Quantum Trajectory Analysis Research Articles

Frequency shift of even-order high harmonic generation in monolayer MoS2.

Sub-optical-cycle electron dynamics in materials driven by intense laser fields can be investigated by high harmonic generation. We observed frequency shift of high harmonic spectrum near the band gap of monolayer MoS2 experimentally. Through semi-classical quantum trajectory analysis, we demonstrated that the phase of transition dipole moment varies according to the recombination timing and momentum of tunneled electrons. It results in either blue- or red-shift of harmonic frequencies, determined by the modulated energy gap by transition dipole phases (TDPs) and Berry connections. Our finding reveals the effect of TDPs on high harmonic frequency in non-central symmetric materials.

Synchronization of persistent oscillations in spin systems with nonlocal dissipation

We explore the synchronization phenomenon in the quantum few-body system of spins with the nonlocal dissipation. Without the external driving, we find that the system can exhibit stable oscillatory behaviors in the long-time dynamics accompanied by the appearance of the purely imaginary eigenvalues of the Liouvillian. Moreover, the oscillations of the next-nearest-neighboring spins are completely synchronized, which is revealed by the quantum trajectory analysis within the stochastic Schr\"odinger equation. The possibility of the appearance of the long-time oscillations in an infinite-size lattice by means of cluster mean-field approximation is also discussed.

Halogenated Baicalein as a Promising Antiviral Agent toward SARS-CoV-2 Main Protease.

The coronavirus disease pandemic is a constant reminder that global citizens are in imminent danger of exposure to emerging infectious diseases. Therefore, developing a technique for inhibitor discovery is essential for effective drug design. Herein, we proposed fragment molecular orbital (FMO)-based virtual screening to predict the molecular binding energy of potential severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) main protease inhibitors. The integration of quantum mechanical approaches and trajectory analysis from a microsecond molecular dynamics simulation was used to identify potential inhibitors. We identified brominated baicalein as a potent inhibitor of the SARS-CoV-2 main protease and confirmed its inhibitory activity in an in vitro assay. Brominated baicalein did not demonstrate significant toxicity in either in vitro or in vivo studies. The pair interaction energy from FMO-RIMP2/PCM and inhibitory constants based on the protease enzyme assay suggested that the brominated baicalein could be further developed into novel SARS-CoV-2 protease inhibitors.

Quantum Trajectory Analysis of Single Microwave Photon Detection by Nanocalorimetry.

We apply quantum trajectory techniques to analyze a realistic setup of a superconducting qubit coupled to a heat bath formed by a resistor, a system that yields explicit expressions of the relevant transition rates to be used in the analysis. We discuss the main characteristics of the jump trajectories and relate them to the expected outcomes ("clicks") of a fluorescence measurement using the resistor as a nanocalorimeter. As the main practical outcome, we present a model that predicts the time-domain response of a realistic calorimeter subject to single microwave photons, incorporating the intrinsic noise due to the fundamental thermal fluctuations of the absorber and finite bandwidth of a thermometer.

Time-reversed quantum trajectory analysis of micromaser correlation properties and fluctuation relations

The micromaser is examined with the aim of understanding certain of its properties based on a time-reversed quantum trajectory analysis. The background theory of master equations derived from a repeated interaction model perspective is briefly reviewed and extended by taking into account the more general renewal process description of the sequence of interactions of the system with incoming ancilla, and results compared with other recent (and not so recent) approaches that use this generalisation. The results are then specialised to the micromaser, and a quantum trajectory unravelling of the micromaser dynamics is formulated that enables time-reversed quantum trajectories, defined according to the Crooks approach, to, first, be shown to arise naturally in the analysis of micromaser and atomic beam correlations, and second used in the formulation of a fluctuation relation for the probabilities of trajectories and their time-reversed counterparts.

Quantum-trajectory analysis for charge transfer in solid materials induced by strong laser fields

We investigate the dependence of charge transfer on the intensity of driving laser field when SiO2 crystal is irradiated by an 800 nm laser. It is surprising that the direction of charge transfer undergoes a sudden reversal when the driving laser intensity exceeds critical values with different carrier–envelope phases. By applying quantum-trajectory analysis, we find that the Bloch oscillation plays an important role in charge transfer in solids. Also, we study the interaction of a strong laser with gallium nitride (GaN), which is widely used in optoelectronics. A pump–probe scheme is applied to control the quantum trajectories of the electrons in the conduction band. The signal of charge transfer is controlled successfully by means of a theoretically proposed approach.

Photon bunching and anti-bunching with two dipole-coupled atoms in an optical cavity**Project supported by the National Natural Science Foundation of China (Grant Nos. 11305037, 11347114, and 11374054) and the Natural Science Foundation of Fujian Province, China (Grant No. 2013J01012).

