Open Quantum System Approach Research Articles

Topological plasmons in dimerized chains of nanoparticles: robustness against long-range quasistatic interactions and retardation effects

We present a simple model of collective plasmons in a dimerized chain of spherical metallic nanoparticles, an elementary example of a topologically nontrivial nanoplasmonic system. Taking into account long-range quasistatic dipolar interactions throughout the chain, we provide an exact analytical expression for the full quasistatic bandstructure of the collective plasmons. An explicit calculation of the Zak phase proves the robustness of the topological physics of the system against the inclusion of long-range Coulomb interactions, despite the broken chiral symmetry. Using an open quantum systems approach, which includes retardation through the plasmon-photon coupling, we go on to analytically evaluate the resulting radiative frequency shifts of the plasmonic spectrum. The bright plasmonic bands experience size-dependent radiative shifts, while the dark bands are essentially unaffected by the light-matter coupling. Notably, the upper transverse-polarized band presents a logarithmic singularity where the quasistatic spectrum intersects the light cone. At wavevectors away from this intersection and for subwavelength nanoparticles, the plasmon-photon coupling only leads to a quantitative reconstruction of the bandstructure and the topologically-protected states at the edge of the first Brillouin zone are essentially unaffected.

A comparative study on the reliability of non-Hermitian effective Hamiltonian approach for modeling open quantum systems

In this paper, we conduct a comprehensive analysis on the reliability of non-Hermitian effective Hamiltonian approach for modeling quantum dissipative dynamics. It is found that one of the major drawbacks to adopting this theoretical approach is that it fails to reproduce correctly both the dynamics and the time evolution of observables of the system. With this in mind, we propose a method that allows correcting the non-Hermitian effective Hamiltonian approach when there exists a conserved quantity in the system. In order to illustrate the performance of our corrected non-Hermitian effective Hamiltonian approach, we consider a two-level system interacting with an electromagnetic cavity mode where the effects of the environment are included in a phenomenological manner. More precisely, the dissipation and pump in the system are considered through non-Hermitian Hamiltonian terms. Our numerical results have been focused on the time evolution of density matrix elements, observables as well as the emission spectrum of the system, and they demonstrate that our proposed methodology is in excellent agreement with the predictions of the Lindblad master equation approach.

Universal Origin for Environment-Assisted Quantum Transport in Exciton Transfer Networks.

Environment-assisted quantum transport (ENAQT) is the possibility of an external environment to enhance transport efficiency of quantum particles. This idea has generated much excitement over recent years, especially due to the experimentally motivated possibility of ENAQT in photosynthetic exciton transfer complexes. Many theoretical calculations have shown ENAQT, but the explanations for its origin differ, and a universal explanation has been elusive. Here we demonstrate a universal origin for ENAQT in quantum networks with a dephasing environment, based on a relation between exciton current and occupation within a Markovian open quantum system approach. We show that ENAQT appears due to two competing processes, namely, the tendency of dephasing to make the exciton population uniform, and the formation of an exciton density gradient, defined by the source and the sink. Furthermore, we find a geometric condition on the network for the appearance of ENAQT, relevant to natural and artificial systems.

Reduced density matrix identification of open quantum system

Identification of performance parameter of a multi-level open quantum system is a central problem in a growing number of applications of information engineering. Based on the quantum tomography, this paper aims at finding a method for identifying reduced density matrix of open quantum system. State identification of open quantum system approaches is presented for two-level, three-level and N-level systems, respectively. The results show that not only the reduced density matrix can be reestablished, but also the quantum state information can be received in quantum tomography experiment.

Retardation effects on the dispersion and propagation of plasmons in metallic nanoparticle chains

We consider a chain of regularly-spaced spherical metallic nanoparticles, where each particle supports three degenerate localized surface plasmons. Due to the dipolar interaction between the nanoparticles, the localized plasmons couple to form extended collective modes. Using an open quantum system approach in which the collective plasmons are interacting with vacuum electromagnetic modes and which, importantly, readily incorporates retardation via the light-matter coupling, we analytically evaluate the resulting radiative frequency shifts of the plasmonic bandstructure. For subwavelength-sized nanoparticles, our analytical treatment provides an excellent quantitative agreement with the results stemming from laborious numerical calculations based on fully-retarded solutions to Maxwell’s equations. Indeed, the explicit expressions for the plasmonic spectrum which we provide showcase how including retardation gives rise to a logarithmic singularity in the bandstructure of transverse-polarized plasmons. We further study the impact of retardation effects on the propagation of plasmonic excitations along the chain. While for the longitudinal modes, retardation has a negligible effect, we find that the retarded dipolar interaction can significantly modify the plasmon propagation in the case of transverse-polarized modes. Moreover, our results elucidate the analogy between radiative effects in nanoplasmonic systems and the cooperative Lamb shift in atomic physics.

