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arXiv:2512.17959 · Classical and Quantum Gravity

Detecting the Unruh effect via an engineered low-mass field in a superconducting qubit

Vladimir Toussaint

Published Apr 2, 2026• 1 citation

Abstract

Abstract Detecting the Unruh effect is a major challenge in fundamental physics. It is known that exciting massive fields with the Unruh thermal bath is heavily suppressed when the field’s rest energy is much larger than the acceleration energy scale, M c 2 ≫ ℏ a / c . However, the standard literature lacks an explicit quantitative derivation of this suppression. In this work, we first fill this gap by deriving the exponential suppression, ∼ exp ⁡ ( − constant × M c 2 / ( ℏ a / c ) ) , in two different frameworks: a (3+1)-dimensional Unruh–deWitt detector and a (1+1)-dimensional cavity QED setup. This shows the suppression is universal and sets an insurmountable barrier for any detection method that relies on exciting massive fields. For an electron-mass field at achievable accelerations ( a ∼ 10 20 m s −2 ), the suppression exceeds 10 9 orders of magnitude. To avoid this suppression, the field’s rest energy must be less than or of the order of the acceleration energy scale, M c 2 ≲ ℏ a / c . Achieving this condition, however, requires astronomically high accelerations. For example, detecting the effect for an electron-mass field would require accelerations of a ≳ 4.6 × 10 29 m s −2 , which is far beyond experimental reach. While using a massless field avoids this suppression, we show the best strategy is not to avoid mass, but to engineer a small effective mass that satisfies the optimal condition ℏ a / c ≫ M eff c 2 . We propose a concrete implementation using a superconducting circuit with a Josephson persistent-current qubit (the analog of a UdW detector) coupled to a microwave resonator (the analog of the scalar field). For this system, the optimal condition is 2 I p ΔΦ ≫ Δ , where I p is the persistent current, Δ Φ is the magnetic flux swing, and Δ is the qubit’s tunneling energy gap. For a fixed experimental setup

DOI: 10.1088/1361-6382/ae5b1c

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Abstract Detecting the Unruh effect is a major challenge in fundamental physics. It is known that exciting massive fields with the Unruh thermal bath is heavily suppressed when the field’s rest energy is much larger than the acceleration energy scale, M c 2 ≫ ℏ a / c . However, the standard literature lacks an explicit quantitative derivation of this suppression. In this work, we first fill this gap by deriving the exponential suppression, ∼ exp ⁡ ( − constant × M c 2 / ( ℏ a / c ) ) , in two different frameworks: a (3+1)-dimensional Unruh–deWitt detector and a (1+1)-dimensional cavity QED setup. This shows the suppression is universal and sets an insurmountable barrier for any detection method that relies on exciting massive fields. For an electron-mass field at achievable accelerations ( a ∼ 10 20 m s −2 ), the suppression exceeds 10 9 orders of magnitude. To avoid this suppression, the field’s rest energy must be less than or of the order of the acceleration energy scale, M c 2 ≲ ℏ a / c . Achieving this condition, however, requires astronomically high accelerations. For example, detecting the effect for an electron-mass field would require accelerations of a ≳ 4.6 × 10 29 m s −2 , which is far beyond experimental reach. While using a massless field avoids this suppression, we show the best strategy is not to avoid mass, but to engineer a small effective mass that satisfies the optimal condition ℏ a / c ≫ M eff c 2 . We propose a concrete implementation using a superconducting circuit with a Josephson persistent-current qubit (the analog of a UdW detector) coupled to a microwave resonator (the analog of the scalar field). For this system, the optimal condition is 2 I p ΔΦ ≫ Δ , where I p is the persistent current, Δ Φ is the magnetic flux swing, and Δ is the qubit’s tunneling energy gap. For a fixed experimental setup

The Unruh effect predicts that an accelerating observer perceives the Minkowski vacuum as a thermal bath, yet direct detection remains experimentally inaccessible. Its timelike counterpart, arising from the entanglement of massless fields between the future and past light cones, offers a more feasible route but requires a detector whose transition frequency follows a specific conformal-time scaling. We propose and analyze a practical implementation of such a detector using superconducting fluxonium circuits, which naturally provide two quasi-degenerate ground states and a tunable excited state, forming an effective

Λ

-system. By modulating the excited-state transition frequency in Minkowski time, the detector accumulates a geometric phase associated with the timelike Unruh effect. Open-system simulations predict

\sim 10\%

shift in the ground-state population within

530

ns, representing a three-order-of-magnitude sensitivity enhancement over two-level Unruh-DeWitt detectors. These results establish a realistic quantum-circuit platform for experimentally probing the timelike Unruh effect and, more broadly, for testing fundamental nature of quantum fields using engineered quantum systems.

