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Journal of the Optical Society of America B

Super-resolution and super-sensitivity of quantum LiDAR with a multi-photonic state and binary outcome photon counting measurement

Priyanka Sharma, Manoj Kumar Mishra, Devendra Kumar Mishra

Published Apr 29, 2024• 8 citations
Publisher

Abstract

Here, we are investigating the enhancement in resolution and phase sensitivity of a Mach-Zehnder interferometer (MZI) based quantum LiDAR. We are using a multi-photonic state (MPS), superposition of four coherent states [ Int. J. Quantum Inf. 19 , 2150013 ( 2021 ) 0219-7499 10.1142/S0219749921500131 ], as the input state and binary outcome parity photon counting measurement and binary outcome zero non-zero photon counting measurement as the measurement schemes. We have thoroughly investigated the results in lossless as well as lossy cases. We found enhancement in resolution and phase sensitivity in comparison to the coherent state and even coherent superposition state (ECSS) based quantum LiDAR. Our analysis shows that MPS may be an alternative nonclassical resource in the field of quantum imaging and quantum sensing technologies, like in quantum LiDAR.

DOI
10.1364/josab.507405

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Here, we are investigating the enhancement in resolution and phase sensitivity of a Mach-Zehnder interferometer (MZI) based quantum LiDAR. We are using a multi-photonic state (MPS), superposition of four coherent states [ Int. J. Quantum Inf. 19 , 2150013 ( 2021 ) 0219-7499 10.1142/S0219749921500131 ], as the input state and binary outcome parity photon counting measurement and binary outcome zero non-zero photon counting measurement as the measurement schemes. We have thoroughly investigated the results in lossless as well as lossy cases. We found enhancement in resolution and phase sensitivity in comparison to the coherent state and even coherent superposition state (ECSS) based quantum LiDAR. Our analysis shows that MPS may be an alternative nonclassical resource in the field of quantum imaging and quantum sensing technologies, like in quantum LiDAR.
Here we are investigating the enhancement in phase sensitivity and resolution in Mach-Zehnder interferometer (MZI) based quantum LiDAR. We are using multi-photonic state (MPS), superposition of four coherent states [1], as the input state and binary outcome parity photon counting measurement and binary outcome zero-nonzero photon counting measurement as the measurement schemes. We thoroughly investigate the results in lossless as well as in lossy cases. We found enhancement in resolution and phase sensitivity in comparison to the coherent state and even coherent superposition state (ECSS) based quantum LiDAR. Our analysis shows that MPS may be an alternative nonclassical resource in the field of quantum imaging and quantum sensing technologies, like in quantum LiDAR.
We investigate the performance of the super-resolving quantum lidar with the entangled coherent states of light in the presence of loss and noise, especially in the noisy case. An exact analytical expression of the output signal has been derived with the binary-outcome photon counting measurements. Numerical results show that the resolution of our scheme with parity detection is √N (N) times enhanced relative to that of the coherent-state strategy with the same (intensity) detection in the lossless and noiseless cases. The influences of phase diffusion on resolution and sensitivity have been analyzed and discussed. It is found that the super-resolution emerges in the whole diffusion rate regions, whereas the super-sensitivity just exists in the high and low diffusion rate regimes. Comparisons are made with the well known N00N states, the results show that the entangled coherent states performs better resolution and sensitivity than those of the N00N scheme in the whole diffusion regimes. In addition, the effects of photon loss on resolution and sensitivity have also been studied. The phase sensitivity can beat the shot noise limit and the resolution is much better than the Rayleigh diffraction limit in the whole loss regions. Finally, the zero-nonzero photon counting measurement gives much worse sensitivity than that of the parity detection, which is just opposite from the case as demonstrated in a recent coherent-light Mach-Zehnder experiment.
Introducing a novel Z4nZ_{4n}Z4n​-detection scheme to enhance the performance of quantum LiDAR systems
In a quantum LiDAR system, to achieve a better resolution and sensitivity, detection scheme plays an important role. We propose a novel detection scheme in which the photo detector considers only the 4n4n4n number of photons, where n∈Nn \in \mathbb{N}n∈N, as a click and the rest of them as a no-click. Similar to the ZZZ-detection scheme, where we get a click for any number of photons, we termed this measurement as Z4nZ_{4n}Z4n​-detection scheme. By employing superposition of four coherent states (SFCS) and vacuum as input we investigate the performance of Mach-Zehnder interferometer (MZI) based quantum LiDAR systems. We found a significant enhancement in resolution and broader working point for the phase sensitivity in comparison to the ZZZ-detection scheme. Our findings highlight the advantages of our approach and suggest promising advancements in the field of quantum LiDAR sensing technology, providing a pathway for more accurate and sensitive measurement capabilities.
We study the phase super–sensitivity of a Mach–Zehnder interferometer (MZI) with the squeezed Kerr state (SKS) and coherent state as the inputs. We discuss the lower bound in phase sensitivity by considering the quantum Fisher information and the corresponding quantum Cramér–Rao bound. With the help of single intensity detection, intensity difference detection, and homodyne detection schemes, we find that our scheme gives a better sensitivity under both lossless and lossy conditions as compared to the well–known results of the combinations of inputs, such as coherent plus vacuum, coherent plus squeezed vacuum, and double coherent states. Because of the possibility of the generation of SKS with the present available quantum optical techniques, we expect that SKS may be an alternative nonclassical resource for the improvement in the phase super–sensitivity of the MZI in realistic scenarios.
We study the improvement in the phase sensitivity of a Mach–Zehnder interferometer using the superposition of Schrödinger’s cat-like state with the Fock state (SCFS) and the coherent state as inputs. With this setup, we examine the effect on phase sensitivity of the interferometer using a two-channel detection (TCD) scheme [ Opt. Express 29 , 95 ( 2021 ) OPEXFF 1094-4087 10.1364/OE.413391 ] in which we take the optimal combination of the intensities of both output ports. We find better phase sensitivity under some conditions for this setup as compared to other known combinations of inputs such as squeezed vacuum and coherent states, vacuum and coherent states, etc. Therefore, we expect that the SCFS may be an alternative nonclassical resource for improvement in the phase sensitivity of a Mach–Zehnder interferometer, having potential application in quantum sensing.
For the precision-based measurements, Mach-Zehnder interferometry is a widely used technique. There are various ways to enhance the precision of Mach-Zehnder interferometer (MZI), e.g., having a non-classical input state is one of the ways to enhance the precision of the phase estimation performed by MZI. The phase estimation performed by MZI is investigated here by considering that the input states of MZI are different combinations of photon added and subtracted squeezed coherent states (PASCS and PSSCS). Using quantum Fisher information, it is shown that the use of PASCS in both the input modes of MZI, provides the most precise estimate of the unknown phase. This system is also analyzed in two different measurement scenarios -- single intensity detection (SID) and intensity difference detection (IDD). Systematic analysis has established that the intensity measurement might not be an optimal measurement scheme for phase estimation in MZI as phase and intensity correspond to non-commuting observables. The impact of the photon loss on the MZI-based phase estimation setup is also studied and it is found that PASCS is robust against photon loss, when the loss in MZI is low.