Diamagnetic micro-chip traps for levitated nanoparticle entanglement experiments (2411.02325v1)

Abstract: The Quantum Gravity Mediated Entanglement (QGEM) protocol offers a novel method to probe the quantumness of gravitational interactions at non-relativistic scales. This protocol leverages the Stern-Gerlach effect to create $\mathcal{O}(\sim \mu m)$ spatial superpositions of two nanodiamonds (mass $\sim 10^{-15}$ kg) with NV spins, which are then allowed to interact and become entangled solely through the gravitational interaction. Since electromagnetic interactions such as Casimir-Polder and dipole-dipole interactions dominate at this scale, screening them to ensure the masses interact exclusively via gravity is crucial. In this paper, we propose using magnetic traps based on micro-fabricated wires, which provide strong gradients with relatively modest magnetic fields to trap nanoparticles for interferometric entanglement experiments. The design consists of a small trap to cool the center-of-mass motion of the nanodiamonds and a long trap with a weak direction suitable for creating macroscopic superpositions. In contrast to permanent-magnet-based long traps, the micro-fabricated wire-based approach allows fast switching of the magnetic trapping and state manipulation potentials and permits integrated superconducting shielding, which can screen both electrostatic and magnetic interactions between nanodiamonds in a gravitational entanglement experiment. The setup also provides a possible platform for other tests of quantum coherence in macroscopic systems and searches for novel short-range forces.

• The paper introduces a novel diamagnetic micro-chip trap that leverages superconducting shielding to isolate electromagnetic forces.
• It employs micro‐fabricated wire configurations to generate strong magnetic gradients, allowing precise nanoparticle manipulation and cooling.
• The research demonstrates potential for advanced quantum coherence tests and probing short-range gravitational forces in macroscopic systems.

Diamagnetic Micro-Chip Traps for Levitated Nanoparticle Entanglement Experiments

Introduction

This paper explores the development of a diamagnetic micro-chip trap system designed for levitated nanoparticle entanglement experiments, targeting the probing of quantum gravity via the Quantum Gravity Mediated Entanglement (QGEM) protocol. The innovation lies in using magnetic traps based on micro-fabricated wires to facilitate gravitational interactions between nanodiamonds, incorporating electromagnetic screening to isolate gravitational effects.

Figure 1: Schematic drawing of the two diamagnetically trapped nanodiamonds on either side of a microfabricated chip, functioning as an electromagnetic screen.

Trapping and Screening Mechanism

The proposed chip-based approach employs micro-fabricated wires for magnetic trapping. This setup enables the creation of strong magnetic gradients, facilitating the trapping and manipulation of nanoparticles:

• Magnetic Shielding: A superconducting (SC) shield is integrated to screen electromagnetic interactions, crucial for ensuring gravitational interactions dominate at the experimental scale. This configuration allows reducing the separation between the test masses, enhancing the entanglement potential by isolating gravitational influence.

  Figure 2: A comparison of the potentials such as electric dipole-dipole (DD), Casimir-Polder (CP), and magnetic dipole-dipole (MM) between two spheres compared to gravitational (GR) interaction.

Micro-Fabricated Wire Design

The traps are based on configurations akin to those in Bose-Einstein Condensates (BEC) traps, using wire arrangements to provide dynamic electromagnetic fields:

• Trapping Potential: The diamagnetic properties of diamonds enable magnetic trapping. The optimal balance between electromagnetic interactions and diamagnetic trapping is critical, with potential fluctuations requiring meticulous control.

  Figure 3: Chip-based magnetic trap with micro-fabricated wires, including three traps with specific dimensions to enhance trapping efficiency.

Experimental Setup and Constraints

In designing the diamagnetic trapping systems, specific constraints are addressed to ensure operational efficiency:

• Superconducting Shield: The shield must operate in the Meissner state to provide effective electromagnetic screening while maintaining a magnetic field below the critical threshold.

  Figure 4: Visual representation of the potential shifts and magnetic field configuration due to superconducting shielding and wire arrangement.

• Nanodiamond Manipulation: Nanodiamonds can be manipulated for cooling and interferometric experiments, using a combination of short and long traps to achieve quantum superpositions and entanglement.

Prospects and Challenges

The potential of this setup extends beyond QGEM experiments:

• Quantum Coherence Tests: The system provides a platform for testing quantum coherence and exploring non-classical states in macroscopic systems.
• Short-Range Force Investigations: The capability of the setup for fine control at micron scales offers a promising tool for investigating novel short-range forces.

Conclusion

This research presents an integrated approach to trapping and manipulating nanoparticles, crucial for gravity-mediated entanglement experiments. The design leverages high-precision magnetic fields and superconducting shielding to enable substantial advancements in macroscopic quantum experiments. Future research will focus on refining control mechanisms and further exploring the scalability of this approach for broader applications in quantum physics.

In conclusion, the development of diamagnetic micro-chip traps for levitated nanoparticles highlights a significant step towards practical implementations of quantum gravity experiments, offering both a robust experimental framework and a versatile tool for exploring quantum mechanics at macroscopic scales.