Three-state System Research Articles

Controllable and shortcut-based population transfers with a composite system of a nitrogen-vacancy electron spin and microwave photons

Optimal population transfer is of critical importance for quantum information processing. Here an efficient scheme is proposed for implementing controllable and shortcut-based population transfers with a nitrogen-vacancy (NV) electron spin and cavity photons. The electron spin is placed inside a setup of circuit quantum electrodynamics (QED). Under a suitable magnetic field bias, the ground state of electron spin constitutes an effective triplet. By means of the quantized cavity field and classical drivings, we obtain a $$\Delta $$ -configuration interaction within a composite three-state system. Based on the adjustable Rabi couplings, the shortcut-based population transfers can be performed controllably. Moreover, compared with the adiabatic counterparts, the operations assisted by counter-diabatic drivings need much shorter times and then are less susceptible to decoherence effects. Our scheme provides a promising avenue toward optimized transfer operations on NV center electron spins in circuit QED.

Morris-Shore transformation for nondegenerate systems

The Morris-Shore (MS) transformation is a powerful tool for decomposition of the dynamics of multistate quantum systems to a set of two-state systems and uncoupled single states. It assumes two sets of states wherein any state in the first set can be coupled to any state in the second set but the states within each set are not coupled between themselves. Another important condition is the degeneracy of the states in each set, although all couplings between the states from different sets can be detuned from resonance by the same detuning. The degeneracy condition limits the application of the MS transformation in various physically interesting situations, e.g. in the presence of electric and/or magnetic fields or light shifts, which lift the degeneracy in each set of states, e.g. when these sets comprise the magnetic sublevels of levels with nonzero angular momentum. This paper extends the MS transformation to such situations, in which the states in each of the two sets are nondegenerate. To this end, we develop an alternative way for the derivation of Morris-Shore transformation, which can be applied to non-degenerate sets of states. We present a generalized eigenvalue approach, by which, in the limit of small detunings from degeneracy, we are able to generate an effective Hamiltonian that is dynamically equivalent to the non-degenerate Hamiltonian. The effective Hamiltonian can be mapped to the Morris-Shore basis with a two-step similarity transformation. After the derivation of the general framework, we demonstrate the application of this technique to the popular Lambda three-state system, and the four-state tripod, double-Lambda and diamond systems. In all of these systems, our formalism allows us to reduce their quantum dynamics to simpler two-state systems even in the presence of various detunings, e.g. generated by external fields of frequency drifts.

Memory effects in glasses: Insights into the thermodynamics of out-of-equilibrium systems revealed by a simple model of the Kovacs effect.

Glasses are interesting materials because they allow us to explore the puzzling properties of out-of-equilibrium systems. One of them is the Kovacs effect in which a glass, brought to an out-of-equilibrium state in which all its thermodynamic variables are identical to those of an equilibrium state, nevertheless evolves, showing a hump in some global variable before the thermodynamic variables come back to their starting point. We show that a simple three-state system is sufficient to study this phenomenon using numerical integrations and exact analytical calculations. It also brings some light on the concept of fictive temperature, often used to extend standard thermodynamics to the out-of-equilibrium properties of glasses. We confirm that the concept of a unique fictive temperature is not valid, an show it can be extended to make a connection with the various relaxation processes in the system. The model also brings further insights on the thermodynamics of out-of-equilibrium systems. Moreover, we show that the three-state model is able to describe various effects observed in glasses such as the asymmetric relaxation to equilibrium discussed by Kovacs, or the reverse crossover measured on B_{2}O_{3}.

Chiral resolution by composite Raman pulses

We present two methods for efficient detection of chiral molecules based on sequences of single pulses and Raman pulse pairs. The chiral molecules are modelled by a closed-loop three-state system with different signs in one of the couplings for the two enantiomers. One method uses a sequence of three interaction steps: a single pulse, a Raman pulse, and another single pulse. The other method uses a sequence of only two interaction steps: a Raman pulse, and a single pulse. The second method is simpler and faster but requires a more sophisticated Raman pulse than the first one. Both techniques allow for straightforward generalizations by replacing the single and Raman pulses with composite pulse sequences. The latter achieve very high signal contrast and far greater robustness to experimental errors than by using single pulses. We demonstrate that both constant-rotation (i.e., with phase compensation) and variable-rotation (i.e., with phase distortion) composite pulses can be used, the former being more accurate and the latter being simpler and faster.

