Semiclassical Density Research Articles

Effect of optical pumping on alkali-atom Doppler-limited spectra

Using a three-level model and semiclassical density matrix formalism, we show that optical pumping influences both line positions and amplitudes in Doppler-broadened alkali-atom D1 and D2 spectra for intensities much lower than the two-level atom saturation intensity. The influence on the D2 spectrum is particularly interesting due to the presence of closed hyperfine transitions unaffected by optical pumping. This effect is of importance for example when lasers are frequency stabilized using linear absorption or when the alkali-atom vapour pressure is determined using absorption measurements.

Independent Trajectory Implementation of the Semiclassical Liouville Method: Application to Multidimensional Reaction Dynamics

We describe an independent trajectory implementation of semiclassical Liouville method for simulating quantum processes using classical trajectories. In this approach, a single ensemble of trajectories describes all semiclassical density matrix elements of a coupled electronic state problem, with the ensemble evolving classically under a single reference Hamiltonian chosen on the basis of physical grounds. In this paper, we introduce an additional uncoupled trajectory approximation, allowing the members of the ensemble to evolve independently of one another and eliminating the major computational costs of our previous coupled trajectory implementation. The accuracy of the method is demonstrated for model one-dimensional problems. In addition, the approach is applied to the chemical reaction dynamics of a collinear triatomic system, yielding excellent agreement with exact calculations. This method allows molecular dynamics involving coupled electronic surfaces to be modeled with essentially the same effort as classical molecular dynamics and ensemble averaging.

Temperature dependence of the photoluminescence properties of self-assembled InGaAs∕GaAs single quantum dot

Based on the semiclassical density matrix approach, a detailed theoretical investigation is made to analyze the effect of temperature and strain on photoluminescence (PL) spectra of an InxGa1−xAs∕GaAs single quantum dot. The temperature effects have been incorporated via temperature dependent (i) dephasing mechanism, (ii) band gap energy, and (iii) population density. A redshift of the PL peak is found to occur with increasing temperature. In our case, the full width at half maximum of the PL spectrum exhibits anomalous behavior at low temperature. The present analysis further reveals the disappearance of biexciton peaks at higher temperatures due to the quenching effect.

Connection between the Strutinsky level density and the semiclassical level density

We establish an analytical link between the level density obtained by means of the Strutinsky averaging method, and the semiclassical level density. This link occurs only in the so-called "asymptotic limit". It turns out that the Strutinsky method amounts to an approximation to the semiclassical method. This approximation contains an unavoidable remainder which constitutes an intrinsic noise in comparison to the semiclassical method. Thus, the "old" problem of the dependency of the Strutinsky procedure on the two free smoothing parameters of the averaging is intimately connected to this noise. On the other hand, we demonstrate that the noise of the method is small in the average density of states and in the average energy, whereas it might be non-negligible in the shell correction itself. In order to improve this method, we give a "rule" which consists simply of minimizing the relative error made on the average energy.

Theoretical calculation of saturated absorption spectra for multi-level atoms

We have developed a model for calculating saturated absorption spectra for dipole transitions in multi-level atoms. Using a semiclassical density matrix formalism, we derive a set of coupled differential equations for the internal state of the atom in a standing wave light field. The equations are solved using standard integration techniques. The absorption at each laser detuning is found from an average of the absorption for a number of velocities along the laser field, thermally weighted. The method is relatively efficient computationally yet quantitatively predicts important details of saturated absorption spectra including saturation, crossover resonances, merging of absorption lines at high intensity and optical pumping between hyperfine levels. We have measured saturated absorption and fluorescence spectra of 85Rb, and compare to our computational results for a 36-level model.

The Break Down of Semiclassical Density Matrix of a Particle Moving in Barrier Potential at Temperature T

The Break Down of Semiclassical Density Matrix of a Particle Moving in Barrier Potential at Temperature T

Semiclassical Liouville method for the simulation of electronic transitions: Single ensemble formulation

In this paper, we describe a single ensemble implementation of the semiclassical Liouville method for simulating quantum processes using classical trajectories. In this approach, one ensemble of trajectories supports the evolution of all semiclassical density matrix elements, rather than employing a distinct ensemble for each. The ensemble evolves classically under a single reference Hamiltonian, which is chosen based on physical grounds; for electronic relaxation of an initially excited state, the initially populated upper surface Hamiltonian is the natural choice. Classical trajectories evolving on the reference potential then represent the time-dependent upper state population density and also the electronic coherence and the ground state density created by electronic transition. The error made in the classical motion of the trajectories for these latter distributions is compensated for by incorporating the difference between the correct and reference Liouville propagators into the calculation of the coefficients of the individual trajectories. This approach gives very accurate results for a number of model problems and cases describing ultrafast electronic relaxation dynamics.

