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

Introduction to Quantum Trajectories

Springer eBooksMay 27, 20060 citations

Collective decay as a stochastic process

F. E. van Dorsselaer, Gerard Nienhuis

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 Trajectories

Miguel Orszag

Springer eBooksJan 1, 20240 citations

Statistical analysis of quantum trajectories in dissipative Landau-Zener model

Laleh Memarzadeh, Rosario Fazio

We present statistics of quantum jumps in the two-level system with landau-Zener Hamiltonian that undergoes a Markovian process. For the Landau-Zener model, which is successful in simulating adiabatic/non-adiabatic evolution and quantum annealing, we consider two types of dissipation. In the first one, the jump operators project states to the initial ground state and excited state of the Hamiltonian at $t\to -\infty$ . In the second type, the jump operators project to the instantaneous eigenstates of the Hamiltonian. By the quantum trajectories approach, we present the probability of the number of jumps in adiabatic and non-adiabatic regimes for both models. Furthermore, we demonstrate the statistics of jumps in time intervals of the evolutions. Also, we show the role of bath temperature, coupling strength to the environment, and spin-coupling directions on the statistics of quantum jumps.We present statistics of quantum jumps in the two-level system with landau-Zener Hamiltonian that undergoes a Markovian process. For the Landau-Zener model, which is successful in simulating adiabatic/non-adiabatic evolution and quantum annealing, we consider two types of dissipation. In the first one, the jump operators project states to the initial ground state and excited state of the Hamiltonian at $t\to -\infty$. In the second type, the jump operators project to the instantaneous eigenstates of the Hamiltonian. By the quantum trajectories approach, we present the probability of the number of jumps in adiabatic and non-adiabatic regimes for both models. Furthermore, we demonstrate the statistics of jumps in time intervals of the evolutions. Also, we show the role of bath temperature, coupling strength to the environment, and spin-coupling directions on the statistics of quantum jumps.

arXiv:2410.03582Oct 4, 20240 citations

\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 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.

t\to -\infty

. In the second type, the jump operators project to the instantaneous eigenstates of the Hamiltonian. By the quantum trajectories approach, we present the probability of the number of jumps in adiabatic and non-adiabatic regimes for both models. Furthermore, we demonstrate the statistics of jumps in time intervals of the evolutions. Also, we show the role of bath temperature, coupling strength to the environment, and spin-coupling directions on the statistics of quantum jumps.