Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America B

Comparative photon statistics of several ultraviolet laser systems determined by transient two-photon absorption

Douglas J. Bamford, A. P. Hickman, Mark J. Dyer, William K. Bischel

Published Jul 1, 1988• 16 citations
Publisher

Abstract

The photon statistics of several different laser systems operating at 226 nm are probed by measuring absolutely the fluorescence following two-photon absorption in atomic oxygen. The integrated fluorescence, obtained by scanning the laser frequency through the two-photon resonance, is theoretically shown to be proportional to G(2) (0) σ0(2). The second-order intensity-correlation function at time zero, G(2)(0), characterizes the laser, and σ0(2) is a fundamental atomic property. Measurement of the integrated fluorescence permits determination of the relative value of G(2) (0) for each laser. The assumption that G(2)(0) = 1 for one of the lasers, a single-frequency source, allows G(2)(0) for the other lasers to be placed on an absolute scale. The values thereby obtained range from 0.8 ± 0.2 to 3.2 ± 0.4. Different values are obtained when the radiation is generated by frequency mixing or Raman shifting of the same frequency-doubled visible dye laser, suggesting that frequency-conversion processes have a significant effect on G(2)(0).

DOI
10.1364/josab.5.001369

Related papers

Two-photon absorption of ultrashort pulses in a gas

E. V. Baklanov, V. P. Chebotaev

Two-photon absorption of a continuous train of ultrashort pulses in a gas gives rise to resonances when the sum of the frequencies of two locked modes coincides with the transition frequency in the gas. It is shown that the width of these resonances is not governed by the pulse duration but by the width of the twophoton transition. Resonance intensities are of the same order of magnitude as in the single-frequency regime at the same power level. It is worth noting an important feature of the use of ultrashort pulses in studies of two-photon resonances due to the 1S-2S transition in the hydrogen atom: there is a strong increase in the efficiency of conversion of dye laser radiation to the ultraviolet range.

Soviet Journal of Quantum Electronics•Oct 31, 1977•19 citations

Investigation of photon statistics and correlations of a dye laser

Katsuji Kaminishi, Rajarshi Roy, R. Short +1 more

The probability distribution $p(n)$ for the detection of $n$ photons emitted by a single-mode dye laser in a short time at various excitations is measured, together with the distribution of time intervals between pairs of detected photons. The first measurement yields the probability density $\mathcal{p}(I)$ and the moments of the light intensity $I$, and the second one the two-time intensity-correlation function. Measurements are also performed at three different wavelengths. $\mathcal{p}(I)$ is found to have a two-component structure, and the relative intensity fluctuations $\frac{〈{(\ensuremath{\Delta}I)}^{2}〉}{{〈I〉}^{2}}$ grow, apparently without limit, as the excitation tends to zero, so that no thermal state is reached. A possible explanation in terms of pumping fluctuations is discussed. The correlation function has the form of a sum of three exponential functions, and the amplitudes and decay constants of the three components are derived. The effective decay-time constant exhibits a thirteenth-power-law dependence on frequency of the laser light.

Physical Review A•Jul 1, 1981•96 citations

Theory for Wavelength-Resolved Photon Emission Statistics in Single-Molecule Fluorescence Spectroscopy

Golan Bel, Frank L. H. Brown

We derive the moment generating function for photon emissions from a single molecule driven by laser excitation. The frequencies of the fluoresced photons are explicitly considered. Calculations are performed for the case of a two-level dye molecule, showing that measured photon statistics will display a strong and nonintuitive dependence on detector bandwidth. Moreover, it is demonstrated that the antibunching phenomenon, associated with negative values of Mandel's Q parameter, results from correlations between photons with well separated frequencies.

arXiv:0908.1924•Physical Review Letters•Jan 9, 2009•47 citations

Distribution of photoelectron separation times and photoelectron counting probabilities for resonance fluorescence

H. J. Carmichael

In recent papers by Cohen-Tannoudji and Dalibard1 and Zoller et al.2 the statistics of quantum jumps in a three-level atom are analyzed in terms of the joint probability density W(t + τ;t) for a photon emission at time t followed by the next photon emission at time t+ τ. W(t+ τ;t) differs from the second-order correlation function G(2) (t + τ;t) often used to characterize photon statistics; the latter gives the joint emission probability without the condition that there be no emissions in the interval t to t + τ. Alter dividing by the density for single-photon emission, W(t + τ;t) gives the probability density for a delay τ between photon emissions.