Bound on dissipative effects from semileptonic neutral B-meson decays

The semileptonic decay asymmetry mathcal {A}_{{Delta }m} is studied within the open quantum systems approach to the physics of the neutral meson B^0–overline{B^0} system: this extended treatment takes into account possible non-standard, dissipative effects induced by the presence of an external environment. A bound on these effects is provided through the analysis of available experimental data from the Belle Collaboration.

Chaos in a quantum neuron: An open system approach

Researches in natural neuron dynamics have shown that phase transition and chaos provide optimal behaviour for information processing. In artificial neural models that behavior is expected also to maximize the neuron learnability. By employing an open quantum systems approach, we propose a new quantum information extraction method in the quantum RAM node dynamics where complex values are iterated. We experimentally show bifurcation and chaos emergence by varying their parameters.

Nonradiative limitations to plasmon propagation in chains of metallic nanoparticles

We investigate the collective plasmonic modes in a chain of metallic nanoparticles that are coupled by near-field interactions. The size- and momentum-dependent nonradiative Landau damping and radiative decay rates are calculated analytically within an open quantum system approach. These decay rates determine the excitation propagation along the chain. In particular, the behavior of the radiative decay rate as a function of the plasmon wavelength leads to a transition from an exponential decay of the collective excitation for short distances to an algebraic decay for large distances. Importantly, we show that the exponential decay is of a purely nonradiative origin. Our transparent model enables us to provide analytical expressions for the polarization-dependent plasmon excitation profile along the chain and for the associated propagation length. Our theoretical analysis constitutes an important step in the quest for the optimal conditions for plasmonic propagation in nanoparticle chains.

Computer-aided cluster expansion: An efficient algebraic approach for open quantum many-particle systems

We introduce an equation of motion approach that allows for an approximate evaluation of the time evolution of a quantum system, where the algebraic work to derive the equations of motion is done by the computer. The introduced procedures offer a variety of different types of approximations applicable for finite systems with strong coupling as well as for arbitrary large systems where augmented mean-field theories like the cluster expansion can be applied. Program summaryProgram Title: EoM_main.frmProgram Files doi:http://dx.doi.org/10.17632/fjwxr28j3d.1Licensing provisions: CC By 4.0Programming language:FORMNature of problem: Quantum many-particle systems are an important subject in fundamental and applied research. The calculation of the time evolution of such systems is a key aspect to investigate and understand their properties. In most cases the Hilbert space that represents the quantum mechanical system is too big to be processed by numerically exact methods and approximation methods have to be used.Solution method: The program automates an equation-of-motion technique that uses the generalized Ehrenfest equation to derive the time evolution for expectation values of physical observables. The cluster expansion is used to close the hierarchy of the equations of motion. The offered method allows for a variety of different types of approximations to solve such problems with small numerical effort [1]. [1] Leymann, H.A.M., Foerster, A., Wiersig, J., 2014. Expectation value based equation-of-motion approach for open quantum systems: A general formalism. Phys. Rev. B 89 (8), 085308.

Brownian motion of a matter-wave bright soliton moving through a thermal cloud of distinct atoms

Taking an open quantum systems approach, we derive a collective equation of motion for the dynamics of a matter-wave bright soliton moving through a thermal cloud of a distinct atomic species. The reservoir interaction involves energy transfer without particle transfer between the soliton and thermal cloud, thus damping the soliton motion without altering its stability against collapse. We derive a Langevin equation for the soliton centre of mass velocity in the form of an Ornstein-Uhlenbeck process with analytical drift and diffusion coefficients. This collective motion is confirmed by simulations of the full stochastic projected Gross-Pitaevskii equation for the matter-wave field. The system offers a pathway for experimentally observing the elusive energy-damping reservoir interaction, and a clear realization of collective Brownian motion for a mesoscopic superfluid droplet.

