We propose a method to enhance the phase sensitivity of a Mach-Zehnder interferometer, independent of its input states. This is achieved by applying squeezing sequences to one arm of the interferometer. By alternating between squeezing along orthogonal quadratures, we demonstrate that the phase sensitivity of a Mach-Zehnder interferometer can be generically enhanced. Since this enhancement is independent of the input states, the proposed dynamic squeezing method allows for further improvement in phase sensitivity when combined with non-classical input states. We compare the dynamic squeezing approach with existing quantum sensing protocols and show that super-Heisenberg scaling can be achieved. Finally, we demonstrate that the scheme is robust against moderate photon loss.
We propose a method to enhance the phase sensitivity of a Mach-Zehnder interferometer, independent of its input states. This is achieved by applying squeezing sequences to one arm of the interferometer. By alternating between squeezing along orthogonal quadratures, we demonstrate that the phase sensitivity of a Mach-Zehnder interferometer can be generically enhanced. Since this enhancement is independent of the input states, the proposed dynamic squeezing method allows for further improvement in phase sensitivity when combined with non-classical input states. We compare the dynamic squeezing approach with existing quantum sensing protocols and show that super-Heisenberg scaling can be achieved. Finally, we demonstrate that the scheme is robust against moderate photon loss.
ABSTRACT Photon addition operations applied to squeezed states have been shown to significantly enhance phase sensitivity. In this work, we extend this approach by applying photon addition not only to coherent states but also within a Mach–Zehnder interferometer, using coherent and squeezed vacuum states as input. Both intensity‐difference and homodyne detection are used to evaluate photon addition schemes, and their phase sensitivities are compared under ideal and lossy conditions. We also analyze the quantum Fisher information of these two schemes. Results show that both schemes improve phase sensitivity, quantum Fisher information, and robustness against losses. In particular, photon addition within the interferometer performs better. Homodyne detection outperforms intensity difference detection under photon losses. Notably, the two schemes exhibit distinct parameter dependencies, rendering them suitable for different operational scenarios. When the squeezing parameter is small, photon addition employed at the coherent input with intensity difference detection can approach the Heisenberg limit in ideal conditions and can exceed the standard quantum limit in high‐loss conditions. The proposed scheme represents a valuable method for quantum precision measurements. PACS : 03.67.‐a, 05.30.‐d, 42.50,Dv, 03.65.Wj
Abstract A scheme is proposed based on a Mach–Zehnder interferometer with high phase sensitivity, utilizing a two-mode squeezed coherent state, generated by four-wave mixing, as input. The phase sensitivity of this scheme easily surpasses the Heisenberg limit when intensity difference detection is applied. Under phase-matching conditions, the quantum Cramér–Rao bound significantly exceeds the Heisenberg limit. Additionally, the scheme exhibits robustness against photon loss. When compared with the modified SU(1,1) interferometer with two coherent state inputs, this approach demonstrates superior measurement sensitivity, evaluated through various detection methods and the quantum Cramér–Rao bound. This work holds potential applications in quantum metrology.
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.
Abstract We propose a photon subtraction scheme within the Mach–Zehnder interferometer using a coherent state and a squeezed vacuum state as inputs. By systematically comparing intensity detection and homodyne detection methods, we demonstrate that strategically applied photon subtraction ( a -mode subtraction) significantly enhances the phase sensitivity of all detection methods. Under this configuration, homodyne detection achieves superior phase sensitivity and loss robustness compared to intensity detection. Remarkably, under 30% photon loss, the system surpasses the Heisenberg limit, enabled by the synergy among the squeezed vacuum state, non-Gaussian operations, and detection optimization. Furthermore, we quantify performance through the quantum Fisher information and the quantum Cramér-Rao bound analyses under both ideal and lossy conditions.
Based on the conventional Mach-Zehnder interferometer, we propose a metrological scheme to improve phase sensitivity. In this scheme, we use a coherent state and a squeezed vacuum state as input states, employ multi-photon-subtraction operations and make intensity-detection or homodyne-detection. We study phase sensitivity, quantum Fisher information and quantum Cramér-Rao bound under both ideal and lossy conditions. The results indicate that choosing an appropriate detection method and photon subtraction scheme can significantly enhance the phase sensitivity and robustness against photon losses. Even under lossy conditions, the multi-photon subtraction schemes can surpass the standard quantum limit. Notably, the homodyne detection method can even break through the Heisenberg limit. Moreover, increasing the number of photon-subtracted can enhance both phase sensitivity and quantum Fisher information. This research highlights the significant value of this scheme in quantum precision measurement.
Abstract A novel scheme for the enhancement of phase sensitivity based on a Mach–Zehnder interferometer (MZI) and intensity detection is proposed. With the input of bright entangled twin beams from four wave mixing (FWM), the phase sensitivity can beat shot noise limit (SNL) and approach Heisenberg limit. This scheme is special due to that only one of bright entangled twin beams enters into the MZI and the other one is employed for measurement. In addition, by altering the parametric strength of FWM and the implementation of maximum quantum squeezing, the optimal phase sensitivity can reach sub-SNL. Optical intensity depletion of photon detectors and internal intensity depletion of the MZI are also discussed. The scheme displays that by employing external resources, while one input of the MZI is an vacuum beam, the phase sensitivity still can beat SNL.