Journal of the Optical Society of America B•Feb 1, 1987•0 citations

Two-Photon Absorption and Field Correlation Functions

B. R. Mollow

The probability of an atom undergoing a transition to a given final state by means of two-photon absorption is expressed for arbitrary field states in terms of the second-order normally-ordered field correlation function, evaluated at the position of the atom. In the case of stationary fields, an expression for the absorption rate is found which reduces to a particularly simple form for narrow-bandwidth fields near resonance. The effect of field statistics is illustrated by comparing the absorption rate $w_{2}^{}{}_{}{}^{(\mathrm{ch})}$ for chaotic or Gaussian light to the rate $w_{2}^{}{}_{}{}^{(l)}$ for laser light. The rate for laser light is calculated within the context of a particular model based on the assumption of fixed field amplitude and random frequency modulation, and the chaotic light to which it is compared is assumed to have the same (Lorentzian) power spectrum. When the width ${\ensuremath{\kappa}}_{f}$ of the final atomic level is much greater than the bandwidth $b$ of the field, we obtain the previously derived result $\frac{w_{2}^{}{}_{}{}^{(\mathrm{ch})}}{w_{2}^{}{}_{}{}^{(l)}}=2$. When ${\ensuremath{\kappa}}_{f}\ensuremath{\ll}b$, on the other hand, the ratio between the two rates depends on the (mean) frequency of the field, and assumes the (maximum) value 4 when the field is exactly on resonance.

Physical Review•Nov 1, 1968•212 citations

Two-photon Excited Fluorescence of Nitrogen-Vacancy Centers in Proton-Irradiated Type Ib Diamond

Tse-Luen Wee, Yan‐Kai Tzeng, C.-C. Han +5 more

Two-photon fluorescence spectroscopy of negatively charged nitrogen-vacancy [(N-V)-] centers in type Ib diamond single crystals have been studied with a picosecond (7.5 ps) mode-locked Nd:YVO(4) laser operating at 1064 nm. The (N-V)- centers were produced by radiation damage of diamond using a 3 MeV proton beam, followed by thermal annealing at 800 degrees C. Prior to the irradiation treatment, infrared spectroscopy of the C-N vibrational modes at 1344 cm(-1) suggested a nitrogen content of 109 +/- 10 ppm. Irradiation and annealing of the specimen led to the emergence of a new absorption band peaking at approximately 560 nm. From a measurement of the integrated absorption intensity of the sharp zero-phonon line (637 nm) at liquid nitrogen temperature, we determined a (N-V)- density of (4.5 +/- 1.1) x 10(18) centers/cm3 (or 25 +/- 6 ppm) for the substrate irradiated at a dose of 1 x 1016) H(+)/cm(2). Such a high defect density allowed us to observe two-photon excited fluorescence and measure the corresponding fluorescence decay time. No significant difference in the spectral feature and fluorescence lifetime was observed between one-photon and two-photon excitations. Assuming that the fluorescence quantum yields are the same for both processes, a two-photon absorption cross section of sigma(TPA) = (0.45 +/- 0.23) x 10(-50) cm(4).s/photon at 1064 nm was determined for the (N-V)- center based on its one-photon absorption cross section of sigma(OPA) = (3.1 +/- 0.8) x 10(-17) cm2 at 532 nm. The material is highly photostable and shows no sign of photobleaching even under continuous two-photon excitation at a peak power density of 3 GW/cm(2) for 5 min.

