The detection of Planck-scale physics facilitated by nonlinear quantum optics

Abstract

A tenet of contemporary physics is that novel physics beyond the Standard Model lurks at a scale related to the Planck length. The development and validation of a unified framework that merges general relativity and quantum physics is contingent upon the observation of Planck-scale physics. Here, we present a fully quantum model for measuring the nonstationary dynamics of a ng-mass mechanical resonator, which will slightly deviate from the predictions of standard quantum mechanics induced by modified commutation relations associated with quantum gravity effects at low-energy scalar. The deformed commutator is quantified by the oscillation frequency deviation, which is amplified by the nonlinear mechanism of the detection field. The measurement resolution is optimized to a precision level that is $15$ orders of magnitude below the electroweak scale.

Figures (3)

• Figure 1: Schematic of the detection scheme: an oscillator modified by GUP that is coupled to two cavity fields through significantly disparate coupling strengths ($g_m\ll g_a$). The probe field $E_m$ is frequency modulated by an EOM with the parameters $\Omega$ and $\phi$. The dotted box indicates the time sequence of $E_1$ and $E_2$ which are two components of driving field. The measured spectrum $S_a$ and $S_{M_c}$ are shown at the bottom.
• Figure 2: Demonstration of the optimization provided by higher-order sidebands through comparison with results from Ref. Li2025. (a) Linear regression coefficients from the fitting process for each value of $\beta_{\text{NL}}$. (b) Estimated $\beta'_{\text{NL}}$ versus $\beta_{\text{NL}}$. The inset in (b) shows the time evolution of the purity $\mathcal{P}(t)$. Blue points are from data in Ref. Li2025, with our model corresponding to $g_a=0$. Red points are obtained with $g_m/g_a=40$. In addition to the parameters in Tab. \ref{['table:1']}, simulations and data processing use $\tau=5.25\times 10^{-6}\gamma^{-1}$, $t_c=0$, $t_p=5.25\times 10^{-4}\gamma^{-1}$, $\Delta t=5.25\times 10^{-4}\gamma^{-1}$, $E_1/\omega_b\simeq 124$, $E_2/\omega_b\simeq 3931$, $E_c/\omega_b\simeq 768$, and $E_p/\omega_b\simeq 38.4$.
• Figure 3: Three sets of simulated measurement results: two of which correspond to EOMs with different parameters (designated as EOMs1 and EOMs2), while the other one corresponds to OMMs. (a): The linear regression coefficient between $\omega_{u,t}$ and $\vert A_t'\vert^2$. (b): The expected value (point) and standard deviation ($68\%$ confidence interval, shaded region) of the measurement error $Er$ obtained from $15$ repetitions. The inset in (b) plots the corresponding average measurement results of the dimensionless parameter $\beta_{\text{NL}}$. In addition to the parameters outlined in Tab. \ref{['table:1']}, the remaining parameters utilized in the simulation and data processing are: $\tau=10^{-4}$ s, $t_c=10^{-2}$ s, $t_p=0.3$ s, $\Delta t=0.01$ s, $E_1/\omega_b\simeq 3.8\times 10^{2} (8.0\times 10^{3})$, $E_2/\omega_b\simeq 1.3\times 10^4$, $E_c/\omega_b=E_p/\omega_b\simeq 8.0\times 10^{-1}$ for EOMs1(2), and $\tau=2.5\times10^{-5}$ s, $t_c=2.5\times 10^{-3}$ s, $t_p=0.075$ s, $\Delta t=0.0025$ s $E_1/\omega_b\simeq 3.8\times 10^5$, $E_2/\omega_b\simeq 1.3\times 10^{6}$, $E_c/\omega_b=E_p/\omega_b\simeq 3.2\times 10^2$ for OMMs.