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Journal of Experimental and Theoretical Physics

Some Remarks Concerning the Interference of Independent Light Beams

В. Г. Барышевский, M.I. Podgoretskii

Published Jan 1, 1969• 0 citations
OpenAlex

Abstract

Some phenomena resulting from the interference of independent photon beams are considered. It is found that depending on the delay time the delayed coincidences undergo damped beats. The nature of the damping depends on the processes occurring in the source. The area under the delayed coincidence curve depends on the frequency difference of the interfering beams and on the damping mechanism.

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Some phenomena resulting from the interference of independent photon beams are considered. It is found that depending on the delay time the delayed coincidences undergo damped beats. The nature of the damping depends on the processes occurring in the source. The area under the delayed coincidence curve depends on the frequency difference of the interfering beams and on the damping mechanism.
The conditions are examined under which interference effects should be observable in the superposition of two light beams derived from independent sources. The quantum-mechanical description of these effects differs from the classical description principally in that it is necessarily based on expectation values of the light intensity at one or more space-time points. It is shown that pure states of the radiation field which are not energy states give rise to interference effects, but in that case the two beams cannot meaningfully be described as statistically independent. For a realistic description mixed states have to be introduced, when the expectation value of the intensity gives no indication of interference effects. On the other hand, the intensity correlation at two space-time points is a periodic function of the separation of the points and indicates the presence of transient interference effects. The effects become readily observable only when the average photon occupation number of each cell of phase space is appreciably greater than 1, and this explains why laser beams were needed for the experimental observations. It is pointed out that, even in these experiments, each photon may be regarded as interfering only with itself.
Beamsplitting Interference phenomena are certainly among the most exciting phenomena in the whole of physics. In the following we will concentrate mainly on interference of weak fields; i.e. the beams contain, on average, only a few photons. The principle of classical interference is as follows: a light beam is split by an optical element, for example by a semitransparent mirror or a screen with several very small apertures, into two or more partial beams. These beams will take different paths and are then reunited and form interference patterns. The first step, the splitting of the beam into partial beams, plays a decisive role; light beams coming from different sources (or from different spatial areas of the same source) do not interfere with each other! We start our discussion of interference with an analysis of the action of a beamsplitter. To form a realistic idea of this device, let us imagine a semitransparent mirror. (Our considerations apply equally well to a screen with two apertures. We could also generalize to cases of unbalanced mirrors, with reflectivity different from 1/2, or screens with apertures of different size.) The classical wave picture can describe interference phenomena without any great effort: the incoming beam is split into the reflected and the transmitted partial wave, and each of these waves contains half of the energy. The process of splitting becomes conceptually difficult only when we think of the beam as consisting of spatially localized energy packets, or photons.
The Rayleigh criterion is a widely known limit in the resolution of incoherent sources with classical measurements in the spatial domain. Unsurprisingly the estimation of the time delay between two weak incoherent signals is afflicted by an analogue problem. In this work, we show the emergence of two-photon quantum beats in the frequency domain from the interference at a beam splitter of a photon emitted by a reference source and one from the two incoherent weak signals. We demonstrate, based on this phenomena, that with a relatively low number of measurements of the frequencies of the interfering photons either bunching or antibunching at the beam splitter output one can achieve a precision amounting to half of the quantum limit, independently of both the mode structure of the photonic wavepackets and the time delay to be estimated. The feasibility of the technique makes it applicable in astronomy, microscopy, remote clocks synchronization and radar ranging
We consider photons as wave packets in time domain and analyze the Hong-Ou-Mandel–type interferences in different conditions. The general analytic formula of the 2 N -photon interference is deduced. It is shown that the widths of the time interval distributions of the 2 N -fold coincidence are proportional to the widths of the photon wave packets and inversely proportional to . Good agreement between previous experimental results and our theory for 2- and 4-photon interferences confirms the validity of this method. The method is also generalized to multi-beam interference and some new phenomena compared with two-beam interference are obtained.
Interferometry has been used widely in sensing application. However, the technique is limited by the finite coherence time of the light sources when the interference paths are not balanced. Higher-order interference effects involve intensity correlations between multiple detectors and may have the advantage over the traditional second-order interference effect exhibited in only one detector. We discuss various scenarios with unbalanced delays in different paths in fourth-order interference exhibited in coincidence between two detectors. We find, in some cases, interference effect persists even when the delays are much larger than the coherence time of the sources. We also extend the discussion to nonstationary pulsed fields, which need to consider the pulse shape and require a different treatment. These results will be useful in remote sensing applications.