non-Markovian Quantum State Diffusion Research Articles

Linear optical properties of organic microcavity polaritons with non-Markovian quantum state diffusion

Abstract Hybridisation of the cavity modes and the excitons to polariton states together with the coupling to the vibrational modes determine the linear optical properties of organic semiconductors in microcavities. In this article we compute the refractive index for such system using the Holstein–Tavis–Cummings model and determine then the linear optical properties using the transfer matrix method. We first extract the parameters for the exciton in our model from fitting to experimentally measured absorption of a 2,7-bis[9,9-di(4-methylphenyl)-fluoren-2-yl]-9,9-di(4-methylphenyl) fluorene (TDAF) molecular thin film. Then we compute the reflectivity of such a thin film in a metal clad microcavity system by including the dispersive microcavity mode to the model. We compute susceptibility of the model systems evolving just a single state vector by using the non-Markovian quantum state diffusion. The computed location and height of the lower and upper polaritons agree with the experiment within the estimated errorbars for small angles ( ≤ 30 ° ) $(\le 30{}^{\circ})$ . For larger angles the location of the polariton resonances are within the estimated error.

Non-Markovian quantum state diffusion for spin environments

We introduce an exact open system method to describe the dynamics of quantum systems that are strongly coupled to specific types of environments comprising of spins, such as central spin systems. Our theory is similar to the established non-Markovian quantum state diffusion theory, but for a spin bath instead of a Gaussian bath. The method allows us to represent the time-evolved reduced state of the system as an ensemble average of stochastically evolving pure states. We present a comprehensive theory for arbitrary linear spin environments at both zero and finite temperatures. Furthermore, we introduce a hierarchical expansion method that enables the numerical computation of the time evolution of the stochastic pure states, facilitating a numerical solution of the open system problem in relevant strong coupling regimes.

Quantum Information Scrambling in Non-Markovian Open Quantum System.

In this paper, we investigate the dynamics of a spin chain whose two end spins interact with two independent non-Markovian baths by using the non-Markovian quantum state diffusion (QSD) equation approach. Specifically, two issues about information scrambling in an open quantum system are addressed. The first issue is that tripartite mutual information (TMI) can quantify information scrambling properly via its negative value in a closed system, whether it is still suitable to indicate information scrambling in an open quantum system. We find that negative TMI is not a suitable quantifier of information scrambling in an open quantum system in some cases, while negative tripartite logarithmic negativity (TLN) is an appropriate one. The second one is that up to now almost all information scrambling in open quantum systems reported were focus on a Markovian environment, while the effect of a non-Markovian environment on information scrambling is still elusive. Our results show that the memory effect of an environment will be beneficial to information scrambling. Moreover, it is found that the environment is generally detrimental for information scrambling in the long-term, while in some cases it will be helpful for information scrambling in the short-term.

Quantum Energy Current Induced Coherence in a Spin Chain under Non-Markovian Environments

We investigate the time-dependent behaviour of the energy current between a quantum spin chain and its surrounding non-Markovian and finite temperature baths, together with its relationship to the coherence dynamics of the system. To be specific, both the system and the baths are assumed to be initially in thermal equilibrium at temperature and , respectively. This model plays a fundamental role in study of quantum system evolution towards thermal equilibrium in an open system. The non-Markovian quantum state diffusion (NMQSD) equation approach is used to calculate the dynamics of the spin chain. The effects of non-Markovianity, temperature difference and system-bath interaction strength on the energy current and the corresponding coherence in cold and warm baths are analyzed, respectively. We show that the strong non-Markovianity, weak system-bath interaction and low temperature difference will help to maintain the system coherence and correspond to a weaker energy current. Interestingly, the warm baths destroy the coherence while the cold baths help to build coherence. Furthermore, the effects of the Dzyaloshinskii–Moriya () interaction and the external magnetic field on the energy current and coherence are analyzed. Both energy current and coherence will change due to the increase of the system energy induced by the interaction and magnetic field. Significantly, the minimal coherence corresponds to the critical magnetic field which causes the first order phase transition.

Calculating nonlinear response functions for multidimensional electronic spectroscopy using dyadic non-Markovian quantum state diffusion.

