Density Matrix Equations Research Articles

Quantum kinetic theory of nonlinear optical currents: Finite Fermi surface and Fermi sea contributions

The quantum kinetic framework provides a versatile method for investigating the dynamical optical and transport currents of crystalline solids. In this paper, starting from the density-matrix equations of motion, we present a general theoretical path to obtain the nonlinear optical response in an elegant and transparent manner. We devise an extensive kinetic theory that can be applied to materials with arbitrary band structures and captures intraband and interband coherence effects, finite Fermi surfaces, and disorder effects. We present a classification of the nonlinear optical currents arising from the interference of the interband and intraband components of the density matrix with distinct symmetry and quantum geometrical origin for each contribution. In this context, we report the following four primary findings: (i) The Fermi golden rule approach is insufficient to derive the correct expression for the injection current, a shortcoming that we remedy in our theory while associating the injection current with the intraband-interband contribution to the second-order density matrix. (ii) The interband-intraband contribution yields a resonant current that survives irrespective of any symmetry constraint in addition to the well-known anomalous nonlinear current (nonresonant), which requires time-reversal symmetry. (iii) Quite generally, the nonlinear current is significantly enhanced by contributions arising from the finite Fermi surface. (iv) The finite Fermi surface and Fermi sea additionally lead to sizable novel nonlinear effects via contributions we term double resonant and higher-order pole. We investigate such effects in sum frequency and difference frequency generation. As an illustration, we compute the nonlinear response of the topological antiferromagnet CuMnAs and thin film tilted Weyl semimetals as model systems dominated by interband coherence contributions. We find that the nonlinear response of CuMnAs is responsive to the direction of the finite magnetization field and the response of Weyl semimetal to the tilt. In addition, the choice of the polarization angle of the beam is crucial to have a nonlinear current in CuMnAs, while it is not the case for Weyl semimetals.

Analysis of laser-induced transient population gratings by different types of exciting pulse

Motivated by atomic response to different initial coherent optical fields, we comparatively studied transient population grating (TPG) induced by successive pulse train. Time delay and pump pulse duration dependence of TPG is achieved by numerically solving the density matrix equations. Results reveal that the creation and erasure of TPG is possible by choosing the appropriate pulse parameters, which is illustrated by Bloch sphere model and quantitative validation. To obtain desired large grating amplitude for rectangular pulse, the allowed pulse duration can be extended to one order wider than that of Gaussian pulse. Population grating can be erased to near zero by a third pulse with time delay by an odd multiple of half the pulse width, and it also can be erased further to recover atom assembly back to the initial state by a fourth pulse with time delay equal to an integer multiple of pulse width. Atomic behaviors excited by different types of pulse presented here may be significant to manipulate TPG during coherent light-matter interaction.

Coherence controlled generation of Gaussian quantum discord in a quantum beat laser

Quantum discord, an appropriate measure of quantum correlation, is analyzed in a two-mode Gaussian state of the cavity field evolved by a system of quantum beat laser. In the laser system, two arbitrary single-mode Gaussian states of the cavity fields and an external classical field couple to the atomic lasing medium. We calculate the time-dependent expression for the quantum discord both analytically and numerically, by following the reduced density matrix equation of the resulting cavity field. In this framework, we investigate the generation and control of Gaussian quantum discord in the two-mode Gaussian state of the cavity field at the output in terms of the purity and non-classicality of the two input cavity modes, the Rabi frequency of the classical driving field, the relative phase of the coupling parameters, and the damping rates of the cavity modes. The behaviour of quantum discord appears oscillatory due to the quantum beats in the output cavity field developed by the classical driving field in the medium as time passes. Moreover, we find that quantum discord switches on and off while adjusting the relative phase of the coupling parameters. Analysis of the analytical results agrees well with our numerical simulations.

