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:quant-ph/0203081 · Physical Review A

Near-optimal two-mode spin squeezing via feedback

Dominic William Berry, Barry C. Sanders

Published Jul 25, 2002• 20 citations
arXivHTMLPDF

Abstract

We propose a feedback scheme for the production of two-mode spin squeezing. We determine a general expression for the optimal feedback, which is also applicable to the case of single-mode spin squeezing. The two-mode spin squeezed states obtained via this feedback are optimal for $j=1/2$ and are very close to optimal for $j>1/2.$ In addition, the master equation suggests a Hamiltonian that would produce two-mode spin squeezing without feedback, and is analogous to the two-axis countertwisting Hamiltonian in the single-mode case.

DOI
10.1103/physreva.66.012313

Related papers

Two-axis two-spin squeezed states

Jonas Kitzinger, Manish Chaudhary, Manikandan Kondappan +2 more

This paper examines the properties of the states generated by the two-spin generalization of the two-axis countertwisting Hamiltonian. The spin squeezing produces correlations for arbitrary spin directions, and can violate the Bell-CHSH inequality with quadratic spin correlators

arXiv:2006.03852•Physical Review Research•Sep 28, 2020•24 citations

Squeezed spin states

Masahiro Kitagawa, Masahito Ueda

The basic concept of squeezed spin states is established and the principles for their generation are discussed. Two proposed mechanisms, referred to as one-axis twisting and two-axis countertwisting, are shown to reduce the standard quantum noise S/2 of the coherent S-spin state down to 1/2(S/3${)}^{1/3}$ and 1/2, respectively. Implementations of spin squeezing in interferometers are also discussed.

Physical Review A•Jun 1, 1993•1,740 citations

Analytical solvability of the two-axis countertwisting spin squeezing Hamiltonian

Mishkatul Bhattacharya

There is currently much interest in the two-axis countertwisting spin squeezing Hamiltonian suggested originally by Kitagawa and Ueda, since it is useful for interferometry and metrology. No analytical solution valid for arbitrary spin values seems to be available. In this article we systematically consider the issue of the analytical solvability of this Hamiltonian for various specific spin values. We show that the spin squeezing dynamics can be considered to be analytically solved for angular momentum values upto $21/2$, i.e. for $21$ spin half particles. We also identify the properties of the system responsible for yielding analytic solutions for much higher spin values than based on naive expectations. Our work is relevant for analytic characterization of squeezing experiments with low spin values, and semi-analytic modeling of higher values of spins.

arXiv:1509.08530•Sep 28, 2015•2 citations

Optimal spin squeezing in cavity QED based systems

Vincenzo Macrí, Franco Nori, Salvatore Savasta +1 more

An advantageous architecture for producing deterministic spin squeezing is cavity QED. We show that the recently discovered one photon - two atom excitation process can be used to generate optimal squeezing (scaling as $1/N$) of an ensemble of $N$ spins coupled to a single-mode cavity. This method has some remarkable features. It is a resonant phenomenon mediated by real photons, which provides the advantage of tunability. This allows to create a sizeable squeezing already at the single-photon limit. Finally, in the strong cavity-driving regime the effective theory is similar to a two-axis Hamiltonian. We calculate that reaching $-30$dB is possible already with the known reported spin-cavity and decoherence rates in magnetic molecules coupled to superconducting circuit resonators. This system represents an attractive on-chip architecture for the realization of technological solutions in sensing.

•Feb 27, 2019•1 citation

Squeezing with classical Hamiltonians

Tomáš Opatrný

A simple formula is derived for the maximum squeezing rate which occurs at the initial stages of the squeezing process: the rate only depends on the second partial derivatives of a classical Hamiltonian. Rules for optimum rotation of the phase space are found to keep the state optimally located and oriented for fastest squeezing. These operations transform the phase-space point of interest into a saddle point with opposite principal curvatures. Similar results are found for the Bloch-sphere phase space and spin squeezing. Application of the general formulas is illustrated by several model examples including parametric down conversion, Kerr nonlinearity, Jaynes-Cummings interaction, and spin squeezing by one-axis twisting and two-axis countertwisting.

