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arXiv:1410.4640 · Physical Review A

Precision measurements using squeezed spin states via two-axis countertwisting interactions

Emi Yukawa, Gerard J Milburn, Catherine A. Holmes, Masahito Ueda, Kae Nemoto

Published Dec 29, 2014• 17 citations
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Abstract

We show that the two-axis countertwisting interaction squeezes a coherent spin state into three states of interest in quantum information, namely, the equally weighted superposition state, the state close to the twin-Fock state, and the state achieving the Heisenberg limit of optimal sensitivity defined by the Cram\'er-Rao inequality, in addition to the well-known Heisenberg-limited state of spin fluctuations.

DOI
10.1103/physreva.90.062132

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We show that the two-axis countertwisting interaction squeezes a coherent spin state into three states of interest in quantum information, namely, the equally weighted superposition state, the state close to the twin-Fock state, and the state achieving the Heisenberg limit of optimal sensitivity defined by the Cram'er-Rao inequality, in addition to the well-known Heisenberg-limited state of spin fluctuations.
We study the quantum dynamics generated by the two-axis countertwisting Hamiltonian from an initial spin coherent state in a spin-1/21/21/2 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 propose a robust approach to spin squeezing with local interactions that approaches the Heisenberg limit of phase sensitivity. To generate the requisite entanglement, we generalize the paradigmatic two-axis countertwisting Hamiltonian -- akin to squeezing by parametric amplification -- to systems with power-law interactions, incorporating a Heisenberg coupling that aids in spreading correlations and protects the collective spin coherence. The resulting time to approach the Heisenberg limit scales sublinearly with particle number in 2D dipolar and 3D van der Waals interacting systems. Our protocol is robust to disorder and density fluctuations, and can be implemented in near-term experiments with molecules, Rydberg atoms, and solid-state spins.
Two well-known mechanisms, one-axis twisting (OAT) and two-axis countertwisting (TACT), generate spin-squeezed states dynamically. The latter provides better spin squeezing (SS) but has not been demonstrated as the form of its interaction does not occur naturally in known physical systems. Several proposals for realizing effective TACT transformed from OAT require stringent experimental conditions in order to overcome the resulting nonstationary (oscillating) SS and continuously varying mean spin directions. This work presents a simple scheme that solves both problems by freezing SS at an optimal point and realizing effectively persistent SS by inhibiting further squeezing dynamics. Explicit procedures are outlined for persistent SS of the TACT limit. Protocols based on our scheme favorably relax experimental demands, which significantly brighten the prospects for realizing TACT.
We analyze a model for spin squeezing based on the so-called countertwisting Hamiltonian, including the effects of dissipation and finite system size. We discuss the conditions under which the Heisenberg limit, i.e., phase sensitivity $\ensuremath{\propto}1/N,$ can be achieved. A specific implementation of this model based on atom-atom interactions via quantized photon exchange is presented in detail. The resulting excitation corresponds to the creation of spin-flipped atomic pairs and can be used for fast generation of entangled atomic ensembles, spin squeezing, and applications in quantum information processing. The conditions for achieving strong spin squeezing with this mechanism are also analyzed.
Spin squeezing in collective atomic ensembles enables quantum-enhanced metrology by reducing noise below the standard quantum limit through nonlinear interactions. Extending the one-axis and two-axis twisting paradigms of Kitagawa and Ueda, we introduce a general class of three-axis spin squeezed states within the anisotropic Lipkin-Meshkov-Glick model. The model features direction-dependent quadratic couplings that interpolate between uniaxial and biaxial regimes and can be interpreted as an asymmetric quantum rotor. Using semiclassical dynamics, Majorana representations, and Husimi-Q distributions, we analyze the structure and metrological properties of the resulting states. The three-axis framework reproduces the known N^(-2/3) scaling of one-axis twisting and the Heisenberg-limited N^(-1) scaling of two-axis twisting, while allowing additional tunability and enhanced entanglement generation in low-spin systems. We further show that tuning the anisotropy parameters induces ground-state and excited-state quantum phase transitions, including a second-order transition associated with level clustering and critical dynamics. These results unify spin squeezing, quantum criticality, and rotor analogies, and suggest implementations in Rydberg arrays and cavity-QED platforms for precision sensing and quantum simulation.