January 18, 2024 | Hudson Loughlin1,* and Vivishek Sudhir1,2
The paper discusses the performance of exceptional point (EP) sensors, which are systems that exhibit a degenerate spectrum with a single complex eigenvalue. EP sensors are claimed to offer enhanced sensitivity due to the $\sqrt{\epsilon}$ scaling near the EP, where $\epsilon$ is a perturbation proportional to an external parameter of interest. However, the authors argue that the efficacy of a sensor is determined by its imprecision, which depends on both sensitivity and noise.
The paper analyzes various types of EP sensors, including passive and active EP sensors, and concludes that passive EP sensors do not show observable $\sqrt{\epsilon}$ bifurcation and thus do not offer any fundamental sensing improvement over traditional sensors. For active EP sensors, the authors consider two scenarios: one where the sensor operates above the lasing threshold and another where it operates below the threshold. They find that in both cases, the excess noise exactly cancels any enhancement from the frequency splitting near the EP.
The authors then focus on PT-symmetric EP sensors, which have balanced gain and loss rates. They show that the utility of such sensors as sensors depends on which elements of the coupling matrix are perturbed. The analysis reveals that the only type of EP sensor that has not been ruled out and offers enhanced signal near the EP is a PT-symmetric EP sensor where the quantity being sensed alters the coupling between the sensor's modes.
However, the authors find that quantum (and thermal) frequency noise scales as $\sqrt{\bar{\epsilon}}$, nullifying any reduction in imprecision in measuring $\bar{\epsilon}$. Therefore, PT-symmetric EP sensors do not offer any advantage in parameter estimation or weak-force sensing if the sensor is limited by fundamental noises such as quantum and thermal fluctuations.
The paper concludes that while PT-symmetric EP sensors do not offer a fundamental advantage in overcoming these limitations, they can potentially be advantageous when limited by technical noises. Additionally, the authors outline a phase-sensitive generalization of an EP sensor that does confer an advantage by harnessing the square-root bifurcation near an EP.The paper discusses the performance of exceptional point (EP) sensors, which are systems that exhibit a degenerate spectrum with a single complex eigenvalue. EP sensors are claimed to offer enhanced sensitivity due to the $\sqrt{\epsilon}$ scaling near the EP, where $\epsilon$ is a perturbation proportional to an external parameter of interest. However, the authors argue that the efficacy of a sensor is determined by its imprecision, which depends on both sensitivity and noise.
The paper analyzes various types of EP sensors, including passive and active EP sensors, and concludes that passive EP sensors do not show observable $\sqrt{\epsilon}$ bifurcation and thus do not offer any fundamental sensing improvement over traditional sensors. For active EP sensors, the authors consider two scenarios: one where the sensor operates above the lasing threshold and another where it operates below the threshold. They find that in both cases, the excess noise exactly cancels any enhancement from the frequency splitting near the EP.
The authors then focus on PT-symmetric EP sensors, which have balanced gain and loss rates. They show that the utility of such sensors as sensors depends on which elements of the coupling matrix are perturbed. The analysis reveals that the only type of EP sensor that has not been ruled out and offers enhanced signal near the EP is a PT-symmetric EP sensor where the quantity being sensed alters the coupling between the sensor's modes.
However, the authors find that quantum (and thermal) frequency noise scales as $\sqrt{\bar{\epsilon}}$, nullifying any reduction in imprecision in measuring $\bar{\epsilon}$. Therefore, PT-symmetric EP sensors do not offer any advantage in parameter estimation or weak-force sensing if the sensor is limited by fundamental noises such as quantum and thermal fluctuations.
The paper concludes that while PT-symmetric EP sensors do not offer a fundamental advantage in overcoming these limitations, they can potentially be advantageous when limited by technical noises. Additionally, the authors outline a phase-sensitive generalization of an EP sensor that does confer an advantage by harnessing the square-root bifurcation near an EP.