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:1203.3797 · Physical Review A

Macroscopic singlet states for gradient magnetometry

Iñigo Urizar-Lanz, Philipp Hyllus, I. L. Egusquiza, Morgan W. Mitchell, Géza Tóth

Published Jul 17, 2013• 59 citations
arXivHTMLPDF

Abstract

We present a method for measuring magnetic field gradients with macroscopic singlet states realized with ensembles of spin-$j$ particles. While the singlet state is completely insensitive to homogeneous magnetic fields, the variance of its collective spin components is highly sensitive to field gradients. We compute the dynamics of this variance analytically for a chain of spins and also for an ensemble of particles with a given density distribution. We find an upper bound on how precisely the field gradient can be estimated from the measured data. Based on our calculations, differential magnetometry can be carried out with cold atomic ensembles using a multipartite singlet state obtained via spin squeezing. On the other hand, comparing the metrological properties of the experimentally prepared state to that of the ideal singlet can be used as further evidence that a singlet state has indeed been created.

DOI
10.1103/physreva.88.013626

Related papers

Precision bounds for gradient magnetometry with atomic ensembles

Iagoba Apellaniz, Iñigo Urizar-Lanz, Zoltán Zimborás +2 more

We study gradient magnetometry with an ensemble of atoms with arbitrary spin. We calculate precision bounds for estimating the gradient of the magnetic field based on the quantum Fisher information. For quantum states that are invariant under homogeneous magnetic fields, we need to measure a single observable to estimate the gradient. On the other hand, for states that are sensitive to homogeneous fields, a simultaneous measurement is needed, as the homogeneous field must also be estimated. We prove that for the cases studied in this paper, such a measurement is feasible. We present a method to calculate precision bounds for gradient estimation with a chain of atoms or with two spatially separated atomic ensembles. We also consider a single atomic ensemble with an arbitrary density profile, where the atoms cannot be addressed individually, and which is a very relevant case for experiments. Our model can take into account even correlations between particle positions. While in most of the discussion we consider an ensemble of localized particles that are classical with respect to their spatial degree of freedom, we also discuss the case of gradient metrology with a single Bose-Einstein condensate.

arXiv:1703.09056•Physical Review A•May 8, 2018•45 citations

Estimation of gradients in quantum metrology

Sanah Altenburg, Michał Oszmaniec, Sabine Wölk +1 more

We develop a general theory to estimate magnetic field gradients in quantum metrology. We consider a system of $N$ particles distributed on a line whose internal degrees of freedom interact with a magnetic field. Usually gradient estimation is based on precise measurements of the magnetic field at two different locations, performed with two independent groups of particles. This approach, however, is sensitive to fluctuations of the offset field determining the level splitting of the particles and results in collective dephasing. In this work, we use the framework of quantum metrology to assess the maximal accuracy for gradient estimation. For arbitrary positioning of particles, we identify optimal entangled and separable states, allowing the estimation of gradients with maximal accuracy, quantified by the quantum Fisher information. We also analyze the performance of states from the decoherence-free subspace (DFS), which are insensitive to the fluctuations of the magnetic offset field. We find that these states allow us to measure a gradient directly, without the necessity of estimating the magnetic offset field. Moreover, we show that DFS states attain a precision for gradient estimation comparable to the optimal entangled states. Finally, for the above classes of states, we find simple and feasible measurements saturating the quantum Cram\'er-Rao bound.

arXiv:1703.09123•Physical Review A•Oct 13, 2017•23 citations

Generation of macroscopic singlet states in atomic ensembles

Géza Tóth, Morgan W Mitchell

We study squeezing of the spin uncertainties by quantum non-demolition (QND) measurement in non-polarized spin ensembles. Unlike the case of polarized ensembles, the QND measurements can be performed with negligible back-action, which allows, in principle, perfect spin squeezing as quantified by Tóth et al (2007 Phys. Rev. Lett. 99 250405). The generated spin states approach many-body singlet states and contain a macroscopic number of entangled particles even when individual spin is large. We introduce the Gaussian treatment of unpolarized spin states and use it to estimate the achievable spin squeezing for realistic experimental parameters. Our proposal might have applications for magnetometry with a high spatial resolution or quantum memories storing information in decoherence free subspaces.

arXiv:0901.4110•New Journal of Physics•May 6, 2010•67 citations

Scalable Spin Squeezing for Quantum-Enhanced Magnetometry with Bose-Einstein Condensates

