LEVITAS: Levitodynamics for Accurate Individual Particle Sensing in Space

TL;DR

LEVITAS targets direct in-situ sensing of neutral particles in space by tracking a single levitated nanoparticle with quantum-limited interferometric readout. The approach uses a damped harmonic oscillator model for the nanoparticle, Kalman filtering, and Bayesian inference to recover impulse moments $p_I$ and times $t_I$, from which gas density, temperature, velocity, and composition are inferred via a shifted Maxwell–Boltzmann framework. Demonstrative simulations cover LEO and interstellar neutral flows, showing high precision for dense regimes and feasible measurements for sparse regimes with multiplexing. The architecture (delivery, trapping, electronics) supports extension to higher densities, 3D momentum resolution, and quantum-enhanced sensing, enabling precise characterisation of upper-atmosphere, exosphere, and heliospheric neutral distributions.

Abstract

Accurately observing the rarefied media of the upper atmosphere, exosphere, and planetary and solar system environments and beyond requires highly sensitive metrological techniques. We present the operating concept and architecture of an in-situ sensing solution based on the dynamics of a levitated nanoparticle (levitodynamics). It can detect and measure impacts of individual particles in rarefied media. Dubbed `LEVITAS', our sensor consists of a dispenser of dielectric nanoparticles and optical trapping of a single nanoparticle in the focus of a laser beam. The trapped nanoparticle constitutes a harmonic oscillator at frequencies in the kilohertz range whose position can be tracked at the standard quantum limit by interferometric detection of the laser photons it scatters. Here, we simulate microcanonical impacts on the nanoparticle and show that the density, velocity, temperature, and composition of the surrounding medium can be estimated accurately. We illustrate the performance of LEVITAS in circumstances ranging from low Earth orbit out to exospheric distances, across which individual impacts can be detected at favourable rates. Furthermore, LEVITAS may be employed to accurately measure highly rarefied neutral distributions within vastly different areas of momentum space. This we demonstrate by simulating the measurement of high-velocity neutral gas particles from the interstellar medium penetrating the heliosphere and flowing through our solar system.

Figures (9)

• Figure 1: Schematic demonstrating the operation of LEVITAS in one dimension; a dielectric nanoparticle is trapped at the focus of a laser beam, and exposed to a rarefied medium outside the spacecraft. Collisions with individual neutral species therein lead to nanoparticle recoil with momentum $p_\text{I}$ at time $t_\text{I}$. The objective of LEVITAS is to provide their estimates $p'_\text{I}$ and $t'_\text{I}$ respectively. These can be used to estimate the density, velocity, temperature, and composition of the target medium or enable high fidelity reconstructions of the underlying distribution function itself. See Fig. \ref{['fig:design']} for the full sensor head.
• Figure 2: Recoil momentum estimation from a trajectory subject to four individual impacts, simulated for the parameters in Table \ref{['table:sim_params']}. Top: A record of the nanoparticle's dispacement. Middle: a Kalman filter is used to obtain a moving average (over a quarter the trap cycle) estimate of the recoil momentum $\tilde{p}_\text{I}$, with impact times flagged by peaks above the threshold level $p_{\text{th}} =$ 18 u km/s denoted by the black dashed line. Bottom: flagged impact times are used as initial guesses for a Bayesian inference calculation, used to compute final estimates of $t_\text{I}'$ and $p_\text{I}'$ and the corresponding errors. Red squares and dashed lines mark the momenta and times of the true impacts respectively. The horizontal errors in the impact times are magnified to represent $100\sigma$.
• Figure 3: Detection of individual impacts applied uniformly in time at a rate 3000/s, and identical momentum of $p_\text{I}=$ 36.73 u km/s (denoted with the red dashed line). The error bars on the points in the top plot are hidden for clarity. The histogram contains 2996 events with sample mean $36.84\pm3.15$ u km/s and mean recoil estimated error of $\sigma_\text{det}=3.15\pm0.03$ u km/s. The momentum threshold was set to $p_{\text{th}} =$ 18 u km/s as in Fig. \ref{['fig:kick-demo']}.
• Figure 4: Inference of parameters $\bm{\theta}=\{T,w,c_0,\cdots,c_5\}$ in LEO at 600 km altitude with $n=2.71\times 10^6/\text{cm}^3$ with 2.01% H, 11.5% He, 1.97% N, 83.2% O, 1.33% $\text{N}_2$, and 0.13% $\text{O}_2$. The error-bars shown represent sample standard deviation for 100 repeated runs of the simulation. In the case of wind speed, the relative error is taken w.r.t. the spacecraft speed $|v_s|=7.5$ km/s. Left: Variation of the relative error in the best estimates $\bm{\theta}_\text{MLE}$ with measurement time $\tau$ at $T=1045$ K and $w=0$ m/s. Top right: Example data histogram at $\tau=60$ s, $T=1045$ K, and $w=0$ m/s. The black dashed curve shows the Eq. \ref{['eq:measurement-process']} evaluated at $\bm{\theta}_\text{MLE}$, while the coloured curves with shaded areas correspond to the different terms contributing to the sum in Eq. \ref{['eq:recoil_distribution']} evaluated at $\bm{\theta}_\text{MLE}$. Bottom right: Relative error for different values of $T$ (middle) and $w$ (right), at $\tau=$ 60 s.
• Figure 5: Inference of parameters $\bm{\theta}=\{T,w,c_0,\cdots,c_3\}$ in LEO at 1000 km altitude with $n=1.21\times 10^5/\text{cm}^3$ with 31.6% H, 61.9% He, 0.3% N, and 6.17% O. The error-bars shown represent the sample standard deviation for 100 repeated runs of the simulation. In the case of wind speed, the relative error is taken w.r.t. the spacecraft speed $|v_s|=7.3$ km/s. Left: Variation of the relative error in the best estimates $\bm{\theta}_\text{MLE}$ with measurement time $\tau$ at $T=1045$ K and $w=0$ m/s. Top right: example data histogram at $\tau=300$ s, $T=1045$ K, and $w=0$ m/s. The black dashed curve shows the Eq. \ref{['eq:measurement-process']} evaluated at $\bm{\theta}_\text{MLE}$, while the coloured curves with shaded areas correspond to the different terms contributing to the sum in Eq. \ref{['eq:recoil_distribution']} evaluated at $\bm{\theta}_\text{MLE}$. Bottom right: Relative error for different values of $T$ (middle) and $w$ (right), at $\tau=$ 600 s.