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International Journal of Optics

Interference of Light in a Michelson-Morley Interferometer: A Quantum Optical Approach

Øystein Langangen, Asle Heide Vaskinn, B.-S. Skagerstam

Published Jan 1, 2012• 3 citations
Publisher

Abstract

The temporal coherence interference properties of light as revealed by single detector intensity measurements in a Michelson-Morley interferometer (MMI) is often described in terms of classical optics. We show, in a pedagogical manner, how such features of light also can be understood in terms of a more general quantum-optics framework. If a thermal reference source is used in the MMI local oscillator port in combination with a thermal source in the signal port, the interference pattern revealed by single detector intensity measurements shows a distinctive dependence on the differences in the temperature of the two sources. A related method has actually been used to perform high-precision measurements of the cosmic microwave background radiation. The general quantum-optics framework allows us to consider any initialquantum state. As an example, we consider the interference of single photons as a tool to determine the peak angular-frequency of a single-photon pulse interfering with a single-photon reference pulse. A similar consideration for laser pulses, in terms of coherent states, leads to a different response in the detector. The MMI experimental setup is therefore an example of an optical device where one, in terms of intensity measurements, can exhibit the difference between classical and quantum-mechanical light.

DOI
10.1155/2012/408067

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The temporal coherence interference properties of light as revealed by single detector intensity measurements in a Michelson-Morley interferometer (MMI) is often described in terms of classical optics. We show, in a pedagogical manner, how such features of light also can be understood in terms of a more general quantum-optics framework. If a thermal reference source is used in the MMI local oscillator port in combination with a thermal source in the signal port, the interference pattern revealed by single detector intensity measurements shows a distinctive dependence on the differences in the temperature of the two sources. A related method has actually been used to perform high-precision measurements of the cosmic microwave background radiation. The general quantum-optics framework allows us to consider any initialquantum state. As an example, we consider the interference of single photons as a tool to determine the peak angular-frequency of a single-photon pulse interfering with a single-photon reference pulse. A similar consideration for laser pulses, in terms of coherent states, leads to a different response in the detector. The MMI experimental setup is therefore an example of an optical device where one, in terms of intensity measurements, can exhibit the difference between classical and quantum-mechanical light.
We investigate how the temporal coherence interference properties of light in a Michelson-Morley interferometer (MMI), using only a single-photon detector, can be understood in a quantum-optics framework in a straightforward and pedagogical manner. For this purpose we make use of elementary quantum field theory and Glaubers theory for photon detection in order to calculate the expected interference pattern in the MMI. If a thermal reference source is used in the MMI local oscillator port in combination with a thermal source in the signal port, the interference pattern revealed by such an intensity measurement shows a distinctive dependence on the differences in the temperature of the two sources. The MMI can therefore be used in order to perform temperature measurements. A related method was actually used to carry out high precision measurements of the cosmic micro-wave background radiation on board of the COBE satellite. The theoretical framework allows us to consider any initial quantum state. The interference of single photons as a tool to determine the angular peak-frequency of a one-photon pulse interfering with a single-photon reference pulse is, e.g., considered. A similar consideration for coherent laser pulses leads to a different response in the detector. The MMI experimental setup is therefore in a sense an example of an optical device where one can exhibit the difference between classical and quantum-mechanical light using only intensity measurements.
The Michelson-Morley experiment is considered via a single photon interferometer and we propose the interpretation of the Michelson-Morley experimental results using de Broglie-Bohm picture. We point out that the Michelson-Morley experiment revealed the interference of photons, however, it did not reveal the photons simultaneous arrival at the beam splitter. According to the de Broglie-Bohm picture, the quantum potential nonlocally determines the interference of photons. The interference of the photons is not governed by the arrival time of the photons; rather, it is governed by the quantum potential. Therefore, there is a possibility for another interpretation of the Michelson-Morley experimental results.
A Michelson's interference experiment has been performed using a single-photon counting under the condition that at most one photon is present in the interferometer. A CW mode-locked Ar + laser has been employed as a light source. It has been found that the dependence of the visibility on the difference in the two arm lengths measured on a single-photon level is the same as that for the multi-photon interference experiment. This dependence and the distribution of the photon detection time measured simultaneously by a time-correlated single-photon counting method have been found to be explained well by assuming that all the photons in the mode-locked laser pulse examined have the same temporal and spectral characteristics. A quantum mechanical analysis of this kind of experiment is also presented.
The interference of two photons in the optical gating Michelson interferometer is investigated. The phenomenon is studied using two different representations of photons: the space-time domain and a step-by-step two photon state evolution. Both representations lead to an equivalent description of the two-photon states which is the interference of four cases of two-photon traveling states, as implied by the evolution analysis. Additionally, the space-time domain analysis reveals that the classical interference of high-intensity light source is identical to the two-photon interference in the quantum regime except for a multiplicative factor of (n 2), where n is the number of photons.
The interference of entangled photon pairs permits the study of the fundamental properties of quantum mechanics. The process is also finding practical applications in optical imaging. The Michelson interferometer provides an elegant means for characterizing the degree of two-photon entanglement, but the technique has not yet been described and analyzed in detail. Here we provide a full description of the interference of collinear down-converted photons in a Michelson interferometer. We explain the basic elements that characterize the interference pattern and complement the theory with experimental measurements. The two-photon Michelson interferometer can be used in quantum optical coherence tomography for dispersion-free imaging and localization.
We investigate the interference of two photons in an optical gating Michelson interferometer. The phenomenon is studied using two different representations of photons: the space-time domain and a step-by-step two-photon state evolution. Both representations lead to identical results. The evolution analysis describes the result by the interference of four two-photon traveling states, whereas the space-time domain analysis reveals that the classical interference of the high-intensity light source is identical to two-photon interference in the quantum regime, except for a multiplicative factor of (n2), where n is the number of photons.