We investigate the effect of the dipole–dipole interaction (DDI) on the photon statistics with two atoms trapped in an optical cavity driven by a laser field and subjected to cooperative emission. By means of the quantum trajectory analysis and the second-order correlation functions, we show that the photon statistics of the cavity transmission can be flexibly modulated by the DDI while the incoming coherent laser selectively excites the atom–cavity system’s nonlinear Jaynes–Cummings ladder of excited states. Finally, we find that the effect of the cooperatively atomic emission can also be revealed by the numerical simulations and can be explained with a simplified picture. The DDI induced nonlinearity gives rise to highly nonclassical photon emission from the cavity that is significant for quantum information processing and quantum communication.

Quantum trajectories for high-order-harmonic generation from multiple rescattering events in the long-wavelength regime

We have performed the quantum trajectory analysis for high-order-harmonic generation (HHG) with different driving laser wavelengths. By defining the ratio of HHG yields of the $N$th and first rescattering events (${Y}_{N}/{Y}_{1}$), we quantitatively evaluate the HHG contributions from multiple rescatterings. The results show that the HHG yield ratio increases gradually with the increase of the laser wavelength, which demonstrates that high-order rescatterings provide ascendent contributions to HHG at longer wavelength. By calculating the classical electron trajectories, we find significant differences exist in the electron behaviors between the first and high-order rescatterings. Further investigations have demonstrated that the increasing HHG yield ratio is mainly attributed to the relatively smaller contributions from the short path of the first electron rescattering at longer laser wavelength.

Estimation of atomic interaction parameters by photon counting

Detection of radiation signals is at the heart of precision metrology and sensing. In this article we show how the fluctuations in photon-counting signals can be exploited to optimally extract information about the physical parameters that govern the dynamics of the emitter. For a simple two-level emitter subject to photon counting, we show that the Fisher information and the Cram\'er-Rao sensitivity bound based on the full detection record can be evaluated from the waiting-time distribution in the fluorescence signal which can, in turn, be calculated for both perfect and imperfect detectors by a quantum trajectory analysis. We provide an optimal estimator achieving that bound.

Effects of excitation frequency on high-order terahertz sideband generation in semiconductors

We theoretically investigate the effects of the excitation frequency on the plateau of high-order terahertz sideband generation (HSG) in semiconductors driven by intense terahertz (THz) fields. We find that the plateau of the sideband spectrum strongly depends on the detuning between the near-infrared laser field and the band gap. We use the quantum trajectory theory (three-step model) to understand the HSG. In the three-step model, an electron–hole pair is first excited by a weak laser, then driven by the strong THz field, and finally recombined to emit a photon with energy gain. When the laser is tuned below the band gap (negative detuning), the electron–hole generation is a virtual process that requires quantum tunneling to occur. When the energy gained by the electron–hole pair from the THz field is less than 3.17 times the ponderomotive energy (Up), the electron and the hole can be driven to the same position and recombined without quantum tunneling, so that the HSG will have large probability amplitude. This leads to a plateau feature of the HSG spectrum with a high-frequency cutoff at about 3.17Up above the band gap. Such a plateau feature is similar to the case of high-order harmonics generation in atoms where electrons have to overcome the binding energy to escape the atomic core. A particularly interesting excitation condition in HSG is that the laser can be tuned above the band gap (positive detuning), corresponding to the unphysical ‘negative’ binding energy in atoms for high-order harmonic generation. Now the electron–hole pair is generated by real excitation, but the recombination process can be real or virtual depending on the energy gained from the THz field, which determines the plateau feature in HSG. Both the numerical calculation and the quantum trajectory analysis reveal that for positive detuning, the HSG plateau cutoff depends on the frequency of the excitation laser. In particular, when the laser is tuned more than 3.17Up above the band gap, the HSG spectrum presents no plateau feature but instead sharp peaks near the band edge and near the excitation frequency.

Quantum trajectory analysis of the two-mode three-level atom microlaser

We consider a single atom laser (microlaser) operating on three-level atoms interacting with a two-mode cavity. The quantum statistical properties of the cavity field at steady state are investigated by the quantum trajectory method which is a Monte Carlo simulation applied to open quantum systems. It is found that a steady state solution exists even when the detailed balance condition is not guaranteed. The differences between a single mode microlaser and a two-mode microlaser are highlighted. The second-order correlation function g^2(T) of a single mode is studied and special attention is paid to the one-photon trapping state, for which a simple formula is derived for its correlation function. We show the effects of the velocity spread of the atoms used to pump the microlaser cavity on the second-order correlation function, trapping states, and phase transitions of the cavity field.

