In this paper, we will show how finite-temperature corrections and spin-dependent/independent noise will affect the contrast in a matter-wave interferometer, especially with massive objects and large spatial superposition sizes. Typically, spin is embedded in a nanoparticle as a defect, which can be manipulated by the external magnetic field to create a macroscopic quantum superposition. These massive matter-wave interferometers are the cornerstone for many new fundamental advancements in physics; particularly, macroscopic quantum superposition can use entanglement features to, e.g., test physics beyond the Standard Model, test the equivalence principle, improve quantum sensors, and test the quantum nature of spacetime in a lab. We will consider a Stern-Gerlach type apparatus to create macroscopic quantum superposition in a harmonic oscillator trap, and figure out the spin contrast loss due to linear spin-independent and spin-dependent noise in a single interferometer. We will show that spin contrast loss due to spin-independent noise does not depend on the initial thermal state of the matter wave function. However, spin contrast loss due to spin-dependent fluctuations do depend on the initial thermal occupation of the quantum state. We will keep our discussion general as far as the noise parameters are concerned.In this paper, we will show how finite-temperature corrections and spin-dependent/independent noise will affect the contrast in a matter-wave interferometer, especially with massive objects and large spatial superposition sizes. Typically, spin is embedded in a nanoparticle as a defect, which can be manipulated by the external magnetic field to create a macroscopic quantum superposition. These massive matter-wave interferometers are the cornerstone for many new fundamental advancements in physics; particularly, macroscopic quantum superposition can use entanglement features to, e.g., test physics beyond the Standard Model, test the equivalence principle, improve quantum sensors, and test the quantum nature of spacetime in a lab. We will consider a Stern-Gerlach type apparatus to create macroscopic quantum superposition in a harmonic oscillator trap, and figure out the spin contrast loss due to linear spin-independent and spin-dependent noise in a single interferometer. We will show that spin contrast loss due to spin-independent noise does not depend on the initial thermal state of the matter wave function. However, spin contrast loss due to spin-dependent fluctuations do depend on the initial thermal occupation of the quantum state. We will keep our discussion general as far as the noise parameters are concerned.

arXiv:2503.13656Mar 17, 20250 citations

Magnetic noise in macroscopic quantum spatial superpositions

Sneha Narasimha Moorthy, Andrew A. Geraci, Sougato Bose +1 more

In this paper, we will show how random fluctuations in the magnetic field will jitter the paths of a matter-wave interferometer randomly, hence, decohere the quantum superposition. To create a large spatial superposition with nanoparticles, we envisage embedding a spin in a nanoparticle as a defect and applying an inhomogeneous magnetic field as in a Stern-Gerlach type experiment to create a macroscopic quantum superposition. Such matter-wave interferometers are the cornerstone for many new fundamental advancements in physics; particularly, adjacent matter-wave interferometers can use entanglement features to test physics beyond the Standard Model, test the equivalence principle, improve quantum sensors, and test the quantum nature of spacetime in a lab. In particular, we will use white and flicker noise to study the decoherence and constrain the parameters keeping in mind ambient temperatures suitable for superconducting wires embedded on a chip. We will show that to obtain a tiny spatial superposition of a nanometer separation, $Δx \sim {\cal O} (10^{-9})$ m and to minimize decoherence, $Γ\leq {\cal O}(\frac{ω_0}{2π})$ , where $Γ$ is the decoherence and $ω_0$ is the frequency of the oscillator, we will need current fluctuations to be $δI/I\leq {\cal O}(10^{-8})$ , which is not impossible to obtain in superconducting wire arrangements. For such tiny fluctuations, we demonstrate that the Humpty-Dumpty problem in a matter-wave interferometer arising from a mismatch in position and momentum does not cause a loss in contrast.In this paper, we will show how random fluctuations in the magnetic field will jitter the paths of a matter-wave interferometer randomly, hence, decohere the quantum superposition. To create a large spatial superposition with nanoparticles, we envisage embedding a spin in a nanoparticle as a defect and applying an inhomogeneous magnetic field as in a Stern-Gerlach type experiment to create a macroscopic quantum superposition. Such matter-wave interferometers are the cornerstone for many new fundamental advancements in physics; particularly, adjacent matter-wave interferometers can use entanglement features to test physics beyond the Standard Model, test the equivalence principle, improve quantum sensors, and test the quantum nature of spacetime in a lab. In particular, we will use white and flicker noise to study the decoherence and constrain the parameters keeping in mind ambient temperatures suitable for superconducting wires embedded on a chip. We will show that to obtain a tiny spatial superposition of a nanometer separation, $Δx \sim {\cal O} (10^{-9})$m and to minimize decoherence, $Γ\leq {\cal O}(\frac{ω_0}{2π})$, where $Γ$ is the decoherence and $ω_0$ is the frequency of the oscillator, we will need current fluctuations to be $δI/I\leq {\cal O}(10^{-8})$, which is not impossible to obtain in superconducting wire arrangements. For such tiny fluctuations, we demonstrate that the Humpty-Dumpty problem in a matter-wave interferometer arising from a mismatch in position and momentum does not cause a loss in contrast.