Influence of spontaneously generated coherence on absorption, dispersion, and group index in a five-level cascade atomic system

By solving the density matrix equations in the steady state, we have derived analytical expressions for the absorption, dispersion, and group index of a five-level cascade-type atomic system as functions of laser intensity and frequency, spontaneously generated coherence (SGC), and relative phase of applied fields. The influences of SGC and relative phase on absorption, dispersion, and group index of this system under electromagnetically induced transparency (EIT) are studied. It is shown that the three EIT windows of system become deeper and narrower as the strength of SGC increases. These lead to an increase in the slope and the amplitude of the dispersion curves at three EIT windows. As a result, the amplitude of the group index at these three EIT windows also becomes larger when the strength of SGC increases. In particular, the group index can easily be switched between negative and positive values i.e., the light propagation can easily be converted between superluminal to subluminal modes by adjusting the strength of SGC, relative phase or the coupling laser intensity.

Probing Rashba spin-orbit coupling by subcycle lightwave control of valley polarization

We perform nonperturbative calculations of light-field driven valley-polarization process in monolayer ${\mathrm{MoS}}_{2}$ which has additional Rashba spin-orbit couplings (SOCs). The ultrafast electron dynamics is simulated within the independent particle picture by solving density-matrix equations in the basis of linear combination of atomic orbitals, where tight-binding (TB) models including both intrinsic atomic and Rashba SOCs are used to calculate relevant matrix elements. We demonstrate that the Rashba-type SOCs can be manifested by suboptical-cycle control of valley selectivity excitations, in particular necessary via using few-cycle linearly polarized pulse with controlled carrier-envelope phase (CEP). This procedure will lead to a CEP-dependent valley Hall conductivity (VHC), which exhibits an important phase shift among different Rashba coupling strengths. The additional analysis shows that this phase shift is mainly determined by the ${d}_{z}^{2}$-orbital TB Rashba parameter from Mo atom and originates from contribution of conduction bands to VHC, where the Berry curvature modified by Rashba SOC plays a crucial role. Moreover, we also provide a qualitative interpretation on the Rashba-dependent VHC in terms of suboptical-cycle Landau-Zener-St\"uckelberg interference. Our results suggest a feasible approach for probing Rashba SOCs in hexagonal two-dimensional materials, and might pave the way of achieving more controls in the future valleytronics application.

Optical Absorption Coefficient and Refractive-Index Change in a Coupled Quantum Dot-Metallic Nanoparticle Structure

In the present work, we investigate the problem of the optical absorption coefficient (OAC) and refractive-index change (RIC) in a semiconductor quantum dot placed in the vicinity of a spherical metallic nanoparticle. We derive the total OAC and RIC from the density-matrix equations through different approaches, one without approximations and the other keeping only linear and third-order nonlinear terms. The derived formulae are then applied in a specific hybrid nanostructure to calculate the OAC and RIC. The results obtained from the derived formulae are used to compare cases of various interparticle distance values and applied light intensities and find that, although for specific distances and intensities the formulae may give similar results, in general, they give different results. Moreover, it becomes clear that the distance between the quantum dot and the metallic nanoparticle, in combination with the polarisation of the light field, plays a significant role in the OAC and RIC of the quantum dot. Expressly, conditional on the polarisation of the applied electric field, the OAC and RIC of the quantum dot can be either enhanced or suppressed close to the metallic nanoparticle compared to their values in the absence of the metallic nanoparticle.

Phonon Blockade in Parametrically Pumped Acoustic Cavity at Finite Temperature

In this study, we investigated the phonon blockade effect in a parametrically driven and dissipative acoustic cavity at finite temperature. With the approximated analytical results based on the steady-state density-matrix master equation, we found that a quantum-interference-induced phonon blockade exists at finite temperature. We found a crossover between the quantum and thermal regimes on the curve of the second-order correlation function of the acoustic mode as the temperature increases. This phenomenon implies an asymmetry about the quantum and classic regimes. We also numerically simulated the single-phonon emission using the Monte Carlo wave function method. The results showed that a wide and deep dip around the zero time delay exists on the curve of the time-delayed second-order correlation function, which implies the possibility of observing a strong phonon blockade with pulse driving. Our study outlines a potential candidate for a efficient single-phonon source and applications in quantum information and phononic quantum networks.

