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:1005.0603 · New Journal of Physics

Spin squeezing of high-spin, spatially extended quantum fields

Jay Deep Sau, Sabrina R. Leslie, Marvin L. Cohen, Dan Stamper-Kurn

Published Aug 25, 2010• 32 citations
arXivHTMLPDF

Abstract

Investigations of spin squeezing in ensembles of quantum particles have been limited primarily to a subspace of spin fluctuations and a single spatial mode in high-spin and spatially extended ensembles. Here, we show that a wider range of spin squeezing is attainable in ensembles of high-spin atoms, characterized by sub-quantum-limited fluctuations in several independent planes of spin-fluctuation observables. Further, considering the quantum dynamics of an f =1 ferromagnetic spinor Bose–Einstein condensate, we demonstrate theoretically that a high degree of spin squeezing is attained in multiple spatial modes of a spatially extended quantum field and that such squeezing can be extracted from spatially resolved measurements of magnetization and nematicity, i.e. the vector and quadrupole magnetic moments, of the quantum gas. Taking into account several experimental limitations, we predict that the variance of the atomic magnetization and nematicity may be reduced as far as 20 dB below the standard quantum limits.

DOI
10.1088/1367-2630/12/8/085011

Related papers

Spin-Nematic Squeezing in a Quantum Gas

Christopher D. Hamley, Corey Gerving, Thai M. Hoang +2 more

Exotic types of magnetic order and phases resulting from collective behaviour of quantum spins are an important focus of many-body physics. Nematic or quadrupolar ordering of spins is one such example [1], which breaks O(3) rotational symmetry, has no magnetic moment and is analogous to the well-known ordering of molecules in nematic phases of liquid crystals [2]. Spin nematic phases have been posited for a variety of condensed matter systems including frustrated quantum magnets [3–5], and heavyfermion [6] and iron-based superconductors [7], although they are challenging to detect directly [8]. Spin-1 atomic Bose-Einstein condensates [9– 11] provide a natural system to investigate spinnematic quantum phases with a key advantage that the nematic tensor is directly measurable. Here, we measure spin-nematic fluctuations in a spin-1 condensate following a quench through a nematic to ferromagnetic quantum phase transition and observe quadrature squeezing in the variance of the fluctuations up to −8.3 −0.7 dB (−10.3 −0.9 dB corrected for detection noise) below the standard quantum limit. Previous work in atomic squeezing has employed two-level systems exhibiting SU(2) symmetry on the Bloch sphere [12, 13], while the squeezing observed here is an example of squeezing in an SU(3) system. These results demonstrate spin-nematic dynamics in the quantum regime and could form the basis of a quantum-enhanced magnetometer.

•Nov 7, 2011•1 citation

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

Spin-nematic squeezing in a spin-1 Bose-Einstein condensate

Christopher D. Hamley

The primary study of this thesis is spin-nematic squeezing in a spin-1 condensate. \nThe measurement of spin-nematic squeezing builds on the success of previous experiments of spin-mixing together with advances in low noise atom counting. \nThe major contributions of this thesis are linking theoretical models to experimental results and the development of the intuition and tools to address the squeezed subspaces. \nUnderstanding how spin-nematic squeezing is generated and how to measure it has required a review of several theoretical models of spin-mixing as well as extending these existing models. This extension reveals that the squeezing is between quadratures of a spin moment and a nematic (quadrapole) moment in abstract subspaces of the SU(3) symmetry group of the spin-1 system. \nThe identification of the subspaces within the SU(3) symmetry allowed the development of techniques using RF and microwave oscillating magnetic fields to manipulate the phase space in order to measure the spin-nematic squeezing. Spin-mixing from a classically meta-stable state, the phase space manipulation, and low noise atom counting form the core of the experiment to measure spin-nematic squeezing. Spin-nematic squeezing is also compared to its quantum optics analogue, two-mode squeezing generated by four-wave mixing. \n \nThe other experimental study in this thesis is performing spin-dependent photo-association spectroscopy. Spin-mixing is known to depend on the difference of the strengths of the scattering channels of the atoms. Optical Feshbach resonances have been shown to be able to alter these scattering lengths but with prohibitive losses of atoms near the resonance. The possibility of using multiple nearby resonances from different scattering channels has been proposed to overcome this limitation. However there was no spectroscopy in the literature which analyzes for the different scattering channels of atoms for the same initial states. Through analysis of the initial atomic states, this thesis studies how the spin state of the atoms affects what photo-association resonances are available to the colliding atoms based on their scattering channel and how this affects the optical Feshbach resonances. From this analysis a prediction is made for the extent of alteration of spin-mixing achievable as well as the impact on the atom loss rate.