arXiv:2504.13252Physical Review AJul 15, 20255 citations

Magnetic noise in macroscopic quantum spatial superposition induced by inverted harmonic oscillator potential

Sneha Narasimha Moorthy, Anupam Mazumdar

We investigate a Stern-Gerlach type matter-wave interferometer where an inhomogeneous magnetic field couples to an embedded spin in a nanoparticle to create spatial superpositions. Employing a sequence of harmonic and inverted harmonic oscillator potentials created by external magnetic fields, we aim to enhance the one-dimensional superposition of a nanodiamond with mass $\sim 10^{-15}$ kg to $\sim 1 μ$ m. However, random fluctuations of the magnetic field stochastically perturbs the interferometer paths and induce dephasing. We quantitatively estimate the susceptibility of the interferometer to white noise arising from magnetic-field fluctuations. Constraining the dephasing rate $Γ$ to be low enough that the final coherence $e^{-Γτ}\leq 0.1$ (where $τ$ is the experimental time duration), we obtain the following bounds on the noise to signal ratios: $δη_\text{IHP}/η_\text{IHP}\lesssim 10^{-13}$ , where $η_\text{IHP}$ is the magnetic field curvature that gives rise to the inverted harmonic potential, and $δη_\text{HP}/η_\text{HP}\lesssim 10^{-6}$ , where $η_\text{HP}$ is the linear magnetic field gradient that gives rise to the harmonic potential. For such tiny fluctuations, we demonstrate that the Humpty-Dumpty problem arising from a mismatch in position and momentum does not cause a loss in contrast of the interferometer. Further, we show that constraining the dephasing rate leads to stricter bounds on the noise parameters than enforcing a contrast threshold, indicating that good dephasing control ensures high interferometric contrast.We investigate a Stern-Gerlach type matter-wave interferometer where an inhomogeneous magnetic field couples to an embedded spin in a nanoparticle to create spatial superpositions. Employing a sequence of harmonic and inverted harmonic oscillator potentials created by external magnetic fields, we aim to enhance the one-dimensional superposition of a nanodiamond with mass $\sim 10^{-15}$ kg to $\sim 1 μ$m. However, random fluctuations of the magnetic field stochastically perturbs the interferometer paths and induce dephasing. We quantitatively estimate the susceptibility of the interferometer to white noise arising from magnetic-field fluctuations. Constraining the dephasing rate $Γ$ to be low enough that the final coherence $e^{-Γτ}\leq 0.1$ (where $τ$ is the experimental time duration), we obtain the following bounds on the noise to signal ratios: $δη_\text{IHP}/η_\text{IHP}\lesssim 10^{-13}$, where $η_\text{IHP}$ is the magnetic field curvature that gives rise to the inverted harmonic potential, and $δη_\text{HP}/η_\text{HP}\lesssim 10^{-6}$, where $η_\text{HP}$ is the linear magnetic field gradient that gives rise to the harmonic potential. For such tiny fluctuations, we demonstrate that the Humpty-Dumpty problem arising from a mismatch in position and momentum does not cause a loss in contrast of the interferometer. Further, we show that constraining the dephasing rate leads to stricter bounds on the noise parameters than enforcing a contrast threshold, indicating that good dephasing control ensures high interferometric contrast.

arXiv:2509.02670Sep 2, 20250 citations

Phonon-induced contrast in a matter-wave interferometer

Qian Xiang, Run Zhou, Sougato Bose +1 more

Utilizing the Stern-Gerlach apparatus to create matter-wave superposition states is a long-sought-after goal, not only due to its potential applications in the quantum realm, but also because of its fundamental implications for studying the quantum properties of gravity. The main challenge in creating a macroscopic quantum interferometer arises from the loss of coherence, primarily through two channels. One channel involves strong coupling with the environment for macroscopic matter, leading to decoherence. The other channel relates to the precision of wave-packet overlap, which can occur due to external and internal fluctuations of various sources. The latter introduces a unique challenge for larger-scale masses by perturbing the center of mass motion of the macroscopic object. Here we study a particular challenge, namely, the issue of internal degrees of freedom, specifically phonon fluctuations and contrast reduction. This work investigates the contrast reduction caused by spin--magnetic-field--phonon and diamagnetism-phonon interactions in the quantum gravity-induced entanglement of masses protocol configuration.Utilizing the Stern-Gerlach apparatus to create matter-wave superposition states is a long-sought-after goal, not only due to its potential applications in the quantum realm, but also because of its fundamental implications for studying the quantum properties of gravity. The main challenge in creating a macroscopic quantum interferometer arises from the loss of coherence, primarily through two channels. One channel involves strong coupling with the environment for macroscopic matter, leading to decoherence. The other channel relates to the precision of wave-packet overlap, which can occur due to external and internal fluctuations of various sources. The latter introduces a unique challenge for larger-scale masses by perturbing the center of mass motion of the macroscopic object. Here we study a particular challenge, namely, the issue of internal degrees of freedom, specifically phonon fluctuations and contrast reduction. This work investigates the contrast reduction caused by spin--magnetic-field--phonon and diamagnetism-phonon interactions in the quantum gravity-induced entanglement of masses protocol configuration.

