This work explores the phase uncertainty of lossy SU(1,1) interferometers in the low gain regime. We show that coincidence measurement can reach the lowest phase uncertainty possible in the system, regardless of the internal losses.
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/NwhereNis 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.
We study the effect of losses on the phase sensitivity of the SU(1,1) interferometer for different configurations. We find that this type of interferometer is robust against losses that result from an inefficient detection system. This type of loss only introduces an overall prefactor to the sensitivity but does not change the 1/n scaling, where n is the average number of particles inside the interferometer, characteristic of the Heisenberg limit. In addition, we show that under some conditions the SU(1,1) interferometer with coherent state inputs is also robust against internal losses. These results show that the SU(1,1) interferometer is a viable candidate for experimentally reaching the Heisenberg limit with current technology. Possible implementations of this interferometer using four-wave mixing in atomic vapors or an atom interferometer in a spinor Bose-Einstein condensate are compared.
We study the phase sensitivity of an SU(1,1) interferometer with photon loss by using three different photon operations schemes, i.e., performing photon-addition operation on the input port of the SU(1,1) interferometer (Scheme A), the interior of SU(1,1) interferometer (Scheme B), and both of them (Scheme C). We compare the performance of the three schemes in phase estimation by performing the same times of photon-addition operation to the mode b. The results show that Scheme B improves the phase sensitivity best in ideal case, and Scheme C performs well against internal loss, especially in the case of strong loss. All the three schemes can beat the standard quantum limit in the presence of photon loss, but Scheme B and Scheme C can break through the standard quantum limit in a larger loss range.
The quantum correlation of light and atomic collective excitation can be used to compose an SU(1,1)-type hybrid light-atom interferometer, where one arm in the optical SU(1,1) interferometer is replaced by the atomic collective excitation. The phase-sensing probes include not only the photon field but also the atomic collective excitation inside the interferometer. For a coherent squeezed state as the phase-sensing field, the phase sensitivity can approach the Heisenberg limit under the optimal conditions. We also study the effects of the loss of light field and the dephasing of atomic excitation on the phase sensitivity. This kind of active SU(1,1) interferometer can also be realized in other systems, such as circuit quantum electrodynamics in microwave systems, which provides a different method for basic measurement using the hybrid interferometers.
We analyse a nonlinear interferometer, also known as an SU(1,1) interferometer, in the presence of internal losses and inefficient detectors. To overcome these limitations, we consider the effect of seeding one of the interferometer input modes with either a number state or a coherent state. We derive analytical expressions for the interference visibility, contrast, phase sensitivity, and signal-to-noise ratio, and show a significant enhancement in all these quantities as a function of the seeding photon number. For example, we predict that, even in the presence of substantial losses and highly inefficient detectors, we can achieve the same quantum-limited phase sensitivity of an unseeded nonlinear interferometer by seeding with a few tens of photons. Furthermore, we observe no difference between a number or a coherent seeding state when the interferometer operates in the low-gain regime, which enables seeding with an attenuated laser. Our results expand the nonlinear interferometry capabilities in the field of quantum imaging, metrology, and spectroscopy under realistic experimental conditions.