Exact broken-symmetry states and Hartree–Fock solutions for quantum dots at high magnetic fields

Wigner molecules formed at high magnetic fields in circular and elliptic quantum dots are studied by exact diagonalization (ED) and unrestricted Hartree–Fock (UHF) methods with multicenter basis of displaced lowest Landau level wave functions. The broken symmetry states with semi-classical charge density constructed from superpositions of the ED solutions are compared to the UHF results. UHF overlooks the dependence of the few-electron wave functions on the actual relative positions of electrons localized in different charge puddles and partially compensates for this neglect by an exaggerated separation of charge islands which are more strongly localized than in the exact broken-symmetry states.

The extended Thomas–Fermi kinetic energy density functional with position-dependent effective mass in one dimension

The point canonical transformations map the Schrodinger equation with constant mass to a wave equation with a position-dependent effective mass. Using such a technique we derive, for a one-dimensional inhomogeneous system of noninteracting fermions with density ρ(x) and spatially dependent effective mass distribution m(x), the semiclassical kinetic energy density functional τ(ρ) in the so-called extended Thomas–Fermi model up to order 2. For a given position-dependent mass, we compare numerically the total semiclassical kinetic energy with its exact quantum mechanical counterpart. The qualitative agreement is excellent.

Nonlinear dynamics in lasing without inversion

We review lasing in homogeneously broadened coherently driven three-level systems in the framework of semiclassical density matrix formalism and using a nonlinear dynamics point of view. We discuss the following features of these systems: (i) self-pulsing lasing without inversion near the first lasing threshold, (ii) giant pulse lasing based on the population inversion without lasing phenomenon, and (iii) the enlargement of the cavity detuning range where lasing without inversion occurs by using broad-area cavities.

Temperature and Mass Factor of Buffer Gas Effect in Optically Pumped Submillimeter Wave Laser

Based on semi-classical density matrix theory and SSH theory, the effect of buffer gas in optically pumped submillimeter wave laser was theoretically studied and the effect of temperature and mass on the effect of buffer gas was analyzed, then the selection rules of buffer gas were achieved. The results could do favor to find high-efficient buffer gas of miniature optically pumped submillimeter wave laser and also had some instruction to its application.

Anisotropic quantum dots: Correspondence between quantum and classical Wigner molecules, parity symmetry, and broken-symmetry states

We study electron systems confined in anisotropic quantum dots at high magnetic fields using the configuration-interaction scheme with a multicenter basis of single-electron functions centered around different sites. Elliptical, triangular, and square quantum dots are investigated. We study the relation between the quantum and classical charge density and conclude that at high magnetic field the quantum charge density reproduces all the equivalent lowest-energy configurations of classical point charges. Quantum systems with a classical counterpart of a unique lowest-energy configuration exhibit a smooth convergence of the charge density to the classical limit at high magnetic field. In quantum systems with several equivalent classical configurations the magnetic field induces discontinuous transformations of the ground-state symmetry associated with crossings of the corresponding few-electron energy levels. A linear combination of states with the crossing levels yields a semiclassical charge density with a broken symmetry. At the magnetic field corresponding to the level crossing this combination is an exact eigenstate of the Hamiltonian. For circular dots the present findings give an additional insight into the properties of the magic-angular-momenta states and into the physics behind the broken-symmetry mean-field solutions.

CURRENTS, SPIN DENSITIES AND MEAN-FIELD FORM FACTORS IN ROTATING NUCLEI: A SEMI-CLASSICAL APPROACH

We present self-consistent semi-classical local densities characterising the structure of rotating nuclei. A particular emphasis is put on those densities which are generated by the breaking of time-reversal symmetry through the cranking piece of the Routhian, namely the current density and the spin vector density. Our approach which is based on the Extended-Thomas-Fermi method goes beyond the Inglis cranking approach and contains naturally the Thouless-Valatin self-consistency terms expressing the response of the mean field to the time-odd part of the density matrix.

