Radiation field states

To see this connection in more detail we extend the model of Figs 9.1 and Eq. (9.2) to include two discrete states, the ground state g) and an excited state lx), and a continuum of states I/) that may represent the ground state dressed by environmental or radiation field states. We assume that l ) is the only excited state in the relevant spectral region that is radiatively coupled to the ground state g) so it can be initially prepared as explained in Section 9.2.4. In the subspace that encompasses the state [s ) and the continuum Z), the former plays the same role as state 11) in Fig. 9.1. We now focus on the excitation from g to s specifically we pose the question What is the corresponding absorption lineshape ... 

The basis state vectors are expressed as direct products of molecular and radiation field states. In the present discussion, only single particle states are taken into account, which can be separated into the following natural... 

If, instead of (1.12), the total Hamiltonian for the molecule in the presence of light were H = Hq + the eigenstates of the system would become simple products of molecular and radiation field states T (r, t)>IXrad)> where the radiation field states Xrad> would depend on photon occupation numbers, energies and polarizations. Since no coupling of light with molecular states is implied in such a Hamiltonian, no transitions can occur between molecular states due to absorption or emission of light in this description. The simplest Hamiltonian that can account for spectroscopic transitions is therefore the one in Eq. 1.12. 

Probably the most interesting of the pathways shown in Fig. 11.6 is 3. Although this pathway yields state c on the fourth interaction with the radiation field, state b is never actually populated the route proceeds entirely through the coherences pab, Pac and pi,c The pathway should, therefore, be particularly sensitive to dephasing... 

In the previous section we discussed light and matter at equilibrium in a two-level quantum system. For the remainder of this section we will be interested in light and matter which are not at equilibrium. In particular, laser light is completely different from the thennal radiation described at the end of the previous section. In the first place, only one, or a small number of states of the field are occupied, in contrast with the Planck distribution of occupation numbers in thennal radiation. Second, the field state can have a precise phase-, in thennal radiation this phase is assumed to be random. If multiple field states are occupied in a laser they can have a precise phase relationship, something which is achieved in lasers by a teclmique called mode-locking Multiple frequencies with a precise phase relation give rise to laser pulses in time. Nanosecond experiments... 

Semiconductor devices ate affected by three kinds of noise. Thermal or Johnson noise is a consequence of the equihbtium between a resistance and its surrounding radiation field. It results in a mean-square noise voltage which is proportional to resistance and temperature. Shot noise, which is the principal noise component in most semiconductor devices, is caused by the random passage of individual electrons through a semiconductor junction. Thermal and shot noise ate both called white noise since their noise power is frequency-independent at low and intermediate frequencies. This is unlike flicker or ///noise which is most troublesome at lower frequencies because its noise power is approximately proportional to /// In MOSFETs there is a strong correlation between ///noise and the charging and discharging of surface states or traps. Nevertheless, the universal nature of ///noise in various materials and at phase transitions is not well understood. 

Here the sum runs over all possible initial states and the operator describes the interaction of the electrons and the radiation field with wave vector q and polarization A. In Eq. (1) it has been assumed that the detector selectively counts photo electrons with energy E, wave vector k, and spin polarization The corresponding final... 

Here, a primary ion P+ formed by the radiation field reacts with a gas molecule M to give an intermediate complex [PM +] which can either dissociate to a secondary species S + and a neutral fragment N or react with another molecule to produce another complex [PM2 + ]. The latter then dissociates into a tertiary ion T+ or propagates the chain by forming a third intermediate [PM3 + ]. A quaternary ion Q+ may result from dissociation of [PM3 + ], or the chain may continue through reaction of [PM3 + ]. Wexler and Jesse (38), on the other hand, have suggested a model which states that reactive intermediate complexes are not involved in the propagation, but rather the polymerization proceeds by chains of simple consecutive and competitive ion-molecule reactions,... 

Consider a two level atom that initially has a ground state n containing N atoms and an empty upper state m. The atom is then excited by a radiation field tuned to the transition v = Wm — W /h, where hiy kT. In equilibrium, — mn m A i where... 

