Quantum Phase Sensitivity with Generalized Coherent States Based on Deformed su(1,1) and Heisenberg Algebras

TL;DR

The paper addresses the problem of achieving high-precision phase estimation in quantum interferometry by introducing generalized coherent states derived from a perturbed harmonic oscillator via deformed Heisenberg and su(1,1) algebras. It develops explicit quantum Fisher information formalism for both two-parameter (symmetric) and single-parameter phase estimation scenarios, deriving closed-form QFIs for inputs of generalized coherent states in a Mach-Zehnder interferometer and showing that GHA states can outperform generalized SU(1,1) states. Three practical detection schemes—difference intensity, single-mode intensity, and balanced homodyne—are analyzed, with explicit phase-sensitivity expressions that connect to the QCRB; balanced homodyne detection, especially with an external phase reference, best tracks the quantum limit across operating points. The results demonstrate the tunability and nonclassical features of the deformed-coherent-state framework and highlight the potential of balanced-homodyne readout for robust, high-precision quantum sensing, while pointing to future work involving entanglement-enhanced strategies to surpass coherent-state limits.

Abstract

We investigate the phase sensitivity of a Mach-Zehnder interferometer using a special class of generalized coherent states constructed from generalized Heisenberg and deformed $su(1,1)$ algebras. These states, derived from a perturbed harmonic oscillator with a four parameter deformed spectrum, provide enhanced tunability and nonclassical features. The quantum Fisher information and its associated quantum Cramer-Rao bound are computed to define the fundamental precision limits in phase estimation. We analyze the phase sensitivity under three realistic detection methods: difference intensity detection, single mode intensity detection, and balanced homodyne detection. The performance of each method is compared with the quantum Cramer Rao bound to evaluate their optimality. Our results demonstrate that, for suitable parameter regimes, these generalized coherent states enable phase sensitivities approaching the quantum limit. This offers a flexible framework for precision quantum metrology and potential applications in quantum enhanced sensing.

Figures (8)

• Figure 1: This is a schematic setup of a MZI, which includes two independent phase shifts and two beam splitters (BS1 and BS2) with an adjustable transmission coefficient. The input state evolves through the interferometric paths before measurement.
• Figure 2: This is a schematic of a Mach–Zehnder interferometer featuring three practical detection methods: intensity-difference detection, single-mode intensity detection and balanced homodyne detection. The input state, $|\psi_{\text{in}}\rangle$, evolves through a unitary transformation into the output state $|\psi_{\text{out}}\rangle$. The main objective is to estimate the phase shift $\theta$ between the interferometer arms using appropriate measurements.
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