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arXiv:1906.01447

Adiabatic Sensing Enhanced by Quantum Criticality

Luca Pezzè, A. Trenkwalder, M. Fattori

Published Jun 4, 2019• 5 citations
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Abstract

We propose an optimal method exploiting second order quantum phase transitions to perform high precision measurements of the control parameter at criticality. Our approach accesses the high fidelity susceptibility via the measurement of first- and second-moments of the order parameter and overcomes the difficulties of existing methods based on the overlap between nearby quantum states, which is hardly detectable in many-body systems. We experimentally demonstrate the feasibility of the method with a Bose-Einstein condensate undergoing a symmetry-breaking quantum phase transition as a function of the attractive inter-particle interaction strength. Our moment-based fidelity susceptibility shows a clear peak that, at the same time, detects the quantum critical point at finite temperature without any model-dependent fit to the data and certifies high sensitivity in parameter-estimation.

DOI
10.48550/arxiv.1906.01447

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We propose an optimal method exploiting second order quantum phase transitions to perform high precision measurements of the control parameter at criticality. Our approach accesses the high fidelity susceptibility via the measurement of first- and second-moments of the order parameter and overcomes the difficulties of existing methods based on the overlap between nearby quantum states, which is hardly detectable in many-body systems. We experimentally demonstrate the feasibility of the method with a Bose-Einstein condensate undergoing a symmetry-breaking quantum phase transition as a function of the attractive inter-particle interaction strength. Our moment-based fidelity susceptibility shows a clear peak that, at the same time, detects the quantum critical point at finite temperature without any model-dependent fit to the data and certifies high sensitivity in parameter-estimation.
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Critical metrology relies on the high sensitivity of systems to parameter changes near a phase transition to extract information with high precision. Such methods usually require working under adiabatic conditions, which implies long preparation times due to critical slowing down. Here instead we demonstrate how favorable sensitivity can be maintained for preparation rates exceeding the adiabatic limit by exploiting knowledge of the nonequilibrium dynamics of the system. Our work focuses on a model of collective dissipation (superradiance) balanced by collective pumping, analyzing the sensitivity around a first order dissipative phase transition. We devise a sensing protocol based on characterizing the hysteresis formed beyond adiabatic conditions, finding the sensing uncertainty r^{α}/N, exhibiting a favorable Heisenberg-like scaling with the particle number N and only a weak power-law dependence α≈0.17 on the preparation rate r. We discuss the implementation of the model and potential applications to metrology within cavity QED setups.
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Abstract Quantum systems can be used as probes in the context of metrology for enhanced parameter estimation. In particular, the delicacy of critical systems to perturbations can make them ideal sensors. Arguably the simplest realistic probe system is a spin- 1 2 impurity, which can be manipulated and measured in-situ when embedded in a fermionic environment. Although entanglement between a single impurity probe and its environment produces nontrivial many-body effects, criticality cannot be leveraged for sensing. Here we introduce instead the two-impurity Kondo model as a novel paradigm for critical quantum metrology, and examine the multiparameter estimation scenario at finite temperature. We explore the full metrological phase diagram numerically and obtain exact analytic results near criticality. Enhanced sensitivity to the inter-impurity coupling driving a second-order phase transition is evidenced by diverging quantum Fisher information (QFI) and quantum signal-to-noise ratio (QSNR). However, with uncertainty in both coupling strength and temperature, the multiparameter QFI matrix becomes singular—even though the parameters to be estimated are independent—resulting in vanishing QSNRs. We demonstrate that by applying a known control field, the singularity can be removed and measurement sensitivity restored. For general systems, we show that the degradation in the QSNR due to uncertainties in another parameter is controlled by the degree of correlation between the unknown parameters.