Critical Quantum Metrology with Fully-Connected Models: From Heisenberg to Kibble-Zurek Scaling

Garbe, Louis; Abah, Obinna; Felicetti, Simone; Puebla, Ricardo

doi:10.48550/arxiv.2110.04144

Cited by 5 publications

(13 citation statements)

References 113 publications

(246 reference statements)

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“…The exponential advantage stems from the breakdown of the adiabatic condition close to a critical point. As we demonstrate, this exponential scaling is well captured by the new bound derived in [1], which in turn allows us to obtain approximate analytical expressions for the quantum Fisher information that agree with exact numerical simulations. In addition, we discuss the limitations to the exponential scaling when considering a finite-size system as well as its robustness against decoherence effects.…”

supporting

confidence: 53%

“…We provide an explanation to the exponential timescaling of the QFI using the bound recently introduced in Ref. [1], showing that it is made possible by the exponential growth of the number of excitations generated by the control strategy. This general understanding also covers the results of a recent work where exponential scaling of the QFI is achieved [25].…”

mentioning

confidence: 85%

“…Current solid-state and atomic technology allow for the implementation of these models in a controllable way, where their parameters can be tuned in real time. Intense research efforts [1,[25][26][27][28][29][30] are now dedicated to identifying the optimal control strategies that maximize the estimation precision.…”

mentioning

confidence: 99%

“…These fully-connected systems admit a simple description in terms of an effective bosonic mode whose potential depends on a rescaled and dimensionless coupling strength g. These models constitute a suitable test-bed for the exploration of different aspects of quantum critical phenomena [42,43,45,46,[48][49][50][51][52][53][54][55][56][57][58][59][60][61][62]. Within the normal phase 0 ≤ g ≤ 1 and in the thermodynamic limit, the effective Hamiltonian describing these systems can be written as [1,35,60]…”

mentioning

confidence: 99%

“…Therefore, the rescaled coupling depends itself on ω as g ∝ 1/ √ ω. In the following, we assume this dependence, which makes the sensing protocol critically dependent on the value of ω [1].…”

mentioning

confidence: 99%

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Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point

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Busch

2022

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We carefully examine critical metrology and present an improved critical quantum metrology protocol which relies on quenching a system exhibiting a superradiant quantum phase transition beyond its critical point. We show that this approach can lead to an exponential increase of the quantum Fisher information in time with respect to existing critical quantum metrology protocols relying on quenching close to the critical point and observing power law behaviour. We demonstrate that the Cramér-Rao bound can be saturated in our protocol through the standard homodyne detection scheme. We explicitly show its advantage using the archetypal setting of the Dicke model and explore a quantum gas coupled to a single-mode cavity field as a potential platform. In this case an additional exponential enhancement of the quantum Fisher information can in practice be observed with the number of atoms N in the cavity, even in the absence of N-body coupling terms.

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Squeezing by Critical Speeding-up: Applications in Quantum Metrology

Gietka

2021

Preprint

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We present an alternative protocol allowing for the preparation of critical states that instead of suffering from the critical slowing-down benefits from the critical speeding-up. Paradoxically, we prepare these states by going away from the critical point which allows for the speedup. We apply the protocol to the paradigmatic quantum Rabi model and its classical oscillator limit as well as the Lipkin-Meshkov-Glick model. Subsequently, we discuss the application of the adiabatic speed-up protocol in quantum metrology and compare its performance with critical quantum metrology. We show that critical quantum metrology with the Lipkin-Meshkov-Glick model cannot even overcome the standard quantum limit, and we argue that, in general, critical metrology is a suboptimal metrological strategy. Finally, we conclude that systems exhibiting a phase transition are indeed interesting from the viewpoint of quantum technologies, however, it may not be the critical point that should attract the most attention.

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Critical Quantum Metrology with Fully-Connected Models: From Heisenberg to Kibble-Zurek Scaling

Cited by 5 publications

References 113 publications

Exponential precision by reaching a quantum critical point

Exponential precision by reaching a quantum critical point

Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point

Squeezing by Critical Speeding-up: Applications in Quantum Metrology

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