We present a methodology for simulating multidimensional electronic spectra of molecular aggregates with coupling of electronic excitation to a structured environment using the stochastic non-Markovian quantum state diffusion (NMQSD) method in combination with perturbation theory for the response functions. A crucial aspect of our approach is that we propagate the NMQSD equation in a doubled system Hilbert space but with the same noise. We demonstrate that our approach shows fast convergence with respect to the number of stochastic trajectories, providing a promising technique for numerical calculation of two-dimensional electronic spectra of large molecular aggregates.

Effects of Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions on the non-markovian dynamics of quantum entanglement and communication

By using the non-Markovian Quantum State Diffusion method, the non-Markovian dynamics of entanglement, quantum dense coding and quantum teleportation in the spin chain system with Kaplan-Shekhtman-Entin-wohlman-Aharony interactions and Dzyaloshinskii-Moriya in- teractions are studied. In particular, the joint effects of Kaplan-Shekhtman-Entin-wohlman-Aharony interactions and different external magnetic fields are discussed under zero and finite temperatures, respectively. The results show that the concurrence, channel capacity of quantum dense coding and average fidelity of quantum teleportation can be effectively increased via the increasing of Kaplan-Shekhtman-Entin-wohlman-Aharony interactions along the z-direction which can be attributed to the constructive role of Kaplan-Shekhtman-Entin-wohlman-Aharony interactions on the O(3) invariance in the spin chain. Non-uniform magnetic fields with the combination of Kaplan-Shekhtman-Entin-wohlman-Aharony interactions are found to be more effective in the increasing of the parameters under discussion.

Many-Body Quantum State Diffusion for Non-Markovian Dynamics in Strongly Interacting Systems.

Capturing non-Markovian dynamics of open quantum systems is generally a challenging problem, especially for strongly interacting many-body systems. In this Letter, we combine recently developed non-Markovian quantum state diffusion techniques with tensor network methods to address this challenge. As a first example, we explore a Hubbard-Holstein model with dissipative phonon modes, where this new approach allows us to quantitatively assess how correlations spread in the presence of non-Markovian dissipation in a 1D many-body system. We find regimes where correlation growth can be enhanced by these effects, offering new routes for dissipatively enhancing transport and correlation spreading, relevant for both solid state and cold atom experiments.

Non-Markovian Dynamics of Geometric Quantum Discord in a Double Quantum Dot System

In this paper, we study the geometric quantum discord dynamics of the double quantum dot charge qubit in the non-Markovian environment. We apply the non-perturbative non-Markovian quantum state diffusion method to obtain the exact master equation of the double quantum dot system coupled to two independent non-zero temperature electronic baths. Then, we use this master equation to investigate the effects of non-Markovianity, inter-dot coupling strength and bath temperature on the dynamics of geometric quantum discord. Our studies show that the geometric quantum discord of a double quantum dot system can be modified and enhanced in some cases via these factors.

Effects of Kaplan-Shekhtman-Entin-Wohlman-Aharony interaction on quantum discord of non-markovian dynamics under different magnetic fields

Since the discovery of symmetric helical interactions in the spin-orbit coupled single-band Hubbard model by Moriya and Kaplan, Shekhtman, Entin, Aharony et al. have successfully used this non-negligible symmetric helical exchange interaction to explain the weak ferromagnetism of La<sub>2</sub>CuO<sub>4</sub>. By using the non-Markovian quantum state diffusion method, the quantum discord of non-Markovian dynamics in the spin chain system that has Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions and Dzyaloshinskii-Moriya interactions is studied. The effects of Kaplan–Shekhtman–Entin-Wohlman–Aharony interaction on the quantum discord under different external magnetic fields at zero and finite temperatures are discussed. The results show that the quantum discord in the system can be increased via the increasing of Kaplan–Shekhtman–Entin-Wohlman–Aharony interaction in the case of zero or uniform magnetic field, while the case is opposite under the nonuniform magnetic field. More importantly, the ideal discord state can be obtained by modulating the uniform magnetic field and Kaplan–Shekhtman–Entin-Wohlman–Aharony interaction. Moreover, the Markovian case and the effect of temperature on the quantum discord are also discussed, respectively.