Four-wave mixing properties in bilayer graphene nanosystem

Graphene thin films are often used to manufacture various optoelectronic nanodevices owing to their advantages such as light weight, small size, high quality factor, and good conductivity. So far, there have been few studies of the four-wave mixing characteristics in a bilayer graphene nanosystem, especially theoretical research. In this work, we study theoretically the four-wave mixing properties in a bilayer graphene nanosystem. Firstly, the analytical formula of the four-wave mixing signal is derived by quantum mechanical method, which is divided into three steps. 1) Total Hamiltonian of the system is written in the rotating wave approximation. 2) By using the Heisenberg equation of motion and the commutation relations between different operators, the corresponding density matrix equations are obtained. 3) To solve these density matrix equations, we make an ansatz and obtain the analytical formula of the four-wave mixing signal. Secondly, we explore the dependence of the four-wave mixing signal on the phonon-exciton coupling strength, pumping intensity and the detuning between the exciton and the pump field. The calculated results show that the lineshape of four-wave mixing spectrum can be switched among two-peaked, three-peaked, four-peaked, five-peaked and six-peaked by adjusting the phonon-exciton coupling strength, the pumping intensity, and the detuning between the exciton and the pump field. In a weak phonon-exciton coupling regime (i.e. phonon-exciton coupling strength <i>g</i> < dephasing rate of exciton <i>Γ</i><sub>2</sub>), the intensity of the left peak and right peak of four-wave mixing signal first increase and then decrease with the increase of the pumping intensity <inline-formula><tex-math id="M1">\begin{document}$ {\varOmega }_{{\text{pu}}}^{\text{2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M1.png"/></alternatives></inline-formula>. In the intermediate and strong phonon-exciton coupling regime (i.e. <i>g</i> = <i>Γ</i><sub>2</sub> and <i>g</i> > <i>Γ</i><sub>2</sub>), the four-wave mixing spectrum exhibits a two-peaked structure. The maximum values of these two peaks increase as <inline-formula><tex-math id="M2">\begin{document}$ {\varOmega }_{{\text{pu}}}^{\text{2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M2.png"/></alternatives></inline-formula> increases, and their spacing is equal to 2<i>g</i>. Especially, for a given pumping intensity <inline-formula><tex-math id="M3">\begin{document}$ {\varOmega }_{{\text{pu}}}^{\text{2}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20230012_M3.png"/></alternatives></inline-formula> (= 10 THz<sup>2</sup>), the maximum value of the peak for <i>g</i> = 4 THz becomes 0.4% of that for <i>g</i> = 1 THz, indicating that the phonon-exciton coupling inhibits the enhancement of the four-wave mixing signal to a certain extent. Our findings can not only offer an efficient way to measure the phonon-exciton coupling strength in the bilayer graphene system, but also help one to further explore the underlying physical mechanism in such a nanosystem.

DYNAMICS OF THE THREE-QUBITS TAVIS — CUMMINGS MODEL

In this article, we have studied the entanglement dynamics of three identical qubits (natural or artificial two-level atoms) resonantly interacting with the one mode of the thermal field of a microwave lossless resonator via one-photon transitions. An exact solution of the quantum time Schrodinger equation is found for the total wave function of the system for the initial separable and entangled states of qubits and the Fock initial state of the resonator. On the basis of this solution, an exact solution of the quantum Liouville equation for the total time-dependent density matrix of the system in the case of a thermal field of the resonator is constructed. The exact solution for the full density matrix is used to calculate the criterion of entanglement of pairs of qubits negativity. The resultsof numerical simulation of the time dependence of the negativity of pairs of qubits showed that with an increase in the intensity of the thermal resonator field, the degree of entanglement of pairs of qubits decreases. It is also shown that In the model under consideration, for any initial states of qubits and intensities of the thermal field of the resonator, the effect of sudden death of entanglement takes place. This behavior of the entanglement parameter in the model under consideration differs from that in the two-qubit model. For two-qubit model, the effect of the sudden death of entanglement takes place only for the initial entangled states of qubits and intense thermal fields of the resonator.

