Molecular photoexcitation in a medium: Density operator approach

Inner composition law of pure states as a purification of impure states

Molecular photoexcitation in a medium: Density operator approach

In the quantum information theory operates with qubits and N-qubits that can be express through coherent states. Density operator admits a representation in terms of coherent states formalism. Consequently, in this paper the notions of qubit and density operators are described in the framework of coherent states. We have expressed a qubit as a coherent state, and thus a sequence of qubits becomes the tensor product of the coherent states. For the ensembles of qubits, it could be used the density operator, in order to describe the informational content of the ensemble. The coherent states representation may play an important role in the quantum information theory and the use of this formalism is not only theoretical, but also, due to its applications, of some practical relevance.

Consider two interacting sub-systems with nonoverlapping charge distributions. How can the properties of the combined system be expressed in terms of properties of the individual sub-systems alone? This general problem appears in a wide variety of physical, chemical, and biological systems [Joester 2003, Stone 1996, Moore 2001]. In this chapter we provide a prescription for addressing this issue by the computation of (i) response functions and (ii) correlation functions of spontaneous fluctuations of relevant degrees of freedom in the individual sub-systems. The computation of response and correlation functions is greatly simplified by using the density matrix in Liouville space [Mukamel 1995]. Hilbert and Liouville spaces offer very different languages for the description of nonlinear response. Computing dynamical observables in terms of the wavefunction in Hilbert space requires both forward and backward propagations in time. In contrast, the density matrix calculated in Liouville space should only be propagated forward. The choice is between following only the ket, moving it both forward and backward, or following the joint forward dynamics of the ket and the bra. Artificial time variables (Keldysh loops) commonly used in many-body theory [Haug 1996] are connected with the wavefunction. The density matrix which uses the real laboratory time throughout the calculation offers a more intuitive picture. Wavefunction-based theories calculate transition amplitudes, which by themselves are not observable. The density matrix, on the other hand directly calculates physical observables. Moreover, dephasing processes (damping of off-diagonal elements of the density matrix caused by phase fluctuations) which are naturally included into the Liouville space formulation may not be described in terms of the wavefunction. The “causality paradox” of TDDFT [Gross 1996] can be clearly resolved in Liouville space [Mukamel 2005]. In this chapter we present a method for expressing the joint response of two interacting sub-systems in terms of their correlation and response functions. This factorization appears quite naturally in Liouville space. The p order response of the individual systems is a linear combination of 2 distinct (p + 1)-point correlation functions known as Liouville space pathways [Mukamel 1995], which differ by whether the interaction at each time

The first part of the chapter is devoted to the discussion of density operators. We first introduce the definition of a density operator and the unitary evolution of a quantum state. We then examine the measurement of a quantum system using the density operator approach. We present the density operator associated with a qubit and a harmonic oscillator at thermal equilibrium. The second part of the chapter focuses on bipartite systems. We show that the quantum state of a subsystem is given by the partial trace of the density operator of the global system. Finally, we explain the concept of purification of a density operator

The development of tunable diode laser absorption sensors for measurements in industrial boilers, both through direct absorption and evanescent wave absorption have been performed in the work presented here. These sensors use both direct and indirect absorption through the use of evanescent interactions within a coal firing combustion environment. For the direct absorption sensor, wavelength modulation absorption spectroscopy with second-harmonic detection was implemented within a physical probe designed to be placed with the flue stack of a power plant. Measurements were taken of carbon dioxide and water vapor concentration during operation at a local industrial facility. The design of this sensor probe overcomes problems of beam steering and permits a reference gas measurement. Extracted concentration data and design elements from the direct absorption measurements are presented. In addition, development of a sapphire fiber-based sensor using evanescent wave absorption along the outside of the fiber is presented. Evanescent absorption allows for the laser transmission to be maintained in the fiber at all times and may alleviate problems of background emission, beam steering, and especially scattering of the laser beam from solid particles experienced through free path direct absorption measurements in particulated flows. Laboratory measurements using evanescent fiber detection are presented.

Monoclinic $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ has a large band gap of 4.8 eV, and can therefore be used as a contact material that is transparent to visible and UV light. However, indirect free-carrier absorption processes, mediated by either phonons or charged impurities, will set a fundamental limit on transparency. We use first-principles calculations to accurately assess the absorption cross section and to elucidate the microscopic origins of these processes. Phonon-assisted absorption is dominated by the emission of phonons, and is therefore always possible. This indirect absorption is inversely proportional to the cube of the wavelength. The presence of charged impurities, whether intentional or unintentional, leads to additional absorption, but for realistic concentrations, phonon-assisted absorption remains the largest contribution. Direct free-carrier absorption also leads to below-gap absorption, with distinct peaks where optical transitions match energy differences to higher conduction bands. In contrast, indirect absorption uniformly reduces transparency for all sub-band-gap wavelengths.

