Proposal for macroscopic delocalisation of a large mass in a RF trap

TL;DR

The paper investigates engineering a spatial quantum superposition of a mesoscopic charged nanoparticle by co-trapping it with a single atomic ion in a dual-frequency RF Paul trap. The authors propose a protocol in which a spin-dependent displacement of the ion, implemented via a state-dependent kick, induces a distance-dependent Coulomb interaction that coherently displaces the nanoparticle, yielding a three-way entangled ion-spin–ion–nanoparticle state and a measurable nanoparticle delocalisation. Using experimentally accessible parameters, they show the nanoparticle can be displaced by a few nanometers, larger than its ground-state wavefunction width, while remaining smaller than the particle size. They discuss decoherence mechanisms and note that under ultrahigh vacuum and controlled voltages, the coherence can persist long enough to enable the readout and validation of macroscopic delocalisation, marking a step toward tests of quantum-classical boundaries and potential sensing applications.

Abstract

Engineering coherent spatial superpositions of levitated large masses is an ongoing challenge. Borrowing from recent experimental work, we consider a charged mass of hundreds of nanometers size (``nanoparticle'') co-trapped with an ion in a Paul trap, and propose a scheme to manipulate its spatial state through the Coulomb interaction with the ion. We focus on the achievable delocalisation, only sketching the other challenges of the protocol (initial cooling, preservation of coherence for long-enough times, and detection). We prove that our scheme can displace coherently the nanoparticle by a few nanometers, with state-of-the-art parameters. Though smaller than the nanoparticle's size, this is much larger than the wavefunction of the trap's ground state. Thus the co-trapping scheme is in principle able to demonstrate macroscopic delocalisation of a charged nanoparticle.

Figures (6)

• Figure 1: Exemplary schematic of the setup, showing a linear dual frequency Paul trap. The blue electrodes are driven by the fast voltage while the purple-colour electrodes are driven by the slow voltage. The green-colour electrodes are the end-cap electrodes driven by a DC voltage. The distances and co-trapped particles are indicated in the figure; the figure is not to scale. Such a setup was proposed an realized in Ref. bykov2024nanoparticle.
• Figure 2: For different displacements in the ion equilibrium state. The end-cap voltage is taken to be $500$ V, which (solving the equations of motion) gives an equilibrium separation of $\sim 40\,µm$ between the particles. The dashed line indicates the width of the nanoparticle's wavefunction cooled in the ground state of the trap, $z_{0,\text{NP}} = \sqrt{\hbar/(2m_\text{NP}\omega_{z,\text{NP}})}$.
• Figure 3: Impression to accompany eq. \ref{['eq:delz-res']}, which gives the superposition size created via the protocol proposed in this work. The Coulomb interaction induces a superposition of equilibrium positions $d_\text{eq}^\pm$ (purple/blue) in the initial state (black).
• Figure 4: For different displacements in the ion equilibrium state. The end-cap voltage is taken to be $400$ V, which (solving the equations of motion) gives an equilibrium separation of $\sim 43\,µm$ if $Q_\text{NP}=800e$ and $\sim 33\,µm$ if $Q_\text{NP}=300e$. The horizontal lines indicate the width of the wave-packet, $z_{0,\text{NP}} = \sqrt{\hbar/(2m_\text{NP}\omega_{z,\text{NP}})}$, which also depends on the number of charges (solid for $800e$, dashed for $300e$).
• Figure 5: A visual representation of the regime $\abs{a_{x,y}}\ll q_{x,y}^2/2$ (the approximate stability condition for trapping in the radial plane) and $a_z>0$ (stability for the axial direction), as shown by the shaded black and blue areas, respectively. The points represent correspond to the values of $a$, $q$ for the experimental parameters given in sec. \ref{['sec:protocol']}.