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IEEE Journal of Quantum Electronics

Intensity interferometry by two-photon excitation of fluorescence

Heinz P Weber, René Dändliker

Published Dec 1, 1968• 38 citations
Publisher

Abstract

Two-photon fluorescence traces used for picosecond pulse-width measurement are analyzed and described by intensity correlation functions, also known as second-order coherence functions. The correlation functions and the fluorescence traces are discussed for three special types of light emission and calculated in detail for a three-mode laser model in free-running, mode-locking, and FM-like operation. A rigorous calculation for the fluorescence intensity excited by a laser oscillating in a large number of modes with arbitrary amplitudes and phases is also given. The shapes of the fluorescence traces are found to be essentially the same for both, free-running and ideally mode-locked emission, but with different contrast ratios of 1.5 : 1 and 3 : 1, respectively.

DOI
10.1109/jqe.1968.1075012

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Two-photon fluorescence traces used for picosecond pulse-width measurement are analyzed and described by intensity correlation functions, also known as second-order coherence functions. The correlation functions and the fluorescence traces are discussed for three special types of light emission and calculated in detail for a three-mode laser model in free-running, mode-locking, and FM-like operation. A rigorous calculation for the fluorescence intensity excited by a laser oscillating in a large number of modes with arbitrary amplitudes and phases is also given. The shapes of the fluorescence traces are found to be essentially the same for both, free-running and ideally mode-locked emission, but with different contrast ratios of 1.5 : 1 and 3 : 1, respectively.
We calculate the second-order correlation function for the atomic fluorescence in the two-photon resonance operation of a driven dissipative Jaynes–Cummings oscillator. We employ a minimal four-level model comprising the driven two-photon transition alongside two intermediate states visited in the dissipative cascaded process, in the spirit of Shamailov et al. (2010). We point to the difference between the output of a JC oscillator exhibiting two-photon blockade and the scattered field of ordinary resonance fluorescence, and discuss the quantum interference effect involving the intermediate states, which is also captured in the axially transmitted light. The spectrum and intensity correlation of atomic emission explicitly reflect the particulars of the cascaded model.
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 present a detailed discussion of a recently demonstrated experimental technique capable of measuring the correlation function of a pulsed light source with picosecond time resolution. The measurement involves a streak camera in single photon counting mode, which is modified such that a signal at a fixed repetition rate, and well defined energy, can be monitored after each pulsed laser excitation. The technique provides further insight into the quantum optical properties of pulsed light emission from semiconductor nanostructures, and the dynamics inside a pulse, on the sub-nanosecond time scale.
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The second-order correlation function of light g(2)(τ) constitutes a pivotal tool to quantify the quantum behavior of an emitter and in turn its potential for quantum information applications. The experimentally accessible time resolution of g(2)(τ) is usually limited by the jitter of available single-photon detectors. Here, we present a versatile technique allowing g(2)(τ) to be measured from a large variety of light signals with a time resolution given by the pulse length of a mode-locked laser. The technique is based on frequency upconversion in a nonlinear waveguide, and we analyze its properties and limitations by modeling the pulse propagation and the frequency conversion process. We measure g(2)(τ) from various signals including light from a quantum emitter—a confined exciton-polariton structure—revealing its quantum signatures at a scale of a few picoseconds and demonstrating the capability of the technique.
A method of calculation of multiple-time correlation functions of the resonance fluorescence light from a two-level atom driven by a realistic laser field with phase and amplitude fluctuations is developed. Both kinds of fluctuations are assumed to be Gaussian. The phase fluctuations are treated in the phase-diffusion model. The averaging over the amplitude fluctuations can be performed in a closed way when the relative mean-square amplitude fluctuation is small compared with the ratio of the amplitude correlation decay rate to the characteristic atomic relaxation rate. There is no restriction to Markovian amplitude fluctuations. Arbitrary values for the mean Rabi frequency are allowed. Results are presented for the intensity, the intensity correlation function, and the spectrum of the fluorescent light. It is shown that even in the case when the relative strength of the amplitude fluctuations is small, significant effects can occur due to the finite correlation length of the fluctuations. The results for fast amplitude correlation decay correspond to the situation without amplitude fluctuations. When the correlation time of the amplitude fluctuations becomes comparable with the atomic relaxation times, the Rabi oscillations of the intensity and the intensity correlation function are nearly washed out, and non-Lorentzian line shapes for the side peaks in the spectrum are observed. It is found that the ratio of the heights of the central peak to the side peak increases with increasing correlation time.