Wolfgang Muessel, Helmut Strobel, Daniel Linnemann +2 more

A major challenge in quantum metrology is the generation of entangled states with a macroscopic atom number. Here, we demonstrate experimentally that atomic squeezing generated via nonlinear dynamics in Bose-Einstein condensates, combined with suitable trap geometries, allows scaling to large ensemble sizes. We achieve a suppression of fluctuations by 5.3(5) dB for 12,300 particles, from which we infer that similar squeezing can be obtained for more than 10(7) atoms. With this resource, we demonstrate quantum-enhanced magnetometry by swapping the squeezed state to magnetically sensitive hyperfine levels that have negligible nonlinearity. We find a quantum-enhanced single-shot sensitivity of 310(47) pT for static magnetic fields in a probe volume as small as 90 μm3.

arXiv:1405.6022•Physical Review Letters•Sep 5, 2014•253 citations

Generation of Macroscopic Singlet States in a Cold Atomic Ensemble

N. Behbood, Ferran Martin Ciurana, Giorgio Colangelo +4 more

We report the generation of a macroscopic singlet state in a cold atomic sample via quantum nondemolition measurement-induced spin squeezing. We observe 3 dB of spin squeezing and detect entanglement with 5σ statistical significance using a generalized spin-squeezing inequality. The degree of squeezing implies at least 50% of the atoms have formed singlets.

arXiv:1403.1964•Physical Review Letters•Aug 25, 2014•76 citations

Generation of macroscopic spin singlets in cold atomic ensembles

N. Behbood

(English) This thesis describes the generation of macroscopic spin singlets in a cold atomic ensemble by performing quantum non-demolition measurement. Toward this goal we have implemented a realtime shot-nose limited detection system, incoherent feedback and spin state preparation via optical pumping, an upgraded absorption imaging system and coherent rotation of atomic spin via magnetic field control. Working with a magnetically sensitive atomic system triggered the development of a vector field magnetometry technique. We demonstrate a fast three-axis optical magnetometer using cold, optically trapped 87Rb gas as a sensor. By near-resonant Faraday rotation we record the free-induction decay following optical pumping to obtain the three field components and one gradient component. A single measurement achieves shot-noise limited sub-nT sensitivity in 1 ms, with transverse spatial resolution of about 20 micrometer. We make a detailed analysis of the shot-noise-limited sensitivity. We apply entropy removal by measurement and feedback to a cold atomic spin ensemble. Using quantum non-demolition probing by Faraday rotation measurement, and feedback by weak optical pumping, we drive the initially random collective spin variable F toward the origin F = 0. We use inputoutput relations and ensemble quantum noise models to describe this quantum control process and identify an optimal two-round control procedure. We observe 12 dB of spin noise reduction, or a factor of 63 reduction in phase-space volume. The method offers a non-thermal route to generation of exotic entangled states in ultra-cold gases, including macroscopic singlet states and strongly correlated states of quantum lattice gases. We generate approximate singlet states using the tools of measurementinduced spin squeezing: quantum non-demolition measurement and coherent magnetic rotations . By squeezing all three spin components, we approach the zero spin noise. Using a cold Rubidium atomic ensemble and nearresonant Faraday rotation probing, we have observed up to 3 dB of squeezing relative to the standard quantum limit, and a violation of the generalized spin squeezing inequality by more than 5 standard deviations. (Español) Esta tesis describe la generación del estado singlete de espín macroscópico formado por conjunto de átomos fríos mediante medidas cuánticas no destructivas. Para tal objetivo hemos implementado un sistema de detección en tiempo real limitado por propiedades fundamentales de la luz, "shot noise", así como un sistema de retroalimentación (feedback) incoherente, una preparación del estado de espín mediante bombeo óptico, una mejora del sistema de absorción de imágenes y un control del campo magnético para rotar de forma coherente el espín de los átomos. Trabajar con átomos sensibles al campo magnético desencadenó la necesidad de desarrollar una técnica pare medir el vector del campo magnético. Hemos demostrado un magnetómetro rápido, óptico, tri-axial que utiliza átomos de 87Rb atrapados ópticamente como sensor. Midiendo el decaimiento libre de la inducción (FID) a través de la rotación de Faraday con pulsos casi-resonantes obtenemos las tres componentes del campo así como una componente del gradiente. Una única medida está limitada por shot-noise y sensible en el rango sub-nT en 1 mili segundo, con una resolución espacial transversa de 20 micrómetros. En el cuerpo de la tesis estudiamos con detalle la sensibilidad en el límite shot-noise. Reducimos la entropía en un conjunto de átomos fríos con medidas y feedback. Utilizando medidas cuánticas no destructivas con la rotación de Faraday, y aplicando un leve feedback por bombeo óptico, llevamos la distribución inicial aleatoria de la variable colectiva de espín F hacia el origen de coordenadas F = 0. Utilizando relaciones de entrada-salida y modelos colectivos de ruido cuántico para describir la interacción identificamos como rutina óptima repetir el proceso de medir y feedback dos veces. Experimentalmente observamos 12 dB de reducción del ruido del espín, o una reducción en el espacio de fases de un factor 63. Éste método ofrece un procedimiento no térmico para la generación de estados entrelazados exóticos en gases ultrafríos, incluyendo un estado de singlete macroscópico y estados fuertemente correlacionados en quantum lattice gases. Generamos aproximadamente estados singlete utilizando los recursos que inducen spin squeezing: medidas no destructivas y rotaciones magnéticas coherentes. Al reducir el ruido en las tres componentes del espín, nos acercamos al cero ruido de espín. Utilizando un conjunto de átomos fríos de Rubidio y rotaciones de Faraday casi-resonantes, hemos observado hasta 3 dB de squeezing relativos al límite cuántico estándar, y una violación de la generalización de la desigualdad para spin squeezing de más de 5 desviaciones estándar.