arXiv:2404.04210Physical Review AOct 15, 20248 citations

Magnetic noise in macroscopic quantum spatial superposition induced by an inverted harmonic oscillator potential

Sneha Narasimha Moorthy, Anupam Mazumdar

We investigate a Stern-Gerlach type matter-wave interferometer where an inhomogeneous magnetic field couples to an embedded spin in a nanoparticle to create spatial superpositions. Employing a sequence of harmonic and inverted harmonic-oscillator potentials created by external magnetic fields, we aim to enhance the one-dimensional superposition of a nanodiamond with mass ≈10−15 kg to ≈1 µm. However, random fluctuations of the magnetic field stochastically perturbs the interferometer paths and induce dephasing. We quantitatively estimate the susceptibility of the interferometer to white noise arising from magnetic-field fluctuations. Constraining the dephasing rate Γ to be low enough that the final coherence e−Γτ > 0.1 (where τ is the experimental time duration), we obtain the following bounds on the noise to signal ratios: δηIHP/ηIHP ≾ 10−13, where ηIHP is the magnetic-field curvature that gives rise to the inverted harmonic potential, and δηHP/ηHP ≾ 10−6, where ηHP is the linear magnetic-field gradient that gives rise to the harmonic potential. For such tiny fluctuations, we demonstrate that the Humpty-Dumpty problem arising from a mismatch in position and momentum does not cause a loss in contrast of the interferometer. Furthermore, we show that constraining the dephasing rate leads to stricter bounds on the noise parameters than enforcing a contrast threshold, indicating that good dephasing control ensures high interferometric contrast.We investigate a Stern-Gerlach type matter-wave interferometer where an inhomogeneous magnetic field couples to an embedded spin in a nanoparticle to create spatial superpositions. Employing a sequence of harmonic and inverted harmonic-oscillator potentials created by external magnetic fields, we aim to enhance the one-dimensional superposition of a nanodiamond with mass ≈10−15 kg to ≈1 µm. However, random fluctuations of the magnetic field stochastically perturbs the interferometer paths and induce dephasing. We quantitatively estimate the susceptibility of the interferometer to white noise arising from magnetic-field fluctuations. Constraining the dephasing rate Γ to be low enough that the final coherence e−Γτ > 0.1 (where τ is the experimental time duration), we obtain the following bounds on the noise to signal ratios: δηIHP/ηIHP ≾ 10−13, where ηIHP is the magnetic-field curvature that gives rise to the inverted harmonic potential, and δηHP/ηHP ≾ 10−6, where ηHP is the linear magnetic-field gradient that gives rise to the harmonic potential. For such tiny fluctuations, we demonstrate that the Humpty-Dumpty problem arising from a mismatch in position and momentum does not cause a loss in contrast of the interferometer. Furthermore, we show that constraining the dephasing rate leads to stricter bounds on the noise parameters than enforcing a contrast threshold, indicating that good dephasing control ensures high interferometric contrast.

Physical Review ADec 9, 20254 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.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:2603.05595Mar 9, 20260 citations

Δx \sim {\cal O} (10^{-9})

m and to minimize decoherence,

Γ\leq {\cal O}(\frac{ω_0}{2π})

, where

Γ

is the decoherence and

ω_0

is the frequency of the oscillator, we will need current fluctuations to be

δI/I\leq {\cal O}(10^{-8})

, which is not impossible to obtain in superconducting wire arrangements. For such tiny fluctuations, we demonstrate that the Humpty-Dumpty problem in a matter-wave interferometer arising from a mismatch in position and momentum does not cause a loss in contrast.

\sim 10^{-15}

kg to

\sim 1 μ

m. However, random fluctuations of the magnetic field stochastically perturbs the interferometer paths and induce dephasing. We quantitatively estimate the susceptibility of the interferometer to white noise arising from magnetic-field fluctuations. Constraining the dephasing rate

Γ

to be low enough that the final coherence

e^{-Γτ}\leq 0.1

(where

τ

is the experimental time duration), we obtain the following bounds on the noise to signal ratios:

δη_\text{IHP}/η_\text{IHP}\lesssim 10^{-13}

, where

η_\text{IHP}

is the magnetic field curvature that gives rise to the inverted harmonic potential, and

δη_\text{HP}/η_\text{HP}\lesssim 10^{-6}

, where

η_\text{HP}

is the linear magnetic field gradient that gives rise to the harmonic potential. For such tiny fluctuations, we demonstrate that the Humpty-Dumpty problem arising from a mismatch in position and momentum does not cause a loss in contrast of the interferometer. Further, we show that constraining the dephasing rate leads to stricter bounds on the noise parameters than enforcing a contrast threshold, indicating that good dephasing control ensures high interferometric contrast.

\sim 0.21~{\rm μm}

for mass

m=10^{-17}

kg in less than

t\sim 0.013