We apply two quantum-trajectory methods to a decaying system of $N$ two-level atoms described by the Dicke model. Such a system is known to be superfluorescent, which is characterized by the $\mathrm{tanh}$ -like decay of the inversion for large $N$ . This $\mathrm{tanh}$ behavior is also found for the jump-free evolution for a single atom using the quantum-jump method, which has been identified with the neoclassical theory of spontaneous emission. However, we find that this behavior of superfluorescence is governed by the jump statistics. The jump-free evolution of the Dicke system displays other atypical behavior. We find that the energy of the system can in fact increase during the jump-free evolution and we propose an experiment that can detect this behavior. Applying the state-diffusion method to the system, we find that the trajectories keep the system in a spin coherent state, which confirms the picture of superfluorescence for single trajectories as a toppling needle point. This enables us to write an approximate analytic expression for the decay of the energy for any $N$ . Finally, we discuss the calculation of two-time correlation functions per trajectory and as an illustration we calculate the single-trajectory spectra. In the quantum-jump method, these single-trajectory spectra do not correspond to intuition, which we ascribe to the incompatibility of photon counting and spectral measurement.We apply two quantum-trajectory methods to a decaying system of $N$ two-level atoms described by the Dicke model. Such a system is known to be superfluorescent, which is characterized by the $\mathrm{tanh}$-like decay of the inversion for large $N$. This $\mathrm{tanh}$ behavior is also found for the jump-free evolution for a single atom using the quantum-jump method, which has been identified with the neoclassical theory of spontaneous emission. However, we find that this behavior of superfluorescence is governed by the jump statistics. The jump-free evolution of the Dicke system displays other atypical behavior. We find that the energy of the system can in fact increase during the jump-free evolution and we propose an experiment that can detect this behavior. Applying the state-diffusion method to the system, we find that the trajectories keep the system in a spin coherent state, which confirms the picture of superfluorescence for single trajectories as a toppling needle point. This enables us to write an approximate analytic expression for the decay of the energy for any $N$. Finally, we discuss the calculation of two-time correlation functions per trajectory and as an illustration we calculate the single-trajectory spectra. In the quantum-jump method, these single-trajectory spectra do not correspond to intuition, which we ascribe to the incompatibility of photon counting and spectral measurement.

Physical Review AJul 1, 19972 citations

Quantum trajectory theory

Perry R. Rice

Institute of Physics eBooksJul 1, 20250 citations

Non-Markovian quantum jump method for driven-dissipative two-level systems

Huanyuan Zhang, Jiasen Jin

We propose a modified non-Markovian quantum jump method to overcome the obstacle of dramatically increased trajectory number in conventional quantum trajectory simulations. In our method the trajectories are classified into the trajectory classes characterized by the number of quantum jumps. We derive the expression of the existence probability of each trajectory (class), which is essential to construct the density matrix of the open quantum system. This modified method costs less computational resources and is more efficient than the conventional quantum trajectory approach. As applications we investigate the dynamics of spin- $\frac{1}{2}$ systems subject to Lorentzian reservoirs with considering only the no-jump and one-jump trajectories. The revival of coherence and entanglement induced by the memory effect is observed.We propose a modified non-Markovian quantum jump method to overcome the obstacle of dramatically increased trajectory number in conventional quantum trajectory simulations. In our method the trajectories are classified into the trajectory classes characterized by the number of quantum jumps. We derive the expression of the existence probability of each trajectory (class), which is essential to construct the density matrix of the open quantum system. This modified method costs less computational resources and is more efficient than the conventional quantum trajectory approach. As applications we investigate the dynamics of spin-$\frac{1}{2}$ systems subject to Lorentzian reservoirs with considering only the no-jump and one-jump trajectories. The revival of coherence and entanglement induced by the memory effect is observed.

arXiv:2502.00764Physical Review ADec 2, 20251 citation

Between Probabilistic and Trajectory Pictures: Revisiting Prigogine's Theory of Irreversibility

Akihiro Koide

One of the key objectives in the study of time in physics is to understand the emergence of macroscopic irreversibility from microscopic reversible dynamics. Prigogine proposed a worldview based on the probabilistic picture, in which irreversibility appears as a fundamental property of the dynamical system itself. This idea was formulated through the use of the complex spectral representation. On the other hand, contemporary physics in the study of isolated quantum systems with a small number of degrees of freedom explains irreversibility from the trajectory picture by using the concept of typicality. This paper reviews Prigogine's theory of irreversibility and compares it with the concept of typicality. By placing Prigogine's approach at the center, it provides a conceptual overview of how irreversibility is treated in physics, focusing on the contrast between probabilistic and trajectory pictures.One of the key objectives in the study of time in physics is to understand the emergence of macroscopic irreversibility from microscopic reversible dynamics. Prigogine proposed a worldview based on the probabilistic picture, in which irreversibility appears as a fundamental property of the dynamical system itself. This idea was formulated through the use of the complex spectral representation. On the other hand, contemporary physics in the study of isolated quantum systems with a small number of degrees of freedom explains irreversibility from the trajectory picture by using the concept of typicality. This paper reviews Prigogine's theory of irreversibility and compares it with the concept of typicality. By placing Prigogine's approach at the center, it provides a conceptual overview of how irreversibility is treated in physics, focusing on the contrast between probabilistic and trajectory pictures.

Annals of the Japan Association for Philosophy of ScienceJan 1, 20251 citation

We apply two quantum-trajectory methods to a decaying system of

N

two-level atoms described by the Dicke model. Such a system is known to be superfluorescent, which is characterized by the

\mathrm{tanh}

-like decay of the inversion for large

N

. This

\mathrm{tanh}

behavior is also found for the jump-free evolution for a single atom using the quantum-jump method, which has been identified with the neoclassical theory of spontaneous emission. However, we find that this behavior of superfluorescence is governed by the jump statistics. The jump-free evolution of the Dicke system displays other atypical behavior. We find that the energy of the system can in fact increase during the jump-free evolution and we propose an experiment that can detect this behavior. Applying the state-diffusion method to the system, we find that the trajectories keep the system in a spin coherent state, which confirms the picture of superfluorescence for single trajectories as a toppling needle point. This enables us to write an approximate analytic expression for the decay of the energy for any

N

. Finally, we discuss the calculation of two-time correlation functions per trajectory and as an illustration we calculate the single-trajectory spectra. In the quantum-jump method, these single-trajectory spectra do not correspond to intuition, which we ascribe to the incompatibility of photon counting and spectral measurement.

\frac{1}{2}

systems subject to Lorentzian reservoirs with considering only the no-jump and one-jump trajectories. The revival of coherence and entanglement induced by the memory effect is observed.