We study the quantum Fisher information (QFI) of acceleration, in the open quantum systems, for a two-level atom with the circular motion coupled to a massless scalar field in the Minkowski vacuum without and with a reflecting boundary in the ultra-relativistic limit. As we amplify a, the saturation time decreases for θ≠π, but first increases and then decreases for θ=π. Without a boundary, there exists a peak value of QFI with a certain time. The QFI varies with the initial state parameter θ, and firstly takes peak value in the ground state of the atom. The variation of QFI with respect to θ gradually fades away with the evolution of time. With a boundary, the detection range of acceleration has been expanded. The QFI firstly takes the maximum in the excited state of the atom. In addition, we study the QFI of temperature for a static atom immersed in a thermal bath without and with a boundary. The relation between the saturation time and T is similar to a. Without a boundary, the QFI of temperature is similar to that of acceleration. With a boundary, the QFI firstly takes peak value in the ground state of the atom, which is different from the behavior of acceleration. The results provide references for the detection of Unruh-like effect.
We study the quantum Fisher information (QFI) of acceleration, in the open quantum systems, for a two-level atom with the circular motion coupled to a massless scalar field in the Minkowski vacuum without and with a reflecting boundary in the ultra-relativistic limit. As we amplify a, the saturation time decreases for θ≠π, but first increases and then decreases for θ=π. Without a boundary, there exists a peak value of QFI with a certain time. The QFI varies with the initial state parameter θ, and firstly takes peak value in the ground state of the atom. The variation of QFI with respect to θ gradually fades away with the evolution of time. With a boundary, the detection range of acceleration has been expanded. The QFI firstly takes the maximum in the excited state of the atom. In addition, we study the QFI of temperature for a static atom immersed in a thermal bath without and with a boundary. The relation between the saturation time and T is similar to a. Without a boundary, the QFI of temperature is similar to that of acceleration. With a boundary, the QFI firstly takes peak value in the ground state of the atom, which is different from the behavior of acceleration. The results provide references for the detection of Unruh-like effect.
In an open quantum system, we study the evolution of a two-level atom as a detector which interacts with given environments. For a uniformly accelerated two-level atom coupled to a massless scalar field in the Minkowski vacuum, when it evolves for a certain time, we find that there exists a peak value for the quantum Fisher information (QFI) of acceleration, which indicates that the optimal precision of estimation is achieved when choosing an appropriate acceleration a. QFI has different behaviors for different initial state parameters $\ensuremath{\theta}$ of the atom, displaying periodicity. However, the periodicity fades away with the evolution of time, which means that the initial state cannot affect the later stable quantum state. Furthermore, adding a boundary, we observe that the peak value of QFI increases when the atom is close to the boundary, which shows that QFI is protected by the boundary. Here, QFI fluctuates, and there may exist two peak values with a certain moment, which expands the detection range of the acceleration. Therefore, we can enhance the estimation precision of acceleration by choosing an appropriate position and acceleration a. The periodicity of QFI with respect to the initial state parameter $\ensuremath{\theta}$ lasts a longer time than the previous unbounded case, which indicates that the initial state is protected by the boundary. Finally, for a thermal bath with a boundary, QFI of temperature has no more than one peak value with a certain moment, which is different from QFI of acceleration with a boundary. The periodicity also lasts a longer time than unbounded case, which shows the initial quantum state of the atom is protected by the boundary for two cases.
In open quantum systems, we study the quantum Fisher information of acceleration for a uniformly accelerated two-level atom coupled to fluctuating electromagnetic fields in the Minkowski vacuum. With the time evolution, for the initial atom state parameter θ=π, the quantum Fisher information can exist a maximum value and a local minimum value before reaching a stable value. In addition, in a short time, the quantum Fisher information varies with the initial state parameter, and the quantum Fisher information can take a maximum value at θ=0. The quantum Fisher information may exist two peak values at a certain moment. These features are different from the massless scalar fields case. With the time evolution, Fmax firstly increases, then decreases, and finally, reaches the same value. However, Fmax will arrive at a stable maximum value for the case of the massless scalar fields. Although the atom response to the vacuum fluctuation electromagnetic fields is different from the case of massless scalar fields, the quantum Fisher information eventually reaches a stable value.
Quantum Fisher information (QFI) associated with local metrology has been used to parameter estimation in open quantum systems. In this work, we calculated the QFI for a moving Unruh–DeWitt detector coupled with massless scalar fields in n-dimensional spacetime, and analyzed the behavior of QFI with various parameters, such as the dimension of spacetime, evolution time, and Unruh temperature. We discovered that the QFI of state parameter decreases monotonically from 1 to 0 over time. Additionally, we noted that the QFI for small evolution times is several orders of magnitude higher than the QFI for long evolution times. We also found that the value of QFI decreases at first and then stabilizes as the Unruh temperature increases. It was observed that the QFI depends on initial state parameter θ, and Fθ is the maximum for θ = 0 or θ = π, Fϕ is the maximum for θ = π/2. We also obtain that the maximum value of QFI for state parameters varies for different spacetime dimensions with the same evolution time.
We explore the changes of Quantum Fisher information (QFI) for an uniformly accelerating atom coupling to fluctuating massless scalar field with a perfectly reflecting boundary. We first deduce the master equation that the system obeys. For the unbounded case, the vacuum fluctuation and Unruh thermal bath can rapidly degrade the QFI. However, with a boundary, the degradation, preservation, fluctuation and enhancement of QFI are dependent on the evolution time, boundary and acceleration. In addition, the existing boundary can effectively shield QFI from the influence of the vacuum fluctuation and Unruh thermal effect. Especially, the QFI seems to be unaffected by the vacuum fluctuation and acceleration when the atom is very close to the boundary. The efficient control of the boundary and acceleration can provide the feasible scheme of improving the parameter estimation precision.
Abstract In this work, we devote to understand how boundaries can help improve parameter estimation against atomic decoherence and dissipation caused by relativistic motion. The system we considered is a two-level atom in uniform linear acceleration parallel to a planar wall in (3+1)-dimensional Minkowski spacetime, which is coupled to a massless scalar field with Dirichlet, Neumann or transparent boundary conditions at the wall. We find that the quantum Fisher information (QFI), which determines the ultimate estimation precision, depends on various factors, such as atomic motional trajectories, evolution time, atomic initial state, and the boundary condition. We identify the optimal estimation strategies that maximize the QFI through all the associated parameters, thus optimizing the estimation precision. Our results show that the QFI has different behaviors and even different magnitudes for different boundary cases. We also determine the boundary conditions that can effectively suppress the influence of atomic relativistic motion on the QFI. Our investigation may help advance the study of relativistic quantum information in cavity quantum electrodynamics.
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.