•Jan 17, 2012•4 citations

Relative number squeezing in a spin-1 Bose-Einstein condensate

Eva Bookjans

The quantum properties of matter waves, in particular quantum correlations and entanglement are an important frontier in atom optics with applications in quantum metrology and quantum information. In this thesis, we report the first observation of sub-Poissonian fluctuations in the magnetization of a spinor 87Rb condensate. The fluctuations in the magnetization are reduced up to 10 dB below the classical shot noise limit. This relative number squeezing is indicative of the predicted pair-correlations in a spinor condensate and lay the foundation for future experiments involving spin-squeezing and entanglement measurements. We have investigated the limits of the imaging techniques used in our lab, absorption and fluorescence imaging, and have developed the capability to measure atoms numbers with an uncertainly < 10 atoms. Condensates as small as ≈ 10 atoms were imaged and the measured fluctuations agree well with the theoretical predictions. Furthermore, we implement a reliable calibration method of our imaging system based on quantum projection noise measurements. We have resolved the individual lattice sites of a standing-wave potential created by a CO2 laser, which has a lattice spacing of 5.3 µm. Using microwaves, we site-selectively address and manipulate the condensate and therefore demonstrate the ability to perturb the lattice condensate of a local level. Interference between condensates in adjacent lattice sites and lattice sites separated by a lattice site are observed.

Bulletin of the American Physical Society•Nov 15, 2010•2 citations

Persistent and enhanced spin-nematic squeezing in a spinor Bose–Einstein condensate

Xinfang Li, Jianning Liu, Seth Osei +3 more

Abstract We propose a simple scheme to realize the persistent spin-nematic squeezing in a spinor Bose–Einstein condensate by rapidly turning-off the external magnetic field at a time that maximal spin-nematic squeezing occurs. We observe that the optimal spin-nematic squeezing can be maintained in a nearly fixed direction. For a proper initial magnetic field, the optimal squeezing can be obviously enhanced. We further construct a spin-mixing interferometer, where the quantum correlation of the squeezed state (generated by our scheme) is fully utilized in the phase measurement, and show the phase sensitivity of the interferometer has a significant enhancement.

Communications in Theoretical Physics•Dec 20, 2021•1 citation

Spatial dynamics and spin squeezing in Bose-Einstein condensates

Sulakshana Thanvanthri, Zachary Dutton

We develop a cumulant based formalism to deterministically calculate the lowest order quantum fluctuations of a two-component Bose-Einstein condensate. We use this to study spin squeezing induced by the atom-atom interaction nonlinearity. Our formalism naturally accounts for the multimode spatial description of the condensate, extending previous spin squeezing work which assumed a single spatial mode. We study spin squeezing in both the miscible and immiscible (phase separating) regimes for the scattering lengths. In the miscible regime, we find the squeezing parameter deviates very little from the single spatial mode approach, while in the phase separating regime, we find the squeezing is slightly reduced, though significant squeezing still occurs.