The Journal of Physical Chemistry A•Aug 18, 2007•196 citations
The photon statistics of several different laser systems operating at 226 nm are probed by measuring absolutely the fluorescence following two-photon absorption in atomic oxygen. The integrated fluorescence, obtained by scanning the laser frequency through the two-photon resonance, is theoretically shown to be proportional to G(2) (0) σ0(2). The second-order intensity-correlation function at time zero, G(2)(0), characterizes the laser, and σ0(2) is a fundamental atomic property. Measurement of the integrated fluorescence permits determination of the relative value of G(2) (0) for each laser. The assumption that G(2)(0) = 1 for one of the lasers, a single-frequency source, allows G(2)(0) for the other lasers to be placed on an absolute scale. The values thereby obtained range from 0.8 ± 0.2 to 3.2 ± 0.4. Different values are obtained when the radiation is generated by frequency mixing or Raman shifting of the same frequency-doubled visible dye laser, suggesting that frequency-conversion processes have a significant effect on G(2)(0).
Two-photon absorption of a continuous train of ultrashort pulses in a gas gives rise to resonances when the sum of the frequencies of two locked modes coincides with the transition frequency in the gas. It is shown that the width of these resonances is not governed by the pulse duration but by the width of the twophoton transition. Resonance intensities are of the same order of magnitude as in the single-frequency regime at the same power level. It is worth noting an important feature of the use of ultrashort pulses in studies of two-photon resonances due to the 1S-2S transition in the hydrogen atom: there is a strong increase in the efficiency of conversion of dye laser radiation to the ultraviolet range.
The probability distribution p(n)p(n)p(n) for the detection of nnn photons emitted by a single-mode dye laser in a short time at various excitations is measured, together with the distribution of time intervals between pairs of detected photons. The first measurement yields the probability density p(I)\mathcal{p}(I)p(I) and the moments of the light intensity III, and the second one the two-time intensity-correlation function. Measurements are also performed at three different wavelengths. p(I)\mathcal{p}(I)p(I) is found to have a two-component structure, and the relative intensity fluctuations $\frac{〈{(\ensuremath{\Delta}I)}^{2}〉}{{〈I〉}^{2}}$ grow, apparently without limit, as the excitation tends to zero, so that no thermal state is reached. A possible explanation in terms of pumping fluctuations is discussed. The correlation function has the form of a sum of three exponential functions, and the amplitudes and decay constants of the three components are derived. The effective decay-time constant exhibits a thirteenth-power-law dependence on frequency of the laser light.
We derive the moment generating function for photon emissions from a single molecule driven by laser excitation. The frequencies of the fluoresced photons are explicitly considered. Calculations are performed for the case of a two-level dye molecule, showing that measured photon statistics will display a strong and nonintuitive dependence on detector bandwidth. Moreover, it is demonstrated that the antibunching phenomenon, associated with negative values of Mandel's Q parameter, results from correlations between photons with well separated frequencies.
In recent papers by Cohen-Tannoudji and Dalibard1 and Zoller et al.2 the statistics of quantum jumps in a three-level atom are analyzed in terms of the joint probability density W(t + τ;t) for a photon emission at time t followed by the next photon emission at time t+ τ. W(t+ τ;t) differs from the second-order correlation function G(2) (t + τ;t) often used to characterize photon statistics; the latter gives the joint emission probability without the condition that there be no emissions in the interval t to t + τ. Alter dividing by the density for single-photon emission, W(t + τ;t) gives the probability density for a delay τ between photon emissions.
The probability of an atom undergoing a transition to a given final state by means of two-photon absorption is expressed for arbitrary field states in terms of the second-order normally-ordered field correlation function, evaluated at the position of the atom. In the case of stationary fields, an expression for the absorption rate is found which reduces to a particularly simple form for narrow-bandwidth fields near resonance. The effect of field statistics is illustrated by comparing the absorption rate w2(ch)w_{2}^{}{}_{}{}^{(\mathrm{ch})}w2​​(ch) for chaotic or Gaussian light to the rate w2(l)w_{2}^{}{}_{}{}^{(l)}w2​​(l) for laser light. The rate for laser light is calculated within the context of a particular model based on the assumption of fixed field amplitude and random frequency modulation, and the chaotic light to which it is compared is assumed to have the same (Lorentzian) power spectrum. When the width ${\ensuremath{\kappa}}_{f}$ of the final atomic level is much greater than the bandwidth bbb of the field, we obtain the previously derived result w2(ch)w2(l)=2\frac{w_{2}^{}{}_{}{}^{(\mathrm{ch})}}{w_{2}^{}{}_{}{}^{(l)}}=2w2​​(l)w2​​(ch)​=2. When ${\ensuremath{\kappa}}_{f}\ensuremath{\ll}b$, on the other hand, the ratio between the two rates depends on the (mean) frequency of the field, and assumes the (maximum) value 4 when the field is exactly on resonance.
Two-photon fluorescence spectroscopy of negatively charged nitrogen-vacancy [(N-V)-] centers in type Ib diamond single crystals have been studied with a picosecond (7.5 ps) mode-locked Nd:YVO(4) laser operating at 1064 nm. The (N-V)- centers were produced by radiation damage of diamond using a 3 MeV proton beam, followed by thermal annealing at 800 degrees C. Prior to the irradiation treatment, infrared spectroscopy of the C-N vibrational modes at 1344 cm(-1) suggested a nitrogen content of 109 +/- 10 ppm. Irradiation and annealing of the specimen led to the emergence of a new absorption band peaking at approximately 560 nm. From a measurement of the integrated absorption intensity of the sharp zero-phonon line (637 nm) at liquid nitrogen temperature, we determined a (N-V)- density of (4.5 +/- 1.1) x 10(18) centers/cm3 (or 25 +/- 6 ppm) for the substrate irradiated at a dose of 1 x 1016) H(+)/cm(2). Such a high defect density allowed us to observe two-photon excited fluorescence and measure the corresponding fluorescence decay time. No significant difference in the spectral feature and fluorescence lifetime was observed between one-photon and two-photon excitations. Assuming that the fluorescence quantum yields are the same for both processes, a two-photon absorption cross section of sigma(TPA) = (0.45 +/- 0.23) x 10(-50) cm(4).s/photon at 1064 nm was determined for the (N-V)- center based on its one-photon absorption cross section of sigma(OPA) = (3.1 +/- 0.8) x 10(-17) cm2 at 532 nm. The material is highly photostable and shows no sign of photobleaching even under continuous two-photon excitation at a peak power density of 3 GW/cm(2) for 5 min.