Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2407.15813

Gyroscopic stability for nanoparticles in Stern-Gerlach Interferometry and spin contrast

Zhou, Tian, Sougato Bose, Anupam Mazumdar

Published Jul 22, 2024• 0 citations
arXivHTMLPDF

Abstract

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. $10^{3}-10^{6}$~Hz for a mass of order $10^{-14}-10^{-17}$ 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.

DOI
10.48550/arxiv.2407.15813

Related papers

Gyroscopic stability for nanoparticles in Stern-Gerlach interferometry and spin contrast

Tian Zhou, Sougato Bose, Anupam Mazumdar

There is a severe impediment in Stern-Gerlach interferometry with a spin-embedded nanoparticle. This is because particle rotation creates a significant mismatch of the wave function of angular degrees of freedom during the creation and recombination of the spatial superposition, resulting in an inferior visibility contrast. We show that imparting angular momentum along the direction of a defect, such as the nitrogen-vacancy (NV) center, during the Stern-Gerlach interferometry provides excellent gyroscopic quantum stability to a nanodiamond, which opens up a way to maintain significant visibility in the quantum interference. The spin contrast improves by many folds for a wide-ranging value of the initial angular momentum, e.g., 10^3–10^6 Hz for a mass of order 10^{-14}–10^{-17} kg nanodiamond. Our scheme is independent of the material and is pertinent to any nanoparticle that can be used to create massive and large spatial superpositions with an embedded spin defect.

Physical Review A•Jun 30, 2025•9 citations

Two-dimensional matter-wave interferometer, rotational dynamics, and spin contrast

Ryan Rizaldy, Shrestha Mishra, Anupam Mazumdar

We investigate a two-dimensional matter-wave interferometer where both spatial and rotational dynamics of a nanoparticle are intertwined in closing the one-loop interferometer in the Stern-Gerlach type setup. We consider the spin-contrast of the nitrogen-vacancy (NV) centred nanodiamond in combination with a two-dimensional magnetic field setup to extend the one-dimensional Stern--Gerlach interferometry. We analyse the dynamical motion along with the rigid rotation under the influence of the external magnetic field. Regarding rotation, we incorporate Euler-angle dynamics to analyse the stability of rotational degrees of freedom and their influence on the spin contrast to address the Humpty-Dumpty problem. We show that by imparting external rotation provides the gyroscopic stability to the liberating mode of the NV-spin and hence helps to improve the contrast. Our scheme creates a tiny spatial superposition of size $\sim 0.21~{\rm μm}$ for mass $m=10^{-17}$kg in less than $t\sim 0.013$s.

quant-pharXiv:2603.05595•Mar 9, 2026•0 citations

Role of rotations in Stern-Gerlach interferometry with massive objects

Yonathan Japha, R. Folman

Realizing a spatial superposition with massive objects is one of the most fundamental challenges, as it will test quantum theory in new regimes, probe quantum-gravity, and enable to test exotic theories like gravitationally induced collapse. A natural extension of the successful implementation of an atomic Stern-Gerlach interferometer (SGI), is a SGI with a nano-diamond (ND) in which a single spin is embedded in the form of a nitrogen-vacancy center (NV). As the ND rotation, and with it the rotation of the NV spin direction, may inhibit such a realization, both in terms of Newtonian trajectories and quantum phases, we analyze here the role of rotations in the SGI. We take into account fundamental limits, such as those imposed by the quantum angular uncertainty relation and thermal fluctuations. We provide a detailed recipe for which a superposition of massive objects is enabled. This may open the door not only to fundamental tests, but also to new forms of quantum technology.

arXiv:2202.10535•Feb 21, 2022•2 citations

Spatial superposition for a two-dimensional matter-wave interferometer in an inverted harmonic potential with gyroscopic rotational stability