Optimal preventive maintenance policy for a system subject to two-phase imperfect inspections

Inspections are essential to finding the health status of a system. However, inspections are usually imperfect, which may not always reveal the true state of the system. Most of research on imperfect inspections of degrading systems focuses on one-phase inspections, but a multi-phase inspection strategy may be more flexible and efficient. In this paper, a two-phase imperfect inspection strategy is considered along with a hybrid preventive maintenance policy for a three-state system. To minimize the maintenance cost, the optimal inspection interval and number of inspections in each phase are obtained based on the renewal reward theorem. Numerical examples are provided to illustrate the proposed method and to explore some managerial insights. To show the advantages of the proposed method, several special models, such as perfect inspection model, one-phase inspection model, and pure inspection model, are presented for comparison. One can see that taking account of imperfect inspections in maintenance management is important, the two-phase inspection policy is generally better than the one-phase inspection, and the pure inspection model might be cost-optimal for the system with a constant defect rate.

Closed-loop three-level charged quantum battery

Quantum batteries are energy storage or extraction devices in a quantum system. Here, we present a closed-loop quantum battery by utilizing a circularly coupled three-state quantum system, and investigate its charging dynamics. The charging performance is greatly improved due to the existence of the third field in the system to form a closed-contour interaction. Through appropriately selecting the third control field, the maximum average power can be increased, even far beyond the ideal maximum power value of non-closed-loop three-level quantum battery. We study the effect of the global driving-field phase on the charging process and find that both the maximum extractable work (“ergotropy”) and the charging power vary periodically under different control fields, with a period of . Possible experimental implementation in nitrogen-vacancy spin is discussed as well.

Optical Potts machine through networks of three-photon down-conversion oscillators

AbstractIn recent years, there has been a growing interest in optical simulation of lattice spin models for applications in unconventional computing. Here, we propose optical implementation of a three-state Potts spin model by using networks of coupled parametric oscillators with phase tristability. We first show that the cubic nonlinear process of spontaneous three-photon down-conversion is accompanied by a tristability in the phase of the subharmonic signal between three states with 2π/3 phase contrast. The phase of such a parametric oscillator behaves like a three-state spin system. Next, we show that a network of dissipatively coupled three-photon down-conversion oscillators emulates the three-state planar Potts model. We discuss potential applications of the proposed system for all-optical optimization of combinatorial problems such as graph 3-COL and MAX 3-CUT.

Acoustic Adiabatic Propagation Based on Topological Pumping in a Coupled Multicavity Chain Lattice

Stimulated adiabatic passage, as an efficient energy transfer in correlated systems, was intensively studied in condensed matter physics and quantum optics. Recently, a paradigm shift has been made to bring up quantum-classical analogs, giving rise to the acoustic version of stimulated Raman adiabatic passage and others. In this work, we focus on the adiabatic propagation of sound under topological protection, i.e., topological-pumping-based acoustic adiabatic propagation. We first study the topological pumping of sound in a two-state multicavity chain lattice, including the Su-Schrieffer-Heeger model, in which the acoustic energy is adiabatically transferred between the two topological end states under specific coupling interactions. Then, we consider the adiabatic propagation of sound via a dark mode in a three-state system. The three states correspond to two end states and one interface state in a heterostructured multicavity chain lattice, which is topologically protected. In a finite system, the three states strongly hybridize with the threefold energy degeneracy lifted. The hybridized states reside in the band gap of the systematic Hamiltonian spectrum in the topological pumping process, leading to a strong robustness against nonadiabatic perturbation, which allows for a faster and more efficient topological adiabatic propagation of acoustic waves.

