Density Matrix Of Quantum System Research Articles

Equivalence of quantum and classical third order response for weakly anharmonic coupled oscillators.

Two-dimensional (2D) infrared (IR) spectra are commonly interpreted using a quantum diagrammatic expansion that describes the changes to the density matrix of quantum systems in response to light-matter interactions. Although classical response functions (based on Newtonian dynamics) have shown promise in computational 2D IR modeling studies, a simple diagrammatic description has so far been lacking. Recently, we introduced a diagrammatic representation for the 2D IR response functions of a single, weakly anharmonic oscillator and showed that the classical and quantum 2D IR response functions for this system are identical. Here, we extend this result to systems with an arbitrary number of bilinearly coupled, weakly anharmonic oscillators. As in the single-oscillator case, quantum and classical response functions are found to be identical in the weakly anharmonic limit or, in experimental terms, when the anharmonicity is small relative to the optical linewidth. The final form of the weakly anharmonic response function is surprisingly simple and offers potential computational advantages for application to large, multi-oscillator systems.

Nonrelativistic quantum mechanics with consideration of influence of fundamental environment

Spontaneous transitions between bound states of an atomic system, the “Lamb Shift” of energy levels and many other phenomena in real nonrelativistic quantum systems are connected with the influence of the quantum vacuum fluctuations (fundamental environment (FE)), which are impossible to consider in the framework of standard quantum-mechanical approaches. The joint system quantum system (QS) and FE is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrodinger type and is defined on the extended space ℝ3⊗Ξn, where ℝ3 and Ξn are the Euclidean and functional spaces, respectively. The method of stochastic density matrix is developed and the von Neumann equation for reduced density matrix of QS with FE is generalized. The entropy of QS entangled with FE is defined and investigated. It is proved that the interaction of QS with the environment leads to emerging structures of various topologies which present new quantum-field properties of QS. It is shown that when the physical system (irrelatively to its being micro ormacro) breaks up into two fragments by means of FE, there arises between these fragments a nonpotential interaction which does not disappear at large distances.

Floquet-Liouville supermatrix approach: Time development of density-matrix operator and multiphoton resonance fluorescence spectra in intense laser fields.

A Floquet-Liouville supermatrix (FLSM) approach is presented for nonperturbative treatment of the time development of the density-matrix operator of atoms and molecules exposed to intense polychromatic fields. By extending the many-mode Floquet theory (MMFT) recently developed, the time-dependent Liouville equation for the density matrix of quantum systems undergoing relaxations (due to radiative decays and collisional dampings, etc.) can be transformed into an equivalent time-independent non-Hermitian FLSM eigenvalue problem. This yields a numerically stable and computationally efficient approach for the unified treatment of nonresonant and resonant, one- and multiple-photon, steady-state and transient phenomena in nonlinear optical processes, much beyond the conventional rotating-wave-approximation (RWA) method. Connections of the FLSM approach to the MMFT in the limit of zero relaxations are also made, providing the understanding of the physical significance of FLSM supereigenvalues and eigenvectors. In addition to the exact FLSM formalism, we have also presented higher-order perturbative results, based on the extension of the generalized Van Vleck (GVV) nearly degenerate perturbation theory, appropriate for somewhat weaker fields and near-resonant processes, but beyond the RWA limit. The implementation of the GVV method in the time-independent Floquet-Liouvillian allows the reduction of the infinite-dimensional FLSM into a finite-dimensional GVV-Liouville matrix, from which essential analytical results are readily obtained. As an illustration of the usefulness of the new formalism, we extend both the FLSM and the GVV methods to a formal study of the multiphoton-induced resonance fluorescence spectra of two-level systems subject to purely radiation relaxations. Both the time-averaged power spectrum and the time-dependent physical spectrum are exploited in details, and novel new features in intense fields are pointed out.

New effects of spontaneous relaxation of quantum systems in a strong laser field

It is shown that the laser field influences spontaneous relaxation of quantum systems and alters the relaxation scheme. New quantum kinetic equations are obtained for the density matrix of quantum systems and it follows from these equations that an additional frequency shift appears in the dispersion function of a quantum system. This shift is over an order of magnitude larger than the familiar Bloch-Siegert shift and the absorption line profile of a quantum system is found to be an asymmetric function of the laser field frequency.