Ryan Rizaldy, Tian Zhou, Run Zhou +1 more

This study presents a mathematical model of the spatial and rotational motion of a nanodiamond in an inverted harmonic potential to create a macroscopic quantum spatial superposition. The model is based on the Stern-Gerlach Interferometer (SGI) scheme, which utilises linear and quadratic magnetic fields to generate a harmonic potential (linear magnetic field) and a non-linear potential (non-linear/quadratic magnetic field). By incorporating two-dimensional dynamics into the model, we provide a more realistic and accurate depiction of nanoparticle dynamics in linear and inverted harmonic potentials and explore the interaction between motion in a two-dimensional plane. Importantly, we derive the equations of motion for the rotational degrees of freedom, i.e. libration, precession, and rotation. The results show that adding a magnetic-field bias term to the magnetic-field profile in the linear stage affects the classical equations of motion but does not affect the width of the wave packet. Moreover, the libration mode always forms a harmonic potential at each stage because the applied initial angular velocity is dominated by the nanoparticle's defect axis, making it more stable in the presence of the trap frequency in the orthogonal direction along the axis that enables the creation of a macroscopic quantum superposition.

quant-pharXiv:2601.20949•APS Open Science•Jan 30, 2026•0 citations

Quantum control of Nitrogen-Vacancy spin in Diamonds: Towards matter-wave interferometry with massive objects

Naor Levi, Omer Feldman, Y. Rosenzweig +4 more

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.

arXiv:2508.15504•Aug 21, 2025•0 citations

Rotational stability in nanorotor and spin contrast in one-loop interferometry in the Stern-Gerlach setup

Ryan Rizaldy, Tian Zhou, Sougato Bose +1 more

The rotation of a nanoparticle in a quantum system has many applications, from theory to experiments. This paper will treat nanoparticle rotational dynamics for spin-embedded nanorotors. We will model it as a rigid body that properly treats the rotation in the coframe of the nanorotor in the presence of external fields. Besides rotation, we will further investigate how to create large spatial superpositions in the inhomogeneous external magnetic field, such as in the case of the Stern-Gerlach apparatus. The spin-embedded nanorotors play a crucial role in creating matter-wave interferometers through their spin and external magnetic field interaction Hamiltonian. We aim to provide a holistic interpretation of the dynamics of three Euler angles, their quantum evolution, and the nanorotor's spatial motion in a Stern-Gerlach-type setup, where we will consider one-full-loop interferometry. We will then study how the quantum evolution of all the Euler angles leads to a spin coherence loss upon interference and what manifests the Einstein-de Haas effect in an external magnetic field. In particular, we show that by imparting rotation along the direction of the magnetic field, we can stabilize the nanorotor's libration mode. We will also extend our analysis to a case where the initial state of the libration mode is thermal and discuss the contrast loss due to interference of the nanorotor upon one-loop completion.

