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arXiv:1407.4603 · Physical review. B./Physical review. B

Photon-photon correlation statistics in the collective emission from ensembles of self-assembled quantum dots

Fitria Miftasani, Paweł Machnikowski

Published Feb 29, 2016• 6 citations

Abstract

We present a theoretical analysis of the intensity correlation functions for the spontaneous emission from a planar ensemble of self-assembled quantum dots. Using the quantum jump approach, we numerically simulate the evolution of the system and construct photon-photon delay time statistics that approximates the second-order correlation functions of the field. The form of this correlation function in the case of collective emission from a highly homogeneous ensemble qualitatively differs from that characterizing an ensemble of independent emitters (inhomogeneous ensemble of uncoupled dots). The signatures of collective emission are observed also in the case of an inhomogeneous but sufficiently strongly coupled ensemble. Different forms of the correlation functions are observed in the intensity autocorrelations and in cross correlations between various spectral ranges, revealing the quantum state projection associated with the detection event and the subsequent interaction-induced redistribution of occupations. The predicted effect of collective dynamics on the correlation functions appears under various excitation conditions. Thus, we show that the second-order correlation function of the emitted field provides a sensitive test of cooperative effects.

DOI: 10.1103/physrevb.93.075311

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The photon correlation of photon emission from a single quantum dot with cw excitation and pulsed excitation is investigated in details. To calculate the second-order correlation function for optical pumping, we deduce rate equations with a simplified two-level model under cw excitation and present the master equation approach in the interaction picture to the study of evolution of a three-level system under pulsed excitation. In addition, we report photon correlation measurements on a single self-assembled In 0.5 Ga 0.5 As quantum dot, which show strong antibunching behaviour under both the conditions of cw and pulsed excitations. The calculated results are in agreement with the experimental measurements.

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{g}^{(2)}({\mathbf{r}}_{1},{\mathbf{r}}_{2})

, we characterize the collective spontaneous emission behavior of two ions in free space. We explain the observed contrast of

{g}^{(2)}({\mathbf{r}}_{1},{\mathbf{r}}_{2})

considering independently derived experimental parameters. Our results show how the detection of a single photon can profoundly modify the collective spontaneous emission dynamics of an atomic ensemble.

The time dependence of correlations between the photons emitted from a microcavity with an embedded quantum dot under incoherent pumping is studied theoretically. Analytic expressions for the second-order correlation function g (2)(t) are presented in strong and weak coupling regimes. The qualitative difference between the incoherent and coherent pumping schemes in the strong coupling case is revealed: under incoherent pumping, the correlation function demonstrates pronounced Rabi oscillations, but in the resonant pumping case, these oscillations are suppressed. At high incoherent pumping, the correlations decay monoexponentially. The decay time nonmonotonically depends on the pumping value and has a maximum corresponding to the self-quenching transition.

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The statistic characteristics of single photon emission in single semiconductor quantum dot with pulse excitation have been investigated.With rotating-wave approximation,we deduce the dynamics equations including second-order correlation function from the master equations of the populations and discuss the correlation function of photon emission from the exciton combination under different input pulse areas.There will appear an apparant split peak around zero time delay under strong excitation.For short pulse width,the probability of single photon emission p and the efficiency of single photon emission η oscillate as the excitation intensity increases.It is revealed that high efficient single photon emissions can be realized in this system when excited with input pulse area about π and short pulse width.

The second-order photon correlation function g((2))(tau) of photons emitted by a continuously pumped ensemble of N two-level systems coupled to a single-mode optical cavity well below the lasing threshold is investigated theoretically. A giant photon bunching is found for N < 10 emitters as the microscopic counterpart of spontaneous emission noise driven quasi-periodic superradiant pulse sequences in macroscopic systems of large numbers of emitters N >> 1. The phenomenon of giant photon bunching is preserved even for N = 2 and can be explained by the cooperative evolution via dark and bright two-atom states resulting into emission of superradiant photon pairs. The sensitivity of g((2)) to microscopic dephasing processes and resonance frequency detuning opens the door for photon bunching spectroscopy.