non-Markovian Evolution Research Articles

Quantum turbulence, superfluidity, non-Markovian dynamics, and wave function thermalization

While quantum turbulence has been addressed both experimentally (predominantly for superfluid He4 and He3) and theoretically, the dynamics of various ensembles of quantized vortices has been followed in time only until the vortices have decayed into phonons. How this “thermalization” is achieved is still an unaddressed and thus an unelucidated question. The unitary Fermi gas (UFG) is a unique quantum system, which has no classical counterpart and is of relevance to neutron stars, cold atoms, condensed-matter and nuclear many-body systems. The non-Markovian evolution of an isolated UFG is put in evidence and its entire nonequilibrium evolution can be studied theoretically within a unified theoretical framework. The initial lattice of quantum vortices and antivortices evolves through a couple of vortex tangles and excitation of Kelvin waves, where vortices cross and reconnect, until very slowly thermalization sets in. Published by the American Physical Society 2024

Non-Markovian dynamics of time-fractional open quantum systems

The Time-Fractional Schrödinger Equation (TFSE) is suitable to describe the non-Markovian dynamics of a quantum system exposed to an environment, which is instructive for understanding and characterizing the time behavior of actual physical systems. Three popular TFSEs, namely Naber’s TFSE I, Naber’s TFSE II, and XGF’s TFSE, have been introduced in the form of ∂β∂tβ with β∈0,1. However, they suffer from the drawbacks. In their respective descriptions, the total probability for finding a particle in the entire space equals one only when β=1, implying that time-fractional quantum mechanics violates quantum mechanical probability conservation. By applying the three TFSEs to a basic single-qubit open system model, we discover that in describing the non-Markovian evolution of the system, the three TFSEs are limited by their own applicable ranges of β. This indicates that the three TFSEs cannot effectively describe the non-Markovian quantum dynamics. To address these issues, we introduce a well-performed TFSE by constructing a new analytic continuation of time without iβ combined with the conformable fractional derivative. In its description, for one thing, the total probability for finding the system in any single-qubit state equals one when β∈0,1. For another, the system evolves correctly in the non-Markovian manner at all values of β. Furthermore, we study the performances of the four TFSEs applying to a two-qubit open system model and show that our TFSE still possesses the above two advantages compared with the other three TFSEs.

Quantum speedup dynamics process in multiqubit-interacting system

We investigate the dynamics of an N-qubit interacting system coupled to a common reservoir. In the weak system-environment coupling regime, the crossovers from Markovian to non-Markovian and from no speedup to speedup can be realized by adjusting the controllable parameters (i.e., the coupling strength between qubits and the number of the qubits). However, in the case of strong coupling, the multiple transitions from non-Markovian regime to Markovian regime and from speedup to no speedup can be induced by manipulating controllable parameters. In addition, a phenomenon can be noticed that the number of qubits and the coupling strength between the qubits have the different effect on the non-Markovian dynamics and speedup evolution of the system in the above weak- and strong-coupling regimes. Our results provide an effective theoretical scheme for the realization of non-Markovian speedup dynamic processes. Published by the American Physical Society 2024

Path integral quantum algorithm for simulating non-Markovian quantum dynamics in open quantum systems

Research in open quantum system dynamics has received growing interest in recent years, and its ongoing investigation has uncovered many intriguing physics departing from closed systems. A particularly useful application of the open quantum system theory is to simulate quantum dynamical processes in condensed phase materials. As the quantum degree of freedom is constantly under the influence of its thermal environment, the accurate description of the dynamics often requires non-Markovian time evolution at finite temperature. Such calculation is usually quite challenging on classical computers as extensive memory storage is required. In this work, we focus on a quantum system linearly coupled to its harmonic bath and present a path integral based quantum algorithm that time-evolves the reduced density matrix under finite temperature non-Markovian dynamics. To treat the nonunitary time evolution, the Sz.-Nagy dilation scheme is used for the conversion to unitary dynamics that can be implementable on gate-based quantum computers. The modified Hadamard test is then used to retrieve all the information of the reduced density matrix. Complexity analysis shows that the memory requirement has exponential reduction on the quantum machine whereas the runtime complexity stays roughly the same as for the classical computer. It points to the possibility of using this algorithm to simulate multilevel and multisite non-Markovian quantum dynamics that are beyond the reach of classical computers. The algorithm makes no ad hoc assumptions and extends naturally beyond Markovian and weak coupling regimes. We validated the algorithm on the quantum simulator with the spin-boson model and demonstrated its excellent agreement with the classical computer benchmark. Published by the American Physical Society 2024

