Strong Confinement of a Nanodiamond in a Needle Paul Trap: Towards Matter-Wave Interferometry with Massive Objects

TL;DR

This work addresses the challenge of realizing matter-wave interferometry with massive objects by developing a strongly confining needle Paul trap for levitated nanodiamonds with embedded NV spins. The authors design and characterize a trap with tunable electrode spacing and electrospray charging, achieving trap frequencies up to $40\,\mathrm{kHz}$ and enabling precise angular and positional control. Experimental results yield a charge-to-mass ratio of $Q/m=2.92\ \mathrm{C/kg}$, a DC offset of $9\ \mathrm{V}$, and a center-of-mass localization near $\sigma_z\approx 370\ \mathrm{nm}$ under $0.2\ \mathrm{Torr}$, with potential improvements for deep cooling and interferometry. The work demonstrates that strong confinement in a needle Paul trap can be a valuable tool for advancing massive matter-wave interferometry and tests of quantum principles at macroscopic scales, supporting broader community efforts toward ND-based SG interferometry and gravity-related probes.

Abstract

Quantum mechanics (QM) and General relativity (GR), also known as the theory of gravity, are the two pillars of modern physics. A matter-wave interferometer with a massive particle, can test numerous fundamental ideas, including the spatial superposition principle - a foundational concept in QM - in completely new regimes, as well as the interface between QM and GR, e.g., testing the quantization of gravity. Consequently, there exists an intensive effort to realize such an interferometer. While several paths are being pursued, we focus on utilizing nanodiamonds as our particle, and a spin embedded in the nanodiamond together with Stern-Gerlach forces, to achieve a closed loop in space-time. There is a growing community of groups pursuing this path [1]. We are posting this technical note (as part of a series of seven such notes), to highlight our plans and solutions concerning various challenges in this ambitious endeavor, hoping this will support this growing community. In this work, we achieve strong confinement of a levitated particle, which is crucial for angular confinement, precise positioning, and perhaps also advantageous for deep cooling. We designed a needle Paul trap with a controllable distance between the electrodes, giving rise to a strong electric gradient. By combining it with an effective charging method - electrospray - we reach a trap frequency of up to 40 kHz, which is more than twice the state of the art. We believe that the designed trap could become a significant tool in the hands of the community working towards massive matter-wave interferometry. We would be happy to make more details available upon request.

Figures (3)

• Figure 1: Needle trap design and simulations. A. Microscope image of the needle trap. The tungsten steel needles (WG-38.0-10) are fixed inside the ground sleeves and isolated from them by dielectric PEEK tubes. The diameter of the needle tips is approximately $14\,\rm\mu m$. B. ND (Adamas Nanotechnologies, 40 nm nominal diameter) levitating in the needle Paul trap. The diamond is illuminated with a green laser and observed with a CCD camera at 45 degrees to the needles. The distance between the needles is 730$\,\mu \rm m$. C. Dependence of the voltage efficiency factor, $\eta$, on the distance between the needles, $d$, according to 3D numerical simulations. One can see that, on the one hand, $\eta$ has a reasonable value at large distances and, on the other hand, its decrease at smaller distances (down to $25\,\rm\mu m$) is such that $\frac{\Delta \eta}{\eta}<\frac{\Delta d^2}{d^2}$. Therefore, decreasing $d$ in order to increase the trap frequency [see \ref{['eq:omega_z', 'eq:q_alfa and omega_alfa']}] is still justified. Inset: Electric field distribution in the trap for $d = 50\,\rm\mu m$ at 1 V DC applied to the needles.
• Figure 2: The experimental setup. A. The scheme of the setup. The needles are fixed inside an octagon vacuum chamber on two linear motorized piezo stages (Newport CONEX-AG-LS25-27P), connected to the controllers via vacuum feedthroughs. One of the stages controls the distance between the needles, and another controls the position of both needles. The trap is powered by a signal generator and a voltage amplifier (TREK model 2210). An infrared laser beam ($\lambda = 1550\rm\,nm$) of total power $P\simeq 50\,\rm mW$ is focused into the trap with lens 1 (NA = 0.5). The scattered and unscattered light are collimated by lens 2 (NA = 0.39) and then split by a D-shaped mirror into two inputs of a balanced photodiode. The signal is analyzed with an NI PCI-5922 board serving as a spectrum analyzer. A green laser is used to illuminate the particle. The particle is detected with a visible-range or infrared (IR) camera. B. Photo of the trap inside the octagon chamber. C. Electrospray system. The electrospray system (MolecularSpray UHV4i) is assembled vertically, so that the needle emitting the diamond solution is on top. The high voltage is applied to the solution, so that the charged particles fly from the needle through the grounded entrance capillary (internal diameter 0.25 mm) inside the vacuum. Entrance capillary leads to the "Stage 1" which is separated from the octagon vacuum chamber with an additional differential-pumping aperture and is connected to a separate rotary pump.
• Figure 3: Particle's motion spectrum at different distances between the needles. A. Power spectral density (PSD) of the split-detection signal of a diamond nanoparticle at three different distances between the needles $d$. The particle (Adamas Nanotechnologies, 40 nm nominal diameter) was trapped at a fixed RF voltage and frequency $V_0 = 326\,\rm V_{pp},$$\Omega_{rf}=2\pi \times 114\,\rm kHz$ and at a fixed pressure of $0.2\rm\,Torr$. The distance between the needles was scanned using the piezo stage 1. The secular-motion peaks are clearly visible; all the other sharper peaks correspond to noise independent of the trap's parameters. B. Maximum trap frequency as a function of the distance between the needles. The model takes into account higher-order corrections beyond the pseudopotential approximation according to Lindvall_2022, because $q_z$ reaches a value of 0.75 at the smallest distances. The dependence $\eta(d)$ is also taken into account. The model has two free parameters: the charge-to-mass ratio of the particle estimated by the fit as $Q/m = 2.92\,\rm C/kg$, and DC-shift of the applied voltage, estimated to be $U_0=9\,\rm V$ (the latter coincides with the independently measured value). See \ref{['Appendix']} for the model's details. We observed jumps of the trap frequency between two values separated by approximately 1 kHz, likely corresponding to two stable equilibrium positions, but further study is needed. The graph shows the highest-frequency mode.