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.
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.
A deeper understanding of the physical processes behind the emergence of photoelectron current pulse (PCP) statistics could help relaxing the source requirements for quantum computers, in choosing nonlinear vs. linear processing of light. Einstein’s photoelectric equation is an energy-balancing “bullet model”. The “bullet-model” over-rides both the classical and the quantum Superposition Principle (SP). SP requires first summing the joint amplitude stimulation experienced by the detecting dipoles by all the incident complex amplitudes, followed by the square modulus operation executed by the detecting dipoles to absorb the quantum-cupful of energy. We have been accommodating this “bullet model” via the prevailing belief that wave-particle duality is our new “confirmed knowledge”, instead of acknowledging our ignorance about the true nature of light. We will use the semiclassical model of photons as time-finite random light pulses stimulating a detecting molecule to its excited state of Ѱ. The molecule then absorbs the quantum of energy through the execution of the square modulus operation, Ѱ*Ѱ, and release the quantum mechanically bound electron. The lifetime of releasing the bound electron is very short as they are in quantum bands, rather than in sharp quantum levels. Each one of the released electron is then amplified, through complex electronic processes, by a factor of as much as 109, to generate one easily measurable photoelectric current pulse, or PCP’s. Therefore, the emergence of the PCP statistics is a combined function of (i) fluctuations in the incident light, (ii) fluctuations in the electron emission moments and (iii) noise introduced during the amplification process. In this paper, we will consider a classical linear approach in smoothing the average energy delivery on to a photodetector using the natural pulse replication property of a Fabry-Perot interferometer (FPI) and hence narrow the PCP statistical spread. If our model is correct, we should be able to derive the PCP-statistics for different sources using the fundamental amplitude and phase characteristics of various real sources. We have also proposed specific experiments to validate our model.
We present observational and causality arguments to underscore that a better model for light is a “hybrid photon” wave packet. At the moment of quantum transitions, the electromagnetic energy is embedded in the transient quantum, hν. But, it immediately evolves into a diffractively spreading classical, quasi-exponential, EM wave packet. This hybrid photon accommodates both quantum and classical optics. The quantum formalism has demonstrated staggering successes in modeling the micro world of atoms. The Huygens-Fresnel diffraction integral and Maxwell’s wave equation are also enjoying continued successes since early 1800’s. In this paper, using the model of hybrid photon, we underscore that the photoelectron counting statistics should vary depending upon the relative phases, spacing and amplitudes of the superposed wave packets (hybrid photons) as they simultaneously arrive and stimulate the quantum mechanical dipole complexes on the surface of the photo detectors.
Einstein’s 1905 paper on the photoelectric effect successfully modeled the published data while explicitly defining light as “indivisible light quanta”. One of the key successes of Quantum Mechanics (QM) of 1925-26, is the release of discrete packet of energy hv during any quantum level transitions in atoms and molecules. These two modern successes have overturned the mathematical and experimental knowledge developed over several centuries behind the optical science and engineering, without successfully bridging the knowledge gap epitomized by the still unresolved “wave-particle-duality” (WPD). Note that, optical science and engineering fields are still thriving using Huygens-Fresnel diffraction integral (HF-DI) of 1817 and Maxwell’s wave equations of 1876, without any controversy. This chapter resolves this dichotomy by eliminating the need for WPD. We provide a model for the atomic emission as a discrete packet of energy hv, as required by QM, but which evolves and propagates out as a Maxwellian classical exponential wave packet, while diffractively spreading out obeying the HF-DI. The continuing need to accept the magical WPD arises because we have not been systematically and explicitly exploring the two-step physical processes which take place during light-detector interaction before the photoelectric data is generated by our apparatus. The two steps are: (i) Linear amplitude-amplitude stimulation induced on the detecting dipoles by the light wave vector; (ii) which is then followed by the quadratic energy absorption step by the detector. If the detector is an LCR oscillator (for radio waves), or an old fashioned Bolometer (for higher frequencies), we would not observe any quantumness in the data. But, when we use a modern quantum photodetector using higher frequency EM waves, we can count highly amplified current pulses of electrons, generated out of each one of the released electron, bound quantum mechanically inside the detector.
The synthesis of Newtonian concept of corpuscles during emission with Huygens’ concept of secondary-wavelets during propagation implies that all EM radiations from quantized atoms and molecules are released as discrete amount of energies. However, they propagate out as time-finite Maxwellian light pulses. Huygens also underscored that his secondary wavelets keep propagating as independent pulses in the absence of any interacting medium, or until intercepted by an interface with a medium or a detector. Then we use the Superposition Principle and the coherence theory to derive Einstein’s photoelectric equation by summing innumerable random time-finite pulses. This process driven approach should yield the characteristic statistical variations of photoelectron current pulses, as generated by photodetectors for different kinds of light sources. Lamb & Scully originally proposed this semiclassical approach without assuming that light actually consists of time finite pulses. The quantumness remains confined within the excitation and de-excitations processes in the material particles.
Although light quanta were known since the works by Planck and Einstein, for several decades after these works, there was no need to treat light quantum mechanically, and all experiments could be well explained using the quantum description of matter and classical description of light (the semiclassical approach). The situation changed with the development of sources of so-called nonclassical light, i.e., light whose properties cannot be understood in the framework of the semiclassical approach. Two simple examples can be given here. The first one is the suppression of shot noise in optical detectors. Shot noise, i.e., fluctuations of photocurrent scaling as the square root of the photocurrent mean value, can be, in principle, attributed to the discrete nature of the charge generated by the detector. At the same time, the effect of shot-noise suppression, which is observed with certain light sources (squeezed light) is clearly related to the statistics of light, and quantum mechanics is completely necessary for its description. Another example, which brings us closer to the subject of the present paper, is two-photon light. This type of light contains only pairs of photons (often called biphotons), and hence, a pair of properly aligned photon-counting detectors registering two-photon light, in an ideal case, will produce only simultaneous photocounts. This behavior, again, can only be explained in terms of a quantum-mechanical description for the light.
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.