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arXiv:2403.11587

One Axis Twisting (OAT) spin squeezing for metrology

Garry Goldstein

Published Mar 18, 2024• 0 citations
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Abstract

In this work we study One Axis Twisting (OAT) spin squeezing for metrology in the presence of decoherence. We study Linbladian evolution in the presence of both T_1 and T_2 (longitudinal and transverse relaxation processes). We show that spin squeezing can be an effective way to improve metrological accuracy even in the presence of decoherence for OAT squeezing. We show our results are not sensitive to inhomogeneity of the squeezing strength of the many spin OAT Hamiltonian and that very general squeezed states do not have entanglement enhanced decoherence. We also extend the Kitagawa-Ueda OAT squeezing formula to finite polarization.

DOI
10.48550/arxiv.2403.11587

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In this work we study One Axis Twisting (OAT) spin squeezing for metrology in the presence of decoherence. We study Linbladian evolution in the presence of both T_1 and T_2 (longitudinal and transverse relaxation processes). We show that spin squeezing can be an effective way to improve metrological accuracy even in the presence of decoherence for OAT squeezing. We show our results are not sensitive to inhomogeneity of the squeezing strength of the many spin OAT Hamiltonian and that very general squeezed states do not have entanglement enhanced decoherence. We also extend the Kitagawa-Ueda OAT squeezing formula to finite polarization.
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 SU(2)\text{SU}(2)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 SU(4)\text{SU}(4)SU(4), thereby creating the opportunity for dynamics not possible in typical SU(2)\text{SU}(2)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.
In the absence of decay, the conditional dynamics for an open system is often describable by a non-Hermitian Hamiltonian. This study investigates spin squeezing (SS) in a non-Hermitian one-axis twisting (OAT) model. Somewhat surprisingly, SS close to the limit of Hermitian two-axis counter twisting (TACT) Hamiltonian is achievable for some parameters, which significantly improves upon the optimal value realizable by the Hermitian OAT model. The drawback is like with all conditional schemes, it takes on average longer time to evolve into a steady state, and the probability of no decay or success decreases as the number of atoms (spins) increases. The result above for the steady-state SS in a non-Hermitian OAT Hamiltonian is thus limited to small systems. For other parameter regimes, however, desirable SS arrives dynamically before a steady state is achieved, with a greatly shortened evolution time and enhanced probability of success, while still remains significantly improved over the limit of Hermitian OAT.
In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that measurement-after-interaction techniques, known to amplify the output signals in quantum parameter estimation protocols, are effective in measuring nonlinear spin observables. Including the presence of the relevant decoherence processes from atomic experiments, we determine analytically the quantum enhancement of non-Gaussian over-squeezed states as a function of the noise parameters for arbitrary atom numbers.
In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that measurement-after-interaction techniques, known to amplify the output signals in quantum parameter estimation protocols, are effective in measuring nonlinear spin observables. Including the presence of the relevant decoherence processes from atomic experiments, we determine analytically the quantum enhancement of non-Gaussian over-squeezed states as a function of the noise parameters for arbitrary atom numbers.
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.
We investigate spin squeezing for a one-axis twisting (OAT) model coupled to a general non-Markovian environment in a finite-temperature regime. Using the non-Markovian quantum state diffusion and master equation approach, we numerically study non-Markovian spin-squeezing generation in the OAT model. Our results show that the total spin number NNN, energy kBT{k}_{B}TkB​T, and certain coefficients in the OAT model can play a crucial role in generating spin squeezing. In particular, it shows that the maximum spin squeezing can be significantly enhanced when the participating environment has a relatively long memory time.