Detecting quantum phase localization using Arnold tongue

The dynamical phase localization of a single qubit in a dissipative bath is investigated. We show that phase preference persists in the long time limit only for a non-Markovian evolution with a finite detuning implying that non-Markovianity is required for phase localization. The maximum of the shifted phase distribution exhibits an Arnold tongue like feature where the phase localized and phase delocalized regions are distinctly separated. We show the formation of Arnold tongue using the relative entropy of coherence as well. From our work we propose that Arnold tongue can be used to detect dynamical phase localization even when there is no synchronization present in the system.

Pure non-Markovian evolutions

Non-Markovian dynamics are characterized by information backflows, where the evolving open quantum system retrieves part of the information previously lost in the environment. Hence, the very definition of non-Markovianity implies an initial time interval when the evolution is noisy, otherwise no backflow could take place. We identify two types of initial noise, where the first has the only effect of degrading the information content of the system, while the latter is essential for the appearance of non-Markovian phenomena. Therefore, all non-Markovian evolutions can be divided into two classes: noisy non-Markovian (NNM), showing both types of noise, and pure non-Markovian (PNM), implementing solely essential noise. We make this distinction through a timing analysis of fundamental non-Markovian features. First, we prove that all NNM dynamics can be simulated through a Markovian pre-processing of a PNM core. We quantify the gains in terms of information backflows and non-Markovianity measures provided by PNM evolutions. Similarly, we study how the entanglement breaking property behaves in this framework and we discuss a technique to activate correlation backflows. Finally, we show the applicability of our results through the study of several well-know dynamical models.

Impact of non-Markovian evolution on characterizations of quantum thermodynamics

Here, we study the impact of non-Markovian evolution on prominent characteristics of quantum thermodynamics such as ergotropy and power. These are benchmarked by the behavior of the quantum speed limit time. We make use of both geometric-based, particularly the quantum Fisher and Wigner–Yanase information metric, and physical properties-based measures, particularly the relative purity measure and relative entropy of coherence measure, to compute the quantum speed limit time. A simple non-Markovian model of a qubit in a bosonic bath exhibiting non-Markovian amplitude damping evolution is considered, which, from the quantum thermodynamic perspective with finite initial ergotropy, can be envisaged as a quantum battery. To this end, we explore the connections between the physical properties-based measures of the quantum speed limit time and the coherent component of ergotropy. The non-Markovian evolution is shown to impact the recharging process of the quantum battery. Furthermore, a connection between the discharging–charging cycle of the quantum battery and the geometric measures of the quantum speed limit time is observed.

Universal equilibration dynamics of the Sachdev-Ye-Kitaev model

Equilibrium quantum many-body systems in the vicinity of phase transitions generically manifest universality. In contrast, limited knowledge has been gained on possible universal characteristics in the non-equilibrium evolution of systems in quantum critical phases. In this context, universality is generically attributed to the insensitivity of observables to the microscopic system parameters and initial conditions. Here, we present such a universal feature in the equilibration dynamics of the Sachdev-Ye-Kitaev (SYK) Hamiltonian – a paradigmatic system of disordered, all-to-all interacting fermions that has been designed as a phenomenological description of quantum critical regions. We drive the system far away from equilibrium by performing a global quench, and track how its ensemble average relaxes to a steady state. Employing state-of-the-art numerical simulations for the exact evolution, we reveal that the disorder-averaged evolution of few-body observables, including the quantum Fisher information and low-order moments of local operators, exhibit within numerical resolution a universal equilibration process. Under a straightforward rescaling, data that correspond to different initial states collapse onto a universal curve, which can be well approximated by a Gaussian throughout large parts of the evolution. To reveal the physics behind this process, we formulate a general theoretical framework based on the Novikov–Furutsu theorem. This framework extracts the disorder-averaged dynamics of a many-body system as an effective dissipative evolution, and can have applications beyond this work. The exact non-Markovian evolution of the SYK ensemble is very well captured by Bourret–Markov approximations, which contrary to common lore become justified thanks to the extreme chaoticity of the system, and universality is revealed in a spectral analysis of the corresponding Liouvillian.

