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A quantum mechanical analysis of the coherence de Broglie wavelength for superresolution and enhanced sensitivity in a coupled interferometer scheme

Byoung Seung HAM

Published Apr 13, 2026• 0 citations
Publisher

Abstract

Abstract Quantum sensing has drawn considerable attention as a means to overcome the fundamental limitations in classical sensing. In practice, however, quantum sensing has been strongly constrained by the photon loss, the achievable photon number N in N00N states, and by a finite squeezing level in squeezed states. These limitations are particularly critical to photon-loss-sensitive applications such as LiDAR as well as to general sensing platforms that require large effective N, such as ring-laser gyroscopes. Recently, fundamentally different sensing platforms have been reported to overcome both classical and quantum constraints in a practical regime. One such approach exploits the coherence de Broglie wavelength (CBW) realized in an anti-symmetrically coupled Mach-Zehnder interferometer (MZI) architecture. Here, a pure quantum mechanical analysis of the CBW is presented for a loss-free sensing mechanism of superresolution with enhanced sensitivity. A proof-of-principle demonstration of CBW is also presented.

DOI
10.21203/rs.3.rs-9215675/v1

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Abstract Quantum sensing has drawn considerable attention as a means to overcome the fundamental limitations in classical sensing. In practice, however, quantum sensing has been strongly constrained by the photon loss, the achievable photon number N in N00N states, and by a finite squeezing level in squeezed states. These limitations are particularly critical to photon-loss-sensitive applications such as LiDAR as well as to general sensing platforms that require large effective N, such as ring-laser gyroscopes. Recently, fundamentally different sensing platforms have been reported to overcome both classical and quantum constraints in a practical regime. One such approach exploits the coherence de Broglie wavelength (CBW) realized in an anti-symmetrically coupled Mach-Zehnder interferometer (MZI) architecture. Here, a pure quantum mechanical analysis of the CBW is presented for a loss-free sensing mechanism of superresolution with enhanced sensitivity. A proof-of-principle demonstration of CBW is also presented.
A quantum wavemetry scheme based on the coherence de Broglie wavelength (CBW) is proposed using an M coupled Mach Zehnder interferometer (MZI) architecture to achieve superresolution sensing and metrology. Although CBW does not attain the Heisenberg limit, it circumvents the key practical limitations of N00N state based quantum sensing, including restricted photon number N, reduced fringe visibility, and strong susceptibility to photon loss. The CBW approach enables loss tolerant operation with arbitrarily large M, while maintaining near unity fringe visibility. Fully compatible with coherence optics, the CBW scheme can be directly integrated into conventional wavemetry systems, providing both superresolution and enhanced sensitivity. A proof of principle experiment demonstrating CBW based superresolution is implemented using a Sagnac integrated round trip MZI structure for M=2, validating the feasibility of the proposed quantum wavemetry design.
Quantum sensing exploits nonclassical states of light, including multiphoton entangled states and squeezed states, to achieve superresolution and/or super-sensitivity. However, its practical implementation is constrained by state-generation complexity, photon loss, and detection efficiency. Here, we present a quantum-operator analysis of coherence de Broglie wavelength (CBW) in an anti-symmetrically coupled Mach-Zehnder interferometer (MZI) architecture and clarify the origin of its superresolution and enhanced phase sensitivity. The two-mode SU(2) structure of the MZI, represented by Pauli operators, shows that successive basis-realigned transformations produce an Nth-order unitary U^N(phi), yielding N-fold phase accumulation (1+cosNphi). The quantum-operator description is particularly significant at the single-photon level, where even a single photon undergoes the Nth-order unitary evolution through its coherent evolution in the two-mode state space. This differs from entanglement-based quantum sensing based on photonic de Broglie wavelength interferometry, where N-fold phase accumulation is associated with an N-photon entangled state. The same SU(2) transformation also applies to coherent classical fields, establishing a classical-quantum correspondence of the CBW phase evolution. Fisher-information analysis further shows that the architecture-induced phase transformation yields an order-dependent enhancement of phase sensitivity without increasing the photon number or statistical sampling. CBW therefore provides an architecture-controlled route to high-order interferometric superresolution, accompanied by enhanced phase sensitivity, with potential applications to fringe-counting wavemetry and Fourier-transform-based sensing.