•Apr 17, 2015•2 citations
We present a method for measuring magnetic field gradients with macroscopic singlet states realized with ensembles of spin-jjj particles. While the singlet state is completely insensitive to homogeneous magnetic fields, the variance of its collective spin components is highly sensitive to field gradients. We compute the dynamics of this variance analytically for a chain of spins and also for an ensemble of particles with a given density distribution. We find an upper bound on how precisely the field gradient can be estimated from the measured data. Based on our calculations, differential magnetometry can be carried out with cold atomic ensembles using a multipartite singlet state obtained via spin squeezing. On the other hand, comparing the metrological properties of the experimentally prepared state to that of the ideal singlet can be used as further evidence that a singlet state has indeed been created.
We study gradient magnetometry with an ensemble of atoms with arbitrary spin. We calculate precision bounds for estimating the gradient of the magnetic field based on the quantum Fisher information. For quantum states that are invariant under homogeneous magnetic fields, we need to measure a single observable to estimate the gradient. On the other hand, for states that are sensitive to homogeneous fields, a simultaneous measurement is needed, as the homogeneous field must also be estimated. We prove that for the cases studied in this paper, such a measurement is feasible. We present a method to calculate precision bounds for gradient estimation with a chain of atoms or with two spatially separated atomic ensembles. We also consider a single atomic ensemble with an arbitrary density profile, where the atoms cannot be addressed individually, and which is a very relevant case for experiments. Our model can take into account even correlations between particle positions. While in most of the discussion we consider an ensemble of localized particles that are classical with respect to their spatial degree of freedom, we also discuss the case of gradient metrology with a single Bose-Einstein condensate.
We develop a general theory to estimate magnetic field gradients in quantum metrology. We consider a system of NNN particles distributed on a line whose internal degrees of freedom interact with a magnetic field. Usually gradient estimation is based on precise measurements of the magnetic field at two different locations, performed with two independent groups of particles. This approach, however, is sensitive to fluctuations of the offset field determining the level splitting of the particles and results in collective dephasing. In this work, we use the framework of quantum metrology to assess the maximal accuracy for gradient estimation. For arbitrary positioning of particles, we identify optimal entangled and separable states, allowing the estimation of gradients with maximal accuracy, quantified by the quantum Fisher information. We also analyze the performance of states from the decoherence-free subspace (DFS), which are insensitive to the fluctuations of the magnetic offset field. We find that these states allow us to measure a gradient directly, without the necessity of estimating the magnetic offset field. Moreover, we show that DFS states attain a precision for gradient estimation comparable to the optimal entangled states. Finally, for the above classes of states, we find simple and feasible measurements saturating the quantum Cram\'er-Rao bound.
We study squeezing of the spin uncertainties by quantum non-demolition (QND) measurement in non-polarized spin ensembles. Unlike the case of polarized ensembles, the QND measurements can be performed with negligible back-action, which allows, in principle, perfect spin squeezing as quantified by Tóth et al (2007 Phys. Rev. Lett. 99 250405). The generated spin states approach many-body singlet states and contain a macroscopic number of entangled particles even when individual spin is large. We introduce the Gaussian treatment of unpolarized spin states and use it to estimate the achievable spin squeezing for realistic experimental parameters. Our proposal might have applications for magnetometry with a high spatial resolution or quantum memories storing information in decoherence free subspaces.
A major challenge in quantum metrology is the generation of entangled states with a macroscopic atom number. Here, we demonstrate experimentally that atomic squeezing generated via nonlinear dynamics in Bose-Einstein condensates, combined with suitable trap geometries, allows scaling to large ensemble sizes. We achieve a suppression of fluctuations by 5.3(5) dB for 12,300 particles, from which we infer that similar squeezing can be obtained for more than 10(7) atoms. With this resource, we demonstrate quantum-enhanced magnetometry by swapping the squeezed state to magnetically sensitive hyperfine levels that have negligible nonlinearity. We find a quantum-enhanced single-shot sensitivity of 310(47) pT for static magnetic fields in a probe volume as small as 90 μm3.