Accelerated adiabatic quantum search algorithm via pulse control in a non-Markovian environment

Adiabatic quantum computation requires that the system remains in its ground state. However, an adiabatic process often loses partly or entirely its quantumness, such as entanglement in its long runtime, due to the system-environment interactions. Here we put forward an effective quantum control technique to realize the adiabatic quantum search algorithm in a nonadiabatic regime and in the presence of environment. Using the non-Markovian quantum state diffusion equation approach, we numerically study the system dynamics characterized by the success probability. The results show that the probability increases with decreasing coupling strength and temperature. In particular, non-Markovianity from the environment can help to enhance the success probability. By choosing a suitable pulse intensity and period, a high success probability can be obtained in a short runtime for weak system-bath coupling, low temperature, and strong non-Markovian heat baths.

Almost-exact state transfer by leakage-elimination-operator control in a non-Markovian environment

We investigate the feasibility of using an effective pulse control method to realize an almost exact state transmission through a uniform chain where the communication channel is immersed in a quantum environment. This pulse control is treated in a nonperturbative fashion, allowing for a more precise view. Using the non-Markovian quantum state diffusion equation, we calculate the dynamics of the transmission fidelity. The results show that the memory effects of the environment can support an effective transmission control that can be boosted under a non-Markovian environment. Our scheme provides another way to realize almost exact state transmission in a spin chain system.

Diffusive Limit of Non-Markovian Quantum Jumps.

We solve two long-standing problems for stochastic descriptions of open quantum system dynamics. First, we find the classical stochastic processes corresponding to non-Markovian quantum state diffusion and non-Markovian quantum jumps in projective Hilbert space. Second, we show that the diffusive limit of non-Markovian quantum jumps can be taken on the projective Hilbert space in such a way that it coincides with non-Markovian quantum state diffusion. However, the very same limit taken on the Hilbert space leads to a completely new diffusive unraveling, which we call non-Markovian quantum diffusion. Further, we expand the applicability of non-Markovian quantum jumps and non-Markovian quantum diffusion by using a kernel smoothing technique allowing a significant simplification in their use. Lastly, we demonstrate the applicability of our results by studying a driven dissipative two level atom in a non-Markovian regime using all of the three methods.

Non-Markovian entanglement transfer to distant atoms in a coupled superconducting resonator**Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2018MS056) and the National Natural Science Foundation of China (Grant Nos. 11605055 and 11974108).

We investigate the non-Markovian effects on the entanglement transfer to the distant non-interacting atom qubits, which are embedded in a coupled superconducting resonator. The master equation governing the dynamics of the system is derived by the non-Markovian quantum state diffusion (NMQSD) method. Based on the solution, we show that the memory effect of the environment can lead to higher entanglement revival and make the entanglement last for a longer time. That is to say, the non-Markovian environment can enhance the entanglement transfer. It is also found that the maximum entanglement transferred to distant atoms can be modified by appropriately selecting the frequency of the modulated inter-cavity coupling. Moreover, with the initial anti-correlated state, the entanglement between the cavity fields can be almost completely transferred to the separated atoms. Lastly, we show that the memory effect has a significant impact on the generation of entanglement from the initial non-entangled states.

Persistent spin squeezing of a dissipative one-axis twisting model embedded in a general thermal environment

We investigate spin squeezing for a Lipkin-Meshkov-Glick (LMG) model coupled to a general non-Markovian environment in a finite temperature regime. Using the non-Markovian quantum state diffusion and master equation approach, we numerically study non-Markovian spin squeezing generation in LMG model. Our results show that the total spin number N, energy kBT, and certain coefficients in a LMG model can play a crucial role in generating spin squeezing. In particular, it shows that the maximum spin squeezing can be significantly enhanced when the participating environment has a relatively long memory time.

Macroscopic entanglement in optomechanical system induced by non-Markovian environment.

