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Reducing of the Uncertainty Product of Coherent Light through Multi-Photon Interference

Joachim Stohr, S. Kim, Fabıan Rotermund, Byoung Seung HAM

Published Apr 1, 2024• 2 citations
Publisher

Abstract

We demonstrate theoretically and experimentally how the diffraction and interferometric resolution limit for single-mode coherent cw laser light can be overcome by multi-photon interference. By use of a Mach-Zehnder interferometer, operated in the single input and single or double output port geometries, we observe a fringe width reduction of the conventional interference pattern, predicted by the wave or single photon quantum theory, by a factor of up to $1/\sqrt{2N}$ through coincident detection of N=2,3,4 photons. Our scheme does not require squeezed or entangled light to overcome the standard quantum limit and greatly facilitates precision interferometry experiments.

DOI
10.1364/opticaopen.25513612.v1

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We demonstrate theoretically and experimentally how the diffraction and interferometric resolution limit for single-mode coherent cw laser light can be overcome by multi-photon interference. By use of a Mach-Zehnder interferometer, operated in the single input and single or double output port geometries, we observe a fringe width reduction of the conventional interference pattern, predicted by the wave or single photon quantum theory, by a factor of up to 1/2N1/\sqrt{2N}1/2N​ through coincident detection of N=2,3,4 photons. Our scheme does not require squeezed or entangled light to overcome the standard quantum limit and greatly facilitates precision interferometry experiments.
We demonstrate theoretically and experimentally how the diffraction and interferometric resolution limit for single-mode coherent cw laser light can be overcome by multi-photon interference. By use of a Mach-Zehnder interferometer, operated in the single input and single or double output port geometries, we observe a fringe width reduction of the conventional interference pattern, predicted by the wave or single photon quantum theory, by a factor of up to 1/2N1/\sqrt{2N}1/2N​ through coincident detection of N=2,3,4 photons. Our scheme does not require squeezed or entangled light to overcome the standard quantum limit and greatly facilitates precision interferometry experiments.
We demonstrate theoretically and experimentally how the diffraction and interferometric resolution limit for single-mode coherent cw laser light can be overcome by multi-photon interference. By use of a Mach-Zehnder interferometer, operated in the single input and single or double output port geometries, we observe a fringe width reduction of the conventional interference pattern, predicted by the wave or single photon quantum theory, by a factor of up to 1/2N1/\sqrt{2N}1/2N​ through coincident detection of N=2,3,4N=2,3,4N=2,3,4 photons. Our scheme does not require squeezed or entangled light to overcome the standard quantum limit and greatly facilitates precision interferometry experiments.
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.
We study a Mach-Zehnder interferometer fed by a coherent state in one input port and vacuum in the other. We explore a Bayesian phase estimation strategy to demonstrate that it is possible to achieve the standard quantum limit independently from the true value of the phase shift and specific assumptions on the noise of the interferometer. We have been able to implement the protocol by using parallel operation of two photon-number-resolving detectors and multiphoton coincidence logic electronics at the output ports of a weakly illuminated Mach-Zehnder interferometer. This protocol is unbiased, saturates the Cramer-Rao phase uncertainty bound, and, therefore, is an optimal phase estimation strategy.
Quantum metrology overcomes standard precision limits by exploiting collective quantum superpositions of physical systems used for sensing, with the prominent example of non-classical multiphoton states improving interferometric techniques. Practical quantum-enhanced interferometry is, however, vulnerable to imperfections such as partial distinguishability of interfering photons. Here we introduce a method where appropriate design of the modal structure of input photons can alleviate deleterious effects caused by another, experimentally inaccessible degree of freedom. This result is accompanied by a laboratory demonstration that a suitable choice of spatial modes combined with position-resolved coincidence detection restores entanglement-enhanced precision in the full operating range of a realistic two-photon Mach-Zehnder interferometer, specifically around a point which otherwise does not even attain the shot-noise limit due to the presence of residual distinguishing information in the spectral degree of freedom. Our method highlights the potential of engineering multimode physical systems in metrologic applications.
A two-photon interference experiment is presented in which an entangled pair of photons generated from a parametric down-conversion was incident on two input ports of a Mach-Zehnder interferometer. The experiment was carried out using two photon coincidence detection with two detectors at the two output ports of the interferometer. The measured coincidence counts exhibit an interference effect with visibility of 0.75 at simultaneous inputs and 0.38 at inputs with different arrival times according to the degree of photon number entanglement.