(English) This thesis describes the generation of macroscopic spin singlets in a cold atomic ensemble by performing quantum non-demolition measurement. Toward this goal we have implemented a realtime shot-nose limited detection system, incoherent feedback and spin state preparation via optical pumping, an upgraded absorption imaging system and coherent rotation of atomic spin via magnetic field control. Working with a magnetically sensitive atomic system triggered the development of a vector field magnetometry technique. We demonstrate a fast three-axis optical magnetometer using cold, optically trapped 87Rb gas as a sensor. By near-resonant Faraday rotation we record the free-induction decay following optical pumping to obtain the three field components and one gradient component. A single measurement achieves shot-noise limited sub-nT sensitivity in 1 ms, with transverse spatial resolution of about 20 micrometer. We make a detailed analysis of the shot-noise-limited sensitivity. We apply entropy removal by measurement and feedback to a cold atomic spin ensemble. Using quantum non-demolition probing by Faraday rotation measurement, and feedback by weak optical pumping, we drive the initially random collective spin variable F toward the origin F = 0. We use inputoutput relations and ensemble quantum noise models to describe this quantum control process and identify an optimal two-round control procedure. We observe 12 dB of spin noise reduction, or a factor of 63 reduction in phase-space volume. The method offers a non-thermal route to generation of exotic entangled states in ultra-cold gases, including macroscopic singlet states and strongly correlated states of quantum lattice gases. We generate approximate singlet states using the tools of measurementinduced spin squeezing: quantum non-demolition measurement and coherent magnetic rotations . By squeezing all three spin components, we approach the zero spin noise. Using a cold Rubidium atomic ensemble and nearresonant Faraday rotation probing, we have observed up to 3 dB of squeezing relative to the standard quantum limit, and a violation of the generalized spin squeezing inequality by more than 5 standard deviations. (Español) Esta tesis describe la generación del estado singlete de espín macroscópico formado por conjunto de átomos fríos mediante medidas cuánticas no destructivas. Para tal objetivo hemos implementado un sistema de detección en tiempo real limitado por propiedades fundamentales de la luz, "shot noise", así como un sistema de retroalimentación (feedback) incoherente, una preparación del estado de espín mediante bombeo óptico, una mejora del sistema de absorción de imágenes y un control del campo magnético para rotar de forma coherente el espín de los átomos. Trabajar con átomos sensibles al campo magnético desencadenó la necesidad de desarrollar una técnica pare medir el vector del campo magnético. Hemos demostrado un magnetómetro rápido, óptico, tri-axial que utiliza átomos de 87Rb atrapados ópticamente como sensor. Midiendo el decaimiento libre de la inducción (FID) a través de la rotación de Faraday con pulsos casi-resonantes obtenemos las tres componentes del campo así como una componente del gradiente. Una única medida está limitada por shot-noise y sensible en el rango sub-nT en 1 mili segundo, con una resolución espacial transversa de 20 micrómetros. En el cuerpo de la tesis estudiamos con detalle la sensibilidad en el límite shot-noise. Reducimos la entropía en un conjunto de átomos fríos con medidas y feedback. Utilizando medidas cuánticas no destructivas con la rotación de Faraday, y aplicando un leve feedback por bombeo óptico, llevamos la distribución inicial aleatoria de la variable colectiva de espín F hacia el origen de coordenadas F = 0. Utilizando relaciones de entrada-salida y modelos colectivos de ruido cuántico para describir la interacción identificamos como rutina óptima repetir el proceso de medir y feedback dos veces. Experimentalmente observamos 12 dB de reducción del ruido del espín, o una reducción en el espacio de fases de un factor 63. Éste método ofrece un procedimiento no térmico para la generación de estados entrelazados exóticos en gases ultrafríos, incluyendo un estado de singlete macroscópico y estados fuertemente correlacionados en quantum lattice gases. Generamos aproximadamente estados singlete utilizando los recursos que inducen spin squeezing: medidas no destructivas y rotaciones magnéticas coherentes. Al reducir el ruido en las tres componentes del espín, nos acercamos al cero ruido de espín. Utilizando un conjunto de átomos fríos de Rubidio y rotaciones de Faraday casi-resonantes, hemos observado hasta 3 dB de squeezing relativos al límite cuántico estándar, y una violación de la generalización de la desigualdad para spin squeezing de más de 5 desviaciones estándar.