spectra from single GaAs quantum wells," Phys. Rev. B 65, 2053271-9 (2002).

Elsaesser, Th.

F. Intonti, V. Emiliani, C. Lienau, Th. Elsaesser, V. Savona, E. Runge, R. Zimmermann, R. Notzel, and K. H. Ploog, "Quantum mechanical repulsion of exciton levels in a disordered quantum well," Phys. Rev. Lett. 27, 0768011-4 (2001).

Elson, E. L.

D. Magde, E. L. Elson, and W. W. Webb, "Fluorescence Correlation Spectroscopy 2. Experimental Realization," Biopolymers 33, 29-61 (1974).
[CrossRef]

Emiliani, V.

F. Intonti, V. Emiliani, C. Lienau, Th. Elsaesser, V. Savona, E. Runge, R. Zimmermann, R. Notzel, and K. H. Ploog, "Quantum mechanical repulsion of exciton levels in a disordered quantum well," Phys. Rev. Lett. 27, 0768011-4 (2001).

Gibbs, H. M.

G. von Freymann, U. Neuberth, M. Deubel, M. Wegener, G. Khitrova, and H. M. Gibbs, "Level repulsion in nanophotoluminescence spectra from single GaAs quantum wells," Phys. Rev. B 65, 2053271-9 (2002).

Hermier, J. P.

Intonti, F.

F. Intonti, V. Emiliani, C. Lienau, Th. Elsaesser, V. Savona, E. Runge, R. Zimmermann, R. Notzel, and K. H. Ploog, "Quantum mechanical repulsion of exciton levels in a disordered quantum well," Phys. Rev. Lett. 27, 0768011-4 (2001).

Khitrova, G.

G. von Freymann, U. Neuberth, M. Deubel, M. Wegener, G. Khitrova, and H. M. Gibbs, "Level repulsion in nanophotoluminescence spectra from single GaAs quantum wells," Phys. Rev. B 65, 2053271-9 (2002).

Kozlov, G. G.

Lienau, C.

F. Intonti, V. Emiliani, C. Lienau, Th. Elsaesser, V. Savona, E. Runge, R. Zimmermann, R. Notzel, and K. H. Ploog, "Quantum mechanical repulsion of exciton levels in a disordered quantum well," Phys. Rev. Lett. 27, 0768011-4 (2001).

Magde, D.

D. Magde, E. L. Elson, and W. W. Webb, "Fluorescence Correlation Spectroscopy 2. Experimental Realization," Biopolymers 33, 29-61 (1974).
[CrossRef]

Neuberth, U.

G. von Freymann, U. Neuberth, M. Deubel, M. Wegener, G. Khitrova, and H. M. Gibbs, "Level repulsion in nanophotoluminescence spectra from single GaAs quantum wells," Phys. Rev. B 65, 2053271-9 (2002).

Notzel, R.

F. Intonti, V. Emiliani, C. Lienau, Th. Elsaesser, V. Savona, E. Runge, R. Zimmermann, R. Notzel, and K. H. Ploog, "Quantum mechanical repulsion of exciton levels in a disordered quantum well," Phys. Rev. Lett. 27, 0768011-4 (2001).

Ploog, K. H.

F. Intonti, V. Emiliani, C. Lienau, Th. Elsaesser, V. Savona, E. Runge, R. Zimmermann, R. Notzel, and K. H. Ploog, "Quantum mechanical repulsion of exciton levels in a disordered quantum well," Phys. Rev. Lett. 27, 0768011-4 (2001).

Runge, E.

F. Intonti, V. Emiliani, C. Lienau, Th. Elsaesser, V. Savona, E. Runge, R. Zimmermann, R. Notzel, and K. H. Ploog, "Quantum mechanical repulsion of exciton levels in a disordered quantum well," Phys. Rev. Lett. 27, 0768011-4 (2001).

Savona, V.

F. Intonti, V. Emiliani, C. Lienau, Th. Elsaesser, V. Savona, E. Runge, R. Zimmermann, R. Notzel, and K. H. Ploog, "Quantum mechanical repulsion of exciton levels in a disordered quantum well," Phys. Rev. Lett. 27, 0768011-4 (2001).

von Freymann, G.

G. von Freymann, U. Neuberth, M. Deubel, M. Wegener, G. Khitrova, and H. M. Gibbs, "Level repulsion in nanophotoluminescence spectra from single GaAs quantum wells," Phys. Rev. B 65, 2053271-9 (2002).

Webb, W. W.

D. Magde, E. L. Elson, and W. W. Webb, "Fluorescence Correlation Spectroscopy 2. Experimental Realization," Biopolymers 33, 29-61 (1974).
[CrossRef]

Wegener, M.

G. von Freymann, U. Neuberth, M. Deubel, M. Wegener, G. Khitrova, and H. M. Gibbs, "Level repulsion in nanophotoluminescence spectra from single GaAs quantum wells," Phys. Rev. B 65, 2053271-9 (2002).

Zapasskii, V. S.

Zimmermann, R.