A Review of Quantum-behaved Particle Swarm Optimization

Particle swarm optimization (PSO) is a population-based swarm intelligence algorithm and it has attracted a large number of widespread researchers. As a branch of PSO, a probabilistic PSO algorithm, which is quantum-behaved PSO (QPSO), was proposed on the quantum mechanics and trajectory analysis of PSO. QPSO shines for its simplicity, easy implementation, and fine search ability. QPSO has also gained many researchers on its improvements and has been shown to offer good performance in a variety of applications. This paper attempts to give a compendious and timely review on QPSO by categorizing the publications on the improvements and applications.

A model for measurement of the states in a coupled-dot qubit

We propose a quantum trajectory analysis of a scheme to measure the statesof a coupled-dot device (qubit) where there is a fluctuating energy gapΔ between the two states. The system consists of the qubit and a readout dot coupled tosource and drain leads. The tunnel rate through the detector is conditioned by theoccupation number of the nearer quantum dot (target) of the qubit and therefore probesthe states of the qubit. We derive a Lindblad-form master equation to calculate theunconditional evolution of the qubit and a conditional stochastic master equationcalculating the conditional evolution for different tunneling rates. The results show theeffects of various device parameters and provide the optimum selection and combination ofthe system structure.

Quantum trajectory analysis of single-photon control from a single-molecule source

We investigate theory of single-photon control from a two-level single-molecule source irradiated by laser pulses of various shapes and pulse durations in terms of quantum trajectories which link stochastic dynamics of the radiating source with quantum measurement theory. Using Monte Carlo wave function simulation, we analyze the detailed dissipative dynamics of the single-molecule source and the photon statistics as revealed by repeated Gedanken photon measurement on the single radiating source. We show that much of the photon statistics from the two-level single-molecule single-photon sources, including few-photon emission probability, waiting time distribution, and two-time correlation function of the fluorescent light, can be understood qualitatively from the simple picture of Rabi nutation and pi pulse in terms of pulse areas.

Geometric phase in open systems: Beyond the Markov approximation and weak-coupling limit

Beyond the quantum Markov approximation and the weak coupling limit, we present a general theory to calculate the geometric phase for open systems with and without conserved energy. As an example, the geometric phase for a two-level system coupling both dephasingly and dissipatively to its environment is calculated. Comparison with the results from quantum trajectory analysis is presented and discussed.

Quantum trajectory analysis for electrical detection of single-electron spin resonance

A Monte Carlo simulation on the basis of quantum trajectory approach is carried out for the measurement dynamics of a single electron spin resonance. The measured electron, which is confined in either a quantum dot or a defect trap, is tunnel-coupled to a side reservoir and continuously monitored by a mesoscopic detector. The simulation not only recovers the observed telegraphic signal of detector current, but also predicts unique features in the output power spectrum which are associated with electron dynamics in different regimes.

Comment on “Collective effects and trapping states by a quantum-trajectory treatment of micromaser dynamics”

A quantum trajectory analysis of the steady-state photon statistics of a micromaser by Casagrande and collaborators [F. Casagrande et al., Phys. Rev. A 60, 1582 (1999)] shows a significant suppression of the trapping behavior due to the inclusion of two-atom events. We use numerical integration in our investigation and obtain results that disagree with their analysis and show less suppression of the trapping behavior. A comparison with two extreme cases places our results between the two extremes and gives us confidence that our calculations are correct. The results of Casagrande and collaborators do not satisfy this condition.

Non-Markovian correlation function and direct analysis of spontaneous emission of an excited two-level atom

The appearance of real correlation function for spontaneous emission is explicitly presented. The non-Markovian correction is calculated directly by the integro-differential equation. The results are compared with the previous results obtained by stochastic quantum trajectory analysis. Obvious difference appears for smaller γ A / ω 0. The present analysis is believed more reliable.

Rescattering processes for elliptical polarization: A quantum trajectory analysis

High-harmonic generation and high-order above-threshold ionization spectra calculated in the strong-field approximation are analyzed in terms of the complex space-time orbits that result from a saddle point analysis of the underlying integrals. For elliptical polarization, the plateaus of the spectra of high-harmonic generation and high-order above-threshold ionization each turn into a staircase of very similar appearance. Each step of the stair can be traced to a particular pair of orbits which are almost identical in both cases.

Emergence of Classical Radiation Fields through Decoherence in the Scully± Lamb Laser Model

The quantum theory of the laser of Scully and Lamb is used to determine the longest-lived states of the quantized field in an idealized, single-mode laser cavity. It is shown that quasiclassical states (states with well-defined phase and amplitude) are naturally selected. A quantum trajectory analysis provides some insight as to why this is so.