Study of Neutrino Oscillation and Dissipative Effects in LBNE

In this work we make a brief phenomenological study for three neutrino oscillation taking into account the matter effect from the open quantum system approach. Open quantum system approach has a rigorous set of the statements and when it is applied on neutrino oscillation, due to dissipative phenomena, the neutrinos may exhibit new and peculiar effects, in special, decoherence and relaxation effects. We use the most effective quantum dissipators and we study how change the neutrino behavior considering the LBNE configuration. In particular, we show how each kind of dissipative effect is linked to each mixing angle and consequently, as the new effects are described in the survival and appearance probabilities. Interesting enough, in the LBNE case we present a new behavior at matter resonance region that can be seen even when the dissipative effect is small compared with energy dependent oscillation parameters.

Thermofield-based chain-mapping approach for open quantum systems

We consider a thermofield approach to analyze the evolution of an open quantum system coupled to an environment at finite temperature. In this approach, the finite-temperature environment is exactly mapped onto two virtual environments at zero temperature. These two environments are then unitarily transformed into two different chains of oscillators, leading to a one-dimensional structure that can be numerically studied using tensor network techniques. Compared to previous approaches using a single chain mapping, our strategy offers the advantage of an exact description of the initial state at arbitrary temperatures, which results in a gain in computational efficiency and a reduced truncation error.

Interplay between Dephasing and Geometry and Directed Heat Flow in Exciton Transfer Complexes

The striking efficiency of energy transfer in natural photosynthetic systems and the recent evidence of long-lived quantum coherence in biological light harvesting complexes has triggered much excitement, due to the evocative possibility that these systems—essential to practically all life on earth–use quantum mechanical effects to achieve optimal functionality. A large body of theoretical work has addressed the role of local environments in determining the transport properties of excitons in photosynthetic networks and the survival of quantum coherence in a classical environment. Nonetheless, understanding the connection between quantum coherence, exciton network geometry, and energy transfer efficiency remains a challenge. Here we address this connection from the perspective of heat transfer within the exciton network. Using a nonequilibrium open quantum system approach and focusing on the Fenna–Matthews–Olson complex, we demonstrate that finite local dephasing can be beneficial to the overall power out...

Local temperatures of strongly-correlated quantum dots out of equilibrium

Probes that measure the local thermal properties of systems out of equilibrium are emerging as new tools in the study of nanoscale systems. One can then measure the temperature of a probe that is weakly coupled to a bias-driven system. By tuning the probe temperature so that the expectation value of some observable of the system is minimally perturbed, one obtains a parameter that measures its degree of local statistical excitation, and hence its local heating. However, one anticipates that different observables may lead to different temperatures and thus different local heating expectations. We propose an experimentally realizable protocol to measure such local temperatures and apply it to bias-driven quantum dots. By means of a highly accurate open quantum system approach, we show theoretically that the measured temperature is quite insensitive both to the choice of observable and to the probe-system coupling. In particular, even with observables that are distinct both physically and in their degree of locality, such as the local magnetic susceptibility of the quantum dot and the global spin-polarized current measured at the leads, the resulting local temperatures are quantitatively similar for quantum dots ranging from noninteracting to Kondo-correlated regimes, and are close to those obtained with the traditional "local equilibrium" definition.

The molecular photo-cell: quantum transport and energy conversion at strong non-equilibrium.

The molecular photo-cell is a single molecular donor-acceptor complex attached to electrodes and subject to external illumination. Besides the obvious relevance to molecular photo-voltaics, the molecular photo-cell is of interest being a paradigmatic example for a system that inherently operates in out-of-equilibrium conditions and typically far from the linear response regime. Moreover, this system includes electrons, phonons and photons, and environments which induce coherent and incoherent processes, making it a challenging system to address theoretically. Here, using an open quantum systems approach, we analyze the non-equilibrium transport properties and energy conversion performance of a molecular photo-cell, including both coherent and incoherent processes and treating electrons, photons, and phonons on an equal footing. We find that both the non-equilibrium conditions and decoherence play a crucial role in determining the performance of the photovoltaic conversion and the optimal energy configuration of the molecular system.

