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American Journal of Physics

Sub-Poissonian photocurrent statistics: Theory and undergraduate experiment

Andrew Funk, M. Beck

Published Jun 1, 1997• 17 citations
Publisher

Abstract

We present the results of an experiment in which we observe a sub-Poissonian photocurrent. This photocurrent is generated by detecting the light emitted from a high-quantum-efficiency light-emitting diode driven by a high-impedance current source. We also present classical, semi-classical and quantum mechanical theories of photoelectric detection. The observed sub-Poissonian statistics are in agreement with quantum mechanical predictions, but are unexplainable using the classical and semi-classical theories. The experiment uses only equipment already found in most undergraduate laboratories, making this a nice experiment to demonstrate a purely quantum mechanical effect.

DOI
10.1119/1.18577

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We present the results of an experiment in which we observe a sub-Poissonian photocurrent. This photocurrent is generated by detecting the light emitted from a high-quantum-efficiency light-emitting diode driven by a high-impedance current source. We also present classical, semi-classical and quantum mechanical theories of photoelectric detection. The observed sub-Poissonian statistics are in agreement with quantum mechanical predictions, but are unexplainable using the classical and semi-classical theories. The experiment uses only equipment already found in most undergraduate laboratories, making this a nice experiment to demonstrate a purely quantum mechanical effect.
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The squeezing of the intensity noise in the extremely weak light emanating from a light-emitting diode (LED) was investigated. By the use of a tailor-made high-efficiency LED, in which the active region is heavily doped (∼3.5×1019 cm-3), we successfully observed sub-Poissonian light at an injection current and photocurrent as low as 1 µA and 160 nA, respectively, at room temperature. The experimental results also implied that the theoretical model describing the noise behavior needs to be refined, particularly in the case of extremely low injection levels where the nonradiative recombination process has a serious effect.
We are developing a semi-classical model to explain the physical processes behind the origin of the statistical variations in the photoelectron current pulses that we register for different kinds of light. They are: super-Poissonian thermal light, Poissonian laser light and sub-Poissonian nonlinearly generated light. Einstein’s photoelectron equation is an energy balancing equation. It does not incorporate the E-vector stimulation process before the quantum mechanically bound electrons can be released, which constitutes a key objective of physics. To introduce physics, we postulate that the photons are hybrid entities. They are discrete packets of energy hνmn at the moment of emission. Then they immediately evolve into spatially spreading diffractive wave packets to accommodate Huygens-Fresnel principle. HF principle has been behind the sustained progress in classical optics and photonics engineering. Thus a spatially spread out single wave-packet cannot any more deliver the necessary quantum cupful of energy hνmn to Angstrom-size detecting atoms. We need simultaneous stimulation of the same quantum entity by multiple wave packets. This model of physical interaction process naturally brings into play the significance of the degree of mutual coherence between different photon wave packets, along with their time varying amplitudes that are simultaneously stimulating the detecting quantum entities during any time-interval selected for the detection system. The superposition effects on the detector due to these phase and amplitude fluctuations are the physics-reasons behind the generation of different statistical variations in the photoelectron counts due to different kinds of sources even though the original photons are released randomly by all quantum sources.
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Shot noise sets a fundamental limit on the sensitivity of classical optical measurements, with coherent emitters achieving the lowest possible shot-noise level. Emission from sub-Poissonian light provides a pathway to surpass this limit, and single-photon sources provide a natural platform for generating such light. However, it is commonly assumed that continuously excited single-photon sources exhibit Poissonian statistics. In this work, a theoretical model of a continuously driven two-level single-photon source is developed, treating both excitation and radiative decay as stochastic processes. The analysis demonstrates that photon emission can display sub-Poissonian statistics when excitation and decay rates are comparable, showing that continuous excitation does not inherently preclude nonclassical emission. The model is further extended to include finite detection efficiency and detector dead time, illustrating how these practical non-idealities can affect the experimental observation of sub-Poissonian statistics.