arXiv:1508.04553•Physical Review A•Sep 1, 2015•9 citations

Twisting tensor and spin squeezing

Tomáš Opatrný

A unified tensor description of quadratic spin squeezing interactions is proposed, covering the single- and two-axis twisting as special cases of a general scheme. A closed set of equations of motion of the first moments and variances is derived in Gaussian approximation, and their solutions are discussed from the prospect of fastest squeezing generation. It turns out that the optimum rate of squeezing generation is governed by the difference between the largest and the smallest eigenvalues of the twisting tensor. A cascaded optical interferometer with Kerr nonlinear media is proposed as one of possible realizations of the general scheme.

arXiv:1408.3265•Physical Review A•May 15, 2015•20 citations
We propose a feedback scheme for the production of two-mode spin squeezing. We determine a general expression for the optimal feedback, which is also applicable to the case of single-mode spin squeezing. The two-mode spin squeezed states obtained via this feedback are optimal for j=1/2j=1/2j=1/2 and are very close to optimal for j>1/2.j>1/2.j>1/2. In addition, the master equation suggests a Hamiltonian that would produce two-mode spin squeezing without feedback, and is analogous to the two-axis countertwisting Hamiltonian in the single-mode case.
The basic concept of squeezed spin states is established and the principles for their generation are discussed. Two proposed mechanisms, referred to as one-axis twisting and two-axis countertwisting, are shown to reduce the standard quantum noise S/2 of the coherent S-spin state down to 1/2(S/3)1/3{)}^{1/3})1/3 and 1/2, respectively. Implementations of spin squeezing in interferometers are also discussed.
There is currently much interest in the two-axis countertwisting spin squeezing Hamiltonian suggested originally by Kitagawa and Ueda, since it is useful for interferometry and metrology. No analytical solution valid for arbitrary spin values seems to be available. In this article we systematically consider the issue of the analytical solvability of this Hamiltonian for various specific spin values. We show that the spin squeezing dynamics can be considered to be analytically solved for angular momentum values upto 21/221/221/2, i.e. for 212121 spin half particles. We also identify the properties of the system responsible for yielding analytic solutions for much higher spin values than based on naive expectations. Our work is relevant for analytic characterization of squeezing experiments with low spin values, and semi-analytic modeling of higher values of spins.
An advantageous architecture for producing deterministic spin squeezing is cavity QED. We show that the recently discovered one photon - two atom excitation process can be used to generate optimal squeezing (scaling as 1/N1/N1/N) of an ensemble of NNN spins coupled to a single-mode cavity. This method has some remarkable features. It is a resonant phenomenon mediated by real photons, which provides the advantage of tunability. This allows to create a sizeable squeezing already at the single-photon limit. Finally, in the strong cavity-driving regime the effective theory is similar to a two-axis Hamiltonian. We calculate that reaching −30-30−30dB is possible already with the known reported spin-cavity and decoherence rates in magnetic molecules coupled to superconducting circuit resonators. This system represents an attractive on-chip architecture for the realization of technological solutions in sensing.
A simple formula is derived for the maximum squeezing rate which occurs at the initial stages of the squeezing process: the rate only depends on the second partial derivatives of a classical Hamiltonian. Rules for optimum rotation of the phase space are found to keep the state optimally located and oriented for fastest squeezing. These operations transform the phase-space point of interest into a saddle point with opposite principal curvatures. Similar results are found for the Bloch-sphere phase space and spin squeezing. Application of the general formulas is illustrated by several model examples including parametric down conversion, Kerr nonlinearity, Jaynes-Cummings interaction, and spin squeezing by one-axis twisting and two-axis countertwisting.
A unified tensor description of quadratic spin squeezing interactions is proposed, covering the single- and two-axis twisting as special cases of a general scheme. A closed set of equations of motion of the first moments and variances is derived in Gaussian approximation, and their solutions are discussed from the prospect of fastest squeezing generation. It turns out that the optimum rate of squeezing generation is governed by the difference between the largest and the smallest eigenvalues of the twisting tensor. A cascaded optical interferometer with Kerr nonlinear media is proposed as one of possible realizations of the general scheme.