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Physical Review A

Non-Markovian enhanced temperature sensing in a dipolar Bose-Einstein condensate

Lan Xu, Ji-Bing Yuan, Shi-Qing Tang, Wei Wu, Qing-Shou Tan, Le‐Man Kuang

Published Aug 10, 2023• 16 citations
Publisher

Abstract

We present a method for implementing quantum temperature sensing for extremely low temperatures in a quasi-1D dipolar Bose-Einstein condensate reservoir with a magnetic field-driven impurity atom acting as a quantum sensor. By analyzing the quantum signal-to-noise ratio (QSNR) as a metric for temperature sensing performance, we demonstrate that the presence of an attractive dipolar interaction in the reservoir, which includes the effects of non-Markovian dynamics on the sensor, significantly enhances estimation efficiency. We also investigate the steady-state estimation efficiency for long-encoding times through an analytical expression, which shows that the optimal QSNR depends on the driving magnetic field of the impurity atom. Our method can achieve high-efficiency temperature sensing for any low temperature by tuning the magnetic field. These findings suggest that our approach has potential applications in high-resolution quantum thermometry.

DOI
10.1103/physreva.108.022608

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We present a method for implementing quantum temperature sensing for extremely low temperatures in a quasi-1D dipolar Bose-Einstein condensate reservoir with a magnetic field-driven impurity atom acting as a quantum sensor. By analyzing the quantum signal-to-noise ratio (QSNR) as a metric for temperature sensing performance, we demonstrate that the presence of an attractive dipolar interaction in the reservoir, which includes the effects of non-Markovian dynamics on the sensor, significantly enhances estimation efficiency. We also investigate the steady-state estimation efficiency for long-encoding times through an analytical expression, which shows that the optimal QSNR depends on the driving magnetic field of the impurity atom. Our method can achieve high-efficiency temperature sensing for any low temperature by tuning the magnetic field. These findings suggest that our approach has potential applications in high-resolution quantum thermometry.
We propose a theoretical scheme for quantum sensing of temperature close to absolute zero in a quasi-one-dimensional Bose-Einstein condensate (BEC). In our scheme, a single-atom impurity qubit is used as a temperature sensor. We investigate the sensitivity of the single-atom sensor in estimating the temperature of the BEC. We demonstrate that the sensitivity of the temperature sensor can saturate the quantum Cram\'er-Rao bound by means of measuring quantum coherence of the probe qubit. We study the temperature sensing performance by using quantum signal-to-noise ratio (QSNR). It is indicated that there is an optimal encoding time at which the QSNR can reach its maximum in the full-temperature regime. In particular, we find that the QSNR reaches a finite upper bound in the weak coupling regime even when the temperature is close to absolute zero, which implies that the sensing-error-divergence problem is avoided in our scheme. Our work opens a way for quantum sensing of temperature close to absolute zero in the BEC.
We investigate the sensing performance of a single-qubit quantum thermometer within a non-Markovian dynamical framework. By employing an exactly numerical hierarchical equations of the motion method, we go beyond traditional paradigms of the Born-Markov theory, the pure dephasing mechanism, and the weak-coupling approximation, which were commonly used in many previous studies of quantum thermometry. We find (i) the non-Markovian characteristics may boost the estimation efficiency, (ii) the sensitivity of quantum thermometry can be effectively optimized by engineering the proportions of different coupling operators in the whole sensor-reservoir interaction Hamiltonian, and (iii) a threshold, above which the strong sensor-reservoir coupling can significantly enhance the sensing precision in the long-encoding-time regime. Our results may have certain applications for high-resolution quantum thermometry.
Accurate measurement at low temperatures is essential for both gaining a fundamental understanding of physical processes and developing technological applications. In this paper, we propose a theoretical framework for quantum temperature sensing in a composite environment with non-Markovian dynamics. Our suggested system uses a single qubit as a temperature sensor to test its sensitivity in calculating the temperature of a composite environment. We show that the temperature sensor's sensitivity can saturate the quantum Cramér-Rao bound by measuring the σ[over ̂]_{z} observable of the probe qubit. Temperature sensing performance is measured using the quantum signal-to-noise ratio. We underline how non-Markovianity can enhance the performance of our thermometers. Furthermore, we emphasize that nonequilibrium conditions do not always result in the best sensitivities in temperature estimation.
We explore the impact of spatial separation between two sensor qubits on quantum sensing performance within a quasi-one-dimensional Bose-Einstein condensate reservoir. By analyzing the quantum Fisher information and quantum signal-to-noise ratio for sensor qubits initialized in both entangled and product states, we reveal distinct behaviors in estimating key reservoir parameters, including spectral density coupling strength and temperature. For coupling strength estimation, smaller spatial distances between the sensor qubits enhance sensing precision. In contrast, for temperature sensing, the spatial separation emerges as a valuable resource, enabling significant improvements in estimation accuracy. Additionally, we discover that product states may outperform entangled states for parameter estimation in quantum reservoir sensing. These findings provide insights into leveraging spatial configurations and state initialization for optimizing quantum sensing protocols in quantum reservoirs.
Quantum thermometry based on single-qubit sensor configurations enables the precise estimation of the temperature of a cosmological Anti-de Sitter (AdS) spacetime. In this work, we characterize the achievable estimation accuracy using the Quantum Fisher Information (QFI) and the associated quantum signal-to-noise ratio. For the first time, we introduce an ancillary Unruh-DeWitt detector between the sensor and the thermal bath, enhancing thermometric sensitivity by channeling temperature-dependent information into the probe qubit's coherence. We examine how detector acceleration in AdS space and the choice of boundary conditions modify the probe's thermal sensitivity. Despite the differing geometries, a unified phenomenology emerges: we characterize the scaling of the QFI with respect to temperature, detector energy gap, spacetime curvature, and interaction time. Finally, we identify optimal state preparation and measurement strategies that maximize the QFI, thereby establishing the fundamental limits of precision for non-Markovian sensing in curved spacetime.
We examine a system in which an impurity qubit is immersed in a quasi-two-dimensional dipolar Bose-Einstein condensate whose collective excitations act as a depasing reservoir for the qubit. The relative dipole-dipole interaction strength is estimated by the probe qubit dephasing. The ultimate precision of this estimation is quantified by the quantum Fisher information, which can be obtained by means of measuring quantum coherence of the probe qubit. Our findings indicate that, in the interval where roton excitations appear, the quantum Fisher information oscillates periodically with the encoding time ttt, and the amplitude of these oscillations increases alongside the extension of ttt. Moreover, we analytically determine that the envelope curve formed by the local maximum points satisfies the functional relationship At+Bt1/2+CAt+Bt^{1/2}+CAt+Bt1/2+C during long-term encoding scenarios, where AAA, BBB, CCC are positive numbers. It is also revealed that the highly non-Markovian effects caused by the roton softening of the excitation spectrum allow long encoding time to serve as a resource for enhancing sensing precision. Our work provides a new pathway for enhancing the sensing precision of dephasing qubits.