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Instantaneous Quantum Description of Photonic Wavefronts and Applications

Andre Vatarescu

Published Nov 8, 2018• 10 citations
Publisher

Abstract

By imposing the condition of non-vanishing expectation values for the amplitude and phase of field operators, pure quantum states are identified composed of two consecutive number states. These pure states also deliver noise-free radiation modes restricting the “half-photon noise” to the expectation value of the lowest level of dynamic and coherent number states. As a result, instantaneous phase-sensitive amplification of photons is easily controlled and direct evaluation of time or distance - varying wavefront distributions of photons and phases can be carried out for sub-Poissonian distributions of photons without the need for quasi-probabilities.

DOI
10.20944/preprints201811.0196.v1

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By imposing the condition of non-vanishing expectation values for the amplitude and phase of field operators, pure quantum states are identified composed of two consecutive number states. These pure states also deliver noise-free radiation modes restricting the “half-photon noise” to the expectation value of the lowest level of dynamic and coherent number states. As a result, instantaneous phase-sensitive amplification of photons is easily controlled and direct evaluation of time or distance - varying wavefront distributions of photons and phases can be carried out for sub-Poissonian distributions of photons without the need for quasi-probabilities.
Three physical elements are missing from the conventional formalism of quantum photonics: 1) the quantum Rayleigh spontaneous and stimulated emissions; 2) the unavoidable parametric amplification; and 3) the mixed time-frequency spectral structure of a photonic field which specifies its duration or spatial extent. As a single photon enters a dielectric medium, the quantum Rayleigh scattering prevents it from propagating in a straight-line, thereby destroying any possible entanglement. A pure dynamic and coherent state composed of two consecutive number states, delivers the correct expectation values for the number of photons carried by a photonic wave front, its complex optical field, and phase quadratures. The intrinsic longitudinal and lateral field profiles associated with a group of photons for any instantaneous number of photons are independent of the source. These photonic properties enable a step-by-step analysis of the correlation functions characterizing counting of coincident numbers of photons or intensities with unity visibility interference, spanning the classical and quantum optic regimes
Three physical elements are missing from the conventional formalism of quantum photonics: 1) the quantum Rayleigh spontaneous and stimulated emissions; 2) the unavoidable parametric amplification; and 3) the mixed time-frequency spectral structure of a photonic field which specifies its duration or spatial extent. As a single photon enters a dielectric medium, the quantum Rayleigh scattering prevents it from propagating in a straight-line, thereby destroying any possible entanglement. A pure dynamic and coherent state composed of two consecutive number states, delivers the correct expectation values for the number of photons carried by a photonic wave front, its complex optical field, and phase quadratures. The intrinsic longitudinal and lateral field profiles associated with a group of photons for any instantaneous number of photons are independent of the source. These photonic properties enable a step-by-step analysis of the correlation functions characterizing counting of coincident numbers of photons or intensities with unity visibility interference, spanning the classical and quantum optic regimes
Three physical elements are missing from the conventional formalism of quantum photonics: (1) the quantum Rayleigh spontaneous and stimulated emissions; (2) the unavoidable parametric amplification; and (3) the mixed time-frequency spectral structure of a photonic field which specifies its duration or spatial extent. As a single photon enters a dielectric medium, the quantum Rayleigh scattering prevents it from propagating in a straight-line, thereby destroying any possible entanglement. A pure dynamic and coherent state composed of two consecutive number states, delivers the correct expectation values for the number of photons carried by a photonic wave front, its complex optical field, and phase quadratures. The intrinsic longitudinal and lateral field profiles associated with a group of photons for any instantaneous number of photons are independent of the source. These photonic properties enable a step-by-step analysis of the correlation functions characterizing counting of coincident numbers of photons or intensities with unity visibility interference, spanning the classical and quantum optic regimes.
Three physical elements are missing from the conventional formalism of quantum photonics: 1) the quantum Rayleigh spontaneous and stimulated emissions; 2) the unavoidable parametric amplification; and 3) the mixed time-frequency spectral structure of a photonic field which specifies its duration or spatial extent. As a single photon enters a dielectric medium, the quantum Rayleigh scattering prevents it from propagating in a straight-line, thereby destroying any possible entanglement. A pure dynamic and coherent state composed of two consecutive number states, delivers the correct expectation values for the number of photons carried by a photonic wave front, its complex optical field, and phase quadratures. The intrinsic longitudinal and lateral field profiles associated with a group of photons for any instantaneous number of photons are independent of the source. These photonic properties enable a step-by-step analysis of the correlation functions characterizing counting of coincident numbers of photons or intensities with unity visibility interference, spanning the classical and quantum optic regimes
At the end of the preceding chapter, we showed that the photon number states | n 〉 have a uniform phase distribution over the range 0 to 2π. Essentially, then, there is no well-defined phase for these states and, as we have already shown, the expectation value of the field operator for a number state vanishes. It is frequently suggested (see, for example, Sakurai) that the classical limit of the quantized field is the limit in which the number of photons becomes very large such that the number operator becomes a continuous variable. However, this cannot be the whole story since the mean field 〈 n | Ê x | n 〉 = 0 no matter how large the value of n . We know that at a fixed point in space a classical field oscillates sinusoidally in time. Clearly this does not happen for the expectation value of the field operator for a number state. In this chapter we present a set of states, the coherent states, which do give rise to a sensible classical limit; and, in fact, these states are the “most classical” quantum states of a harmonic oscillator, as we shall see. Eigenstates of the annihilation operator and minimum uncertainty states In order to have a non-zero expectation value of the electric field operator or, equivalently, of the annihilation and creation operators, we are required to have a superposition of number states differing only by ±1.