Back-reflection in dipole fields and beyond

TL;DR

The paper addresses the challenge of detecting quantum vacuum nonlinearities via light-by-light scattering in realistic optical setups by focusing on back-reflection signals. It employs the vacuum emission picture combined with Maxwell solvers to compute channel-separated, polarization-insensitive signal photons and investigates dipole pulses, belt configurations, and three-pulse collisions to maximize discernibility against backgrounds. Bayesian optimization is used to identify optimal pulse orientations, polarizations, and energy distributions, revealing that three-pulse collisions offer the most favorable balance between signal strength and experimental feasibility. Overall, the work provides quantitative benchmarks and methodological tools for realizing and optimizing back-reflected signatures of quantum vacuum effects in multi-pulse optical experiments.

Abstract

Quantum reflection is a fascinating signature of the quantum vacuum that emerges from inhomogeneities in the electromagnetic fields. In pursuit of the prospective real-world implementation of quantum reflection in the back-reflection channel, we provide the first numerical estimates for the light-by-light scattering with dipole pulses, which are known to provide the tightest focusing of light possible. For an all-optical setup with a dipole pump and Gaussian probe of the same frequency, we find that the dominant signal signature is related mainly to the back-reflection channel from 4-wave mixing. Focusing on this, we study the particular case of a multiple focusing pulses configuration (belt configuration) as an approximation to the idealized dipole pulse. Using Bayesian optimization methods, we determine optimal parameters that maximize the detectability of a discernible back-reflection signal. Our study indicates that the optimization favors a three-beam collision setup, which we further investigate both numerically and analytically.

Figures (17)

• Figure 1: Electromagnetic energy density of a magnetic dipole pulse in three planes ($xz$ at $y=0$, $xy$ at $z=0$, and $yz$ at $x=0$) at two time steps: (left column) $t = 0$ (focus), (right column) $t = \tau$. Dipole pulse parameters: $W = 40\, \rm{J}$, $\lambda = 800\, \rm{nm}$, $\mathbf{d} \: \| \: \mathbf{e}_y$, $\tau_{\rm{FWHM}} = 20\, \rm{fs}$.
• Figure 2: Angular signal photon spectrum from the collision of a Gaussian probe with a dipole pump. Probe pulse has the following parameters: $\hat{\mathbf{k}} = \mathbf{e}_{\rm{x}}$, $W = 20\, \rm{J}$, $\lambda = 800\, \rm{nm}$, $\tau_{\rm{FWHM}} = 20\, \rm{fs}$, $w_0 = 2\lambda$, $\beta = 0^{\circ}$. The probe collides with the magnetic dipole pulse ($W = 40\, \rm{J}$, $\lambda = 800\, \rm{nm}$, $\tau_{\rm{FWHM}} = 20\, \rm{fs}$) with different dipole moment orientations. Green crosses show the dipole moment axis. The blue square shows a $10^{\circ} \times 10^{\circ}$ detector for which we calculate the reflected signal ($N_{\rm{det}}$). (a) $\mathbf{d} \: \| \: \mathbf{e}_x$, $N_{\rm{tot}} \approx 348, \: N_{\rm{det}} \approx 0.25$; (b) $\mathbf{d} \: \| \: \mathbf{e}_y$, $N_{\rm{tot}} \approx 574, \: N_{\rm{det}} \approx 7.2$; (c) $\mathbf{d} \: \| \: \mathbf{e}_z$, $N_{\rm{tot}} \approx 416, \: N_{\rm{det}} \approx 2.8$.
• Figure 3: Lineout from the angular signal photon spectrum at $\vartheta = 90^{\circ}$. Different lines correspond to different collision scenarios shown in Fig. \ref{['fig:gg-gd']}. The blue-shaded region corresponds to the detector for the back-reflected signal.
• Figure 4: Angular background and signal photon spectrum from a single magnetic dipole pulse. Dipole pulse parameters: $W = 40\, \rm{J}$, $\lambda = 800\, \rm{nm}$, $\mathbf{d} \: \| \: \mathbf{e}_y$, $\tau_{\rm{FWHM}} = 20\, \rm{fs}$. Green crosses show the dipole moment axis. The blue square shows a $10^{\circ} \times 10^{\circ}$ detector. The dipole background results in $N_{\rm{tot}} \approx 4 \times 10^{22}$, $N_{\rm{det}} \approx 1.5 \times 10^{20}$ and the dipole self-scattering results in $N_{\rm{tot}} \approx 289$, $N_{\rm{det}} \approx 1.1$.
• Figure 5: Optimization results in 3-dimensional parameter space: $b$-dipole moment orientation ($\vartheta_d, \varphi_d$) and probe polarization ($\beta_{\rm probe}$). The optimization objective was to maximize the signal in a $10^{\circ} \times 10^{\circ}$ detector around $(\vartheta, \varphi) = (90^{\circ}, 180^{\circ})$. Probe and dipole pulse parameters are similar to Fig. \ref{['fig:gg-gd']}. Found optimum is $(\vartheta_d^*, \varphi_d^*, \beta_{\rm probe}^*) \approx (0^{\circ}, 360^{\circ}, 90^{\circ})$ achieving $N_{\rm{det}} \approx 7.2$. The optimum corresponds to $\mathbf{d}\: ||\: \mathbf{e}_z$ and $\mathbf{E_{\rm probe}\: || \:\mathbf{e}_y}$.