The effect of the indirect interband absorption both below and above the direct gap in Ge/SiGe quantum-well (QW) structures is theoretically investigated in comparison to the direct interband absorption. The theoretical formula for the indirect interband absorption is derived based on the second-order time-dependent perturbation theory. The direct interband absorption is calculated by summing the bound-state exciton contribution based on the variational method and the QW continuum-state contribution in the consideration of the valence band mixing effect and a Sommerfeld excitonic enhancement factor. The calculated indirect interband absorption parabolically increases below the direct bandgap and shows a stair-step-like gradual increase above the direct bandgap. The calculated optical absorption spectra at room temperature are compared with the experimental results measured by Kuo et al. [Nature 437, 1334 (2005)]. Although the indirect interband absorption is very small below the direct bandgap, the contribution of the gradually increasing indirect interband absorption is significant at the high transition energy above the direct bandgap.

In many problems in quantum optics, damping plays an important role. These include, for example, the decay of an atom in an excited state to a lower state and the decay of the radiation field inside a cavity with partially transparent mirrors. In general, damping of a system is described by its interaction with a reservoir with a large number of degrees of freedom. We are interested, however, in the evolution of the variables associated with the system only. This requires us to obtain the equations of motion for the system of interest only after tracing over the reservoir variables. There are several different approaches to deal with this problem.

This paper is concerned with a study of the interaction between collective electronic excitations and collective vibrational excitations in a molecular crystal. A strong coupling theory is developed and is used to calculate the vibrational structure of the collective excitation in the Frenkel limit. The frequency dependence of the self-energy of the excitation and dispersion in the optical phonon branch of the vibrational spectrum are included in the analysis. The line shapes in the absorption spectrum of a molecular crystal are considered for the two limiting cases of exciton–phonon coupling—namely weak and strong coupling. One of the topics considered in detail is the damping of the zero phonon transition.

We investigate the statistical properties of superradiant pulses emitted by a system of many atoms. By using a representation of the atomic density operator in terms of directed angular-momentum states (which are also known as atomic coherent states), we find that the statistical behavior of the atoms is formally equivalent to that of a harmonic oscillator subject to linear amplitude amplification and driven by Gaussian white noise. The emitted light pulses are then found to exhibit very large quantum fluctuations for atomic initial states corresponding to complete or nearly complete excitation. For all other atomic initial states the superradiant pulses show classical behavior.

For a multielectron open-shell system exposed to an external time-dependent perturbation, the Hartree–Fock nonstationary equations are obtained in terms of density operators. Using them as a basis, equations of nonstationary “coupled” perturbation theory are suggested in orbital representation within the framework of the two-operator variant of the Roothaan method for an open shell. The perturbation theory corrections to the orbitals have been found in the form of expansions in unperturbed orbitals which are assumed to be calculated in the LCAO approximation in the basis of Slater-type atomic orbitals. The dynamic polarizability of open-shell atoms of substances from Li to F and Sc has been calculated as an even-power series of the frequency of incident radiation.

The relaxation of the muon spin in a free radical is complicated by the presence of several molecular degrees of freedom. In particular, for muonated ethylene, ${\mathrm{C}}_{2}$${\mathrm{H}}_{4}$Mu, which exemplifies the type of free radical that is being considered, the addition product has an unpaired electron, so the motion of the free radical in an external magnetic field is dominated by the precession of the electron spin. This paper formulates a theory for the muon-spin relaxation of such free radicals. It is based on the Boltzmann equation, so it has a rigorous basis by which both free motion (including all of the angular momentum couplings) and the collisional processes (which cause the decay to equilibrium) can be included. A multipole expansion of the density operator in terms of electron, muon, and rotational angular-momentum operators including terms up to quadratic in the rotational angular momentum is used to represent the state of the system. The multipole coefficients in the Hamiltonian are treated as fitting parameters to give a best interpretation of the experimental data for the longitudinal muon-spin relaxation rate of ${\mathrm{C}}_{2}$${\mathrm{H}}_{4}$Mu.

Monitoring fluid absorption using 1% ethanol-tagged glycine during operative hysteroscopy

Measurements of the infrared absorption spectrum of heavily doped p- and n-type germanium in the free carrier concentration range of 4×1017∼9×1019 cm-3 are reported. Both the indirect and the direct absorption edge in the impure samples of both types differ strongly from that in pure germanium. The shift of the indirect absorption edge is larger than the shift of the direct absorption edge in both types. The shift of the direct absorption edge is almost the same value in both cases but the shift of indirect absorption edge in n-type is about twice as large as that in p-type. The absorption due to indirect transitions rises more rapidly with photon energy in the impure samples of both types than in pure germanium. The highest absorption value in the direct absorption region is less than that in the pure sample.