리(理), 삼국체제(三國體制), 그리고 민본주의(民本主義): 위정척사론(衛正斥邪論)의 철학적 기초

이 글은 조선 시대 사대부들의 관념적 특징을 네 가지 관념축을 중심으로 하는 동역학적 관계에서 서술하려고 시도한다. 이를 바탕으로 조선 후기에 나타난 위정척사론과 동학 사이에 존재했던 이념적 불편성의 의미를 해명하려는 것이 두 번째 목적이다. 이를 위해 이 글은 조선의 주류 성리학자들의 정신세계를 ‘리’개념을 중심으로 하는 관념 체계로 명명하고, 이를 대략 네 가지로 범주화한다. 먼저 「리로서의 국가」로서 조선을 가정한다. 이것은 조선의 성리학자들이 추상적인 리의 현실태로서 조선을 이해한다는 의미에서 리국체제(理國體制)라고 불린다. 이것이 사실가장 중요한 관념 체계이고 다시 이를 바탕으로 세 가지 상호연관된 체제 관념이 나타났다. 리의 기원으로서 중국체제(中國體制), 리의 상징으로서 왕국체제(王國體制), 리의 담지자로서 사대부들이 중심이 된 국가 관념, 즉 사국체제(士國體制)가 그것들이다. 조선의 성리학자들이 강조했던 민본주의적 관념은 이 리를 중심으로 하는 삼국체제(三國體制)의 시각에서 해석될 것이다. 이렇게 볼 때 성리학적 민본주의는 이 네 가지 관념축 위에서 의미를 가질 수 있는 제한적인 개념으로 이해된다. 그리고 이것이 리에 기초한 삼국체제로서의 조선을 긍정했던 위정척사론이 왕국체제와 사국체제를 부정하는 것으로 받아들여졌던 동학과 불화를 겪을 수밖에 없었던 근본 원인이라고 주장할 것이다. 다시 말해 동학은 리에 기초한 삼국체제와는 다른 세계를 지향했던 움직임이었다. 따라서 이 불화는 역사적인 조선을 진리의 구현태로 간주했던 성리학적 역사 서사가 자신의 한계를 드러내는 필연적 현상 가운데 하나로 해석되어야 한다.

Efficient and robust chiral resolution by composite pulses

We introduce a method for the detection of chiral molecules using sequences of three pulses driving a closed-loop three-state quantum system. The left- and right-handed enantiomers have identical optical properties (transition frequencies and transition dipole moments) with the only difference being the sign of one of the couplings. We identify 12 different sequences of resonant pulses for which chiral resolution with perfect contrast occurs. In all of them, the first and third pulses are $\ensuremath{\pi}/2$ pulses and the middle pulse is a $\ensuremath{\pi}$ pulse. In addition, one of the three pulses must have a phase shift of $\ensuremath{\pi}/2$ with respect to the other two. The simplicity of the proposed chiral resolution technique allows for straightforward extensions to more efficient and more robust implementations by replacing the single $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ pulses by composite pulses. We present specific examples of chiral resolution by composite pulses which compensate errors in the pulse areas and the detuning of the driving fields.

Generalized stacked contact process with variable host fitness

AbstractThe stacked contact process is a three-state spin system that describes the co-evolution of a population of hosts together with their symbionts. In a nutshell, the hosts evolve according to a contact process while the symbionts evolve according to a contact process on the dynamic subset of the lattice occupied by the host population, indicating that the symbiont can only live within a host. This paper is concerned with a generalization of this system in which the symbionts may affect the fitness of the hosts by either decreasing (pathogen) or increasing (mutualist) their birth rate. Standard coupling arguments are first used to compare the process with other interacting particle systems and deduce the long-term behavior of the host–symbiont system in several parameter regions. The spatial model is also compared with its mean-field approximation as studied in detail by Foxall (2019). Our main result focuses on the case where unassociated hosts have a supercritical birth rate whereas hosts associated to a pathogen have a subcritical birth rate. In this case, the mean-field model predicts coexistence of the hosts and their pathogens provided the infection rate is large enough. For the spatial model, however, only the hosts survive on the one-dimensional integer lattice.