Fishbone resonance structure in the attosecond transient absorption spectrum of graphene

We investigate the attosecond transient absorption spectroscopy (ATAS) of graphene by numerically solving four-band density-matrix equations, which demonstrates apparent fish bone resonance structures. To gain insight into these interesting structures, we exploit a simplified model that only considers the electrons of $\Gamma$ and M points in the Brillouin zone. With the help of this model, we can analytically express the ATAS spectrum as the sum of zeroth- and first-order Bessel functions in the variables of the strength and frequency of the infrared pump field as well as the effective mass of electrons at the $\Gamma$ and M points. Lorentzian and Fano line shapes in the absorption spectrum are addressed. The fish bone structure consists of periodic V-shaped structure that can be explained by first-order Bessel functions and its tilt angle is solely determined by the frequency of the pump laser. The periodicity of the V-shaped structure in the fish bone originates from the periodic dependence of the Lorentzian and Fano line shapes of the absorption spectrum on the time delay between the pump and probe lasers. Compared with the numerical results, our analytical theory can qualitatively or even quantitatively predict the zeroth- and first-order fringes in the fish bone structures of the ATAS spectrum. The gauge issues in the numerical simulations are also discussed.

Energy absorbed from double quantum dot-metal nanoparticle hybrid system

This work proposes the double quantum dot (DQD)-metal nanoparticle (MNP) hybrid system for a high energy absorption rate. The structure is modeled using density matrix equations that consider the interaction between excitons and surface plasmons. The wetting layer (WL)-DQD transitions are considered, and the orthogonalized plane wave (OPW) between these transitions is considered. The DQD energy states and momentum calculations with OPW are the figure of merit recognizing this DQD-MNP work. The results show that at the high pump and probe application, the total absorption rate ({Q}_{tot}) of the DQD-MNP hybrid system is increased by reducing the distance between DQD-MNP. The high {Q}_{tot} obtained may relate to two reasons: first, the WL washes out modes other than the condensated main mode. Second, the high flexibility of manipulating DQD states compared to QD states results in more optical properties for DQD. The {Q}_{DQD} is increased at a small MNP radius on the contrary to the {Q}_{MNP} which is increased at a wider MNP radius. Under high tunneling, a broader blue shift in the {Q}_{tot} due to the destructive interference between fields is seen and the synchronization between {Q}_{MNP} and {Q}_{DQD} is destroyed. {Q}_{tot} for the DQD-MNP is increased by six orders while {Q}_{DQD} is by eight orders compared to the single QD-MNP hybrid system. The high absorption rate of the DQD-MNP hybrid system comes from the transition possibilities and flexibility of choosing the transitions in the DQD system, which strengthens the transitions and increases the linear and nonlinear optical properties. This will make the DQD-MNP hybrid systems preferable to QD-MNP systems.

Quantum thermodynamics of periodically driven polaritonic systems.

We investigate the energy distribution and quantum thermodynamics in periodically-driven polaritonic systems in the stationary state at room temperature. Specifically, we consider an exciton strongly coupled to a harmonic oscillator and quantify the energy reorganization between these two systems and their interaction as a function of coupling strength, driving force, and detuning. After deriving the quantum master equationfor the polariton density matrix with weak environment interactions, we obtain the dissipative time propagator and the long-time evolution of an equilibrium initial state. This approach provides direct access to the stationary state and overcomes the difficulties found in the numerical evolution of weakly damped quantum systems near resonance, also providing maps on the polariton lineshape. Then, we compute the thermodynamic performance during harmonic modulation and demonstrate that maximum efficiency occurs at resonance. We also provide an expression for the irreversible heat rate and numerically demonstrate that this agrees with the thermodynamic laws.

A Review of Neutrino Decoupling from the Early Universe to the Current Universe

We review the distortions of spectra of relic neutrinos due to the interactions with electrons, positrons, and neutrinos in the early universe. We solve integro-differential kinetic equations for the neutrino density matrix, including vacuum three-flavor neutrino oscillations, oscillations in electron and positron background, a collision term and finite temperature corrections to electron mass and electromagnetic plasma up to the next-to-leading order O(e3). After that, we estimate the effects of the spectral distortions in neutrino decoupling on the number density and energy density of the Cosmic Neutrino Background (CνB) in the current universe, and discuss the implications of these effects on the capture rates in direct detection of the CνB on tritium, with emphasis on the PTOLEMY-type experiment. In addition, we find a precise value of the effective number of neutrinos, Neff=3.044. However, QED corrections to weak interaction rates at order O(e2GF2) and forward scattering of neutrinos via their self-interactions have not been precisely taken into account in the whole literature so far. Recent studies suggest that these neglections might induce uncertainties of ±(10−3–10−4) in Neff.