Observation of Non-Markovian Evolution of Einstein-Podolsky-Rosen Steering.

Einstein-Podolsky-Rosen (EPR) steering is a type of characteristic nonlocal correlation and provides an important resource in quantum information tasks, especially in view of its asymmetric property. Although plenty of works on EPR steering have been reported, the study of non-Markovian evolution of EPR steering, in which the interactions between the quantum system and surrounding environment are taken into consideration, still lacks intuitive experimental evidence. Here, we experimentally observe the non-Markovian evolution of EPR steering including its sudden death and revival processes, during which the degree of memory effect plays a key role in the recovery of steering. Additionally, a strict unsteerable feature is sufficiently verified during the non-Markovian evolution within multisetting measurements. This Letter, revealing the whole evolution of EPR steering under the non-Markovian process, provides incisive insight into the applications of EPR steering in quantum open systems.

Quantum speed limit of Jaynes-Cummings model with detuning for arbitrary initial states

The quantum speed limit (QSL) of the Jaynes-Cummings model with detuning for arbitrary initial states is investigated. We mainly focus on the influences of the detuning, width of Lorentzian spectral density, and coherence of the initial state on the non-Markovian speedup evolution in an open system. It is found that even in the Markovian regime, increasing the detuning parameter leads to quantum speedup. Moreover, we reveal that the QSL has an inverse relation with the population of the initial excited state. Notably, we show that the QSL depends on the quantum coherence of the system's initial state such that the maximal coherent state can saturate its bound.

Non-Markovian speedup evolution of a center massive particle in two-dimensional environmental model

A two-dimensional ray model is introduced to realize the non-Markovian speedup evolution of a center massive particle gravitationally coupled to a controllable environment (multilayer arrangement of the massive particles). By controlling the environment, for instance by choosing a judicious mass of the environmental particles or by changing the separation distance of each massive particle, two dynamical crossover behaviors from Markovian to non-Markovian and from no-speedup to speedup are achieved due to the gravitational interactions between the system particle and environmental particles. It is obvious that the critical mass of the environmental particles or the critical separation distance for these two dynamical crossover behaviors restrict each other directly. The larger the value of the mass of the environmental particles is, the smaller the value of the critical separation distance should be requested. In addition, it should be emphasized that the non-Markovian dynamics is the principal physical reason for the speedup evolution of the system massive particle. Particularly, the non-Markovianity of the dynamics process of the system massive particle in the even ray case has better correspondence with the quantum speed limit time than that in the singular ray case.

Ancillary Gaussian modes activate the potential to witness non-Markovianity

We study how the number of employed modes impacts the ability to witness non-Markovian evolutions via correlation backflows in continuous-variable quantum dynamics. We first prove the existence of non-Markovian Gaussian evolutions that do not show any revivals in the correlations between the mode evolving through the dynamics and a single ancillary mode. We then demonstrate how this scenario radically changes when two ancillary modes are considered. Indeed, we show that the same evolutions can show correlation backflows along a specific bipartition when three-mode states are employed, and where only one mode is subjected to the evolution. These results can be interpreted as a form of activation phenomenon in non-Markovianity detection and are proven for two types of correlations, entanglement and steering, and two classes of Gaussian evolutions, a classical noise model and the quantum Brownian motion model.

