Quantum thermodynamics, quantum correlations and quantum coherence in accelerating Unruh-DeWitt detectors in both steady and dynamical state

TL;DR

This work investigates how quantum thermodynamics, correlations, and coherence interplay in a pair of Unruh–DeWitt detectors interacting with a quantum field. It develops an open-system framework combining a Lindblad-type dynamics and a correlated dephasing channel to study steady and dynamical quantum resources (steering, entanglement, discord, coherence) under the influence of Unruh temperature, energy gaps, and initial states. The authors analyze a quantum Stirling cycle using the detectors as a working substance, deriving thermodynamic quantities and showing that non-Markovian memory effects can enhance resource preservation and engine efficiency. The results illuminate how classical correlations and memory effects can be harnessed to optimize quantum thermal devices in relativistic or open environments, offering guidance for robust quantum technologies. Overall, the paper maps the hierarchy of quantum resources and demonstrates practical implications for quantum heat engines and refrigerators in non-ideal environments.

Abstract

We investigate the interplay between quantum thermodynamics, quantum correlations, and quantum coherence within the framework of the Unruh-DeWitt (UdW) detector model. By analyzing both the steady and dynamical states of various quantum resources (including steerability, entanglement, quantum discord, and coherence), we study how these resources evolve under Markovian and non-Markovian environments. Furthermore, we investigate the impact of both the Unruh temperature and the energy levels on three key quantum phenomena: thermodynamic evolution, quantum correlations, and quantum coherence, considering different initial state preparations. The hierarchical structure relating quantum correlations and quantum coherence is determined. We further examine the thermodynamic performance of a quantum heat engine, highlighting the influence of memory effects and classical correlations on heat exchange, work extraction, and efficiency. Our results reveal that non-Markovian dynamics can enhance the preservation of quantum correlations and improve the engine's efficiency compared to purely Markovian regime. These findings provide insights into the role of quantum correlations and quantum coherence in quantum thermodynamic processes and open avenues for optimizing quantum devices operating in relativistic or open-system settings.

Figures (17)

• Figure 1: (a) Quantum steerability $S_{A \rightarrow B}$ and $S_{B \rightarrow A}$ as a function of temperature $T$ for different values of $\omega$ with fixed $\Delta_0 = -1.9$; (b) Quantum steerability versus $T$ for different values of the initial state parameter $\Delta_0$ with $\omega = 5$; (c) Comparison of $S_{A \rightarrow B}$, $S_{B \rightarrow A}$, and $\Delta_{12}$ for $\Delta_0 =-1.9$ and $\omega =0.2$.
• Figure 2: (a) Quantum steering versus $\Delta_0$ and $T$ with $\omega=1$; (b) Quantum steering versus $\omega$ and $T$ with $\Delta_0=-2.2$; (c) Quantum steering versus $\Delta_0$ and $\omega$ with $T=0.8$.
• Figure 3: (a) Entanglement of formation $\xi$ versus temperature $T$ for different values of $\omega$ with $\Delta_0 = -1$; (b) entanglement of formation versus $T$ for different values of $\Delta_0$ with $\omega= 3$.
• Figure 4: Geometric quantum discord $Q_G$ as a function of the temperature $T$; (a) for different values of $\omega$ with $\Delta_0 = 0.1$. (b) for different values of $\Delta_0$ with $\omega = 1$.
• Figure 5: The quantum coherence $C_{l1}$ as a function of temperature $T$ is presented: (a) for different values of the energy $\omega$, with initial state selection parameter $\Delta_0=1$ ; (b)for different values of the initial state selection parameter $\Delta_0$, with $\omega=0.5$.