Interferometers are widely used as sensors in precision measurement. Compared with a conventional Mach–Zehnder interferometer, the sensitivity of a correlation-enhanced nonlinear interferometer can break the standard quantum limit. Phase sensitivity plays a significant role in the enhanced performance. In this paper, we review improvement in phase estimation technologies in correlation-enhanced nonlinear interferometers, including SU(1,1) interferometer and SU(1,1)-SU(2) hybrid interferometer, and so on, and the applications in quantum metrology and quantum sensing networks.
Interferometers are widely used as sensors in precision measurement. Compared with a conventional Mach–Zehnder interferometer, the sensitivity of a correlation-enhanced nonlinear interferometer can break the standard quantum limit. Phase sensitivity plays a significant role in the enhanced performance. In this paper, we review improvement in phase estimation technologies in correlation-enhanced nonlinear interferometers, including SU(1,1) interferometer and SU(1,1)-SU(2) hybrid interferometer, and so on, and the applications in quantum metrology and quantum sensing networks.
Abstract The SU(1,1) interferometer, a nonlinear analog of the traditional Mach–Zehnder interferometer, has emerged as a powerful tool for achieving phase sensitivity beyond the standard quantum limit. In this work, we propose the use of a superposition of even and odd coherent states as input state to enhance the phase sensitivity of an SU(1,1) interferometer. These non-classical states exhibit unique properties such as squeezing, entanglement, and quantum interference, which can be harnessed to improve metrological precision. Phase sensitivity is analyzed using single-intensity detection and homodyne detection schemes under both ideal and photon loss cases, which demonstrates significant improvements over classical and squeezed-vacuum inputs. In addition, we evaluate the quantum Cramér-Rao lower bound by employing the quantum Fisher information formalism, showing that it surpasses the standard quantum limit and approaches the Heisenberg limit under optimal conditions. Our results highlight the potential of the even and odd coherent states superposition in quantum metrology and provide a pathway for achieving ultra-precise phase measurements in SU(1,1) interferometers for applications in optical sensing, and quantum information processing.
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.
Quantum stochastic phase estimation has many applications in the precise measurement of various physical parameters. Similar to the estimation of a constant phase, there is a standard quantum limit for stochastic phase estimation, which can be obtained with the Mach–Zehnder interferometer and coherent input state. Recently, it has been shown that the stochastic standard quantum limit can be surpassed with nonclassical resources such as squeezed light. However, practical methods to achieve quantum enhancement in the stochastic phase estimation remain largely unexplored. Here we propose a method utilizing the SU(1,1) interferometer and coherent input states to estimate a stochastic optical phase. As an example, we investigate the Ornstein–Uhlenback stochastic phase. We analyze the performance of this method for three key estimation problems: prediction, tracking, and smoothing. The results show significant reduction of the mean square error compared with the Mach–Zehnder interferometer under the same photon number flux inside the interferometers. In particular, we show that the method with the SU(1,1) interferometer can achieve fundamental quantum scaling, achieve stochastic Heisenberg scaling, and surpass the precision of the canonical measurement.
We propose a high-precision phase estimation scheme in a hybrid interferometer by synergistically combining a Kerr nonlinear phase shifter and multi-photon subtraction operations. Using a coherent state and a vacuum state as input resources, we systematically evaluate the phase sensitivity via homodyne detection and analyze the quantum Fisher information as well as the quantum Cramér-Rao bound under both ideal and lossy conditions. Our results show that the joint integration of Kerr nonlinearity and multi-photon subtraction yields remarkable advantages over either technique used alone. The proposed scheme enables the phase sensitivity to surpass the standard quantum limit, exceed the conventional Heisenberg scaling (1/N), and approach the super-Heisenberg scaling (1/N2)-a direct consequence of Kerr nonlinearity. More precisely, the super-Heisenberg scaling $\propto $ 1/N2 is the ultimate precision limit permitted by the k=2 Kerr nonlinearity and does not violate the fundamental Heisenberg limit for linear phase accumulation. Even under moderate internal photon loss, the system maintains high precision and exhibits enhanced robustness to decoherence. The Kerr nonlinearity introduces an intensity-dependent phase shift proportional to the squared photon number, while multi-photon subtraction tailors non-Gaussian states to strengthen phase information extraction. Compared with existing schemes based on hybrid interferometers or SU(1,1) interferometers, our architecture achieves superior precision and stronger loss resilience. All components are experimentally accessible with current quantum optical technologies. This work provides a promising route for practical high-precision quantum metrology and quantum sensing.
Absolute sensitivity is measured for the phase measurement in an SU(1,1) type interferometer, and the results are compared to that of a Mach-Zehnder interferometer operated under the condition of the same intra-interferometer intensity. The interferometer is phase locked to a point with the largest quantum noise cancellation, and a simulated phase modulation is added in one arm of the SU(1,1) interferometer. Both the signal and noise level are estimated at the same frequency range, and we obtained 3 dB improvement in sensitivity for the SU(1,1) interferometer over the Mach-Zehnder interferometer. Our results demonstrate a direct phase estimation and may pave the way for practical applications of a nonlinear interferometer.
Conventional interferometers usually utilize beam splitters for wave splitting and recombination. These interferometers are widely used for precision measurement. Their sensitivity for phase measurement is limited by the shot noise, which can be suppressed with squeezed states of light. Here we study a new type of interferometer in which the beam splitting and recombination elements are parametric amplifiers. We observe an improvement of 4.1±0.3 dB in signal-to-noise ratio compared with a conventional interferometer under the same operating condition, which is a 1.6-fold enhancement in rms phase measurement sensitivity beyond the shot noise limit. The improvement is due to signal enhancement. Combined with the squeezed state technique for shot noise suppression, this interferometer promises further improvement in sensitivity. Furthermore, because nonlinear processes are involved in this interferometer, we can couple a variety of different waves and form new types of hybrid interferometers, opening a door for many applications in metrology. Interferometers play a key role in precision measurements and metrology. Here, the authors demonstrate a new type of interferometer that replaces the standard beam splitter elements with parametric amplifiers, which provides enhanced performance compared with a Mach–Zehnder interferometer.