Strong coupling in the entanglement dynamics of two qubits interacting with a graphene nanodisk

We investigate the entanglement dynamics of two qubits interacting with a graphene nanodisk using the macroscopic quantum electrodynamics method. By modifying the free-space decay rate of each qubit, we study the coupling strength between the nanoparticle and the qubits. We find that as the free-space decay rate increases, the decaying Rabi oscillations featured in the qubit population dynamics change to complex non-Markovian dynamical population evolution. This is also reflected on the concurrence, which at weak or moderate light–matter coupling conditions, attains values up to 0.5, while as the coupling conditions become stronger, larger values are also transiently observed. Our findings indicate that graphene nanostructures can provide a platform for the realization of high degree of entanglement in the strong coupling regime at the nanoscale, essential for quantum technology applications.

Dynamics of quantum Fisher information from a time-local non-Markovian master equation with decoherence rates and operators depending on the estimated parameter

We analyze the dynamics of the quantum Fisher information (QFI) in the case of a two-dimensional open quantum system obeying a time-local non-Markovian master equation in the canonical form, characterized by canonical decoherence rates and operators that depend on the parameter to be estimated. This last condition brings a framework in which the information about the parameter is structurally encoded not only in the open system, but also in the system-environment interaction or/and correlations, and in some environment properties. We derive analytical formulas for the decompositions of the QFI flow and of the purity dynamics in terms associated to the canonical decoherence rates. In contrast to the results presented in X.-M. Lu et al. [Phys. Rev. A 82, 042103 (2010)], we show that, in this extended framework, the QFI flow contains not only the subflows corresponding to the decoherence rates, but also supplementary terms which originate in the state dependence on the estimated parameter; moreover, the signs of the QFI subflows associated to the decoherence rates are not correlated to the signs of the rates. We show that a pertinent connection between the QFI flow and non-Markovianity can be realized using the canonical measures defined from the negative canonical decoherence rates. We employ this theoretical framework to explore the QFI flow and its subflows in two cases of quantum evolutions directed by master equations with decoherence rates or/and operators depending on the estimated parameter: (i) the Markovian nonunital time evolution of a qubit under the generalized amplitude damping channel; (ii) the non-Markovian time evolution of a two-dimensional electronic subsystem entangled with its vibrational environment in a molecule.

Markovian and non-Markovian dynamics of quantum coherence in the extended XX chain

The Markovian and non-Markovian dynamics of quantum coherence, including single-spin coherence, two-spin coherence, and its distribution (collective and localized coherence), are investigated in the $XX$ spin chain with three-spin interaction. We find that the single-spin and localized coherence do not decrease but increase with time, which makes the dynamic evolution of the two-spin coherence more robust than entanglement and quantum discord. The three-spin interaction can lower the values of quantum coherence in Markovian evolution and heighten the oscillation frequency of quantum coherence in non-Markovian evolution because it can speed up the flow of coherence information. Finally, the trade-off relation between the collective and the localized coherence is clearly shown in their dynamic evolution. Thanks to the coherence trade-off, we find the substitution of localized coherence for collective coherence in dominating the dynamics of the two-spin coherence.

Control of quantum dynamics: non-Markovianity and speedup of a massive particle evolution due to gravity

We illustrate two linear configurations (one-side model and two-side model) for implementing a non-Markovian speedup evolution of a massive particle gravitationally coupled with a controllable environment: multiple massive particles. By controlling the environment, for instance by choosing a judicious the mass of the environmental particles or by changing the separation distance of each massive particle, two dynamical crossover behaviors from Markovian to non-Markovian and from no-speedup to speedup are achieved due to the gravitational interactions between the system particle and each environmental particle. Numerical calculation also shows that the critical mass of the environmental particles or the critical separation distance for these two dynamical crossover behaviors restrict each other directly. The larger the value of the mass of the environmental particles is, the smaller the value of the critical separation distance should be requested. In this work, the non-Markovian dynamics is the principal physical reason for the speedup evolution of a quantum system. Particularly, the non-Markovianity of the system mass particle in the two-side model has better correspondence with the quantum speed limit time than that in the one-side model.