Nonequilibrium dynamics of photoinduced forward and backward electron transfer reactions.

The biological functions of photoenzymes are often triggered by photoinduced electron transfer (ET) reactions. An ultrafast backward ET (BET) reaction follows the initial photoinduced forward ET (FET), which dissipates the energy of absorbed photons and terminates the biological function in vain. Based upon our previous works, we reasoned that the dynamics of the BET is coupled with that of the FET and other local motions. In this work, the dynamics of the FET and BET is modeled as the master equation of the reduced density operator of a three-state system coupled with a classical harmonic reservoir. The coupling of the FET and BET is reflected in the time-evolution of the charge-transfer state's population, which is generated by a source, the reaction flux for the FET, and annihilated by a sink, the reaction flux for the BET. Surprisingly, numerical simulations show that when the BET is in the Marcus normal region, the BET can be accelerated by nonequilibrium local motions and becomes faster than what is predicted by the Marcus theory. The experimental confirmation of this novel dynamics would provide qualitative evidence for nonequilibrium effects on ultrafast ET dynamics. Additionally, the effects of quantum vibrational modes on the dynamics are discussed. This work can help understand the dynamical interactions between the chain of ultrafast reactions and the complex local environmental motions, revealing the physical nature underlying biological functions.

Digital adiabatic passage in multi-state systems

Digital adiabatic passage in multi-pod and multi-lambda systems is investigated. We show that using digital variation of control fields, one can create a coherent superposition of ground states in multi-state systems. In order to design the propagator at every step, the multi-state systems are simplified to a three-state system using Morris-Shore transformation. In this method, the number of steps is arbitrary and by increasing the number of steps the population of excited states decreases to negligible small values. Sensitivity of the final fidelity with respect to exact value of tmax decreases by increasing the number of steps.

Series of semi-Markov processes to model infrastructure resilience under multihazards

Civil infrastructure systems are subjected to multiple hazards, including natural and anthropogenic, that disrupt their function or the level of service offered. Estimating the function recovery of these systems (or how soon normalcy of operations will be restored) when subjected to repeated hazard events by considering the inter-event dependencies is an important problem in multihazard infrastructure resilience. However, this problem has been less addressed in the field. This paper proposes a series of semi-Markov processes model to capture the inter-event dependencies in infrastructure recovery when subjected to successive hazard events. Recovery after each new hazard event is represented by a unique semi-Markov process that models the reduced recovery rates and the increased recovery times caused by the system’s incomplete recovery from the preceding event. Two novel formulations of the inter-event dependency modeling, namely Maximal Effects Dependency (considers the worst impact of two successive hazard events) and Cumulative Effects Dependency (considers the aggregated impacts of two successive hazard events), are proposed and discussed. The model is demonstrated by considering the following applications: Three-state system subjected to deterministic and random occurrences of identical hazard events; and Multihazard resilience of a building in Charleston, SC, considering earthquake and hurricane hazards. Results indicate that considering inter-event dependencies in recovery modeling can lead to lesser-predicted resilience, thereby affecting resilience-based decision-making.

Optimal maintenance policy considering imperfect repairs and non-constant probabilities of inspection errors

During system operation, inspections are usually scheduled to detect the signals of defects. Due to the human, measurement or environment errors, inspections are generally imperfect which reveal the real states of the system with non-constant probabilities. When an inspection concludes a defect, necessary preventive maintenance actions should be carried out. In most existing literatures, perfect preventive maintenance, like replacement, is studied. However, in practice, most defects are imperfectly repaired rather than being replaced because of limitations of resources, technologies or time. Thus, considering both imperfect inspections and imperfect repairs, a novel preventive maintenance policy is investigated for a three-state system. Cost rate and reliability of the system are derived by a recursive method. The problem of optimal maintenance policy is formulated by minimizing the cost rate over an infinite time horizon. An algorithm is proposed to obtain the optimal inspection interval and preventive replacement interval. Finally, several numerical examples are given to illustrate the proposed method and verify the correctness of the method.

