Interferometry Concept Within the SU(1,1) Framework

Shuai Wang, Jiandong Zhang, Xue-xiang Xu

G. S. Agarwal

Breaking the standard quantum limit in the sensing of parameters at different spatial locations, such as in a quantum network, is of great importance. Using the framework of quantum Fisher information, many strategies based on squeezed quantum probes and multipath multiphoton or multiqubit entangled states have been considered. In this context there is always the question of what the simplest measurement is that would saturate the quantum Cramér-Rao bound (QCRB). The simplest quantity to measure would be characteristics of photon flux or population distribution in the case of qubits. Previous studies have shown that the error sensitivity in SU(1,1) interferometry, also known by several other terms such as nonlinear interferometry and time-reversed measurements, does saturate the QCRB for single parameters such as phase, displacement, and loss. In this work we reveal the great utility of generalized SU(1,1) interferometry in distributed sensing. Generalized SU(1,1) interferometry is a combination of SU ( m ) and SU(1,1) elements, where m is the number of nodes in the network. The SU ( m ) element is used to produce distributed entanglement starting from a squeezed photonic or matter probe. We demonstrate how error sensitivity measurement or more precisely the method of moment sensitivity at just one output port can saturate or nearly saturate the QCRB and thus results in Heisenberg sensitivity of network sensing.

Bernard Yurke, S. L. McCall, John R. Klauder

Hubert de Guise, Barry C. Sanders, Stephen D. Bartlett +1 more

G. S. Agarwal, L. Davidovich

We present a unified framework, based on quantum metrology concepts, for defining and quantifying deterministic noiseless quantum amplification of parameter-dependent processes, which plays an important role in increasing the precision of quantum sensing.Recent experiments [Burd et al., Science 364, 1163 (2019)] can be encompassed by this concept, which also leads to new suggestions of experimental work.The unified view presented here allows the identification of the basic steps for quantum amplification and of the measurements that lead to the best possible precision, beyond the quantum standard limit, in the estimation of parameters involved in the process.This is applied to the estimation of displacements of trapped ions and of the phase in SU(1,1) optical interferometers and atomic interferometry.

Stuart S. Szigeti, Robert J. Lewis-Swan, Simon A. Haine

Although SU(1,1) interferometry achieves Heisenberg-limited sensitivities, it suffers from one major drawback: Only those particles outcoupled from the pump mode contribute to the phase measurement. Since the number of particles outcoupled to these "side modes" is typically small, this limits the interferometer's absolute sensitivity. We propose an alternative "pumped-up" approach where all the input particles participate in the phase measurement and show how this can be implemented in spinor Bose-Einstein condensates and hybrid atom-light systems-both of which have experimentally realized SU(1,1) interferometry. We demonstrate that pumped-up schemes are capable of surpassing the shot-noise limit with respect to the total number of input particles and are never worse than conventional SU(1,1) interferometry. Finally, we show that pumped-up schemes continue to excel-both absolutely and in comparison to conventional SU(1,1) interferometry-in the presence of particle losses, poor particle-resolution detection, and noise on the relative phase difference between the two side modes. Pumped-up SU(1,1) interferometry therefore pushes the advantages of conventional SU(1,1) interferometry into the regime of high absolute sensitivity, which is a necessary condition for useful quantum-enhanced devices.