© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1509.08530

Analytical solvability of the two-axis countertwisting spin squeezing Hamiltonian

Mishkatul Bhattacharya

Published Sep 28, 2015• 2 citations

Abstract

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.

DOI: 10.48550/arxiv.1509.08530

Related papers

Quantum dynamics generated by the two-axis countertwisting Hamiltonian

Dariusz Kajtoch, Emilia Witkowska

We study the quantum dynamics generated by the two-axis countertwisting Hamiltonian from an initial spin coherent state in a spin-$1/2$ ensemble. A characteristic feature of the two-axis countertwisting Hamiltonian is the existence of four neutrally stable and two saddle unstable fixed points. The presence of the latter is responsible for a high level of squeezing. The squeezing is accompanied by the appearance of several quantum states of interest in quantum metrology with Heisenberg-limited sensitivity, and we show fidelity functions for some of them. We present exact results for the quantum Fisher information and the squeezing parameter. Although the overall time evolution of both changes strongly with the number of particles, we find that they have regular dynamics for short times. We explain scaling with the system size by using a Gaussian approach.

arXiv:1505.04002•Physical Review A•Jul 20, 2015•34 citations

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

The quadratic spin squeezing operators

Pradyumna K. Pathak, Ram Narayan Deb, N. Nayak +1 more

Abstract. We discuss generic spin squeezing operators (quadratic in angular momentum operators) capable of squeezing out quantum mechanical noise from a system of two-level atoms (spins) in a coherent state. Such systems have been considered by Kitagawa and Ueda (Refs. 2) in this context and a Hamiltonian of this nature governs the Lipkin model (Ref. 14) which is relevant to nuclear physics.

•Aug 5, 2013•6 citations

The quadratic spin squeezing operators

P K Pathak, R N Deb, N. Nayak +1 more

We discuss generic spin squeezing operators (quadratic in angular momentum operators) capable of squeezing out quantum-mechanical noise from a system of two-level atoms (spins) in a coherent state. Such systems have been considered by Kitagawa and Ueda (1991 Phys. Rev. Lett. 67 1852, 1993 Phys. Rev. A 47 5138) in this context and a Hamiltonian of this nature governs the Lipkin model (Lipkin et al 1965 Nucl. Phys. 62 188) which is relevant to nuclear physics.

arXiv:0711.0995•Journal of Physics A Mathematical and Theoretical•Mar 26, 2008•8 citations

A Study of Entanglement and Squeezing of Multiqubit Cluster Systems

Mojtaba Jafarpour, Ahmad Akhound

We study entanglement and squeezing of a cluster of spin systems under the influence of the two-axis countertwisting Hamiltonian. The squeezing parameters given by Wineland et al and also by Kitagawa et al. are chosen as the criteria of spin squeezing. The criterion of pairwise entanglement is chosen to be the concurrence and that of the bipartite entanglement the linear entropy. We also define a new squeezing parameter η, which plays a direct role in the investigation of the relationship between squeezing and entanglement. We observe that if the system is squeezed according to the Wineland’s criterion, it is squeezed according to the Kitagawa’s also, but the reverse is not always true. Moreover, if the system is squeezed according to Kitagawa’s criterion, it is pairwise entangled simultaneously and vice versa. It is also observed that the entropy is a linear function of the parameter η2.

•Jan 1, 2009•0 citations

Beyond one-axis twisting: Simultaneous spin-momentum squeezing

John Drew Wilson, Simon B. Jäger, J. Reilly +3 more

The creation and manipulation of quantum entanglement is central to improving precision measurements. A principal method of generating entanglement for use in atom interferometry is the process of spin squeezing whereupon the states become more sensitive to $\text{SU}(2)$ rotations. One possibility to generate this entanglement is provided by one-axis twisting (OAT), where a many-particle entangled state of one degree of freedom is generated by a nonlinear Hamiltonian. We introduce a method which goes beyond OAT to create squeezing and entanglement across two distinct degrees of freedom. We present our work in the specific physical context of a system consisting of collective atomic energy levels and discrete collective momentum states, but also consider other possible realizations. Our system uses a nonlinear Hamiltonian to generate dynamics in $\text{SU}(4)$, thereby creating the opportunity for dynamics not possible in typical $\text{SU}(2)$ one-axis twisting. This leads to three axes undergoing twisting due to the two degrees of freedom and their entanglement, with the resulting potential for a more rich context of quantum entanglement. The states prepared in this system are potentially more versatile for use in multiparameter or auxiliary measurement schemes than those prepared by standard spin squeezing.

arXiv:2206.12491•Physical Review A•Oct 14, 2022•14 citations

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.

We study the quantum dynamics generated by the two-axis countertwisting Hamiltonian from an initial spin coherent state in a spin-

1/2

ensemble. A characteristic feature of the two-axis countertwisting Hamiltonian is the existence of four neutrally stable and two saddle unstable fixed points. The presence of the latter is responsible for a high level of squeezing. The squeezing is accompanied by the appearance of several quantum states of interest in quantum metrology with Heisenberg-limited sensitivity, and we show fidelity functions for some of them. We present exact results for the quantum Fisher information and the squeezing parameter. Although the overall time evolution of both changes strongly with the number of particles, we find that they have regular dynamics for short times. We explain scaling with the system size by using a Gaussian approach.

We study entanglement and squeezing of a cluster of spin systems under the influence of the two-axis countertwisting Hamiltonian. The squeezing parameters given by Wineland et al and also by Kitagawa et al. are chosen as the criteria of spin squeezing. The criterion of pairwise entanglement is chosen to be the concurrence and that of the bipartite entanglement the linear entropy. We also define a new squeezing parameter η, which plays a direct role in the investigation of the relationship between squeezing and entanglement. We observe that if the system is squeezed according to the Wineland’s criterion, it is squeezed according to the Kitagawa’s also, but the reverse is not always true. Moreover, if the system is squeezed according to Kitagawa’s criterion, it is pairwise entangled simultaneously and vice versa. It is also observed that the entropy is a linear function of the parameter η2.

The creation and manipulation of quantum entanglement is central to improving precision measurements. A principal method of generating entanglement for use in atom interferometry is the process of spin squeezing whereupon the states become more sensitive to

\text{SU}(2)

rotations. One possibility to generate this entanglement is provided by one-axis twisting (OAT), where a many-particle entangled state of one degree of freedom is generated by a nonlinear Hamiltonian. We introduce a method which goes beyond OAT to create squeezing and entanglement across two distinct degrees of freedom. We present our work in the specific physical context of a system consisting of collective atomic energy levels and discrete collective momentum states, but also consider other possible realizations. Our system uses a nonlinear Hamiltonian to generate dynamics in

\text{SU}(4)

, thereby creating the opportunity for dynamics not possible in typical

\text{SU}(2)

one-axis twisting. This leads to three axes undergoing twisting due to the two degrees of freedom and their entanglement, with the resulting potential for a more rich context of quantum entanglement. The states prepared in this system are potentially more versatile for use in multiparameter or auxiliary measurement schemes than those prepared by standard spin squeezing.