F. Intonti, V. Emiliani, C. Lienau, Th. Elsaesser, V. Savona, E. Runge, R. Zimmermann, R. Notzel, and K. H. Ploog, "Quantum mechanical repulsion of exciton levels in a disordered quantum well," Phys. Rev. Lett. 27, 0768011-4 (2001).

Biopolymers (1)

D. Magde, E. L. Elson, and W. W. Webb, "Fluorescence Correlation Spectroscopy 2. Experimental Realization," Biopolymers 33, 29-61 (1974).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (1)

G. von Freymann, U. Neuberth, M. Deubel, M. Wegener, G. Khitrova, and H. M. Gibbs, "Level repulsion in nanophotoluminescence spectra from single GaAs quantum wells," Phys. Rev. B 65, 2053271-9 (2002).

Phys. Rev. Lett. (1)

F. Intonti, V. Emiliani, C. Lienau, Th. Elsaesser, V. Savona, E. Runge, R. Zimmermann, R. Notzel, and K. H. Ploog, "Quantum mechanical repulsion of exciton levels in a disordered quantum well," Phys. Rev. Lett. 27, 0768011-4 (2001).

Other (1)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univeristy Press, 1995).

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Figures (5)

Fig. 1.
Fig. 1.

Our approach uses an interferometer to convert fast spectral fluctuations into intensity fluctuations. The cross-correlation of the fluctuations in the interferometer outputs reveals single emitter spectral dynamics with high temporal and spectral resolution.

Fig. 2.
Fig. 2.

Single-emitter and ensemble spectral correlations in the fluorescence of a population of emitters. a) We first consider an ensemble of emitters with the same narrow line shape but different center frequencies. The ensemble spectrum would appear as a broad Gaussian 〈S(ω,t)〉. b) With our setup, intensity correlations from the emission of single emitters flowing under a microscope objective will contribute to the single emitter spectral correlation, Psing (ζ,τ), if the two photons correlated are from the same emitter. Correlations of photons originating from different emitters will provide the ensemble spectral correlation, P ens(ζ).

Fig. 3.
Fig. 3.

The standard FCS intensity correlation function, g (2)(τ). Our method works in situations like FCS, where the ensemble emission exhibits an intensity correlation function g (2)(τ) ≠ 1 at short timescales. In these cases, the single emitter spectral correlation, psingle(ζ, τ), is weighted by g (2)(τ)-1 and can be separated from the background ensemble spectral correlation, p ens(ζ).

Fig. 4.
Fig. 4.

Standard spectroscopy versus spectral correlation measurement. a) Emission spectrum as measured by standard spectroscopy after an acquisition time of 1 s. The corresponding lineshape coincides with the average ensemble spectrum, 〈S(ω, t)〉, and shows no evidence of the underlying single-emitter doublets si (ω,t). b) Using our method, the spectral correlation of the underlying doublet, p single(ζ, τ), is easily seen on top of a broad ensemble pedestal, p ens(δ). The amplitude of p single(ζ, τ) is determined by the intensity correlation function g (2)(τ) of the sample emission.

Fig. 5.
Fig. 5.

Intensity cross-correlations at the ouputs of the scanning interferometer for a population of emitters undergoing both static and dynamic spectral broadening. a) g ×(τ) as measured at different interferometer positions δ. The cross-correlation functions g ×(τ) differ from the standard FCS intensity correlation function g (2)(τ) at long timescales ττD due to the ensemble spectral correlation p ens(ζ) and at short timescales ττD due to the time-dependent single-emitter spectral correlation function p single(ζ, τ). b) Decay of the g ×(τ) with S at short timescale τ = 100 ns (insert). The corresponding Fourier transform of g (2)(τ) - g ×(τ) for increasing values of τ reveals the time dependent single emitter spectral correlation, p single (ζ, τ) .

Equations (9)

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P ( ζ , τ ) = S ( ω , t ) S ( ω + ζ , t + τ ) d ω .
P ( ζ , τ ) = P ens ( ζ , τ ) + P sin gle ( ζ , τ )
I a , b ( t ) = i = 1 N I i ( t ) [ 1 ± 0 S ̂ i ( ω , t ) cos ( ω δ ( t ) / c ) d ω ] ,
g × ( τ ) = I a ( t ) I b ( t + τ ) ̄ I a ( t ) ̄ I b ( t + τ ) ̄ ,
g × ( τ ) = g ens ( τ ) + g sin gle ( τ ) ,
g ens ( τ ) = N 1 N ( 1 1 2 FT [ p ens ( ζ ) ] δ / c )
g sin gle ( τ ) = ( g ( 2 ) ( τ ) 1 + 1 N ) × ( 1 1 2 FT [ p single ( ζ , τ ) ] δ / c )
g × ( τ ) = 1 1 2 FT [ P sin gle ( ζ , τ ) ] δ / c ,
g × ( τ ) = g ( 2 ) ( τ ) 1 2 FT [ P ens ( ζ ) + ( g ( 2 ) ( τ ) 1 ) P sin gle ( ζ , τ ) ] δ / c ,

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