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arXiv:2411.10117

Super-Heisenberg scaling of the quantum Fisher information using spin-motion states

Venelin P. Pavlov, Peter Ivanov

Published Nov 15, 2024• 0 citations
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Abstract

We propose a spin-motion state for high-precision quantum metrology with super-Heisenberg scaling of the parameter estimation uncertainty using a trapped ion system. Such a highly entangled state can be created using the Tavis-Cummings Hamiltonian which describes the interaction between a collective spin system and a single vibrational mode. Our method relies on an adiabatic evolution in which the initial motional squeezing is adiabatically transferred into collective spin squeezing. In the weak squeezing regime, we show that the adiabatic evolution creates a spin-squeezed state, which reduces the quantum projective noise to a sub-shot noise limit. For strong bosonic squeezing we find that the quantum Fisher information follows a super-Heisenberg scaling law $\propto N^{5/2}$ in terms of the number of ions $N$. Furthermore, we discuss the spin squeezing parameter which quantifies the phase sensitivity enhancement in Ramsey spectroscopic measurements and show that it also exhibits a super-Heisenberg scaling with $N$. Our work enables the development of high-precision quantum metrology based on entangled spin-boson states that lead to faster scaling of the parameter estimation uncertainty with the number of spins.

DOI
10.48550/arxiv.2411.10117

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We propose a spin-motion state for high-precision quantum metrology with super-Heisenberg scaling of the parameter estimation uncertainty using a trapped ion system. Such a highly entangled state can be created using the Tavis-Cummings Hamiltonian which describes the interaction between a collective spin system and a single vibrational mode. Our method relies on an adiabatic evolution in which the initial motional squeezing is adiabatically transferred into collective spin squeezing. In the weak squeezing regime, we show that the adiabatic evolution creates a spin-squeezed state, which reduces the quantum projective noise to a sub-shot noise limit. For strong bosonic squeezing we find that the quantum Fisher information follows a super-Heisenberg scaling law ∝N5/2\propto N^{5/2}∝N5/2 in terms of the number of ions NNN. Furthermore, we discuss the spin squeezing parameter which quantifies the phase sensitivity enhancement in Ramsey spectroscopic measurements and show that it also exhibits a super-Heisenberg scaling with NNN. Our work enables the development of high-precision quantum metrology based on entangled spin-boson states that lead to faster scaling of the parameter estimation uncertainty with the number of spins.
We propose an adiabatic Ramsey interferometry technique for detecting weak nonlinearities with trapped ions. The method relies on using the quantum Rabi model as a probe, which is sensitive to nonlinear symmetry-breaking perturbations. We show that the couplings which arise either from anharmonic terms of the trapping potential or due to higher order terms in the Coulomb interaction expansion can be efficiently estimated by measuring the spin state probabilities alone. We show that the spin signal is amplified by the mean-phonon excitations, which results in the estimation precision reaching the super-Heisenberg limit. Notably, achieving such high-precision estimation does not require specific entangled state preparation and can be reached even for initial thermal motion state. Furthermore, we show that the super-Heisenberg scaling can be observed even in the presence of weak spin-dephasing.
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In this dissertation we focused on some quantum states with strong entanglement and robustness to noise. We constructed a spinor BEC Hamiltonian which has already been realized in experiment with several different kinds of atoms and proposed an adiabatic passage method to produce the maximal entangled Dicke state. We also analyzed the entanglement behavior of the Dicke state under various noises and demonstrate its use in high precision measurement experiment. We introduce a new class of quantum many-particle entangled states, called the Dicke squeezed (or DS) states, which can be used to improve the precision in quantum metrology beyond the standard quantum limit. We show that the enhancement in measurement precision is characterized by a single experimentally detectable parameter, called the Dicke squeezing, which also bounds the entanglement depth for this class of states. The measurement precision approaches the ultimate Heisenberg limit as the Dicke squeezing parameter attains the minimum in an ideal Dicke state. Compared with other entangled states, we show that the Dicke squeezed states are more robust to decoherence and give better measurement precision under typical experimental noise. On the other hand, we explore other choices of precision measurement with spin squeezed states. Spin squeezed states have strong manybody entanglement and are good candidates to be used in quantum metrology. A robust squeezing parameter is proposed to characterize the experimental phase measurement precision for spin squeezed states. The behavior of this parameter under various experimental noises is compared with other parameters in the history and it is shown to have better performance. Finally we present a scalable implementation scheme for Boson sampling using local transverse phonon modes in trapped ion system, which is a promising model for quantum computers.
Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian statistics. Here, we report on the creation and characterization of non-Gaussian many-body entangled states. We develop a general method to extract the Fisher information, which reveals that the quantum dynamics of a classically unstable system creates quantum states that are not spin squeezed but nevertheless entangled. The extracted Fisher information quantifies metrologically useful entanglement, which we confirm by Bayesian phase estimation with sub-shot-noise sensitivity. These methods are scalable to large particle numbers and applicable directly to other quantum systems.
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