[Paper Review] Duality in asymmetric Quantum optical Ramsey interferometers

Jesús Martínez-Linares, Julio Vargas-Medina|ArXiv.org|Aug 30, 2003

Quantum Mechanics and Applications1 references3 citations

TL;DR

This paper applies a formalism separating a-priori predictability ($\mathcal{P}$) and quantum detector quality ($\mathcal{Q}$) in asymmetric Quantum Optical Ramsey Interferometers (QORI), where the same Jaynes-Cummings interaction acts as both beam splitter and which-way detector. It shows $\mathcal{Q}$ quantifies quantum which-way information in the detector even when $\mathcal{D}$ is saturated by $\mathcal{P}$, demonstrating that $\mathcal{Q}$ captures intrinsic detector performance independent of classical beam-splitting asymmetry.

ABSTRACT

A formalism have been recently derived [J. Martinez-Linares and D. Harmin, quantum-ph/0306057] allowing one to separate different sources of which-way information contributing to the total distinguishability D of the ways in a two-way interferometer. Here we apply the formalism to a Quantum Optical Ramsey Interferometer where both sources, the a-priori predictability of the ways P and the quantum "Quality" Q of the which-way detector, stems from the same physical interaction. We show that the formalism is able to separate both sources of which-way information. Moreover, it is shown that Q succeeds in quantifying the amount of quantum which-way information stored in the which-way detector even in cases where D does not.

Motivation & Objective

• To analyze the interplay between different sources of which-way information (WWI) in asymmetric Quantum Optical Ramsey Interferometers (QORI).
• To test whether the formalism separating a-priori predictability ($\mathcal{P}$) and quantum detector quality ($\mathcal{Q}$) remains valid when both sources stem from the same physical interaction.
• To demonstrate that $\mathcal{Q}$ can quantify stored WWI even in cases where total distinguishability $\mathcal{D}$ fails due to saturation by $\mathcal{P}$.
• To validate the formalism in a realistic, experimentally relevant setup—specifically, the QORI with a high-finesse cavity mode acting as both beam splitter and which-way detector.

Proposed method

• The formalism from previous work [I] is applied to the QORI, decomposing total distinguishability $\mathcal{D}$ into $\mathcal{P}$ (a-priori predictability) and $\mathcal{Q}$ (quantum detector quality).
• The system is modeled using the Jaynes-Cummings Hamiltonian, describing the interaction between a two-level atom (Quanton) and a quantized cavity mode (acting as both beam splitter and which-way detector).
• The evolution of the system is analyzed through the density matrix formalism, tracing over detector degrees of freedom to compute $\mathcal{D}$, $\mathcal{P}$, and $\mathcal{Q}$.
• Fringe visibility $\mathcal{V}$ is computed as a function of cavity field intensity $\bar{n}_0$ and Rabi phase $\Omega\tau$, linking it to $\mathcal{D}$ and $\mathcal{Q}$ via the duality relation $\left(1-\mathcal{P}^2\right)\mathcal{Q}^2 + \mathcal{P}^2 + \mathcal{V}^2 \leq 1$.
• Numerical plots of $\mathcal{Q}$, $\mathcal{D}$, and $\mathcal{V}^2$ are generated for symmetric ($\mathcal{P}=0$) and asymmetric ($\mathcal{P}=1$) cases to compare behavior across different cavity field intensities.

Experimental results

Research questions

• RQ1 Can the formalism separating $\mathcal{P}$ and $\mathcal{Q}$ be successfully applied to a QORI where both beam splitting and which-way detection arise from the same physical interaction?
• RQ2 How does $\mathcal{Q}$ behave when $\mathcal{D}$ is saturated by $\mathcal{P}$, particularly in the limit of extreme asymmetry ($\mathcal{P}=1$)?
• RQ3 Does $\mathcal{Q}$ remain a valid measure of quantum which-way information storage in the detector even when $\mathcal{D}$ fails to reflect the actual amount of stored information?
• RQ4 What is the relationship between $\mathcal{Q}$, $\mathcal{D}$, and fringe visibility $\mathcal{V}$ in the strong-coupling regime of the QORI?

Key findings

• In the symmetric case ($\mathcal{P}=0$), $\mathcal{Q}^2 = \mathcal{D}^2$ and both decrease with increasing cavity field intensity $\bar{n}_0$, while $\mathcal{V}^2$ increases, showing coherence degradation due to WWI.
• In the high-intensity limit ($\bar{n}_0 \to \infty$), $\mathcal{V}^2 \to 1$ and $\mathcal{Q} \to 0$, indicating that perfect visibility is incompatible with any storage of which-way information in the detector.
• In the vacuum limit ($\bar{n}_0 = 0$), the system reaches maximal entanglement $\frac{1}{\sqrt{2}}(|0\rangle_D|a\rangle_Q + i|1\rangle_D|b\rangle_Q)$, leading to $\mathcal{Q} = 1$ and $\mathcal{D} = 1$, with full WWI stored in the cavity field.
• When $\mathcal{P} = 1$, $\mathcal{D} \geq \mathcal{P} = 1$ saturates the distinguishability, but $\mathcal{Q}$ remains at 1, showing that $\mathcal{Q}$ still quantifies stored WWI even when $\mathcal{D}$ cannot.
• The formalism successfully separates $\mathcal{P}$ and $\mathcal{Q}$ in the QORI, proving that $\mathcal{Q}$ characterizes the intrinsic quantum performance of the which-way detector independently of classical beam-splitting asymmetry.
• The results are experimentally feasible, as visibility measurements in the strong-coupling regime ($\Omega\tau \sim 1$) with $\bar{n}_0$ from 0 to 14 have already been demonstrated by Bertet et al. [9].