In this paper, we propose a nonlinear interferometer with feedback loops and explore its efficiency for phase estimation. We analyse two feedback schemes, one where both modes of the interferometer are fed-back into the device and another where only one mode is fed-back. The quantum Fisher information (QFI) for phase estimation in each feedback scheme increases with each feedback loop, and similar to the standard SU(1,1) nonlinear interferometer, phase estimation in this scheme is sensitive to photon loss when the inputs are vacuum state. In terms of resources, we show that, in the low-loss regime, our scheme performs better than standard nonlinear interferometer. The feedback scheme provides the minimum phase variance when the unknown phase is small. We have also provided a special case where feedback scheme provided enhanced QFI even for large phase values. This is achieved by switching between squeezing and anti-squeezing operators after every few loops.
In this paper, we propose a nonlinear interferometer with feedback loops and explore its efficiency for phase estimation. We analyse two feedback schemes, one where both modes of the interferometer are fed-back into the device and another where only one mode is fed-back. The quantum Fisher information (QFI) for phase estimation in each feedback scheme increases with each feedback loop, and similar to the standard SU(1,1) nonlinear interferometer, phase estimation in this scheme is sensitive to photon loss when the inputs are vacuum state. In terms of resources, we show that, in the low-loss regime, our scheme performs better than standard nonlinear interferometer. The feedback scheme provides the minimum phase variance when the unknown phase is small. We have also provided a special case where feedback scheme provided enhanced QFI even for large phase values. This is achieved by switching between squeezing and anti-squeezing operators after every few loops.
Phase estimation has a wide range of applications. Over the years, several strategies have been studied to improve precision in phase estimation. These strategies include using exotic quantum states to quantum detection schemes. This dissertation summarizes my effort in improving the precision of phase estimation with a linear and nonlinear interferometer. Chapter 1 introduces quantum optics and quantum metrology. I introduce all relevant quantum states of light used. We also look into tools and terminologies of quantum metrology such as Fisher information, shot-noise limit, Heisenberg limit, etc., along with examples of phase estimation with a Mach-Zehnder interferometer. In Chapter 2, I discuss multiple phase estimation using a multimode interferometer. Building upon previous work, our scheme consists of a multimode interferometer with single-photon inputs. By using a quantum Fisher information analysis, we show that our scheme gives a constant improvement over other schemes. We also show that our scheme with photon-number-resolving detection approaches the quantum Cram\'er-Rao bound. Moreover, we also consider the probabilistic nature of photon emission at the input, and we study its effect on phase sensitivity. I discuss phase estimation with SU(1,1) interferometer in Chapter 3. We look at phase sensitivity in this interferometer with different input states. Namely, we consider two different phase estimation scheme, one using thermal and squeezed states, and others using coherent and displaced squeezed states with parity and on-off as a detection scheme. We also look into the effect of photon loss inside the interferometer. In Chapter 4, we revisit phase estimation in SU(1,1) interferometer from the perspective of quantum Fisher information. I discuss in detail a longstanding confusion regarding the use of quantum Fisher information in SU(1,1) interferometer. We show that phase averaging or quantum Fisher information matrix method is needed in general for calculating the phase sensitivity which resolves inconsistencies reported in previously published articles.
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.
Compared with passive interferometers, SU(1,1) interferometers demonstrate superior phase sensitivity due to the incorporation of nonlinear elements that enhance their ability to detect phase shifts. Nevertheless, the measurement precision of these interferometers is considerably impacted by photon losses, particularly internal losses, thereby restricting the overall accuracy of measurements. Addressing these issues is essential to fully realize the advantages of SU(1,1) interferometers in practical applications. Among the available resources in quantum metrology, squeezing stands out as one of the most practical and efficient approaches. We propose a theoretical scheme to improve the precision of phase measurement using homodyne detection by implementing the single-path local squeezing operation (LSO) inside the SU(1,1) interferometer, with the coherent state and the vacuum state as the input states. We not only analyze the effects of the single-path LSO scheme on the phase sensitivity and the quantum Fisher information (QFI) under both ideal and photon-loss cases but also compare the impact of different squeezing parameters r on the system performance. Our findings reveal that the internal single-path LSO scheme can significantly enhance the phase sensitivity and QFI by strengthening intramode correlations while weakening intermode correlations, thereby effectively improving the robustness of the SU(1,1) interferometer against photon losses.
Compared to passive interferometers, SU(1,1) interferometers exhibit superior phase sensitivity due to the incorporation of nonlinear elements that enhance their ability to detect phase shifts. However, the precision of these interferometers is significantly affected by photon losses, especially internal losses, which can limit the overall measurement accuracy. Addressing these issues is essential to fully realize the advantages of SU(1,1) interferometers in practical applications. Among the known resources of quantum metrology, one of the most practical and efficient is squeezing. We propose a theoretical scheme to improve the precision of phase measurement using homodyne detection by implementing the single-path local squeezing operation (LSO) inside the SU(1,1) interferometer, with the coherent state and the vacuum state as the input states. We not only analyze the effects of the single-path LSO scheme on the phase sensitivity and the quantum Fisher information (QFI) under both ideal and photon-loss cases but also compare the effects of different squeezing parameters r on the system performance. Our findings reveal that the internal single-path LSO scheme can enhance the phase sensitivity and the QFI, effectively improving the robustness of the SU(1,1) interferometer against internal and external photon losses. Additionally, a larger squeezing parameter r leads to a better performance of the interferometer.
Quantum metrology employs quantum resources to achieve measurement precision beyond classical limits. This work investigates a Mach--Zehnder interferometer incorporating a Kerr nonlinear phase shifter, with photon-added two-mode squeezed coherent states generated via four-wave mixing as input. We demonstrate that increasing both the photon-addition order and the input resource strength systematically enhances phase sensitivity, quantum Fisher information, and the corresponding quantum Cramér--Rao bound. The proposed system not only surpasses the standard quantum limit but also approaches or exceeds the Heisenberg limit for linear phase shifts, while Kerr nonlinearity enables surpassing the super-Heisenberg limit. Furthermore, the scheme exhibits enhanced robustness against photon loss, providing a promising pathway toward practical high-precision quantum metrology applications.
We propose a theoretical scheme to enhance the phase sensitivity by introducing a Kerr nonlinear phase shift into the traditional SU(1,1) interferometer with a coherent state input and homodyne detection. We investigate the realistic effects of photon losses on phase sensitivity and quantum Fisher information. The results show that compared with the linear phase shift in SU(1,1) interferometer, the Kerr nonlinear case can not only enhance the phase sensitivity and quantum Fisher information, but also significantly suppress the photon losses. We also observe that at the same accessible parameters, internal losses have a greater influence on the phase sensitivity than the external ones. It is interesting that, our scheme shows an obvious advantage of low-cost input resources to obtain higher phase sensitivity and larger quantum Fisher information due to the introduction of nonlinear phase element.