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Optical and Quantum Electronics

Improvement in phase-sensitivity of a Mach–Zehnder interferometer with the superposition of Schrödinger’s cat-like state with vacuum state as an input under parity measurement

Gaurav K. Shukla, Krishna Mohan Mishra, Aviral Kumar Pandey, Taj Kumar, Hemendra Kumar Pandey, Devendra Kumar Mishra

Published Apr 3, 2023• 19 citations
Publisher
DOI
10.1007/s11082-023-04724-w

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We study the phase sensitivity of a Mach–Zehnder interferometer (MZI) with product detection (PD) scheme by using the superposition of Schrödinger’s cat-like state with the vacuum state (SCVS) and the coherent state as the inputs. We compare the results derived from PD with the parity detection scheme’s results. We found that PD performs better than parity detection and approaches the single parameter quantum Cramér-Rao bound in some cases. Therefore, we expect that SCVS may play as an alternative quantum resource with PD for the improvement in the phase sensitivity of an MZI having potential application in quantum metrology and quantum sensing.
We study the improvement in the phase sensitivity of a Mach–Zehnder interferometer using the superposition of Schrödinger’s cat-like state with the Fock state (SCFS) and the coherent state as inputs. With this setup, we examine the effect on phase sensitivity of the interferometer using a two-channel detection (TCD) scheme [ Opt. Express 29 , 95 ( 2021 ) OPEXFF 1094-4087 10.1364/OE.413391 ] in which we take the optimal combination of the intensities of both output ports. We find better phase sensitivity under some conditions for this setup as compared to other known combinations of inputs such as squeezed vacuum and coherent states, vacuum and coherent states, etc. Therefore, we expect that the SCFS may be an alternative nonclassical resource for improvement in the phase sensitivity of a Mach–Zehnder interferometer, having potential application in quantum sensing.
Many works have stated that nonlinear interactions can improve phase sensitivity beyond the Heisenberg limit scaling of 1/N1/N1/N with NNN being the mean photon number. This raises some open questions---among them the conclusive sensitivity limits with respect to single-mode inputs. Namely, when one of two inputs is vacuum, is there a shot-noise-style sensitivity bound on a nonlinear Mach-Zehnder interferometer? Within the reach of second-order nonlinear phase shifts, we make an attempt to provide an answer to this question. Based upon phase-averaging approach, this puzzle is partially resolved with careful calculations of the quantum Fisher information regarding three kinds of common inputs: Gaussian states, squeezed number states, and Schrödinger cat states. The results suggest that shot-noise-style sensitivity limit is no longer available, and the ideal candidate is squeezed vacuum.