Measuring gravitational lensing time delays with quantum information processing

TL;DR

This work tackles measuring gravitational lensing time delays, especially in microlensing, with quantum-information tools to achieve photon-efficient observations. It presents a photon-count–optimal approach that leverages frequency-domain measurements and quantum undersampling, establishing a lower bound of $\Omega(\log(T/t_c))$ photons and achieving $O(\log(T/t_c))$ photon consumption. The analysis includes finite-source effects, noise, and magnification disparities, and provides practical observation plans with M-dwarf flares and a pathway for telescope-array calibration. Experimental pathways are discussed via single-photon spectrometry, linear-optics implementations, and quantum-memory-based quantum computing, highlighting near-term feasibility with current or forthcoming facilities. Overall, the approach broadens the regime of microlensing time-delay measurements and offers a scalable route to direct lens-mass measurements and high-precision telescope calibration.

Abstract

The gravitational fields of astrophysical bodies bend the light around them, creating multiple paths along which light from a distant source can arrive at Earth. Measuring the difference in photon arrival time along these different paths provides a means of determining the mass of the lensing system, which is otherwise difficult to constrain. This is particularly challenging in the case of microlensing, where the images produced by lensing cannot be individually resolved; existing proposals for detecting time delays in microlensed systems are significantly constrained due to the need for large photon flux and the loss of signal coherence when the angular diameter of the light source becomes too large. In this work, we propose a novel approach to measuring astrophysical time delays. Our method uses exponentially fewer photons than previous schemes, enabling observations that would otherwise be impossible. Our approach, which combines a quantum-inspired algorithm and quantum information processing technologies, saturates a provable lower bound on the number of photons required to find the time delay. Our scheme has multiple applications: we explore its use both in calibrating optical interferometric telescopes and in making direct mass measurements of ongoing microlensing events. To demonstrate the latter, we present a fiducial example of microlensed stellar flares sources in the Galactic Bulge. Though the number of photons produced by such events is small, we show that our photon-efficient scheme opens the possibility of directly measuring microlensing time delays using existing and near-future ground-based telescopes.

Figures (9)

• Figure 1: The simplified diagram of a single-lens system showing the light deflection under the gravity of the lens. In the diagram, the black solid line shows a small-angle-approximated light path from the source to the observer, $\theta_1$ and $\theta_2$ are the position angle of the lensed image, $\beta$ is the position angle of the source, and $\hat{\alpha}_1$ and $\hat{\alpha}_2$ are the deflection angles of the light paths.
• Figure 2: Plot of $A(u)$ and $f(u)$, the $u$-dependent parts of the magnification and time delay for a point-source point-lens microlensing configuration.
• Figure 3: (a) Two Gaussian wave packets separated by $\Delta t$ in the time domain correspond to (b) one Gaussian packet in the frequency domain with $(1+\cos(\omega \Delta t ))$ modulation. In the simple example of this figure, we let $\Delta t=3$ and $t_c = 0.15$, hence two adjacent peaks in (b) are separated by $2\pi/\Delta t \approx 2.1$ and the Gaussian envelop has width $2/t_c \approx 13$. All values in this example are unitless.
• Figure 4: An implementation of the protocol with linear optics. Incoming light is routed by a classical switch onto $O(T/t_c)$ different paths. Time delays are introduced such that the paths jointly interfere at a $P$-port, where $P=O(T/t_c$), followed by measurement with photodetectors.
• Figure 5: This figure shows, with two possible values of the signal-to-background ratio $Q$, how the confidence level of $\Delta t$ measurements increases with the number of signal photons. The confidence level for each $n_\mathrm{sig}$ is computed by numerical simulation of a scenario with $A=1.34$ and $T/t_c = 10^4$. Here $Q=1$ corresponds to the scenario with no background or noise photons, and $Q=0.4$ corresponds to the fiducial example of M-dwarf flares considered in our observation proposal. The $95\%$ confidence and $50\%$ confidence are marked by horizontal dashed lines.

Theorems & Definitions (2)

• Theorem 1
• proof