Leptogenesis in SO(10) models with A4 modular symmetry

We study the prediction for leptogenesis in two renormalizable supersymmetric SO(10) × A4 modular models in which the neutrino mass is dominantly generated by the type I seesaw mechanism. The evolution of the lepton asymmetries are described in terms of the three-flavored density matrix equations for three heavy Majorana neutrinos, where both vanishing initial condition and thermal initial condition of the right-handed neutrinos are considered. We also present an analytical approximation based on the Boltzmann equations. We find regions of parameter space compatible with the measured fermion masses and mixing parameters as well as the baryon asymmetry of the Universe. The predictions for the light neutrino masses, the effective mass in neutrinoless double beta decay and the leptonic CP violation phases are discussed.

Knee structure in the laser-intensity dependence of harmonic generation for graphene

We investigate the high-order harmonic generations (HHGs) of graphene irradiated by linearly polarized lasers with intensities in a wide range from $10^{8}$ W/cm$^2$ to $10^{13}$ W/cm$^2$. We find a striking knee structure in the laser intensity dependence of HHGs, which consists of a linear growth regime, followed by a plateau of the saturated HHGs, and then a transition to a nonlinear growth. The knee structure is rather universal for the varied harmonic orders and has been certificated by the calculations of two-band density-matrix equations as well as the \textit{ab initio} calculations of time-dependent density functional theory. Based on the two-band model, we reveal the underlying mechanisms: The behavior of linear growth can be depicted analytically by the perturbative theory of optical conductivity; While, the plateau of saturated HHGs and the transition to a nonlinear growth are caused by the quantum destructive interference and constructive interference of harmonics generated by the electrons corresponding to the lattice momentums around Dirac points and M points in Brillouin zone, respectively. In particular, we find that tuning Fermi energy can effectively alter the knee structure while the profile of the knee structure is not sensitive to the temperature. Our calculations of the third-order harmonic vs. tuning Fermi energy are compared with recent experiment showing a good agreement. Our predicted knee structure and its associated properties are observable with the current experimental techniques.

Efficient Biexciton State Preparation in a Semiconductor Quantum Dot Coupled to a Metal Nanoparticle with Linearly Chirped Gaussian Pulses.

We consider a hybrid nanostructure composed of a semiconductor quantum dot placed near a spherical metallic nanoparticle, and study the effect of the nanoparticle on the population transferral from the ground to the biexciton state of the quantum dot, when using linearly chirped Gaussian pulses. For various values of the system parameters (biexciton energy shift, pulse area and chirp, interparticle distance), we calculate the final population of the biexciton state by performing numerical simulations of the non-linear density matrix equations which describe the coupled system, as well as its interaction with the applied electromagnetic field. We find that for relatively large values of the biexciton energy shift and not very small interparticle distances, the presence of the nanoparticle improves the biexciton state preparation, since it effectively increases the area of the applied pulse. For smaller biexciton energy shifts and smaller distances between the quantum dot and the nanoparticle, the performance is, in general, degraded. However, even in these cases we can still find ranges of parameter values where the population transfer to the biexciton state is accomplished with high fidelity, when using linearly chirped Gaussian pulses. We anticipate that our results may be exploited for the implementation of novel nanoscale photonic devices or future quantum technologies.