arXiv:2412.15335•Physical Review Research•Jul 18, 2025•7 citations
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.
There is a severe impediment in Stern-Gerlach interferometry with a spin-embedded nanoparticle. This is because particle rotation creates a significant mismatch of the wave function of angular degrees of freedom during the creation and recombination of the spatial superposition, resulting in an inferior visibility contrast. We show that imparting angular momentum along the direction of a defect, such as the nitrogen-vacancy (NV) center, during the Stern-Gerlach interferometry provides excellent gyroscopic quantum stability to a nanodiamond, which opens up a way to maintain significant visibility in the quantum interference. The spin contrast improves by many folds for a wide-ranging value of the initial angular momentum, e.g., 10^3–10^6 Hz for a mass of order 10^{-14}–10^{-17} kg nanodiamond. Our scheme is independent of the material and is pertinent to any nanoparticle that can be used to create massive and large spatial superpositions with an embedded spin defect.
We investigate a two-dimensional matter-wave interferometer where both spatial and rotational dynamics of a nanoparticle are intertwined in closing the one-loop interferometer in the Stern-Gerlach type setup. We consider the spin-contrast of the nitrogen-vacancy (NV) centred nanodiamond in combination with a two-dimensional magnetic field setup to extend the one-dimensional Stern--Gerlach interferometry. We analyse the dynamical motion along with the rigid rotation under the influence of the external magnetic field. Regarding rotation, we incorporate Euler-angle dynamics to analyse the stability of rotational degrees of freedom and their influence on the spin contrast to address the Humpty-Dumpty problem. We show that by imparting external rotation provides the gyroscopic stability to the liberating mode of the NV-spin and hence helps to improve the contrast. Our scheme creates a tiny spatial superposition of size ∼0.21 μm\sim 0.21~{\rm μm}∼0.21 μm for mass m=10−17m=10^{-17}m=10−17kg in less than t∼0.013t\sim 0.013t∼0.013s.
Realizing a spatial superposition with massive objects is one of the most fundamental challenges, as it will test quantum theory in new regimes, probe quantum-gravity, and enable to test exotic theories like gravitationally induced collapse. A natural extension of the successful implementation of an atomic Stern-Gerlach interferometer (SGI), is a SGI with a nano-diamond (ND) in which a single spin is embedded in the form of a nitrogen-vacancy center (NV). As the ND rotation, and with it the rotation of the NV spin direction, may inhibit such a realization, both in terms of Newtonian trajectories and quantum phases, we analyze here the role of rotations in the SGI. We take into account fundamental limits, such as those imposed by the quantum angular uncertainty relation and thermal fluctuations. We provide a detailed recipe for which a superposition of massive objects is enabled. This may open the door not only to fundamental tests, but also to new forms of quantum technology.
This study presents a mathematical model of the spatial and rotational motion of a nanodiamond in an inverted harmonic potential to create a macroscopic quantum spatial superposition. The model is based on the Stern-Gerlach Interferometer (SGI) scheme, which utilises linear and quadratic magnetic fields to generate a harmonic potential (linear magnetic field) and a non-linear potential (non-linear/quadratic magnetic field). By incorporating two-dimensional dynamics into the model, we provide a more realistic and accurate depiction of nanoparticle dynamics in linear and inverted harmonic potentials and explore the interaction between motion in a two-dimensional plane. Importantly, we derive the equations of motion for the rotational degrees of freedom, i.e. libration, precession, and rotation. The results show that adding a magnetic-field bias term to the magnetic-field profile in the linear stage affects the classical equations of motion but does not affect the width of the wave packet. Moreover, the libration mode always forms a harmonic potential at each stage because the applied initial angular velocity is dominated by the nanoparticle's defect axis, making it more stable in the presence of the trap frequency in the orthogonal direction along the axis that enables the creation of a macroscopic quantum superposition.
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.
The rotation of a nanoparticle in a quantum system has many applications, from theory to experiments. This paper will treat nanoparticle rotational dynamics for spin-embedded nanorotors. We will model it as a rigid body that properly treats the rotation in the coframe of the nanorotor in the presence of external fields. Besides rotation, we will further investigate how to create large spatial superpositions in the inhomogeneous external magnetic field, such as in the case of the Stern-Gerlach apparatus. The spin-embedded nanorotors play a crucial role in creating matter-wave interferometers through their spin and external magnetic field interaction Hamiltonian. We aim to provide a holistic interpretation of the dynamics of three Euler angles, their quantum evolution, and the nanorotor's spatial motion in a Stern-Gerlach-type setup, where we will consider one-full-loop interferometry. We will then study how the quantum evolution of all the Euler angles leads to a spin coherence loss upon interference and what manifests the Einstein-de Haas effect in an external magnetic field. In particular, we show that by imparting rotation along the direction of the magnetic field, we can stabilize the nanorotor's libration mode. We will also extend our analysis to a case where the initial state of the libration mode is thermal and discuss the contrast loss due to interference of the nanorotor upon one-loop completion.