A bstract We investigated the influence of the massive scalar field on the information degradation concerning the Unruh-DeWitt (UDW) detectors. In this conjecture, we adopted a system with a finite and large interaction time. To accomplish our purpose, one examines the quantum coherence of a uniformly accelerated qubit and the probability of finding the detector in the ground state. In this framework, we consider a quantum interferometric circuit to obtain the probability, visibility, and coherence. Naturally, these measurements provide us with wave-like information. Besides, one modifies the circuit to describe the path distinguishability and the particle-like information. These results are promising, as they allow us to understand the influence of the Unruh effect on the wave-particle duality. Thus, our findings announce that the increase in the scalar field mass induces a decrease in information degradation. Finally, we noted that the information concerning the Unruh effect remains preserved when m ≥ Ω. Therefore, the detector cannot absorb particles with mass equal to or greater than its energy gap. These results indicate that the scalar field mass is a protective factor against information degradation for systems under high acceleration conditions.

A long-standing debate on Unruh effect is about its obscure thermal nature. In this Letter, we use quantum Fisher information (QFI) as an effective probe to explore the thermal nature of Unruh effect from both local and global perspectives. By resolving the full dynamics of UDW detector, we find that the QFI is a time-evolving function of detector's energy gap, Unruh temperature TU and particularities of background field, e.g., mass and spacetime dimensionality. We show that the asymptotic QFI whence detector arrives its equilibrium is solely determined by TU, demonstrating the global side of Unruh thermality alluded by the KMS condition. We also show that the local side of Unruh effect, i.e., the different ways for the detector to approach the same thermal equilibrium, is encoded in the corresponding time-evolution of the QFI. In particular, we find that with massless scalar background the QFI has unique monotonicity in n=3 dimensional spacetime, and becomes non-monotonous for n≠3 models where a local peak value exists at early time and for finite acceleration, indicating an enhanced precision of estimation on Unruh temperature at a relative low acceleration can be achieved. Once the field acquiring mass, the related QFI becomes significantly robust against the Unruh decoherence in the sense that its local peak sustains for a very long time. While coupling to a more massive background, the persistence can even be strengthened and the QFI possesses a larger maximal value. Such robustness of QFI can surely facilitate any practical quantum estimation task.

Abstract We study, in the framework of open quantum systems, the entanglement dynamics for a quantum system composed of two uniformly accelerated Unruh-Dewitt detectors interacting with a bath of massive scalar fields in the Minkowski vacuum. We find that the entanglement evolution for the quantum system coupled with massive fields is always slower compared with that of the one coupled with massless fields, and this time-delay effect brought about by the field being massive can however be counteracted by a large enough acceleration, in contrast to the case of a static quantum system in a thermal bath, where this time delay is not affected by the temperature. Remarkably, the maximal concurrence of the quantum system generated during evolution may increase with acceleration for any inter-detector separation while that for static ones in a thermal bath decreases monotonically with temperature, and this can be considered as an anti-Unruh effect in terms of the entanglement generated.

Uniform acceleration induces a thermal response to the Minkowski vacuum and can thereby modify quantum correlations. For measurement-induced nonlocality (MIN), a form of nonclassical correlation distinct from entanglement, previous field-mode analyses of bosonic fields found that it decreases with increasing acceleration and vanishes in the infinite-acceleration limit. This raises the question of whether the disappearance of MIN is a generic consequence of the Unruh effect or depends on the physical description of the accelerated quantum system. To address this question, we study two uniformly accelerating Unruh-DeWitt detectors interacting with a massless scalar field. We find that the response of MIN to the Unruh temperature depends sensitively on the initial detector state: it can decrease monotonically, vanish at an intermediate temperature and subsequently recover, or increase monotonically. Moreover, for a broad class of initial states, MIN approaches a nonzero value in the high-temperature limit. These results show that the suppression of MIN under strong acceleration is not universal. Instead, Unruh-induced detector dynamics gives rise to a state-dependent response in which measurement-induced nonlocality can be suppressed, restored, or enhanced.

A simple but powerful particle detector model consists of a two-level system coupled to a field, where the detected particles are the field excitations. This is known as the Unruh-DeWitt detector. Research using this model has often focused on either a completely classical description of the external degrees of freedom of the detector, or a full field-theoretic treatment, where the detector itself is described as a field. Recently there has been much interest in quantum aspects of the detector's center of mass---either described as moving in superposition along semiclassical trajectories, or dynamically evolving under a nonrelativistic Hamiltonian. However, the processes of interest---the absorption or emission of field particles---necessarily change the detector's rest mass by the amount of energy of the absorbed or emitted field quanta. Neither of the above models can capture such effects. Here we incorporate the quantization of the detector's mass-energy into the Unruh-DeWitt model. We show that internal energy changes due to emission or absorption are relevant even in the lowest energy limit. Specifically, corrections to transition rates due to the detector's mass changing cannot be ignored unless the entire center of mass dynamics is also ignored. Our results imply that one cannot have a consistent model of the Unruh-DeWitt detector as a massive particle without including the mass-energy equivalence.