Controlling Resonance Fluorescence Spectra and Photon Statistics in a Driven V-Type Quantum Emitter—Metal Nanoparticle Coupled Structure

We study the resonant fluorescence emission spectrum and the intensity-intensity correlations of the emitted fluorescent field by a V-type quantum emitter (QE) which is located near a metal nanosphere. For the description of the studied phenomena, we use the density matrix equations methodology combined with electromagnetic calculations and obtain results for the profile of the resonant fluorescence spectrum and the second-order correlation functions associated with the fluorescent photons. The decay rates and the coupling term exhibit a strong dependence on the distance that separates the QE from the metal nanoparticle. This distance also influences the resonance fluorescence of the V-type QE. We find that, in the general case, the resonant fluorescence spectrum is composed of five Lorentzian-type peaks, for high interparticle distances, while, when the QE is located very close to the surface of the nanosphere, the central resonance becomes dominant, and a single-peaked spectral profile appears. The two-time correlation functions of the fluorescent photons evolve in an oscillatory manner around unity, for non-zero time delay, with a period that decreases with the increase of the field intensity. In the strong driving field regime, the antibunching to bunching crossing time does not depend on the interparticle distance, contrary to the results found in the weak driving field regime. We also find that, for a weak laser field and under specific conditions, the second-order correlation functions constantly remain in the antibunching region.

Decoherence and maintenance of an entangled state in three-spin system coupled to ferromagnetic electrodes

We study the model of three-spin system by using Born-Markov master equation for density matrix. Three-spin system consists of a spin-1/2 quantum dot and two spin-1 magnetic particles arranged in triangular geometry and a quantum dot is also tunnel-coupled to ferromagnetic electrodes, respectively. In this case, we are interested in decoherence of entangled state of the system. Decoherence occurs due to tunneling of electrons through coupling to ferromagnetic electrodes. Therefore, an entangled state undergoes decoherence dependent on the spin polarization as well as magnetization orientations of electrodes. We have established master-equation formalism for the density matrix of three-spin system and calculated spin-spin correlation function between two magnetic particles corresponding to entangled state. The results show that with the increase of spin polarization, spin-spin correlation function for parallel configuration of electrodes’ magnetizations decays more rapidly, while spin-spin correlation function for antiparallel configuration decays more slowly.

Optical susceptibility of metal nanoparticle-double quantum dot hybrid system

This work is modeling the linear optical susceptibility of a double quantum dot (DQD)–metal nanoparticle (MNP) hybrid system using density matrix equations that consider the interaction between excitons and surface plasmons. The wetting layer (WL)-QD interaction is considered.The absorption of the hybrid DQD-MNP system increases by five times compared to the bare DQD system. The absorption peak is reducing in a similar ratio of increasing MNP radius. A Mollow triplet with asymmetric sidebands appears and decreases with increasing MNP radius, which is compatible with recent experimental evidence. The susceptibility peaks at resonance for a small distance between the hybrid MNP-DQD. The susceptibility is increased by one order for the DQD system compared to a single QD. A similar result is obtained under WL-QD detuning compared to the case of the probe between DQD states. Small DQDs give high absorption and dispersion, offering more shifts from resonance.

Dynamics of photosynthetic light harvesting systems interacting with N-photon Fock states.

We develop a method to simulate the excitonic dynamics of realistic photosynthetic light harvesting systems, including non-Markovian coupling to phonon degrees of freedom, under excitation by N-photon Fock state pulses. This method combines the input-output and the hierarchical equations of motion formalisms into a double hierarchy of density matrix equations. We show analytically that under weak field excitation relevant to natural photosynthesis conditions, an N-photon Fock state input and a corresponding coherent state input give rise to equal density matrices in the excited manifold. However, an N-photon Fock state input induces no off-diagonal coherence between the ground and excited subspaces, in contrast with the coherences created by a coherent state input. We derive expressions for the probability to absorb a single Fock state photon with or without the influence of phonons. For short pulses (or, equivalently, wide bandwidth pulses), we show that the absorption probability has a universal behavior that depends only upon a system-dependent effective energy spread parameter Δ and an exciton-light coupling constant Γ. This holds for a broad range of chromophore systems and for a variety of pulse shapes. We also analyze the absorption probability in the opposite long pulse (narrow bandwidth) regime. We then derive an expression for the long time emission rate in the presence of phonons and use it to study the difference between collective vs independent emission. Finally, we present a numerical simulation for the LHCII monomer (14-mer) system under single photon excitation that illustrates the use of the double hierarchy equations.