In this paper, the non-Markovian dynamics of an optomechanical system is analyzed by using the non-Markovian quantum state diffusion (NMQSD) method. An exact solution is obtained for the system composed of a Fabry-Pérot (F-P) cavity with two movable mirrors without the linearization of the Hamiltonian. Based on the solution, we find that the memory effect of the non-Markovian environment can be used to generate macroscopic entanglement between two mirrors. In order to achieve the maximum entanglement generation, the non-Markovian properties of the environment have to be chosen carefully depending on the properties of the system. Then, we also show that the coherence (superposition) in the initial state may produce entanglement in the evolution. At last, we show the entanglement sudden death and revival significantly depend on the strength of the memory effect, and the entanglement revival can be only observed in non-Markovian case. Our treatment, as an example, paves a way to exactly solve a large category of optomechanical systems without the linearization of the Hamiltonian.

Realization of hierarchical equations of motion from stochastic perspectives

The hierarchical equations of motion (HEOM) for a generalized quantum dissipative system is rigorously constructed in the frameworks of two different stochastic dynamical descriptions, i.e., the non-Markovian quantum state diffusion approach as well as the stochastic decoupling scheme. We demonstrated that the HEOMs obtained by these two different stochastic dynamical methods are identical. Moreover, we present some numerical examples to verify the feasibility of our formalism.

Equivalence of stochastic formulations and master equations for open systems

Several stochastic formulations have been developed to investigate the quantum dynamics of open systems. We show the equivalence between the Liouville equation based on the stochastic decoupling of the system-bath interaction and the non-Markovian quantum state diffusion approach. The procedure we use provides not only a means of calculating the unknown functional derivative in the latter, but also a possibility of developing more efficient theoretical schemes. Further, we demonstrate that the stochastic decoupling approach can feasibly be used to derive master equations for the spontaneously decaying multistate systems, which are difficult to obtain by other available methods.

Perturbation expansions of stochastic wavefunctions for open quantum systems.

Based on the stochastic unravelling of the reduced density operator in the Feynman path integral formalism for an open quantum system in touch with harmonic environments, a new non-Markovian stochastic Schrödinger equation (NMSSE) has been established that allows for the systematic perturbation expansion in the system-bath coupling to arbitrary order. This NMSSE can be transformed in a facile manner into the other two NMSSEs, i.e., non-Markovian quantum state diffusion and time-dependent wavepacket diffusion method. Benchmarked by numerically exact results, we have conducted a comparative study of the proposed method in its lowest order approximation, with perturbative quantum master equations in the symmetric spin-boson model and the realistic Fenna-Matthews-Olson complex. It is found that our method outperforms the second-order time-convolutionless quantum master equation in the whole parameter regime and even far better than the fourth-order in the slow bath and high temperature cases. Besides, the method is applicable on an equal footing for any kind of spectral density function and is expected to be a powerful tool to explore the quantum dynamics of large-scale systems, benefiting from the wavefunction framework and the time-local appearance within a single stochastic trajectory.

Stochastic Feshbach Projection for the Dynamics of Open Quantum Systems.

We present a stochastic projection formalism for the description of quantum dynamics in bosonic or spin environments. The Schrödinger equation in the coherent state representation with respect to the environmental degrees of freedom can be reformulated by employing the Feshbach partitioning technique for open quantum systems based on the introduction of suitable non-Hermitian projection operators. In this picture the reduced state of the system can be obtained as a stochastic average over pure state trajectories, for any temperature of the bath. The corresponding non-Markovian stochastic Schrödinger equations include a memory integral over the past states. In the case of harmonic environments and linear coupling the approach gives a new form of the established non-Markovian quantum state diffusion stochastic Schrödinger equation without functional derivatives. Utilizing spin coherent states, the evolution equation for spin environments resembles the bosonic case with, however, a non-Gaussian average for the reduced density operator.

Effects of counter-rotating-wave terms on the non-Markovianity in quantum open systems

We investigate the effect of counter-rotating-wave terms on the non-Markovianity in quantum open systems by employing the hierarchical equations of motion in the framework of the non-Markovian quantum state diffusion approach. As illustrative examples, the non-Markovian memory effect of a qubit embedded in a bosonic and a fermionic environment at zero temperature are analyzed. It is found that the counter-rotating-wave terms are able to enhance the observed non-Markovianity no matter the environment is composed of bosons or fermions. This result suggests that the rotating-wave approximation may inevitably reduce the non-Markovianity in quantum open systems. Moreover, we find that the modification of the non-Markovianity due to the different statistical properties of environmental modes becomes larger with the increase of the system-environment coupling strength.