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arXiv:1302.7187 · Physical Review A

Theory of interferometric photon-correlation measurements: Differentiating coherent from chaotic light

A. Lebreton, Izo I. Abram, Rémy Braive, Isabelle Sagnes, Isabelle Robert-Philip, A. Beveratos

Published Jul 2, 2013• 21 citations
arXivHTMLPDF

Abstract

Interferometric photon-correlation measurements, which correspond to the second-order intensity cross correlations between the two output ports of an unbalanced Michelson (or Mach-Zehnder) interferometer, are sensitive to both amplitude and phase fluctuations of an incoming beam of light. Here, we present the theoretical framework behind these measurements and show that they can be used to unambiguously differentiate a coherent wave undergoing dynamical amplitude and phase fluctuations from a chaotic state of light. This technique may thus be used to characterize the output of nanolasers and monitor the onset of coherent emission.

DOI
10.1103/physreva.88.013801

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Interferometric photon-correlation measurements, which correspond to the second-order intensity cross correlations between the two output ports of an unbalanced Michelson (or Mach-Zehnder) interferometer, are sensitive to both amplitude and phase fluctuations of an incoming beam of light. Here, we present the theoretical framework behind these measurements and show that they can be used to unambiguously differentiate a coherent wave undergoing dynamical amplitude and phase fluctuations from a chaotic state of light. This technique may thus be used to characterize the output of nanolasers and monitor the onset of coherent emission.
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One of the most fundamental quantum features is the two-photon intensity correlation on a beam splitter, resulting in photon bunching into either output port. According to the conventional understanding of quantum mechanics, the origin of photon bunching on a beam splitter is in the indistinguishable characteristics between coincident photons, resulting in destructive quantum interference even without a clear definition of phase information of the paired photons. Here, a completely different approach is presented for the same quantum feature, where a strong mutual phase dependency is the essential requirement for the nonclassical feature of photon bunching. This definite phase relationship is now understood as the origin of this quantum feature resulting from the phase-basis superposition of the photon-BS system, resulting in photon indistinguishability. On behalf of a coherent model with a single input-port BS system, an extended scheme of a Mach-Zehnder interferometer is additionally analyzed for the validity of forbidden phase-basis superposition in the quantum feature.
By using an intensity correlation, or photon coincidence, technique and a Mach-Zehnder interferometer with artificially applied phase fluctuations in one arm, we measured the coherence time of a thermal light beam. The light was derived from the filtered fluorescence of a rhodamine 6G dye solution. The two-photon coincidence rate was measured as a function of path difference and was found to dip 50% when the two arms of the interferometer are balanced. The coherence time of ~100 fs is determined from the measured width of the dip and is consistent with the passband of the filters. The method does not require the stability needed in second-order interference measurements, and its time resolution can be much shorter than that of the photodetectors. The theory of this type of fourth-order interference technique is discussed.
We have studied the sensitivity of four different phase shift measurement schemes with a Mach-Zehnder interferometer. The input light is considered to be in a coherent state and the detectors are assumed to be ideal with the quantum efficiency of unity. It is shown by direct calculation of the operators corresponding to the measurement schemes that the uncertainty of the phase-shift measurement is limited to the classical one 1m\frac{1}{\sqrt{m}}m​1​ (m is the average number of the photons in the input state) regardless of the phase-shift measurement schemes.
When a photon interferes with itself while traversing a Mach-Zehnder interferometer, the output port where it emerges is influenced by the phase difference between the interferometer arms. This allows for highly precise estimation of the path length difference (delay) but is extremely sensitive to phase noise. By contrast, a delay between the arms of the two-photon Hong-Ou-Mandel interferometer directly affects the relative indistinguishability of the photon pair, affecting the rate of recorded coincidences. This likewise allows for delay estimation, notably less precise but with the advantage of being less sensitive to perturbations of the photons' phase. Focusing on two-photon input states, we here investigate to what degree of noise Mach-Zehnder interferometry retains its edge over Hong-Ou-Mandel interferometry. We also explore the competing benefits of different two-photon inputs for a Mach-Zehnder interferometer and under what parameter regimes each input performs best.