The new delightful book by Greenstein and Zajonc(9) contains several examples where the outcome of experiments was not what physicists expected. Careful analysis of the Schrddinger equation revealed what the intuitive argument had overlooked and showed that QM is correct. In Chapter 2, Photons , they tell the story that Einstein got the Nobel Prize in 1922 for the explaining the photoelectric effect with the concept of particle-like photons. In 1969 Crisp and Jaynes(IO) and Lamb and Scullyfl I) showed that the quantum nature of the photoelectric effect can be explained with a classical radiation field and a quantum description for the atom. Photons do exist, but they only show up when the EM field is in a state that is an eigenstate of the number operator, and they do not reveal themselves in the photoelectric effect. 

In Science, every concept, question, conclusion, experimental result, method, theory or relationship is always open to reexamination. Molecules do exist Nevertheless, there are serious questions about precise definition. Some of these questions lie at the foundations of modem physics, and some involve states of aggregation or extreme conditions such as intense radiation fields or the region of the continuum. There are some molecular properties that are definable only within limits, for example, the geometrical stmcture of non-rigid molecules, properties consistent with the uncertainty principle, or those limited by the negleet of quantum-field, relativistic or other effects. And there are properties which depend specifically on a state of aggregation, such as superconductivity, ferroelectric (and anti), ferromagnetic (and anti), superfluidity, excitons. polarons, etc. Thus, any molecular definition may need to be extended in a more complex situation. 

NES is an elastic and coherent scattering process, i.e., it takes place without energy transfer to electronic or vibronic states and is delocalized over many nuclei. Owing to the temporal and spatial coherence of the radiation field in the sample. 

In a continuous wave (CW) magnetic resonance experiment, the radiation field B is continuous and BQ is changed only slowly compared with the relaxation rates (so-called slow passage conditions). Thus a steady-state solution to eqns... 

Photons in quantum optical cavities also constitute excellent qubit candidates [52]. Resonant coupling of atoms with a single mode of the radiation field was experimentally achieved 25 years ago [53], and eventually the coherent coupling of quantum optical cavities with atoms or (simple) molecules was suggested as a means to achieve stable quantum memories in a hybrid quantum processor [54]. There might be a role to play for molecular spin qubits in this kind of hybrid quantum devices that combine solid-state with flying qubits. 

In a celebrated paper, Einstein (1917) analyzed the nature of atomic transitions in a radiation field and pointed out that, in order to satisfy the conditions of thermal equilibrium, one has to have not only a spontaneous transition probability per unit time A2i from an excited state 2 to a lower state 1 and an absorption probability BUJV from 1 to 2 , but also a stimulated emission probability B2iJv from state 2 to 1 . The latter can be more usefully thought of as negative absorption, which becomes dominant in masers and lasers.1 Relations between the coefficients are found by considering detailed balancing in thermal equilibrium... 

The system is prepared at t=0 in the quantum state Pik> and the question is how to calculate the probability that at a later time t the system is in the state Fjn>. By construction, these quantum states are solutions of molecular Hamiltonian in absence of the radiation field, Hc->Ho Ho ik> = e k Fik> and H0 Pjn> = Sjn xPJn>. The states are orthogonal. The perturbation driving the jumps between these two states is taken to be H2(p,A)= D exp(icot), where co is the frequency of the incoherent radiation field and D will be a time independent operator. From standard quantum mechanics, the time dependent quantum state is given by ... 

As a result of self-focusing, power propagating within the core f iz) inereases behind the region of unsteady-state regime (Fig. 10). Meanwhile the total power of the light beam calculated within the computational window decreases due to emitting of radiation field outside the window. 

The field of theoretical molecular sciences ranges from fundamental physical questions relevant to the molecular concept, through the statics and dynamics of isolated molecules, aggregates and materials, molecular properties and interactions, and the role of molecules in the biological sciences. Therefore, it involves the physical basis for geometric and electronic structure, states of aggregation, physical and chemical transformations, thermodynamic and kinetic properties, as well as unusual properties such as extreme flexibility or strong relativistic or quantum-field effects, extreme conditions such as intense radiation fields or interaction with the continuum, and the specificity ofbiochemical reactions. 

The Ea for the dissolution of hematite by mercapto carboxylic acids in acid media in the presence of UV radiation was lower (64 5 kj mol ) than that for dissolution in the absence of radiation (94 8 kJ mol ) (Waite et al. 1986). The reaction in both cases was considered to involve formation of an intermediate organic-Fe surface complex which decomposed as a result of intramolecular electron transfer to release Fe". UV irradiation enhanced the decomposition of the surface complex either through excitation of the ligand field states associated with the free electrons on the S atoms, or through high energy charge transfer states. 

---