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.
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 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.
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.
Quantum computers, hypothesized in 1980s, use concepts of superposition and entanglement phenomena. Although theoretical propositions and associated search algorithms for accurate measurements are being generated, the development of practical quantum computers themselves are advancing very slowly requiring enormous time and investments. The underlying concepts of a quantum computer are not new to the optical domain. However, the crucial enabling concepts of Entanglement and Superposition Principle are remaining clouded under the unresolved postulates, Wave-Particle Duality (WPD), and Wave Packet Reduction (WPR), implicating incompleteness in the interpretations of the mathematical formalism behind Quantum Mechanics. The WPD debate started during late1600 between Newton and Huygens. Young’s resolution of WPD through his double-slit experiment in 1802 was effectively overturned by Einstein’s interpretation of photoelectric effect as due to “indivisible light quanta”. However, Einstein disowned his “light quanta” postulate shortly before his death in1955, even though it had earned him the Nobel Prize. We resolve WPD by synthesizing Newton’s and Maxwell’s concepts and assume atoms do emit quanta but propagate as time-finite exponential pulses. This assumption also resolves WPR for light-matter interaction with the assumption that Schrodinger’s ψ represents atom’s internal dipolar amplitude stimulations. This over-turns Born’s interpretation that ψ only represents the abstract mathematical probability amplitude, rather than the physical “internal amplitude stimulation” of the quantum entity. However, our concept of atomic pulse emission forces us to re-derive the expression for the N-slit grating-spectrometer response since the classical derivation uses CW light, which does not exist. This pulsespectrometric response function strengthens our postulate since the grating response to the exponential pulse appears to be the convolution of a Lorentzian spectrum with the classical CW response function of the grating. The Fourier Transform of an exponential function is Lorentzian and QM predicts spontaneous emission line width to be Lorentzian. Then, conceptually one can extend the grating-expression (with N=2) to get the double-slit pattern. This approach preserves the classical causality that each of the two slits, like the N-signals out of a grating, are physically real and jointly stimulate the quantum detector array at the far field to generate the “Local” cosine fringes. The detector array executes the square modulus operation on its imposed dipolar amplitude stimulation and absorbs the necessary energy to fill up their quantum cups. Hence the double-slit pattern must also be “Local”, just as the N-slit grating spectrum is generated locally at the exit spectral-plane of the spectrometer. This removes the need to believe that “single photons” mysteriously generate the double slit pattern.
Introduction In previous chapters we studied wave propagation in fiber OPAs from a classical standpoint, i.e. starting from Maxwell's equations. That approach provides only a partial view of the rich nature of the electromagnetic field, namely its wave nature. However, a complete description of the electromagnetic field requires quantum mechanics. This quantum description of the electromagnetic field (called quantum electrodynamics, or QED) predicts fluctuations in measurable quantities due to the Heisenberg uncertainty principle and sets ultimate limits on the performance of devices such as optical amplifiers. A remarkable result of this theory is that the statistics and thus the noise performance of a system are affected by the quantum statistics of the source and by the physical measurement that is made. Thus a different analysis is needed depending on whether homodyne, heterodyne, or direct detection (where the field simply impinges on a photodiode) is used. Direct detection reveals the particle nature of the electromagnetic field. More specifically, energy arrives in discrete units, called photons, each of which may create an electron–hole pair in a semiconductor photodetector. In particular, the number of photons in an optical pulse can be thought of as a random variable having a mean and a variance. By deriving the mean and variance of the photocurrent that would be present if one performed direct detection of ideal laser light at the input of an optical amplifier and then a similar measurement at its exit, one can quantify the degradation of the signal-to-noise ratio (SNR) caused by the amplifier.
A relation is derived between the probability distribution of the integrated intensity of light incident on a photoelectric detector and that of the emission of n photoelectrons in a time interval (t, t + T) from the properties of a quantized electromagnetic field. Both the direct and the inverse relations are derived, thereby enabling the statistical properties of light to be determined from photoelectric measurements. An explicit expression is given for the coefficients for calculating the moments ( W k) by means of the moments (n J) (] = 1, 2 ..... k). The correctness of the operations in which generalized functions occur is confirmed by some direct calculations. The significance of photoelectric detectors has been increasing of late. Since their response is proportional to the intensity of incident light (to the square of the amplitude of light) (more exactly, to the local mean time value of the intensity), one speaks of quadratic detectors. These detectors are of basic importance in the theory of the coherence of the electromagnetic field, since if we place N such detectors into N different points in space and if we lead the outputs of these detectors to the correlator we can measure the correlation (coherence) effects of the 2N-th order in the given field [1]. Such correlation measurements provide information on the energy distribution in the radiation spectrum [2], the angular dimensions of stars [3], and the state of polarization [4] and also enable the phase of physically important functions (e.g. the scattering amplitudes) [5] to be determined. Although in such experiments the properties of photoelectrons are studied rather than of photons, they reflect the basic properties of photons. Let the probability distribution Of the emission of n photoelectrons in a time interval (t, t + T) be p(n, T, t) - p(n) and let the probability distribution of the quantity W(T, t) = W = J'tt+r I(t') dr', where I(t) is the intensity of linearly polarized light incident on the photodetector (for simplicity we assume that the sensitivity of the photocathode is a = 1), be P(W). The quantity W can be regarded as a classical characteristic of the field, the quantity n represents the quantum characteristic of the field. Then, on the basis of such a semi-classical description, in which the field is described classically, but its interaction is described quantum-wise, one can derive the following relation [6]