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arXiv:2110.14436 · Quantum Technology: Driving Commercialisation of an Enabling Science

Towards a test of quantum gravity with a levitated nanodiamond containing a spin

Benjamin D. Wood, Gavin W. Morley

Published Oct 6, 2021• 1 citation
arXivHTMLPDF

Abstract

There is significant interest in potential experimental tests of macroscopic quantum effects, both to test potential modifications to quantum theory and to probe the quantum nature of gravity. A proposed platform with which to generate the required macroscopic quantum spatial superposition is a nanodiamond containing a negatively charged nitrogen vacancy (NV-) centre. In this review, methods to fabricate nanodiamonds containing NV­suitable for these quantum applications are discussed. The proposed probes of the macroscopic limits of quantum theory are presented along with the spin physics of the NV- centre relevant to those tests.

DOI
10.1117/12.2601348

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There is significant interest in potential experimental tests of macroscopic quantum effects, both to test potential modifications to quantum theory and to probe the quantum nature of gravity. A proposed platform with which to generate the required macroscopic quantum spatial superposition is a nanodiamond containing a negatively charged nitrogen vacancy (NV-) centre. In this review, methods to fabricate nanodiamonds containing NV­suitable for these quantum applications are discussed. The proposed probes of the macroscopic limits of quantum theory are presented along with the spin physics of the NV- centre relevant to those tests.
We propose a current-carrying-chip scheme for generating spatial quantum superpositions using a levitating nanodiamond with a built-in nitrogen-vacancy (NV) centre defect. Our setup is quite versatile and we aim to create the superposition for a mass range of 10−19 kg<m<10−15 kg10^{-19}~{\rm kg}< m< 10^{-15}~{\rm kg}10−19 kg<m<10−15 kg and a superposition size O(10)μm<Δx<O(1)nm{\cal O}(10) {\rm μm} < Δx < {\cal O}(1){\rm nm}O(10)μm<Δx<O(1)nm, respectively, in t≤0.1t\leq 0.1t≤0.1s, depending on the position we launch from the center of the diamagnetic trap. We provide an in-depth analysis of two parallel chips that can create levitation and spatial superposition along the xxx-axis, while producing a very tight trap in the yyy direction, and the direction of gravity, i.e., the zzz direction. Numerical simulations demonstrate that our setup can create a one-dimensional spatial superposition state along the x-axis. Throughout this process, the particle is stably levitated in the z-direction, and its motion is effectively confined in the y-direction for a Gaussian initial condition. This setup presents a viable platform for a diamagnetically levitated nanoparticle for a table-top experiment exploring the possibility of creating a macroscopic Schrödinger Cat state to test the quantum gravity induced entanglement of masses (QGEM) protocol.
Levitated nanodiamonds containing negatively charged nitrogen-vacancy centers $({\text{NV}}^{\ensuremath{-}})$ have been proposed as a platform to generate macroscopic spatial superpositions. Requirements for this include having a long ${\text{NV}}^{\ensuremath{-}}$ spin coherence time, which necessitates formulating a dynamical decoupling strategy in which the regular spin flips do not cancel the growth of the superposition through the Stern-Gerlach effect in an inhomogeneous magnetic field. Here, we propose a scheme to place a $250\text{\ensuremath{-}}\mathrm{n}\mathrm{m}$-diameter diamond in a superposition with spatial separation of over 250nm250\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{m}250nm, while incorporating dynamical decoupling. We achieve this by letting a diamond fall for 2.4m2.4\phantom{\rule{0.16em}{0ex}}\mathrm{m}2.4m through a magnetic structure, including 1.13m1.13\phantom{\rule{0.16em}{0ex}}\mathrm{m}1.13m in an inhomogeneous region generated by magnetic teeth.
A key open problem in physics is the correct way to combine gravity (described by general relativity) with everything else (described by quantum mechanics). This problem suggests that general relativity and possibly also quantum mechanics need fundamental corrections. Most physicists expect that gravity should be quantum in character, but gravity is fundamentally different to the other forces because it alone is described by spacetime geometry. Experiments are needed to test whether gravity, and hence space-time, is quantum or classical. We propose an experiment to test the quantum nature of gravity by checking whether gravity can entangle two micron-sized crystals. A pathway to this is to create macroscopic quantum superpositions of each crystal first using embedded spins and Stern-Gerlach forces. These crystals could be nanodiamonds containing nitrogen-vacancy (NV) centres. The spins can subsequently be measured to witness the gravitationally generated entanglement. This is based on extensive theoretical feasibility studies and experimental progress in quantum technology. The eventual experiment will require a medium-sized consortium with excellent suppression of decoherence including vibrations and gravitational noise. In this white paper, we review the progress and plans towards realizing this. While implementing these plans, we will further explore the most macroscopic superpositions that are possible, which will test theories that predict a limit to this.
This thesis explores how to create macroscopic matter-wave interferometers (MMWIs) using nanodiamonds with nitrogen-vacancy (NV) centers. MMWIs are important for testing the limits of quantum mechanics and studying the possible quantum nature of gravity. However, building MMWIs with large masses is very challenging because of decoherence and the diamagnetic properties of diamonds. This work presents several experimental schemes to increase the spatial separation of massive quantum objects. The key idea is to use the diamagnetism of diamonds not only as a limitation but also as a tool to help separate wave packets. Methods include catapulting trajectories with nonlinear magnetic fields, using diamagnetic repulsion, combining gravitational acceleration with magnetic fields, and applying inverted harmonic potentials. The results show that it is possible to achieve large spatial superpositions, up to tens of micrometers, in short timescales. While a full-scale MMWI is still difficult to realize, these findings may contribute to future efforts to observe quantum effects in macroscopic systems.
Creating macroscopic spatial quantum superposition with a nanoparticle has a multitude of applications, ranging from testing the foundations of quantum mechanics, matter-wave interferometer for detecting gravitational waves and probing the electromagnetic vacuum, dark matter detection and quantum sensors to testing the quantum nature of gravity in a lab. In this paper, we investigate the role of rotation in a matter-wave interferometer, where we show that imparting angular momentum along the direction of a defect, such as one present in the nitrogen-vacancy centre of a nanodiamond can cause an enhancement in spin contrast for a wide-ranging value of the angular momentum, e.g. 103−10610^{3}-10^{6}103−106~Hz for a mass of order 10−14−10−1710^{-14}-10^{-17}10−14−10−17 Kg nanodiamond. Furthermore, the imparted angular momentum can enhance the spatial superposition by almost a factor of two and possibly average out any potential permanent dipoles in the nanodiamond.
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 previously unexplored regimes. It also opens the possibility of probing the interface between QM and GR, such as testing the quantization of gravity. Consequently, there exists an intensive effort to realize such an interferometer. While several approaches are being explored, we focus on utilizing nanodiamonds with embedded spins as test particles which, in combination with Stern-Gerlach forces, enable the realization of a closed-loop matter-wave interferometer 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. Here we present our work on quantum control of a nitrogen-vacancy spin system in bulk diamonds and in levitated diamonds as a step towards Stern-Gerlach interferometry with levitated nanodiamonds. Our simulations show that the current state of the art for spin coherence time in nanodiamonds of a few tens of microseconds, is good enough to enable an SGI spatial splitting on the order of nanometers for an ND composed of 10^7 atoms. We would be happy to make available more details upon request.