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Physical Review A

Nontrivial intensity correlation from a coherent continuous-wave laser beam

Binod Joshi, Thomas A. Smith, Yanhua H. Shih

Published Sep 4, 2024• 5 citations
Publisher

Abstract

Quantum correlations with a normalized value of ${g}^{(2)}(\ensuremath{\tau})>1$ are typically observed in light in a thermal state (e.g., light from a star or incandescent bulb). Here, the authors demonstrate that similar correlations are present in a continuous-wave laser beam consisting of a large number of longitudinal modes modeled as coherent states.

DOI
10.1103/physreva.110.l031702

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Quantum correlations with a normalized value of g(2)(\ensuremathτ)>1{g}^{(2)}(\ensuremath{\tau})>1g(2)(\ensuremathτ)>1 are typically observed in light in a thermal state (e.g., light from a star or incandescent bulb). Here, the authors demonstrate that similar correlations are present in a continuous-wave laser beam consisting of a large number of longitudinal modes modeled as coherent states.
An intensity-correlation experiment is proposed to test the second-order coherence of laser light from a cw-operated laser based on the Glauber formalism. The calculation utilizes the known form of the density matrix for radiation from a randomly excited source such as a discharge tube which is equivalent to filtered black-body radiation, and represents the laser radiation field by a coherent state. The intensity correlation calculated exhibits the standard Hanbury Brown-Twiss term and an extra term due to intensity interference between the Fourier components of the thermal field and the laser mode.
Introduction The degree of first-order temporal coherence, a function denoted by g (1) ( τ ), provides information about the coherence length and the power spectral density of a light source. However, without additional information, g (1) ( τ ) has no bearing on intensity fluctuations and higher-order statistics of the emitted light. A quasi-monochromatic laser beam and the beam of light from an incandescent light bulb, provided that the latter is properly filtered to match the spectral line-shape of the former, will have identical degrees of first-order coherence. Any interferometric experiment involving the splitting and superposition of amplitudes would yield identical results for the laser beam and the (properly filtered) thermal light. Therefore, on the basis of such experiments alone, there is no way to distinguish the two light sources. It turns out, however, that the intensity fluctuations of laser light are fundamentally different from those of thermal light. The two sources can, therefore, be distinguished based on their second-order coherence properties. An ideal photodetector produces an electrical signal proportional to the “cycle-averaged intensity” of the E -field (or B -field) of the light beam at the location of the detector. Assuming that the electrical bandwidth of the detector (including all associated circuitry) is greater than the bandwidth of the incident light wave by at least a factor of 2, the output of the detector should accurately represent the intensity fluctuations of the light beam as a function of time.
Abstract Quantum optics did not, and could not, flourish without the laser. The present paper is not about the principles of laser construction, still less a history of how the laser was invented. Rather, it addresses the question: what are the fundamental features that distinguish laser light from thermal light? The obvious answer, ‘laser light is coherent’, is, I argue, so vague that it must be put aside at the start, albeit to revisit later. A more specific, quantum theoretic, version, ‘laser light is in a coherent state’, is simply wrong in this context: both laser light and thermal light can equally well be described by coherent states, with amplitudes that vary stochastically in space. Instead, my answer to the titular question is that four principles are needed: high directionality, monochromaticity, high brightness, and stable intensity. Combining the first three of these principles suffices to show, in a quantitative way—involving, indeed, very large dimensionless quantities (up to )—that a laser must be constructed very differently from a light bulb. This quantitative analysis is quite simple, and is easily relatable to ‘coherence’, yet is not to be found in any textbooks on quantum optics to my knowledge. The fourth principle is the most subtle and, perhaps surprisingly, is the only one related to coherent states in the quantum optics sense: it implies that the description in terms of coherent states is the only simple description of a laser beam. Interestingly, this leads to the (not, as it turns out, entirely new) prediction that narrowly filtered laser beams are indistinguishable from similarly filtered thermal beams. I hope that other educators find this material useful; it may contain surprises even for researchers who have been in the field longer than I have.