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CRC Press eBooks

Two-Photon Interferometry II: Two-Photon Interference of Thermal Field

Yanhua H. Shih

Published Dec 16, 2020• 0 citations
Publisher

Abstract

The study of entangled states greatly advanced our understanding about two-photon interferometry. Two-photon interference is not the interference between two photons, it is about a pair of photons interfering with the pair itself. In the language of quantum theory, two-photon interference is the result of superposition between different yet indistinguishable two-photon probability amplitudes. Under certain conditions, the observed second-order interference can be factorized into a product of two individual classic first-order interferences. In this case, the interference is not only observable from the intensity fluctuation correlation measurement, or from the photon number fluctuation correlation measurement, of two photodetectors, but also observable in the counting rate of each individual photodetector. It may not be uneasy to accept the quantum concept of two-photon interference for “classical” thermal radiation. Indeed, the radiation Planck dealt with was “classical” thermal light. Perhaps, no one would even expect observing nontrivial second-order correlation from a laser beam, since laser field is non-Gaussin.

DOI
10.1201/9781003130604-11

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The study of entangled states greatly advanced our understanding about two-photon interferometry. Two-photon interference is not the interference between two photons, it is about a pair of photons interfering with the pair itself. In the language of quantum theory, two-photon interference is the result of superposition between different yet indistinguishable two-photon probability amplitudes. Under certain conditions, the observed second-order interference can be factorized into a product of two individual classic first-order interferences. In this case, the interference is not only observable from the intensity fluctuation correlation measurement, or from the photon number fluctuation correlation measurement, of two photodetectors, but also observable in the counting rate of each individual photodetector. It may not be uneasy to accept the quantum concept of two-photon interference for “classical” thermal radiation. Indeed, the radiation Planck dealt with was “classical” thermal light. Perhaps, no one would even expect observing nontrivial second-order correlation from a laser beam, since laser field is non-Gaussin.
The study of entangled states has greatly improved the basic understanding about two-photon interferometry. Two-photon interference is not the interference of two photons but the result of superposition among indistinguishable two-photon amplitudes. The concept of two-photon amplitude, however, has generally been restricted to the case of entangled photons. In this letter we report an experimental study that may extend this concept to the general case of independent photons. The experiment also shows interesting practical applications regarding the possibility of obtaining high-resolution interference patterns with thermal sources.
We report the observation of a counterintuitive phenomenon in multipath correlation interferometry with thermal light. The intensity correlation between the outputs of two unbalanced Mach-Zehnder interfer- ometers (UMZIs) with two classically correlated beams of thermal light at the input exhibits genuine second-order interference with the visibility of 1=3. Surprisingly, the second-order interference does not degrade at all no matter how much the path length difference in each UMZI is increased beyond the coherence length of the thermal light. Moreover, the second-order interference is dependent on the difference of the UMZI phases. These results differ substantially from those of the entangled-photon Franson interferometer, which exhibits two-photon interference dependent on the sum of the UMZI phases and the interference vanishes as the path length difference in each UMZI exceeds the coherence length of the pump laser. Our work offers deeper insight into the interplay between interference and coherence in multiphoton interferometry.
Two-photon interferometry started to play an important role in quantum optics since 1980’s. In that time, Dirac was criticized to be mistaken because he stated in his book, The Principles of Quantum Mechanics , that “photon only interferes with itself. Interference between two different photons never occurs”. Two-photon interference was considered as the interference between two photons. In fact, neither classical theory nor quantum theory suggested the interference between different photons. Classical theory views optical interference the result of coherent superposition between electromagnetic waves. The two-photon interference picture provided reasonable interpretation to that observation too: under the condition of complete overlapping, when the two biphoton amplitudes superpose in phase the joint-detection of the two distant photodetectors reaches its maximum counting rate as the sign of “correlation”. When the optical path difference is increased from zero to unbalanced values, a coincidence curve of “dip” is observed.
We report observation of a counter-intuitive phenomenon in multi-path correlation interferometry with thermal light. The intensity correlation between the outputs of two unbalanced Mach-Zehnder interferometers (UMZI) with two classically correlated beams of thermal light at the input exhibits genuine second-order interference with the visibility of 1/3. Surprisingly, the second-order inter- ference does not degrade at all no matter how much the path length difference in each UMZI is increased beyond the coherence length of the thermal light. Moreover, the second-order interference is dependent on the difference of the UMZI phases. These results differ substantially from those of the entangled-photon Franson interferometer which exhibits two-photon interference dependent on the sum of the UMZI phases and the interference vanishes as the path length difference in each UMZI exceeds the coherence length of the pump laser. Our work offers deeper insight into the interplay between interference and coherence in multi-photon interferometry.
We report observation of a counter-intuitive phenomenon in multi-path correlation interferometry with thermal light. The intensity correlation between the outputs of two unbalanced Mach-Zehnder interferometers (UMZI) with two classically correlated beams of thermal light at the input exhibits genuine second-order interference with the visibility of 1/3. Surprisingly, the second-order interference does not degrade at all no matter how much the path length difference in each UMZI is increased beyond the coherence length of the thermal light. Moreover, the second-order interference is dependent on the difference of the UMZI phases. These results differ substantially from those of the entangled-photon Franson interferometer which exhibits two-photon interference dependent on the sum of the UMZI phases and the interference vanishes as the path length difference in each UMZI exceeds the coherence length of the pump laser. Our work offers deeper insight into the interplay between interference and coherence in multi-photon interferometry.
We report the observation of a counterintuitive phenomenon in multipath correlation interferometry with thermal light. The intensity correlation between the outputs of two unbalanced Mach-Zehnder interferometers (UMZIs) with two classically correlated beams of thermal light at the input exhibits genuine second-order interference with the visibility of 1/3. Surprisingly, the second-order interference does not degrade at all no matter how much the path length difference in each UMZI is increased beyond the coherence length of the thermal light. Moreover, the second-order interference is dependent on the difference of the UMZI phases. These results differ substantially from those of the entangled-photon Franson interferometer, which exhibits two-photon interference dependent on the sum of the UMZI phases and the interference vanishes as the path length difference in each UMZI exceeds the coherence length of the pump laser. Our work offers deeper insight into the interplay between interference and coherence in multiphoton interferometry.