Maxwell-Bloch system describing the resonant propagation of electromagnetic pulses in both two-level media with degeneracy in angle moment projection and three-level media with equal oscillator forces is considered. The inhomogeneous broadening of energy levels is accounted. Binary Darboux Transformation generating the solutions of the system is constructed. Pulses corresponding to the transition between levels with largest population difference are shown to be stable. The solution describing the propargation of pulses in the medium exited by the periodic wave is obtained. The hierarchy of infinitesimal symmetries is obtained by means of Darboux transformation.
A new strategy, using Darboux transformations, of finding self-switching solutions of $i\dotρ = [H, f(ρ)]$ is introduced. Unlike the previous ones, working for any f but for Hamiltonians whose spectrum contains at least three equally spaced eigenvalues, the strategy does not impose any restriction on the discrete part of the spectrum of H. The strategy is applied to the Bloch-Maxwell system.
A simple algebraic procedure is described for deriving Maxwell-Bloch-type equations from single-atom cavity quantum electrodynamics (cavity QED) master equations via orthogonal projection onto a manifold of semiclassical states. In particular the usual Maxwell-Bloch Equations are obtained--up to a state-dependent correction factor of order unity--straightforwardly from the unconditional Jaynes-Cummings master equation. The technique of projecting onto a semiclassical manifold can also be applied with conditional master equations (quantum filters), leading to stochastic simulation models that i…
The Maxwell-Bloch equations are a valuable tool to model light-matter interaction, where the application examples range from the description of pulse propagation in two-level media to the elaborate simulation of optoelectronic devices, such as the quantum cascade laser (QCL). In this work, we present mbsolve, an open-source solver tool for the Maxwell-Bloch equations. Here, we consider the one-dimensional Maxwell's equations, which are coupled to the Lindblad equation. The resulting generalized Maxwell-Bloch equations are treated without invoking the rotating wave approximation (RWA). Since th…
We present an implementation of the Maxwell-Bloch (MB) formalism for the study of x-ray emission dynamics from periodic multilayer materials whether they are artificial or natural. The treatment is based on a direct Finite-Difference-Time-Domain (FDTD) solution of Maxwell equations combined with Bloch equations incorporating a random spontaneous emission noise. Besides periodicity of the material, the treatment distinguishes between two kinds of layers, those being active (or resonant) and those being off-resonance. The numerical model is applied to the problem of $Kα$ emission in multilayer m…
We present quantum Maxwell-Bloch equations (QMBE) for spatially inhomogeneous optical semiconductor devices taking into account the quantum noise effects which cause spontaneous emission and amplified spontaneous emission. Analytical expressions derived from the QMBE are presented for the spontaneous emission factor beta and the far field pattern of amplified spontaneous emission in broad area quantum well lasers.
The discovery of relativistic spin-1/2 fermions such as Dirac and Weyl fermions in condensed-matter or artificial systems opens a new era in modern physics. An interesting but rarely explored question is whether other relativistic spinal excitations could be realized with artificial systems. Here, we construct twoand three-dimensional tight-binding models realizable with cold fermionic atoms in optical lattices, where the low energy excitations are effectively described by the spin-1 Maxwell equations in the Hamiltonian form. These relativistic (linear dispersion) excitations with unconvention…
We present quantum Maxwell-Bloch equations (QMBE) for spatially inhomogeneous semiconductor laser devices. The QMBE are derived from fully quantum mechanical operator dynamics describing the interaction of the light field with the quantum states of the electrons and the holes near the band gap. By taking into account field-field correlations and field-dipole correlations, the QMBE include quantum noise effects which cause spontaneous emission and amplified spontaneous emission. In particular, the source of spontaneous emission is obtained by factorizing the dipole-dipole correlations into a pr…
We investigate the dynamics of a two-photon laser under conditions where the spatial variation of the cavity field along the cavity axis is important. Main attention is paid to linear stability analysis and numerical investigation of a two-photon laser for the Maxwell-Bloch equations. The model assumes pumping to the upper state of the two-photon transition. We consider the Maxwell-Bloch equations on the basis of which we study the stability analysis of the steady state of the system. The system is taken to be contained in a ring-laser cavity. Asymptotic expansion of the eigenvalue and analyti…
In this article we present a systematic derivation of the Maxwell-Bloch equations describing amplification and laser action in a ring cavity. We derive the Maxwell-Bloch equations for a two-level medium and discuss their applicability to standard three- and four-level systems. After discusing amplification, we consider lasing and pay special attention to the obtention of the laser equations in the uniform field approximation. Finally, the connection of the laser equations with the Lorenz model is considered.
The adiabatic solutions of Maxwell-Bloch equation governing the three-level EIT medium is presented. The time evolution of the density matrix elements of the EIT system and the probe light is thus investigated by using the adiabatic approximation formulation and the slowly varying envelope condition.
We report the Bose-Einstein condensate (BEC) in the Bloch bands with off-diagonal periodic potential (ODPP), which simultaneously plays the role of spin-orbit coupling (SOC) and Zeeman field. This model can be realized using two independent Raman couplings in the same three level system, in which the time-reversal symmetry ensures the energy degeneracy between the two states with opposite momenta. We find that these two Raman couplings can be used to tune the spin polarization in momentum space, thus greatly modifies the effective scatterings over the Bloch bands. We observe a transition from …
We study the topological nature of a class of lattice systems, whose Bloch vector can be expressed as the difference of two independent periodic vector functions (knots) in an auxiliary space. We show exactly that each loop as a degeneracy line generates a polarization field, obeying the Biot-Savart law: The degeneracy line acts as a current-carrying wire, while the polarization field corresponds to the generated magnetic field. Applying the Ampere's circuital law on a nontrivial topological system, we find that two Bloch knots entangle with each other, forming a link with the linking number b…
The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are explicit functions of the probability and degeneracy of each state, and the total number of entities, N. By analysis of the cost of a "binary decision", exact BE and FD statistics are shown to have profound consequences for the behaviour of quantum mechanical systems.
We measure the coherent scattering of low-intensity, near-resonant light by a cloud of laser-cooled two-level rubidium atoms with a size comparable to the wavelength of light. We isolate a two-level atomic structure by applying a 300G magnetic field. We measure both the temporal and the steady-state coherent optical response of the cloud for various detunings of the laser and for atom numbers ranging from 5 to 100. We compare our results to a microscopic coupled-dipole model and to a multi-mode, paraxial Maxwell-Bloch model. In the low-intensity regime, both models are in excellent agreement, …
We focus on the propagation properties of a single-cycle laser pulse through a two-level medium by numerically solving the full-wave Maxwell-Bloch equations. The counter-rotating terms in the spontaneous emission damping are included such that the equations of motion are slightly different from the conventional Bloch equations. The counter-rotating terms can considerably suppress the broadening of the pulse envelope and the decrease of the group velocity rooted from dispersion. Furthermore, for incident single-cycle pulses with envelope area 4$π$, the time-delay of the generated soliton pulse …
