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Optics Express

Improving the phase sensitivity of an SU(1,1) interferometer with photon-added squeezed vacuum light

Lili Guo, Ya‐Fei Yu, Zhi‐Ming Zhang

Published Oct 24, 2018• 46 citations
Publisher

Abstract

We study the phase sensitivity of an SU(1,1) interferometer from two aspects, i.e., the phase estimation determined by the error propagation formula and that by the quantum Cramér-Rao bound (QCRB). The results show that the phase sensitivity by using the intensity detection reaches the sub-shot-noise limit with a coherent state and an m-photon-added squeezed vacuum state (m-PA-SVS) as inputs. The phase sensitivity gradually approaches the Heisenberg limit for increasing m, and the ultimate phase precision improves with the increase of m. In addition, the QCRB can be saturated by the intensity detection with inputting the m-PA-SVS.

DOI
10.1364/oe.26.029099

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We study the phase sensitivity of an SU(1,1) interferometer from two aspects, i.e., the phase estimation determined by the error propagation formula and that by the quantum Cramér-Rao bound (QCRB). The results show that the phase sensitivity by using the intensity detection reaches the sub-shot-noise limit with a coherent state and an m-photon-added squeezed vacuum state (m-PA-SVS) as inputs. The phase sensitivity gradually approaches the Heisenberg limit for increasing m, and the ultimate phase precision improves with the increase of m. In addition, the QCRB can be saturated by the intensity detection with inputting the m-PA-SVS.
We investigate phase estimation in an SU(1,1) interferometer employing mmm-photon-added even and odd coherent states as nonclassical input resources. The phase sensitivity is evaluated through intensity detection and the error propagation method, while the ultimate precision limit is determined from the quantum Cramér-Rao bound with the quantum Fisher information serving as the relevant metrological quantity. Our results demonstrate that photon addition significantly enhances the phase sensitivity, increases the quantum Fisher information, and reduces the quantum Cramér-Rao bound, leading to a clear improvement over the corresponding even and odd coherent states. Furthermore, the achievable sensitivity exceeds the standard quantum limit and gradually approaches the Heisenberg scaling with increasing photon-addition number. We also find that the mmm-photon-added even coherent states exhibit a modest advantage over their odd counterparts. As mmm increases, however, this distinction becomes progressively weaker, suggesting that photon addition diminishes the role of the initial parity of the coherent state in determining the interferometric performance.
We theoretically study the phase estimation based on a Mach-Zehnder interferometer (MZI) with a two-mode squeezed coherent state. By maximizing the quantum Fisher information, we find that the quantum Cramér-Rao bounds (QCRB) can reach sub-Heisenberg limit under the phase-matched condition. The optimal phase sensitivity can reach the sub-shot noise limit (SNL) and approach the QCRB by employing the intensity difference detection. Meanwhile, compared with the MZI fed with a coherent plus a single-mode squeezed vacuum state, this scheme can have better performance by adjusting the squeezing parameter and the mean photon number. With the same parameter, our scheme shows more sensitive phase measurement than the SU(1,1) interferometer with a coherent plus a vacuum state. We also show that the phase sensitivity of our proposal can still reach the SNL when the loss of the photon is 36%. This scheme can provide potential applications in optical sensors.
ABSTRACT We enhance phase sensitivity in an SU(1,1) interferometer by combining a Kerr nonlinear phase shifter with multi‐photon addition. Using coherent and vacuum states as inputs, we analyze phase sensitivity and the quantum Fisher information under ideal and lossy conditions. We show that both phase sensitivity and the quantum Cramér‐Rao bound (QCRB) improve gradually as the total mean photon number increases. For the standard SU(1,1) interferometer, phase sensitivity does not saturate the QCRB, even with multi‐photon addition. In contrast, for the Kerr‐based SU(1,1) interferometer, phase sensitivity nearly saturates the QCRB under ideal conditions and remains optimal at high transmissivity under loss. The Kerr‐based scheme surpasses the standard quantum limit, approaches the sub‐Heisenberg limit, and exhibits enhanced robustness against moderate losses. Our scheme is feasible with current technology and provides a promising route for high‐precision quantum metrology.
We theoretically present the quantum Cramér-Rao bounds (QCRB) of an SU(1,1) interferometer for Gaussian states input with and without the internal photonic losses. The phase shifts in the single arm and in the double arms are studied and the corresponding analytical expressions of quantum Fisher information with Gaussian input states are presented. Different from the traditional Mach-Zehnder interferometer, the QCRB of single arm case is slightly higher or lower than that of double arms case depending on the input states. With a fixed mean photon number and for pure Gaussian state input, the optimal sensitivity is achieved with a squeezed vacuum input in one mode and the vacuum input in the other. We compare the QCRB with the standard quantum limit and Heisenberg limit. In the case of small internal losses the QCRB can beat the standard quantum limit.
In the field of quantum precision measurement, enhancing phase sensitivity is crucial for various applications, including quantum metrology and quantum sensing technologies. We theoretically investigate the improvement in phase sensitivity and quantum Fisher information achieved through multiphoton subtraction operations at the output port of an SU(1,1) interferometer under conditions of photon loss. We use vacuum and coherent states as the inputs and detect the outputs by intensity detection. The results indicate that internal photon losses within the SU(1,1) interferometer have a more significant impact on the phase sensitivity compared to external photon losses. Moreover, increasing the number of photon subtractions m effectively enhances both the phase sensitivity and the quantum Fisher information. Notably, even under conditions of severe photon loss, the multiphoton subtraction operations can enable the phase sensitivity to surpass the standard quantum limit, approaching both the Heisenberg limit and the quantum Cramér-Rao bound. This study provides a new theoretical basis for enhancing the phase sensitivity in the SU(1,1) interferometer.
In the field of quantum precision measurement, enhancing phase sensitivity is crucial for various applications, including quantum metrology and quantum sensing technologies. We theoretically investigate the improvement in phase sensitivity and quantum Fisher information achieved through multiphoton subtraction operations at the output port of an SU(1,1) interferometer under conditions of photon loss. We use vacuum and coherent states as the inputs and detect the outputs by intensity detection. The results indicate that internal photon losses within the SU(1,1) interferometer have a more significant impact on the phase sensitivity compared to external photon losses. Moreover, increasing the number of photon subtractions m effectively enhances both the phase sensitivity and the quantum Fisher information. Notably, even under conditions of severe photon loss, the multiphoton subtraction operations can enable the phase sensitivity to surpass the standard quantum limit, approaching both the Heisenberg limit and the quantum Cramér-Rao bound. This study provides a new theoretical basis for enhancing the phase sensitivity in the SU(1,1) interferometer.