Quantum sensing and metrology have been extensively investigated over the past several decades to surpass the classical shot noise limit and approach the Heisenberg limit. The hallmark of N00N state based quantum sensing is superresolution, characterized by the interference fringe pattern (1+cosNphi). However, practical implementations are severely constrained by the achievable photon number N, reduced fringe visibility, and vulnerability to photon loss. Recently, several coherence-based approaches without using N00N states have been explored as alternative routes to superresolution. Among them, the coherence de Broglie wavelength (CBW) approach is fully compatible with coherence optics. Here, we experimentally demonstrate CBW based superresolution up to N=3. In contrast to N00N state based schemes, the observed CBW fringes exhibit near unity visibility that is essentially independent of N and remain robust against photon loss. Although CBW does not attain the Heisenberg limited phase sensitivity, its phase sensitivity exhibits an N fold enhancement over conventional classical interferometric approaches. These results suggest that CBW provides a practical and scalable platform for superresolution based sensing and metrology.
Abstract Quantum sensing and metrology have been intensively studied over the last several decades to surpass the fundamental shot-noise limit of classical systems and approach the Heisenberg limit. However, implementation of N00N-state-based quantum sensing has been severely constrained by the limited order N , intrinsically imperfect fringe visibility, and vulnerability to photon loss. Recently, the coherence de Broglie wavelength (CBW) has been proposed as an alternative method for achieving superresolution in a coherently coupled interferometer architecture, whose characteristics resemble those of the photonic de Broglie wavelength (PBW) used in quantum sensing. Here, we experimentally demonstrate scalable CBW superresolution up to N =3, with near-perfect fringe visibility that is invariant to photon loss. The observed CBWs have the potential to enable a superresolution sensing platform even if it remains within the shot-noise limit.
Quantum Sensors like Quantum Radar and Lidar based on the interference of non-classical states can achieve super-sensitivity beyond the Standard Quantum Limit (SQL). But as the photons transporting in atmosphere, the environmental interaction causes quantum de-coherence and results in the reduction of super-sensitivity range of the quantum sensors. The most significant effect of atmospheric transmission is photon loss along with phase fluctuation. In this letter, we introduce both the photon loss and phase fluctuation by adding a fictitious beam splitter in the signal arm of Mach- Zehnder interferometer (MZI). The density matrix with N00N and M&M' entangled states being the input states under the condition of photon loss and phase fluctuation is given respectively. Then as the optimal detection schemes parity operator is used as the detector and the formula of the sensitivity is derived. The super-sensitivity range of M&M’ and N00N states with de-coherence are simulated. As a consequence, with high photon loss M&M’ states shows the better phase sensitivity than N00N states but the N00N state is better when the loss is smaller than 20%. And with pure phase fluctuations N00N states get the longer range. M&M’ states is sensitive to the transmittance difference between two arms of the interferometer.
Superresolution is a unique quantum feature generated by N00N states or phase-controlled coherent photons via projection measurements in a Mach-Zehnder interferometer (MZI). Superresolution has no direct relation with supersensitivity in quantum sensing and has a potential application for the precision measurement of an unknown signal frequency. Recently, phase-controlled quantum erasers have been demonstrated for superresolution using classical light of a continuous-wave laser to overcome the diffraction limit in classical physics and to solve the limited scalability in N00N state-based quantum sensing. Here, a quantum spectrometer is presented for the macroscopic superresolution using phase-controlled spatial light modulators (SLMs) in MZI. For validity, a general solution of the superresolution is derived from the SLM-based projection measurements and an unprecedented resolution is numerically confirmed for an unknown frequency of light.