Beyond the Petermann limit: can exceptional points increase sensor precision?

Smith, David; Chang, Hongrok; Михайлов, Е. Е.; Shahriar, Selim M.

doi:10.48550/arxiv.2005.12213

Cited by 3 publications

(10 citation statements)

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“…Of course, no perfectly coherent source exists, and no practical system can supply infinite gain, so nonlinearities, such as gain saturation, are expected to play an important role in eventually determining the superiority of one sensor versus another as we approach the lasing threshold. Sensing in (nonlinear) lasing systems has been addressed by a number of works, , and in some settings EP sensing in the nonlinear limit may be beneficial, but it goes beyond the scope of this paper. We conclude that, if the functionality is limited to a purely linear operation, there appears to be no advantage in operating an active sensor near the EP, similar to the passive scenario.…”

Section: Ep Sensing In Active Systemsmentioning

confidence: 99%

“…In the following, we draw first-principles considerations to establish a fair comparison between EP sensing and other sensing approaches. Although our framework is general and it applies to any approach to sensing, we focus on linear scattering systems, taking into account that sensors operating at a lasing point have already been discussed in this context. , Linear scattering systems have raised the original interest in EP sensing, since it was shown that, despite their linearity, frequency splitting (δ) of the eigenvalues around an EP has a nonlinear variation for certain changes in a parameter ε in systems with gain and/or loss. − ,− Due to the associated scaling of frequency splitting δ ∝ (ε – ε EP ) 1/ n , where n is the order of the EP, the slope of δ(ε) becomes very large for ε ≈ ε EP . As the frequency splitting is extremely sensitive to system parameters around the EP, it has been suggested that such a response may enable very precise measurements.…”

Section: Introductionmentioning

confidence: 99%

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Limitations of Sensing at an Exceptional Point

2022

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With the rapid progress of high-quality superconducting and photonic resonators, it has become possible to sense with extremely high precision a wide range of physical properties. Along with these advances, several proposals have recently been put forward for schemes that maximize the sensitivity of these sensing systems. Of particular recent interest are sensors operating near exceptional points (EPs), which have been shown to provide dramatic variations of their eigenvalues in response to small parameter changes. While there have been theoretical and experimental reports of sensitivity enhancements under these operating conditions, recent work has also cast doubts around the actual benefit of operating near an EP for sensors under realistic conditions. In this paper, we study the fundamentals of sensing in linear scattering systems operating near an EP, analyzing the specific role of EPs and of the associated amplification mechanisms; we specifically show that eigenvalue variations under a perturbation are not a good measure of the overall sensor performance near an EP. Further, we note that sensors with amplification should account for the extra energy usage when comparing to passive sensors.

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Section: Ep Sensing In Active Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Limitations of Sensing at an Exceptional Point

2022

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“…Finally, we remark that understanding the linear response of non-Hermitian systems is a very crucial step towards studying their noise. In this regard, we expect our formalism to provide more insight into the noise behavior in non-Hermitian systems and play a positive role in the active debate on signal to noise ratio of EP-based sensors [121][122][123][124][125][126][127]. We plan to explore some of these interesting directions in future works.…”

Section: Discussionmentioning

confidence: 99%

Linear response theory of open systems with exceptional points

et al. 2022

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Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating the linear response is complicated due to the non-orthogonality of their eigenmodes, and the presence of exceptional points (EPs). Here, we derive a closed form series expansion of the resolvent associated with an arbitrary non-Hermitian system in terms of the ordinary and generalized eigenfunctions of the underlying Hamiltonian. This in turn reveals an interesting and previously overlooked feature of non-Hermitian systems, namely that their lineshape scaling is dictated by how the input (excitation) and output (collection) profiles are chosen. In particular, we demonstrate that a configuration with an EP of order M can exhibit a Lorentzian response or a super-Lorentzian response of order Ms with Ms = 2, 3, …, M, depending on the choice of input and output channels.

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“…By placing a sensor at a specific location in parameter space (the EP), it has been shown that some devices can exhibit significantly increased sensitivity [11,12]. Unfortunately, these enhancements generally come at the expense of increased noise [13,14]. For the specific case of the laser gyroscope, the EP is equivalent to the dead band edge where noise and instability dominate [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, these enhancements generally come at the expense of increased noise [13,14]. For the specific case of the laser gyroscope, the EP is equivalent to the dead band edge where noise and instability dominate [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Intracavity Measurement Sensitivity Enhancement without Runaway Noise

Horstman

Diels

2021

Sensors

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A method to increase the sensitivity of an intracavity differential phase measurement that is not made irrelevant by a larger increase of noise is explored. By introducing a phase velocity feedback by way of a resonant dispersive element in an active sensor in which two ultrashort pulses circulate, it is shown that the measurement sensitivity is elevated without significantly increasing the Petermann excess noise factor. This enhancement technique has considerable implications for any optical phase based measurement; from gyroscopes and accelerometers to magnetometers and optical index measurements. Here we describe the enhancement method in the context of past dispersion enhancement studies including the recent work surrounding non-Hermitian quantum mechanics, justify the method with a theoretical framework (including numerical simulations), and propose practical applications.

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Beyond the Petermann limit: can exceptional points increase sensor precision?

Cited by 3 publications

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Limitations of Sensing at an Exceptional Point

Limitations of Sensing at an Exceptional Point

Linear response theory of open systems with exceptional points

Intracavity Measurement Sensitivity Enhancement without Runaway Noise

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