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arXiv:2402.15041

Observation of the First-Order Interference Fringes Beyond Coherence Length Employing Commercial Continuous-wave Multi-mode Laser Diode: A Sight of Two-photon Interference

Hongmin Liu

Published Feb 23, 2024• 0 citations
arXivHTMLPDF

Abstract

We report an experiment of observation of classical double-slit interference fringes of two-photon interference. In the experiment, a commercial continuous-wave multi-mode F-P laser diode without either mode-locked or frequency-locked is used as the light source, the density of photons is far more than the single-photon level, and the path difference of the long and short paths is far more than the longitudinal coherence length of the laser diode. The temporal stable and clearly visible spatial-distributed pattern, i.e. first-order interference fringes, was observed .Contradict to the prediction of single-photon interference mechanism, the interference happened far beyond the coherence length, the occurrence possibility and time duration of the interference fringes decrease with the reduction of mode number of the LD, and the time difference between the fringes disappearance and the light vanish is equal to the time difference of the two paths. After discussion, we came to the conclusion that the observed phenomena can be understood in time-resolved two-photon interference mechanism. We reveal a new method to perform two-photon first-order interference, and this help to understand the nature of two-photon interference and also can be useful for quantum information science.

DOI
10.48550/arxiv.2402.15041

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We report two-photon interference with continuous-wave multi-mode coherent light. We show that the two-photon interference, in terms of the detection time difference, reveals two-photon beating fringes with the visibility V = 0.5. While scanning the optical delay of the interferometer, Hong-Ou-Mandel dips or peaks are measured depending on the chosen detection time difference. The HOM dips/peaks are repeated when the optical delay and the first-order coherence revival period of the multi-mode coherent light are the same. These results help to understand the nature of two-photon interference and also can be useful for quantum information science.
The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by employing two-photon interference in Feynman's path integral theory. It is concluded that whether the second-order temporal interference pattern can or cannot be retrieved via two-photon coincidence counting rate is dependent on the resolution time of the detection system and the frequency difference between these two lasers. Two identical and tunable single-mode continuous-wave diode lasers are employed to verify the predictions. These studies are helpful to understand the physics of two-photon interference with photons of different spectra.
Over the past several decades, single photon-based path interference in double-slit experiment has been well demonstrated for the particle nature of photons satisfying complementarity theory, where the quantum mechanical interpretation of the single photon interference fringe is given by Born rule for complex amplitudes in measurements. Unlike most conventional methods using entangled photon pairs, here, a classical coherent light source is directly applied for the proof of the same self-interference phenomenon. Instead of double slits, we use a Mach-Zehnder interferometer as usual, where the resulting self-interference fringe of coherent single photons is exactly the same as that of the coherent photon ensemble of the laser, demonstrating that the classical coherence based on the wave nature is rooted in the single photon self-interference. This unexpected result seems to contradict our common understanding of decoherence phenomena caused by multi-wave interference among bandwidth distributed photons in coherence optics.
Interference between different photons occurs and has been observed under diverse experimental conditions. A necessary condition in order to obtain interference fringes is the existence of at least two possible paths and unknown which-path information. If the photon beams have different frequencies, stability of the sources and fast spatially distributed detectors are required in order to detect the time displaced interference fringes. First order optical interference between two truly independent CW laser sources is observed. In contrast with the standard quantum criterion, interference is observed although the photon beams are distinguishable and, from quantum measurements, the path is unequivocally known for each photon beam. Segments of the continuous wave wavetrains are selected with an acousto-optic modulator. Temporal and spatial interference are integrated in a single combined phenomenon via streak camera detection. The displacement of the fringes in the time versus space interferograms evince the trajectories of the labeled photons. These results suggest that in non-degenerate frequency schemes, the ontology has to be refined and the which-path criterion must be precisely formulated. On the one hand, if the query refers to the frequency labeled photons, the path of each red or blue photon is known, whereas on the other hand, if the query is performed in terms of the detected photons, the path is unknown.
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A necessary condition in order to obtain interference fringes in QED is the existence of at least two possible paths and unknown which-path information. If the photon beams have different frequencies, stability of the sources and fast enough detectors are also required. In this experiment, first order interference between two truly independent CW Nd:YAG monomode laser sources was produced. Contrary to what is expected, interference is observed although the photon beams are distinguishable and the path is unequivocally known for each photon beam. Segments of the ultra-stabilized CW wavetrains are selected with an acousto optic modulator. Temporal and spatial interference are integrated in a single combined phenomenon via streak camera detection. In this way, interference fringes and frequency beating are both present in the streak camera images. The photon beams are labeled with two slightly different frequencies. In addition, the inclination of the beams establish the projection of their respective wave vectors in the detection plane, which may be seen as perturbations coming from two different slits. The fringes displacement in the time-space interferograms reveal the trajectories of the frequency labeled photons. Since the detection probability of any one photon is independent from the detection of the rest, the trajectory can be drawn for each frequency labeled event. These results indicate that in non-degenerate frequency schemes, the ontology has to be refined and the which path criterion must be precisely stated. If reference is made to the frequency labeled photons, the path of each photon is known, whereas if the query is stated in terms of the detected photons, the path is unknown.