Reconstructing non-Markovian open quantum evolution from multiple time measurements

For a quantum system undergoing non-Markovian open quantum dynamics, we demonstrate a tomography algorithm based on multi-time measurements of the system, which reconstructs a minimal environment coupled to the system, such that the system plus environment undergoes unitary evolution and that the reduced dynamics of the system is identical to the observed dynamics of it. The reconstructed open quantum evolution model can be used to predict any future dynamics of the system when it is further assumed to be time-independent. We define the memory size and memory complexity for the non-Markovian open quantum dynamics which characterize the complexity of the reconstruction.

Tunable non-Markovian dynamics with a three-level atom mediated by the classical laser in a semi-infinite photonic waveguide

In this work, we investigate the non-Markovian (NM) dynamical evolution of a three-level atom coupled to a semi-infinite one-dimensional photonic waveguide and driven by a classical driving field. The single-end of waveguide behaves as a perfect mirror while light can pass through the opposite end with no backreflection. We derive the exact analytical expressions for the wave function of the driven three-level atom by solving a set of delay differential equations and give the conditions of atom-photon bound state formation that can inhibit the dissipation, which appears in the atom-mirror interspace in order to trap a considerable amount of initial atomic excitation. We show that when the evolution time of the system is shorter than the time delay taken by a photon to perform a round trip between the atom and mirror, the atomic dynamics exhibits Markovian properties, which depend on the driving strength and rescaled parameters. If the evolution time of the system exceeds the time delay, the photon can be reabsorbed by the atom with the photon emitted by the atom having completed the round trip, which exhibits NM memory effects, where the population eventually convergences to the finite-steady values. We also study the influence of the loss and dephasing on the formation of a bound state. Finally, the above results are extended to a more general quantum system involving single-end photonic waveguide coupled to an arbitrary number of noninteracting three-level atoms driven by the driving fields. The presented formalism might open a way to better understand exactly the NM dynamics of driven multilevel atoms coupled to a semi-infinite waveguide.

Optimally preserving quantum correlations and coherence with eternally non-Markovian dynamics

We demonstrate, both analytically and experimentally, the usefulness of non-Markovianity for preserving correlations and coherence in quantum systems. For this, we consider a broad class of qubit evolutions, having a decoherence matrix separated from zero for large times. While any such Markovian evolution leads to an exponential loss of correlations, non-Markovianity can help to preserve correlations even in the limit t → ∞. In fact, under general assumptions, eternally non-Markovian evolution naturally emerges as the one that allows for optimal preservation of quantum correlations. For covariant qubit evolutions, we also show that non-Markovianity can be used to preserve quantum coherence at all times, which is an important resource for quantum metrology. We explicitly demonstrate this effect experimentally with linear optics, by implementing the optimal non-Markovian quantum evolution.

Guaranteeing completely positive quantum evolution

In open quantum systems, it is known that if the system and environment are in a product state, the evolution of the system is given by a linear completely positive (CP) Hermitian map. CP maps are a subset of general linear Hermitian maps, which also include non completely positive (NCP) maps. NCP maps can arise in evolutions such as non-Markovian evolution, where the CP divisibility of the map (writing the overall evolution as a composition of CP maps) usually fails. Positive but NCP maps are also useful as entanglement witnesses. In this paper, we focus on transforming an initial NCP map to a CP map through composition with the asymmetric depolarizing map. We use separate asymmetric depolarizing maps acting on the individual subsystems. Previous work have looked at structural physical approximation (SPA), which is a CP approximation of an NCP map using a mixture of the NCP map with a completely depolarizing map. We prove that the composition can always be made CP without completely depolarizing in any direction. It is possible to depolarize less in some directions. We give the general proof by using the Choi matrix and an isomorphism from a maximally entangled two qudit state to a set of qubits. We also give measures that describe the amount of disturbance the depolarization introduces to the original map. Given our measures, we show that asymmetric depolarization has many advantages over SPA in preserving the structure of the original NCP map. Finally, we give some examples. For some measures and examples, completely depolarizing (while not necessary) in some directions can give a better approximation than keeping the depolarizing parameters bounded by the required depolarization if symmetric depolarization is used.