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arXiv:2010.13133 · Physical Review A

Criticality-enhanced quantum sensing in ferromagnetic Bose-Einstein condensates: Role of readout measurement and detection noise

Safoura Sadat Mirkhalaf, Daniel Benedicto Orenes, Morgan W. Mitchell, Emilia Witkowska

Published Feb 16, 2021• 33 citations
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Abstract

We theoretically investigate estimation of the control parameter in a ferromagnetic Bose-Einstein condensate near second-order quantum phase transitions. We quantify sensitivity by quantum and classical Fisher information and use the error-propagation formula. For these different metrics, we find the same beyond standard quantum limit (SQL) scaling with atom number near critical points and SQL scaling away from critical points. We find that both depletion of the ${m}_{f}=0$ Zeeman sublevel and transverse magnetization provide signals of sufficient quality to saturate the sensitivity scaling. To explore the effect of experimental imperfections, we study the scaling around criticality at nonzero temperature and with nonzero detection noise. Our results suggest the feasibility of sub-SQL sensing in ferromagnetic condensates with current experimental capabilities.

DOI
10.1103/physreva.103.023317

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We theoretically investigate estimation of the control parameter in a ferromagnetic Bose-Einstein condensate near second-order quantum phase transitions. We quantify sensitivity by quantum and classical Fisher information and use the error-propagation formula. For these different metrics, we find the same beyond standard quantum limit (SQL) scaling with atom number near critical points and SQL scaling away from critical points. We find that both depletion of the mf=0{m}_{f}=0mf​=0 Zeeman sublevel and transverse magnetization provide signals of sufficient quality to saturate the sensitivity scaling. To explore the effect of experimental imperfections, we study the scaling around criticality at nonzero temperature and with nonzero detection noise. Our results suggest the feasibility of sub-SQL sensing in ferromagnetic condensates with current experimental capabilities.
We consider an antiferromagnetic Bose-Einstein condensate in a transverse magnetic field with a fixed macroscopic magnetization. The system exhibits two different critical behaviors corresponding to transitions from polar to broken-axisymmetry and from antiferromagnetic to broken-axisymmetry phases, depending on the value of the magnetization. We exploit both types of system criticality as a resource in the precise estimation of the control parameter value. We quantify the achievable precision by the quantum Fisher information. We demonstrate supersensitivity and show that the precision scales with the number of atoms up to N4{N}^{4}N4 around criticality. In addition, we study the precision based on the error-propagation formula, which provides a simple-to-measure signal whose scaling coincides with the quantum Fisher information. Finally, we take into account the effect of nonzero temperature and show that sub-shot-noise sensitivity in the estimation of the control parameter is achievable in the low-temperature limit.
In this work, we study temperature sensing with finite-sized strongly correlated systems exhibiting quantum phase transitions. We use the quantum Fisher information (QFI) approach to quantify the sensitivity in the temperature estimation, and apply a finite-size scaling framework to link this sensitivity to critical exponents of the system around critical points. We numerically calculate the QFI around the critical points for two experimentally-realizable systems: the spin-1 Bose-Einstein condensate and the spin-chain Heisenberg XX model in the presence of an external magnetic field. Our results confirm finite-size scaling properties of the QFI. Furthermore, we discuss experimentally-accessible observables that (nearly) saturate the QFI at the critical points for these two systems.
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.
The sensitivity of quantum sensors is fundamentally constrained by the standard quantum limit (SQL) arising from intrinsic quantum fluctuations. While non-classical resources like squeezing or entanglement can surpass this limit, their utility is often restricted by the extreme fragility of entangled states and the complexity of their preparation. Quantum criticality offers a compelling alternative by harnessing divergent susceptibility to amplify signals without requiring fragile non-classical resources. However, the practical benefit of this approach has remained controversial due to the potential for the simultaneous amplification of quantum noise. Here, we demonstrate a universal protocol for noiseless critical sensing by engineering a light-driven atomic ensemble near a dynamical critical point. Analogous to a Kapitza pendulum near its inverted orientation, the spin system enters a non-equilibrium regime where the signal susceptibility diverges while the quantum noise periodically recedes to its coherent baseline. We exploit this ``noise ebbing'' to create a built-in noiseless amplifier, demonstrating a 3.3 dB metrological gain over the SQL in an atomic magnetometer. Our implementation exhibits intrinsic robustness against common experimental imperfections such as detection losses, establishing non-equilibrium critical dynamics as a practical and versatile paradigm for surpassing the fundamental limits of quantum sensing.
Quantum phase transitions universally exist in the ground and excited states of quantum many-body systems, and they have a close relationship with the nonequilibrium dynamical phase transitions, which however are challenging to identify. In the system of spin-1 Bose-Einstein condensates, though dynamical phase transitions with correspondence to equilibrium phase transitions in the ground state and uppermost excited state have been probed, those taking place in intermediate excited states remain untouched in experiments thus far. Here we unravel that both the ground- and excited-state quantum phase transitions in spinor condensates can be diagnosed with dynamical phase transitions. A connection between equilibrium phase transitions and nonequilibrium behaviors of the system is disclosed in terms of the quantum Fisher information. We also demonstrate that near the critical points parameter estimation beyond the standard quantum limit can be implemented. This work not only advances the exploration of excited-state quantum phase transitions via a scheme that can immediately be applied to a broad class of few-mode quantum systems, but also provides a new perspective on the relationship between quantum criticality and quantum enhanced 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.