Physical Review A•Feb 21, 2007•10 citations
Investigations of spin squeezing in ensembles of quantum particles have been limited primarily to a subspace of spin fluctuations and a single spatial mode in high-spin and spatially extended ensembles. Here, we show that a wider range of spin squeezing is attainable in ensembles of high-spin atoms, characterized by sub-quantum-limited fluctuations in several independent planes of spin-fluctuation observables. Further, considering the quantum dynamics of an f =1 ferromagnetic spinor Bose–Einstein condensate, we demonstrate theoretically that a high degree of spin squeezing is attained in multiple spatial modes of a spatially extended quantum field and that such squeezing can be extracted from spatially resolved measurements of magnetization and nematicity, i.e. the vector and quadrupole magnetic moments, of the quantum gas. Taking into account several experimental limitations, we predict that the variance of the atomic magnetization and nematicity may be reduced as far as 20 dB below the standard quantum limits.
Exotic types of magnetic order and phases resulting from collective behaviour of quantum spins are an important focus of many-body physics. Nematic or quadrupolar ordering of spins is one such example [1], which breaks O(3) rotational symmetry, has no magnetic moment and is analogous to the well-known ordering of molecules in nematic phases of liquid crystals [2]. Spin nematic phases have been posited for a variety of condensed matter systems including frustrated quantum magnets [3–5], and heavyfermion [6] and iron-based superconductors [7], although they are challenging to detect directly [8]. Spin-1 atomic Bose-Einstein condensates [9– 11] provide a natural system to investigate spinnematic quantum phases with a key advantage that the nematic tensor is directly measurable. Here, we measure spin-nematic fluctuations in a spin-1 condensate following a quench through a nematic to ferromagnetic quantum phase transition and observe quadrature squeezing in the variance of the fluctuations up to −8.3 −0.7 dB (−10.3 −0.9 dB corrected for detection noise) below the standard quantum limit. Previous work in atomic squeezing has employed two-level systems exhibiting SU(2) symmetry on the Bloch sphere [12, 13], while the squeezing observed here is an example of squeezing in an SU(3) system. These results demonstrate spin-nematic dynamics in the quantum regime and could form the basis of a quantum-enhanced magnetometer.
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.
The primary study of this thesis is spin-nematic squeezing in a spin-1 condensate. \nThe measurement of spin-nematic squeezing builds on the success of previous experiments of spin-mixing together with advances in low noise atom counting. \nThe major contributions of this thesis are linking theoretical models to experimental results and the development of the intuition and tools to address the squeezed subspaces. \nUnderstanding how spin-nematic squeezing is generated and how to measure it has required a review of several theoretical models of spin-mixing as well as extending these existing models. This extension reveals that the squeezing is between quadratures of a spin moment and a nematic (quadrapole) moment in abstract subspaces of the SU(3) symmetry group of the spin-1 system. \nThe identification of the subspaces within the SU(3) symmetry allowed the development of techniques using RF and microwave oscillating magnetic fields to manipulate the phase space in order to measure the spin-nematic squeezing. Spin-mixing from a classically meta-stable state, the phase space manipulation, and low noise atom counting form the core of the experiment to measure spin-nematic squeezing. Spin-nematic squeezing is also compared to its quantum optics analogue, two-mode squeezing generated by four-wave mixing. \n \nThe other experimental study in this thesis is performing spin-dependent photo-association spectroscopy. Spin-mixing is known to depend on the difference of the strengths of the scattering channels of the atoms. Optical Feshbach resonances have been shown to be able to alter these scattering lengths but with prohibitive losses of atoms near the resonance. The possibility of using multiple nearby resonances from different scattering channels has been proposed to overcome this limitation. However there was no spectroscopy in the literature which analyzes for the different scattering channels of atoms for the same initial states. Through analysis of the initial atomic states, this thesis studies how the spin state of the atoms affects what photo-association resonances are available to the colliding atoms based on their scattering channel and how this affects the optical Feshbach resonances. From this analysis a prediction is made for the extent of alteration of spin-mixing achievable as well as the impact on the atom loss rate.
The quantum properties of matter waves, in particular quantum correlations and entanglement are an important frontier in atom optics with applications in quantum metrology and quantum information. In this thesis, we report the first observation of sub-Poissonian fluctuations in the magnetization of a spinor 87Rb condensate. The fluctuations in the magnetization are reduced up to 10 dB below the classical shot noise limit. This relative number squeezing is indicative of the predicted pair-correlations in a spinor condensate and lay the foundation for future experiments involving spin-squeezing and entanglement measurements. We have investigated the limits of the imaging techniques used in our lab, absorption and fluorescence imaging, and have developed the capability to measure atoms numbers with an uncertainly < 10 atoms. Condensates as small as ≈ 10 atoms were imaged and the measured fluctuations agree well with the theoretical predictions. Furthermore, we implement a reliable calibration method of our imaging system based on quantum projection noise measurements. We have resolved the individual lattice sites of a standing-wave potential created by a CO2 laser, which has a lattice spacing of 5.3 µm. Using microwaves, we site-selectively address and manipulate the condensate and therefore demonstrate the ability to perturb the lattice condensate of a local level. Interference between condensates in adjacent lattice sites and lattice sites separated by a lattice site are observed.
Abstract We propose a simple scheme to realize the persistent spin-nematic squeezing in a spinor Bose–Einstein condensate by rapidly turning-off the external magnetic field at a time that maximal spin-nematic squeezing occurs. We observe that the optimal spin-nematic squeezing can be maintained in a nearly fixed direction. For a proper initial magnetic field, the optimal squeezing can be obviously enhanced. We further construct a spin-mixing interferometer, where the quantum correlation of the squeezed state (generated by our scheme) is fully utilized in the phase measurement, and show the phase sensitivity of the interferometer has a significant enhancement.
We develop a cumulant based formalism to deterministically calculate the lowest order quantum fluctuations of a two-component Bose-Einstein condensate. We use this to study spin squeezing induced by the atom-atom interaction nonlinearity. Our formalism naturally accounts for the multimode spatial description of the condensate, extending previous spin squeezing work which assumed a single spatial mode. We study spin squeezing in both the miscible and immiscible (phase separating) regimes for the scattering lengths. In the miscible regime, we find the squeezing parameter deviates very little from the single spatial mode approach, while in the phase separating regime, we find the squeezing is slightly reduced, though significant squeezing still occurs.