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arXiv:2211.07992 · Quantum Science and Technology

Lossy SU(1,1) interferometers in the single-photon-pair regime

Matteo Santandrea, Kai-Hong Luo, Michael Stefszky, Jan Sperling, Harald Herrmann, Benjamin Brecht, Christine Silberhorn

Published Mar 7, 2023• 12 citations
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Abstract

Abstract The success of quantum technologies is intimately connected to the possibility of using them in real-world applications. This requires the system to be comprehensively modeled including various relevant experimental parameters. To this aim, in this paper, we study the performance of lossy SU(1,1) interferometers in the single-photon pair regime, posing particular attention to the different amount of information contained in the measurement of single counts and of coincidences at the output of the interferometer. To this aim, we derive the classical Fisher information (FI) of both single and coincidence events, and study it as a function of the internal and external losses of the system. Our analysis shows that, in the absence of external losses, the FI of the coincidence events is always higher or equal than the one of single events. On the other hand, in the presence of external losses, the FI of the singles can increase above the one of the coincidences. Moreover, our analysis shows that coincidence measurement can be exploited to partially mitigate the effect of internal losses in the absence of external losses. Finally, comparing SU(1,1) and classical SU(2) interferometers, we find that the former can outperform the classical systems when the internal losses are above 50%.

DOI
10.1088/2058-9565/acc205

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Abstract The success of quantum technologies is intimately connected to the possibility of using them in real-world applications. This requires the system to be comprehensively modeled including various relevant experimental parameters. To this aim, in this paper, we study the performance of lossy SU(1,1) interferometers in the single-photon pair regime, posing particular attention to the different amount of information contained in the measurement of single counts and of coincidences at the output of the interferometer. To this aim, we derive the classical Fisher information (FI) of both single and coincidence events, and study it as a function of the internal and external losses of the system. Our analysis shows that, in the absence of external losses, the FI of the coincidence events is always higher or equal than the one of single events. On the other hand, in the presence of external losses, the FI of the singles can increase above the one of the coincidences. Moreover, our analysis shows that coincidence measurement can be exploited to partially mitigate the effect of internal losses in the absence of external losses. Finally, comparing SU(1,1) and classical SU(2) interferometers, we find that the former can outperform the classical systems when the internal losses are above 50%.
The standard quantum limit (SQL) describes the best precision that can be achieved for phase measurements using a classical interferometer. For such an interferometer, this limit is given by1/N1/\sqrt{N}1/N​whereNNNis the total number of photons launched into the interferometer. The SQL can be circumvented through the utilisation of quantum states combined with advanced low-loss detection schemes. Such overcoming of the SQL has been demonstrated, for example, by replacing the unused vacuum input port of the linear interferometer with a non-classical state [1], and by exploiting nonlinear SU (1,1) interferometers in the high-gain regime [2]. However, the impact of the experimental losses on the ability of nonlinear interferometers to beat the SQL is often neglected, particularly in the low-gain regime. In this work, we close this gap by studying the performance of lossy SU (1,1) interferometers in the single-photon pair regime, with particular attention to the different amount of information contained in the measurement of single counts and of coincidences at the output of the 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.
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.
High-precision laser interferometers are commonly used to search for signatures of random spacetime fluctuations, in an attempt to understand the fundamental nature of gravity. Conventionally, SU(2)SU(2)SU(2) interferometers have been used in such experimental investigations. Motivated by [K. Zheng \textit{et al.}, Photon. Res. \textbf{8}, 1653 (2020)], I assess if there is any advantage to be gained by using an SU(1,1)SU(1,1)SU(1,1) interferometer instead of the SU(2)SU(2)SU(2) interferometer. To this end, I compute the quantum Fisher information for estimating the strength and the correlation length of the spacetime fluctuations, and the corresponding classical Fisher information considering different experimentally relevant measurement schemes, in both types of interferometers. I compare the information metrics corresponding to different parameter regimes that are relevant to both current and possible future experimental setups. This helps me assess if and when the SU(1,1)SU(1,1)SU(1,1) interferometer offers any advantage over the SU(2)SU(2)SU(2) interferometer for estimating either the fluctuation strength or correlation length of the spacetime fluctuations.
We provide a general theoretical derivation of the phase sensitivity achieved by SU(1,1) interferometers under homodyne detection. The general expressions obtained accommodate arbitrary input states and include internal and external losses. In this systematic review, both full SU(1,1) interferometers with two parametric amplifiers and the truncated interferometers with only one parametric amplifier are examined. We investigate scenarios involving both single-output ports and joint homodyne detection, and consider parametric amplifiers with equal gains or with a boosted gain second amplifier. Our analytical formulation provides physical insight and understanding of the improvements in the sensitivity, which are shown to originate from noise reduction and/or signal amplification, depending on the configurations and practical implementations. Surprisingly, the configuration with single-output mode detection and parametric amplifiers with equal gains exhibits the highest robustness to very high internal losses. We finally apply this framework to a ubiquitous ∣α,0⟩|α,0\rangle∣α,0⟩ input two-mode coherent probe state. This approach permits the comparison of different strategies and the optimization of the interferometer performance in the presence of losses. In particular, we determine which amplification and detection configurations provide the best performance, depending on the level of losses. This exemplifies how this general analytical approach provides a powerful tool to design quantum-enhanced interferometers and achieve optimal sensitivity with selected probe states and homodyne detection.