Optimizing phase sensitivity of Mach-Zehnder interferometer having superposition of coherent state with single-photon-added coherent state

Abstract

Precision measurement of an unknown parameter using a Mach-Zehnder interferometer (MZI) plays an important role in quantum metrology. We use hybrid coherent states (HCS), consisting of a superposition of coherent state (CS) and single-photon-added coherent state (SPACS), as well as solely CS, as inputs of the MZI. We computed the phase sensitivity of the MZI for three detection schemes: single intensity detection (SID), intensity difference detection (IDD), and optimal detection (OD). We find that HCS offers improved phase sensitivity under certain conditions, compared to CS combined with SPACS or double CS inputs and CS combined with the squeezed vacuum state as the input of MZI, under lossless and lossy scenarios. Also, we found that SID outperforms the IDD and OD schemes approximately in all cases. Furthermore, we explore the lower bound in phase sensitivity using quantum Fisher information (QFI) and the corresponding quantum Cramér–Rao bound (QCRB). We found that HCS with CS approaches the QCRB for SID and OD cases. Our results suggest that HCS could serve as a promising nonclassical resource for enhancing phase super-sensitivity in MZI, especially in realistic operational environments.