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arXiv:2607.16701

Quantum Metrological Detection of the Unruh Effect with Optimized Accelerated Two-Level Atoms

Yao Jin

quant-phSubmitted Jul 18, 2026• Announced Jul 21, 2026• 0 citations
v1 · Jul 18, 2026v2 · Jul 26, 2026
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Abstract

For a uniformly accelerated two-level probe atom, the acceleration-dependent factor is encoded in the atomic state during the atom-field evolution. If this factor can be estimated through a large number of measurements with an uncertainty smaller than its magnitude, the Unruh effect can be experimentally verified. In this work, we show that the minimal uncertainty is inversely proportional to the square root of the total probe time. For a fixed total probe time, we minimize the estimation uncertainty by optimizing the atom-field interaction time, the initial atomic state, and the measurement basis in each probe. Results show that the uncertainty decreases as the evolution time of each individual probe becomes shorter. The optimal measurement basis is determined by the initial atomic state, while the optimal initial state depends on both the acceleration factor and the evolution time of each probe. For a fixed evolution time, we analyze the estimation uncertainty versus the acceleration factor and identify the optimal factor and minimal uncertainty for each initial state. The initial excited state outperforms other configurations in the small-acceleration regime, whereas the ground state can become advantageous for sufficiently large acceleration and long evolution time of each probe. Finally, we estimate the minimal total probe time required for testing the Unruh effect and demonstrate that it can be significantly reduced by using probe atoms with larger transition dipole moments.

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For a uniformly accelerated two-level probe atom, the acceleration-dependent factor is encoded in the atomic state during the atom-field evolution. If this factor can be estimated through a large number of measurements with an uncertainty smaller than its magnitude, the Unruh effect can be experimentally verified. In this work, we show that the minimal uncertainty is inversely proportional to the square root of the total probe time. For a fixed total probe time, we minimize the estimation uncertainty by optimizing the atom-field interaction time, the initial atomic state, and the measurement basis in each probe. Results show that the uncertainty decreases as the evolution time of each individual probe becomes shorter. The optimal measurement basis is determined by the initial atomic state, while the optimal initial state depends on both the acceleration factor and the evolution time of each probe. For a fixed evolution time, we analyze the estimation uncertainty versus the acceleration factor and identify the optimal factor and minimal uncertainty for each initial state. The initial excited state outperforms other configurations in the small-acceleration regime, whereas the ground state can become advantageous for sufficiently large acceleration and long evolution time of each probe. Finally, we estimate the minimal total probe time required for testing the Unruh effect and demonstrate that it can be significantly reduced by using probe atoms with larger transition dipole moments.
Quantum metrology studies the ultimate limit of precision in estimating a physical quantity if quantum strategies are exploited. Here we investigate the evolution of a two-level atom as a detector which interacts with a massless scalar field using the master equation approach for open quantum system. We employ local quantum estimation theory to estimate the Unruh temperature when probed by a uniformly accelerated detector in the Minkowski vacuum. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over all possible detector preparations and evolution times, and compare its behavior with that of the quantum Fisher information (QFI). We find that the optimal precision of estimation is achieved when the detector evolves for a long enough time. Furthermore, we find that in this case the FI for population measurement is independent of initial preparations of the detector and is exactly equal to the QFI, which means that population measurement is optimal. This result demonstrates that the achievement of the ultimate bound of precision imposed by quantum mechanics is possible. Finally, we note that the same configuration is also available to the maximum of the QFI itself.
We study the estimation of parameters in a quantum metrology scheme based on entangled many-body Unruh-DeWitt detectors. It is found that the precision for the estimation of Unruh effect can be enhanced via initial state preparations and parameter selections. It is shown that the precision in the estimation of the Unruh temperature in terms of the many-body-probe metrology is always better than the precision in two probe estimations. The proper acceleration for Bob's detector and the interaction between the accelerated detector and the external field have significant influences on the precision for the Unruh effect's estimation. In addition, the probe state prepared with more excited atoms in the initial state is found to perform better than less excited initial states. However, different from the estimation of the Unruh temperature, the estimation of the effective coupling parameter for the accelerated detector requires more total atoms but less excited atoms in the estimations.
We study the quantum metrology for a pair of entangled Unruh-Dewitt detectors when one of them is accelerated and coupled to a massless scalar field. Comparing with previous schemes, our model requires only local interaction and avoids the use of cavities in the probe state preparation process. We show that the probe state preparation and the interaction between the accelerated detector and the external field have significant effects on the value of quantum Fisher information, correspondingly pose variable ultimate limit of precision in the estimation of Unruh effect. We find that the precision of the estimation can be improved by a larger effective coupling strength and a longer interaction time. Alternatively, the energy gap of the detector has a range that can provide us a better precision. Thus we may adjust those parameters and attain a higher precision in the estimation. We also find that an extremely high acceleration is not required in the quantum metrology process.
We investigate the thermalization process of two-level probes in de Sitter spacetime from a quantum-metrological perspective. For a static probe separated by a finite distance from a freely falling observer, both the intrinsic Gibbons--Hawking temperature and the position-dependent Unruh temperature are encoded in the probe state. The mutual influence between the encoding rate of the Gibbons--Hawking temperature and that of the Unruh temperature is studied. Results show that the thermalization rate is equal to the sum of the encoding rates of the Gibbons--Hawking temperature and that of the Unruh temperature. Interestingly, a nonzero inherent acceleration induced by the separation between the probe and a freely falling observer does not necessarily suppress the encoding of the Gibbons--Hawking temperature. Instead, there exists an optimal inherent acceleration at which the encoding rate of the Gibbons--Hawking temperature is maximized. Furthermore, the required total probe time of estimating the thermal effect with sufficient precision is shown in relation with the thermalization rate. The required total probe time and the corresponding number of probes remain experimentally feasible when the position-dependent inherent acceleration satisfies a2πω0→0.1\frac{a}{2πω_0}\rightarrow0.12πω0​a​→0.1.
The unknown temperature of a sample can be estimated with minimal disturbance by putting it in thermal contact with an individual quantum probe. If the interaction time is sufficiently long so that the probe thermalizes, the temperature can be read-out directly from its steady state. Here we prove that the optimal quantum probe, acting as a thermometer with maximal thermal sensitivity, is an effective two-level atom with a maximally degenerate excited state. When the total interaction time is insufficient to produce full thermalization, we optimize the estimation protocol by breaking it down into sequential stages of probe preparation, thermal contact, and measurement. We observe that frequently interrogated probes initialized in the ground state achieve the best performance. For both fully and partly thermalized thermometers, the sensitivity grows significantly with the number of levels, though optimization over their energy spectrum remains always crucial.
We address the quantum estimation of parameters encoded into the initial state of two modes of a Dirac field described by relatively accelerated parties. By using the quantum Fisher information (QFI), we investigate how the weak measurements performed before and after the accelerating observer, affect the optimal estimation of information encoded into the weight and phase parameters of the initial state shared between the parties. Studying the QFI, associated with weight parameter [Formula: see text], we find that the acceleration at which the optimal estimation occurs may be controlled by weak measurements. Moreover, it is shown that the post-measurement plays the role of a quantum key for manifestation of the Unruh effect. On the other hand, investigating the phase estimation optimization and assuming that there is no control over the initial state, we show that the weak measurements may be utilized to match the optimal [Formula: see text] to its predetermined value. Moreover, in addition to determination of a lower bound on the QFI with the local quantum uncertainty (LQU), we unveil an important upper bound on the precision of phase estimation in our relativistic scenario, given by the maximal steered coherence (MSC). We also obtain a compact expression of the MSC for general X states.