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Toward Spin-Dependent Macroscopic Matter-Wave Interferometers: Potential Methods and Approaches

Run Zhou

Published Nov 19, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.33612/diss.1431772913

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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.
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.
Creating macroscopic spatial superposition states is crucial for investigating matter-wave interferometry and advancing quantum sensor technology. Currently, two potential methods exist to achieve this objective. The first involves using inverted harmonic potential (IHP) to spatially delocalize quantum states through coherent inflation [New J. Phys. 19, 123029 (2017)]. The second method employs a spin-dependent force to separate two massive wave packets spatially [Phys. Rev. Lett. 111, 180403 (2013)]. The disadvantage of the former method is the slow initial coherent inflation, while the latter is hindered by the diamagnetism of spin-embedded nanocrystals, which suppresses spatial separation. In this study, we integrate two methods: first, we use the spin-dependent force to generate initial spatial separation, and second, we use IHP to achieve coherent inflating trajectories of the wave packets. This approach enables the attainment of massive large spatial superposition in minimal time. For instance, a spatial superposition with a mass of ${10}^{\ensuremath{-}15}\phantom{\rule{0.16em}{0ex}}\mathrm{kg}$ and a size of around $50\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{m}$ is realized in 0.1 s. We also calculate the evolution of wave packets in both harmonic potential (HP) and IHP using the path integral approach.
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 discuss the design considerations for a high-precision enhanced-coherence nanodiamond source, review the fabrication processes used to produce nanodiamond pillars measuring 40 x 65 x 80 nm, summarize the characterization work completed to date, and conclude with an outlook on the remaining steps needed to finalize the source fabrication. We would be happy to make available more details upon request.
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.
A large spatial quantum superposition of size $O(1\text{--}10)\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{m}$ for mass $m\ensuremath{\sim}{10}^{\ensuremath{-}17}\text{--}{10}^{\ensuremath{-}14}$ kg is required to probe the foundations of quantum mechanics and test the classical and quantum nature of gravity via entanglement in a laboratory. In this paper, we will show that it is possible to accelerate the two spin states of a macroscopic nanocrystal sourced by the inhomogeneous nonlinear magnetic field in a Stern-Gerlach-type setup. We will assume that the electronic spin can be embedded at the center of the nanocrystal, such as the nitrogen-vacancy (NV) center of diamond. Our analysis will be generic to any dopant or any material. We will show that we can create a desired superposition size within 1–21\text{--}21–2 s by catapulting the trajectories of the two spin states with a modest magnetic field gradient and then recombine the trajectories for a coherent interference. We will show the demanding nature of the precision required in the magnetic field to recover a 9999%99 spin coherence confidence level at the moment of interference.
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.