Detuning-induced robustness of a three-state Landau-Zener model against dissipation

A three-state system subjected to a time-dependent Hamiltonian whose bare energies undergo one or more crossings, depending on the relevant parameters, is considered, also taking into account the role of dissipation in the adiabatic following of the Hamiltonian eigenstates. Depending on the fact that the bare energies are equidistant or not, the relevant population transfer turns out to be very sensitive to the environmental interaction or relatively robust. The physical mechanisms on the basis of this behavior are discussed in detail.

Organic Redox Systems Based on Pyridinium-Carbene Hybrids.

New redox systems with three oxidation states are highly sought-after, for example, for redox-flow battery applications, selective reducing agents, or organic electronics. Herein, we describe a straightforward and modular synthesis of a new class of such a three-state redox system based on the intermolecular reaction of a large variety of pyridinium salts with carbenes. These hybrids represent organic (super) electron donors with tailored electrochemical properties and feature three stable oxidation states, which could be fully characterized including by X-ray diffraction. We elaborate which electronic factors either promote attainment of stable radicals through one electron transfer or instead favor 2e- processes. Indeed, based on X-ray data, a verification for a potential compression mechanism is given that originates through a large structural distortion in the first oxidation event. By geometrically locking this hybridization change, a potential expansion can be realized. The new class of stable organic radicals are highly persistent and even moderately stable toward air. Additionally, we demonstrate that our modular synthesis approach is also applicable to remarkably strong multielectron (4e-) donors by utilizing bridged pyridinium salts. Based on the stability and reversibility of the new redox system, we could demonstrate by charge-discharge experiments the use of the hybrid molecules as novel anolyte materials for nonaqueous redox-flow batteries.

Conformational Complexity and Dynamics in a Muscarinic Receptor Revealed by NMR Spectroscopy.

The M2 muscarinic acetylcholine receptor (M2R) is a prototypical GPCR that plays important roles in regulating heart rate and CNS functions. Crystal structures provide snapshots of the M2R in inactive and active states, but the allosteric link between the ligand binding pocket and cytoplasmic surface remains poorly understood. Here we used solution NMR to examine the structure and dynamics of the M2R labeled with 13CH3-ε-methionine upon binding to various orthosteric and allosteric ligands having a range of efficacy for both G protein activation and arrestin recruitment. We observed ligand-specific changes in the NMR spectra of 13CH3-ε-methionine probes in the M2R extracellular domain, transmembrane core, and cytoplasmic surface, allowing us to correlate ligand structure with changes in receptor structure and dynamics. We show that the M2R has a complex energy landscape in which ligands with different efficacy profiles stabilize distinct receptor conformations.

Highly Efficient Detection and Separation of Chiral Molecules through Shortcuts to Adiabaticity.

A highly efficient method for optical or microwave detection and separation of left- and right-handed chiral molecules is proposed. The method utilizes a closed-loop three-state system in which the population dynamics depends on the phases of the three couplings. Because of the different signs of the coupling between two of the states for the opposite chiralities the population dynamics is chirality dependent. By using the "shortcuts to adiabaticity" concept applied to the stimulated Raman adiabatic passage technique, one can achieve 100% contrast between the two enantiomers in the population of a particular state. It can be probed by light-induced fluorescence for large ensembles or through resonantly enhanced multiphoton ionization for single molecules.

Three-state Landau-Zener model in the presence of dissipation

A population transfer based on adiabatic evolutions in a three-state system undergoing an avoided crossing is considered. The efficiency of the process is analyzed in connection with the relevant parameters, bringing to light an important role of the phases of the coupling constants. The role of dissipation is also taken into account, focusing on external decays that can be described by effective non-Hermitian Hamiltonians. Though the population transfer turns out to be quite sensitive to the decay processes, for very large decay rates the occurrence of a Zeno-phenomenon allows for restoring a very high efficiency.