Non-Markovian Quantum State Diffusion for temperature-dependent linear spectra of light harvesting aggregates.

Non-Markovian Quantum State Diffusion (NMQSD) has turned out to be an efficient method to calculate excitonic properties of aggregates composed of organic chromophores, taking into account the coupling of electronic transitions to vibrational modes of the chromophores. NMQSD is an open quantum system approach that incorporates environmental degrees of freedom (the vibrations in our case) in a stochastic way. We show in this paper that for linear optical spectra (absorption, circular dichroism), no stochastics is needed, even for finite temperatures. Thus, the spectra can be obtained by propagating a single trajectory. To this end, we map a finite temperature environment to the zero temperature case using the so-called thermofield method. The resulting equations can then be solved efficiently by standard integrators.

Entropic uncertainty relation in de Sitter space

The uncertainty principle restricts our ability to simultaneously predict the measurement outcomes of two incompatible observables of a quantum particle. However, this uncertainty could be reduced and quantified by a new Entropic Uncertainty Relation (EUR). By the open quantum system approach, we explore how the nature of de Sitter space affects the EUR. When the quantum memory A freely falls in the de Sitter space, we demonstrate that the entropic uncertainty acquires an increase resulting from a thermal bath with the Gibbons–Hawking temperature. And for the static case, we find that the temperature coming from both the intrinsic thermal nature of the de Sitter space and the Unruh effect associated with the proper acceleration of A also brings effect on entropic uncertainty, and the higher the temperature, the greater the uncertainty and the quicker the uncertainty reaches the maximal value. And finally the possible mechanism behind this phenomenon is also explored.

Analytic representations of bath correlation functions for ohmic and superohmic spectral densities using simple poles.

We present a scheme to express a bath correlation function (BCF) corresponding to a given spectral density (SD) as a sum of damped harmonic oscillations. Such a representation is needed, for example, in many open quantum system approaches. To this end we introduce a class of fit functions that enables us to model ohmic as well as superohmic behavior. We show that these functions allow for an analytic calculation of the BCF using pole expansions of the temperature dependent hyperbolic cotangent. We demonstrate how to use these functions to fit spectral densities exemplarily for cases encountered in the description of photosynthetic light harvesting complexes. Finally, we compare absorption spectra obtained for different fits with exact spectra and show that it is crucial to take properly into account the behavior at small frequencies when fitting a given SD.

Expectation value based equation-of-motion approach for open quantum systems: A general formalism

We present a new method to formulate equations of motion for open quantum many-particle systems. Our approach allows for a numerically exact treatment as well as for approximations necessary in large systems and can be applied to systems involving both bosonic and fermionic particles. The method generalizes the cluster expansion technique by using expectation values instead of correlation functions. The use of expectation values not only makes the equations more transparent but also considerably reduces the amount of algebraic effort to derive the equations. The proposed formulation offers a unified view on various approximation techniques presented recently in the literature. The microscopic semiconductor model for quantum-dot-based microcavity lasers is extended to higher-order photon-autocorrelation functions and the validity of the cluster expansion is shown for this system. We study photon-autocorrelation functions up to fifth order and monitor the onset of lasing in quantum-dot-based microcavity lasers. We observe a successive vanishing of photon bunching in the higher-order photon-autocorrelation functions with increasing pump rates. Our results reveal that the laser threshold is not only softened in microcavity laser systems but is centered around different pump rates with respect to the photon-autocorrelation functions.

Researching on Hawking Effect in a Kerr Space Time via Open Quantum System Approach

It has been proposed that Hawking radiation from a Schwarzschild or a de Sitter spacetime can be understood as the manifestation of thermalization phenomena in the framework of an open quantum system. Through examining the time evolution of a detector interacting with vacuum massless scalar fields, it is found that the detector would spontaneously excite with a probability the same as the thermal radiation at Hawking temperature. Following the proposals, the Hawking effect in a Kerr space time is investigated in the framework of an open quantum systems. It is shown that Hawking effect of the Kerr space time can also be understood as the the manifestation of thermalization phenomena via open quantum system approach. Furthermore, it is found that near horizon local conformal symmetry plays the key role in the quantum effect of the Kerr space time.