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arXiv:2310.12933 · Physical Review A

Assisted metrology and preparation of macroscopic superpositions with split spin-squeezed states

Jiajie Guo, Feng-Xiao Sun, Qiongyi He, Matteo Fadel

Published Nov 30, 2023• 5 citations
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Abstract

We analyze the conditional states in which one part of a split spin-squeezed state is left, upon performing a collective spin measurement on the other part. For appropriate measurement directions and outcomes, we see the possibility of obtaining states with high quantum Fisher information, even reaching the Heisenberg limit. This allows us to propose a metrological protocol that can outperform standard approaches, for example, in a situation where the number of particles in the probe is bounded. The robustness of this protocol is investigated by considering realistic forms of noise present in cold-atom experiments, such as particle number fluctuations and imperfect detection. Ultimately, we show how this measurement-based state-preparation approach can allow for the conditional (i.e., heralded) preparation of spin Schr\"odinger's cat states even when the initial state before splitting is only mildly squeezed.

DOI
10.1103/physreva.108.053327

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We analyze the conditional states in which one part of a split spin-squeezed state is left, upon performing a collective spin measurement on the other part. For appropriate measurement directions and outcomes, we see the possibility of obtaining states with high quantum Fisher information, even reaching the Heisenberg limit. This allows us to propose a metrological protocol that can outperform standard approaches, for example, in a situation where the number of particles in the probe is bounded. The robustness of this protocol is investigated by considering realistic forms of noise present in cold-atom experiments, such as particle number fluctuations and imperfect detection. Ultimately, we show how this measurement-based state-preparation approach can allow for the conditional (i.e., heralded) preparation of spin Schr"odinger's cat states even when the initial state before splitting is only mildly squeezed.
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The Heisenberg limit of quantum measurement where the measurement precision scales as N-1 with the number of atoms N can be achieved by introducing quantum correlations between the atoms. In the present work, we show how to reach Heisenberg scaling by implementing a new Ramsey measurement scheme for cold-atom metrological devices. The proposed protocol consists of a sequence of one-axis twisting pulses and total collective spin rotations. It results in the creation of atomic Schrödinger-cat states, a superposition of two coherent spin states. Analyzing the Fisher information, we discuss the main features of the states and their interferometric precision.
Spin cat states are promising candidates for quantum-enhanced measurement. Here, we analytically show that the ultimate measurement precision of spin cat states approaches the Heisenberg limit, where the uncertainty is inversely proportional to the total particle number. In order to fully exploit their metrological ability, we propose to use the interaction-based readout for implementing phase estimation. It is demonstrated that the interaction-based readout enables spin cat states to saturate their ultimate precision bounds. The interaction-based readout comprises a one-axis twisting, two $\frac{\ensuremath{\pi}}{2}$ pulses, and a population measurement, which can be realized via current experimental techniques. Compared with the twisting echo scheme on spin squeezed states, our scheme with spin cat states is more robust against detection noise. Our scheme may pave an experimentally feasible way to achieve Heisenberg-limited metrology with non-Gaussian entangled states.
In its simplest form, decoherence occurs when a quantum state is entangled with a second state, but the results of measurements made on the second state are not accessible. As the second state has effectively ``measured'' the first, in this paper we argue that the quantum Fisher information is the relevant metric for predicting and quantifying this kind of decoherence. The quantum Fisher information is usually used to determine an upper bound on how precisely measurements on a state can be used to estimate a classical parameter, and as such it is an important resource. Quantum-enhanced metrology aims to create nonclassical states with large quantum Fisher information and utilize them in precision measurements. In the process of doing this it is possible for states to undergo decoherence; for instance atom-light interactions used to create coherent superpositions of atomic states may result in atom-light entanglement. Highly nonclassical states, such as spin-cat states (Schr\"odinger cat states constructed from superpositions of collective spins) are shown to be highly susceptible to this kind of decoherence. We also investigate the required field occupation of the second state, such that this decoherence is negligible.
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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.