Significance of field and medium asymmetry for the generation of squeezed light

The roles of the asymmetry of coherent light and of an active medium in squeezed-state generation in a weakly noncentrosymmetric semiconductor are discussed. It is suggested that origin of medium asymmetry lies in the parity indefiniteness of the transition states, whereas field asymmetry is due to the polarization property of light. Third-order nonlinear optical susceptibility is obtained from the semiclassical density matrix approach, whereas the light-squeezing process is studied by use of Heisenberg’s equation of motion. The analysis is applied to GaAs that has been duly irradiated by a tunable nanosecond pulsed Co:MgF2 laser with its photon energy off resonant below the semiconductor’s band edge. It has been found that the effect of asymmetry on squeezed-state generation and photon number is finite only when both of the asymmetries are present simultaneously. One may also notice that the asymmetry improves the squeezing level and reduces the time span of squeezed-light generation.

Calculation of Intermolecular Interaction Energies by Direct Numerical Integration over Electron Densities. 2. An Improved Polarization Model and the Evaluation of Dispersion and Repulsion Energies

A procedure to adapt electron densities of isolated molecules for the evaluation of intermolecular energies, first introduced in paper 1 (Gavezzotti, A. J. Phys. Chem. B 2002, 106, 4145) is here improved for polarization energy and extended to dispersion and repulsion terms. Dispersion is evaluated from atomic polarizabilities distributed over the electron density, using an average ionization potential taken as the energy of the highest occupied molecular orbital, in a London-type inverse sixth-power formulation. Repulsion is evaluated from the overlap between electron densities. The method, called semiclassical density sums (SCDS), requires only four disposable numerical parameters and allows a complete evaluation of intermolecular interaction energies for a rather wide range of molecular systems. Calculations on molecular dimers, in comparison with results obtained by high-level quantum chemical methods, show that SCDS energies are quite reliable, at a fraction of the computational cost. The sublimation...

Operating Parameters Optimization of Buffer Gas in Optically Pumped Submillimeter Wave Laser

Based on the basic theory of molecular vibration relaxation and semi-classical density matrix theory, operating parameters optimization of buffer gas in the process of miniature pulsed optically pumped submillimeter wave laser was systemically studied and the theoretical calculated result was tested by experiments. The result would do favor to develop and study high-power and wide-range tunable miniature and high-efficient pulsed optically pumped submillimeter wave laser and also had some instruction to its application.

Spike Phenomenon in Raman Spectrum of Optically Pumped Ear-Infrared Laser

Based on the theory of semi-classical density matrix, spike phenomenon of multi-longitudinal-mode CO2-9R(30) optically pumped miniature NH3 molecules far-infrared cavity laser was theoretically studied and the reason of forming spike phenomenon was approved as two aspects: one was the competitive effect caused by the process of AC Stack splitting two photons, which made that the output optical spectral intensity of one AC Stark splitting peak was stronger than that of the other AC Stark splitting peak; the other was the longitudinal-mode spectral characteristics of laser resonant cavity.

Symmetry Breaking and Bifurcations in the Periodic Orbit Theory. II: Spheroidal Cavity

We derive a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences and discontinuities occurring at bifurcation points and in the spherical limit, the trace integrals over the action-angle variables are performed using an improved stationary phase method. The resulting semiclassical level density oscillations and shell energies are in good agreement with quantum-mechanical results. We find that the births of three-dimensional orbits through the bifurcations of planar orbits in the equatorial plane lead to considerable enhancement of shell effect for superdeformed shapes.

Improved semiclassical density matrix: taming caustics.

We present a simple method to deal with caustics in the semiclassical approximation to the thermal density matrix of a particle moving on the line. For simplicity, only its diagonal elements are considered. The only ingredient we require is the knowledge of the extrema of the Euclidean action. The procedure makes use of complex trajectories, and is applied to the quartic double-well potential.

Double-folding model including the Pauli exclusion principle

A new method for incorporating the Pauli exclusion principle into the double-folding approach to the heavy-ion potential is proposed. The description of the exchange terms at the level of the semiclassical one-body density matrix is used. It is shown that, in order to take into account Pauli blocking properly, the density matrices of free isolated nuclei must be redefined. A solution to the self-consistent incorporation of Pauli blocking effects in the mean-field nucleus-nucleus potential is obtained in the Thomas-Fermi approximation.