Detecting deformed commutators with exceptional points in optomechanical sensors

Abstract

Models of quantum gravity imply a modification of the canonical position-momentum commutation relations. In this manuscript, working with a binary mechanical system, we examine the effect of quantum gravity on the exceptional points of the system. On the one side, we find that the exceedingly weak effect of quantum gravity can be sensed via pushing the system towards a second-order exceptional point, where the spectra of the non-Hermitian system exhibits non-analytic and even discontinuous behavior. On the other side, the gravity perturbation will affect the sensitivity of the system to deposition mass. In order to further enhance the sensitivity of the system to quantum gravity, we extend the system to the other one which has a third-order exceptional point. Our work provides a feasible way to use exceptional points as a new tool to explore the effect of quantum gravity.

Statistical description of ideal gas at Planck scale with strong quantum gravity measurement

“…It has been shown that, the weak effect of quantum gravity induced by the minimal length can be sensed via pushing the system towards a second-order exceptional point, where the spectra of the non-Hermitian system exhibit non-analytic and even discontinuous behavior exceptional point, where the spectra of the non-Hermitian system exhibit non-analytic and even discontinuous behavior. In agreement with this result [32] , the weak quantum gravity measurement shifts quadratically the thermodynamic quantities and at the extremal limit of deformed parameter [18] , [19] , [20] , [21] , [22] , [23] , one recovers the ordinary quantities. This concept of weak quantum gravity measurement can also be observed in general relativity where the weak curvature of the space-time fabric can be approximated as flat.…”

“…In fact, the minimal length induces a weak quantum gravity localization while the maximal length in this context induces a strong quantum gravity localization. Recently, numerically experimentations have been addressed to examine the effect of the minimal length on the exceptional points in optomechanical sensors [32] . It has been shown that, the weak effect of quantum gravity induced by the minimal length can be sensed via pushing the system towards a second-order exceptional point, where the spectra of the non-Hermitian system exhibit non-analytic and even discontinuous behavior exceptional point, where the spectra of the non-Hermitian system exhibit non-analytic and even discontinuous behavior.…”

Problems with modified commutators

“…As stated in the Introduction, we believe that this constitutes the most serious criticism of the modified commutator/modified phase space paradigm yet formulated in the literature. It has immediate real world implications since, to the best of our knowledge, existing experimental bounds on the GUP parameter α have all been obtained by adopting two contradictory assumptions: 1) that the GUP arises from a modified commutation relation, and 2) that the modified commutation relation holds for the uncertainties Δ ψ X i and Δ ψ P j where i, j ∈ {X, Y, Z} refer to global Cartesian coordinates (Pikovski et al, 2012;Bosso et al, 2017;Kumar and Plenio, 2018;Girdhar and Doherty, 2020;Cui et al, 2021;Sen et al, 2022).…”

Squeezing enhanced nonlinearity sensing in dissipatively coupled optical systems

“…Sensitivity enhancement based on EP has been demonstrated both theoretically and experimentally [17][18][19][20][21][45][46][47][48][49][50][51][52][53][54][55] in the particle detector [17], mass sensor [51], and gyroscope [54]. It has been shown that if an EP is subjected to the strength ǫ of the linear perturbation, the frequency splitting (the energy spacing of the two levels) scales as the square root of the perturbation strength ǫ [17][18][19][20][21][45][46][47][48][49][50][51][52][53][54][55]. Recently, in the context of dissipatively coupled APT symmetric systems, a scheme was proposed to efficiently detect the nonlinear perturbations [31].…”

“…Particularly, near the coherence-induced singularity (CIS), the response N behaves as dN dU ∝ |U | −5/3 , where U quantifies the strength of the Kerr nonlinearity [31]. Compared with EP-based sensors [17][18][19][20][21][45][46][47][48][49][50][51][52][53][54][55], the sensitivity of the system to inherent nonlinearities has been greatly improved, and the protocol does not require any gains [31].…”