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arXiv:2305.17656 · Advanced Quantum Technologies

Critical Sensing with a Single Bosonic Mode Without Boson–Boson Interactions

Ken Chen, Jiahao Lu, Xin Zhu, Hao-Long Zhang, Wen Ning, Zhen‐Biao Yang, Shi‐Biao Zheng

Published Aug 1, 2024• 4 citations
arXivHTMLPDF

Abstract

Abstract Critical phenomena of quantum systems are useful for enhancement of quantum sensing. However, experimental realizations of criticality enhancement are confined to very few systems, owing to the stringent requirements, including the thermodynamical or scaling limit, and fine control of interacting quantum subsystems or particles. Here, a simple critical quantum sensing scheme is proposed that requires neither of these conditions. The critical system is realized with a single parametrically‐driven bosonic mode involving many non‐interacting bosons. The quantum Fisher information is calculated, which confirms the criticality‐enabled enhancement. The response of one of the quadratures to the variation of the control parameter is further detailed. The numerical results reveal that its inverted variance exhibits a diverging behavior at the critical point. Based on the presently available control techniques of parametric driving, it is expected that scheme can be realized in different systems, e.g., ion traps and superconducting circuits.

DOI
10.1002/qute.202400105

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Abstract Critical phenomena of quantum systems are useful for enhancement of quantum sensing. However, experimental realizations of criticality enhancement are confined to very few systems, owing to the stringent requirements, including the thermodynamical or scaling limit, and fine control of interacting quantum subsystems or particles. Here, a simple critical quantum sensing scheme is proposed that requires neither of these conditions. The critical system is realized with a single parametrically‐driven bosonic mode involving many non‐interacting bosons. The quantum Fisher information is calculated, which confirms the criticality‐enabled enhancement. The response of one of the quadratures to the variation of the control parameter is further detailed. The numerical results reveal that its inverted variance exhibits a diverging behavior at the critical point. Based on the presently available control techniques of parametric driving, it is expected that scheme can be realized in different systems, e.g., ion traps and superconducting circuits.
Quantum sensing improves the accuracy of measurements of relevant parameters by exploiting the unique properties of quantum systems. The divergent susceptibility of physical systems near a critical point for quantum phase transition enables criticality-enhanced quantum sensing. The quantum Rabi model (QRM), composed of a single qubit coupled to a single bosonic field, represents a good candidate for realizing such critical enhancement for its simplicity, but it is experimentally challenging to achieve the ultrastrong qubit-field coupling required to realize the critical phenomena. In this work, we explore an alternative to construct the analog of the QRM for the sensing, exploiting the criticality appearing in the Jaynes-Cummings (JC) model whose bosonic field is parametrically driven, not necessitating the ultrastrong coupling condition, thus to some extent relaxing the requirement for practical implementation.
ABSTRACT Precision measurement has been a driving force in physics, from the uncertainty principle to modern quantum sensing, enabling the exploration of phenomena across microscopic and cosmic scales. We demonstrate significant sensitivity enhancement in a two‐mode continuous‐variable bosonic system by leveraging a first‐order superradiant phase transition (SPT) induced by parametric nonlinearity. The SPT causes the divergence of quantum fluctuations, enhancing the sensitivity. We characterize the sensitivity through a dimensionless quantum Fisher information. Compared to a continuous‐variable system without SPT, the sensitivity near the critical point exhibits an enhancement of three orders of magnitude. The universal theory represents a truly macroscopic quantum detection approach that can be demonstrated in general quantum systems and applied to a variety of nonlinear models.
Critical systems near quantum phase transitions were predicted to be useful for improvement of metrological precision, thanks to their ultrasensitive response to tiny variations of the control Hamiltonian. However, realizing criticality enhanced quantum metrology is experimentally challenging, mainly owing to decoherence and critical slowing down associated with the corresponding quantum state preparation. We circumvent these problems by making use of the critical behaviors in the Jaynes-Cummings model, to which the signal field is coupled. The information is encoded in the qubit's excitation number, which displays a divergent changing rate at the critical point, and is extremely robust against decoherence and nonadiabatic effects. We demonstrate such a metrological protocol in a superconducting circuit, where an Xmon qubit, interacting with a resonator, is used as a probe for estimating the amplitude of a microwave field. The measured quantum Fisher information exhibits a critical quantum enhancement, confirming the potential for quantum metrology.
Quantum criticality, as a fascinating quantum phenomenon, may provide significant advantages for quantum sensing. Here we propose a dynamic framework for quantum sensing with a family of Hamiltonians that undergo quantum phase transitions (QPTs). By giving the formalism of the quantum Fisher information (QFI) for quantum sensing based on critical quantum dynamics, we demonstrate its divergent feature when approaching the critical point. We illustrate the basic principle and the details of experimental implementation using quantum Rabi model. The framework is applicable to a variety of examples and does not rely on the stringent requirement for particular state preparation or adiabatic evolution. It is expected to provide a route towards the implementation of criticality-enhanced quantum sensing.
Critical properties of a quantum system are recognized as valuable resources for quantum metrology. In this work, we investigate the criticality-enhanced sensing in a quantum Rabi triangle system, which exhibits multiple phases. Around the phase boundary, enhanced parameter estimation precision can be achieved by tuning either the scaled coupling strength or the hopping phase controlled by an artificial magnetic field. We observe that the quantum Fisher information shows divergent scaling near different quantum phase transition points, characterized by distinct critical exponents. When the resource consumption is taken into account, we find that the divergent quantum Fisher information can reach the Heisenberg limit. Furthermore, we propose a measurement scheme of the average photon number and the quantum Cramér-Rao bound can be saturated.
Abstract Critical systems represent a valuable resource in quantum sensing and metrology. Critical quantum sensing (CQS) protocols can be realized using finite-component phase transitions, where criticality arises from the rescaling of system parameters rather than the thermodynamic limit. Here, we show that a collective quantum advantage can be achieved in a multipartite CQS protocol using a chain of parametrically coupled critical resonators in the weak-nonlinearity limit. We derive analytical solutions for the low-energy spectrum of this unconventional quantum many-body system, which is composed of locally critical elements. We then assess the scaling of the quantum Fisher information with respect to fundamental resources. We demonstrate that the coupled chain outperforms an equivalent ensemble of independent critical sensors, achieving quadratic scaling in the number of resonators. Finally, we show that even with finite Kerr nonlinearity or Markovian dissipation, the critical chain retains its advantage, making it relevant for implementing quantum sensors with current microwave superconducting technologies.