The quantum radiation field

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 ... 

The interacting waves from myriads of charge centres constitute the electromagnetic radiation field. In particle physics the field connection between balanced charge centres is called a virtual photon. This equilibrium is equivalent to the postulated balance between classical and quantum potentials in Bohmian mechanics, which extends holistically over all space. 

Thus far we have dealt with the idealized case of isolated molecules that are neither -subject to external collisions nor display spontaneous emission. Further, we have V assumed that the molecule is initially in a pure state (i.e., described by a wave function) and that the externally imposed electric field is coherent, that is, that the " j field is described by a well-defined function of time [e.g., Eq. (1.35)]. Under these. circumstances the molecule is in a pure state before and after laser excitation and S remains so throughout its evolution. However, if the molecule is initially in a mixed4> state (e.g., due to prior collisional relaxation), or if the incident radiation field is notlf fully coherent (e.g., due to random fluctuations of the laser phase or of the laser amplitude), or if collisions cause the loss of quantum phase after excitation, then J phase information is degraded, interference phenomena are muted, and laser controi. is jeopardized. < f... 

T ) obtain the Schrodinger equation for the interaction of a molecule with the quanted radiation field, that is, the Schrodinger equation for the (matter + radiation) fr steni. we need the quantum analog of 77MR, the matter-radiation interaction, hi the 1,1 pole approximation HMR depends, according to Eq. (1.51), on the transverse... 

Now we will introduce quantum electrodynamics. Just as we quantized the atoms and molecules, we must also quantize the electromagnetic radiation field, to deal with field-molecule interactions properly [14,34],... 

This, plus the quantization of the normal modes of vibration of the electromagnetic radiation field (just demonstrated), form, together, the quantum-mechanical basis for the wave-particle duality A wave can become a particle, and vice versa, but you can never make a simultaneous experiment to test both the wave and the particle nature of the same system. 

Photodissociation and exchange reactions are the primary destruction process for interstellar molecules. If photodecomposition is considered to be the only destruction mechanism, then the lifetime of interstellar molecules depends upon three factors the absorption cross section, the quantum yield of dissociation and the interstellar radiation field. A quantitative discussion of this destruction mechanism has been given by Stief (1971) for two diatomic and eight polyatomic molecules. 

The Rayleigh-Jeans picture of the radiation field as an ensemble of different modes of vibration confined to an enclosure was applied to the blackbody problem in Chapter 1. The quantum theory of radiation develops this correspondence more explicitly, identifying each mode of the electromagnetic field with an abstract harmonic oscillator of frequency coa- The Hamiltonian for the entire radiation field can be written... 

The simplest way to show the principal difference between the representations of plane and multipole photons is to compare the number of independent quantum operators (degrees of freedom), describing the monochromatic radiation field. In the case of plane waves of photons with given wavevector k (energy and linear momentum), there are only two independent creation or annihilation operators of photons with different polarization [2,14,15]. It is well known that QED (quantum electrodynamics) interprets the polarization as given spin state of photons [4]. The spin of photon is known to be 1, so that there are three possible spin states. In the case of plane waves, projection of spin on the... 

In this approximation, the molecular hamiltonian is coupled to the radiation field by the three latter terms. They define the molecule-radiation field coupling opo ator, U. The linear term in A acts as external perturbation on the quantum states of Hm prompting for the passage among different eigenstates of Hm. 

Abstract Rapid advances in quantum technology have made possible the control of quantum states of elementary material quantum systems, such as atoms or molecules, and of the electromagnetic radiation field resulting from spontaneous photon emission of their unstable excited states to such a level of precision that subtle quantum electrodynamical phenomena have become observable experimentally. Recent developments in the area of quantum information processing demonstrate that characteristic quantum electrodynamical effects can even be exploited for practical purposes provided the relevant electromagnetic field modes are controlled by appropriate cavities. A central problem in this context is the realization of an ideal transfer of quantum information between a state of a material quantum system and a quantum... 

It turns out that the spontaneous lifetime of the Rydberg levels is shortened if the cavity is tuned into resonance with the frequency a>o of the atomic transition n) n — 1). liis prolonged if no cavity mode matches coq [1297]. This effect, which had been predicted by quantum electrodynamics, can intuitively be understood as follows in the resonant case, that part of the thermal radiation field that is in the resonant cavity mode can contribute to stimulated emission in the transition n) n — 1), resulting in a shortening of the lifetime (Sect. 6.3). For the... 

From this expression, it is seen that the temporal properties of the incident radiation field depend upon the coherence time Atg and the pulse duration AT. It must be pointed out that the physical nature of these times is essentially different. For a given source, At is imposed by the uncertainty principle of quantum theory, whereas AT corresponds to a classical statistical probability distribution, which can in principle be modified by the experimenter. In particular, if one reduces this classical uncertainty" sufficiently, the time resolution conditions can be improved so as to have the lowest possible resolution time given by the quantal uncertainty" value At. This corresponds to the minimum time uncertainty situation, for which one has S(fo) (to) and therefore p to) a(to)-The spectral properties of the incident beam are best described by... 

This effect, which had been predicted by quantum electrodynamics, can intuitively be understood as follows In the resonant case that part of the thermal radiation field which is in the resonant cavity mode, can contribute to stimulated emission in the transition n) n-l) resulting in a... 

Unlike thermal detectors, which sense the power of the absorbed radiation, photon detectors respond to the number of photons arriving per unit time. Photon as well as thermal detectors are incoherent transducers, which means that the detection process is independent of the wave properties of the incident radiation field. Incoherent detectors produce an electrical signal proportional to the intensity of the radiation. In contrast, coherent detectors, such as the nonlinear elements in heterodyne receivers discussed in Section 5.9, register the amplitude and phase of the electric field associated with the absorbed radiation. Due to the simultaneous measurement of amplitude and phase, coherent detection is subject to a fundamental noise limit that has its origin in the quantum mechanical uncertainty principle. Incoherent detectors are free of this particular limit. However, as we shall see, they are subject to othernoise sources. 

The Poynting vector has a dual role for it can be shown that the electromagnetic radiation fields transport momentum as well as energy, and tliat the momentum density is given by R/c. This relationship is most easily derived by making use of the idea tliat radiation consists of photons of energy hu whose momentum in vacuo is tioi/c, which follows from the quantum theory of radiation (Problem 2.7). 

This effect may be explained in terms of the quantum theory of electrodynamics. According to this theory each mode of the quantized radiation field possesses a zero-point energy of hu)/2. This implies that, even in the absence of external radiation, the mean square value of the time-depen-dent electric field is finite and that a hydrogen atom will experience a perturbation produced by the fluctuations in this field. These zero-point fluctuations cause the electron to wobble randomly in its orbit and so smear the charge over a greater volume of space. Since the electron is bound to the nucleus by a non-uniform electric field, the reduction in electron density causes a shift in the atomic energy levels. This Lamb shift, as it is now called, is greatest for those states in which iK0) is finite, i.e. the n states. 

It was found that that in the case of soft beta and X-ray radiation the IPs behave as an ideal gas counter with the 100% absorption efficiency if they are exposed in the middle of exposure range ( 10 to 10 photons/ pixel area) and that the relative uncertainty in measured intensity is determined primarily by the quantum fluctuations of the incident radiation (1). The thermal neutron absorption efficiency of the present available Gd doped IP-Neutron Detectors (IP-NDs) was found to be 53% and 69%, depending on the thicknes of the doped phosphor layer ( 85pm and 135 pm respectively). No substantial deviation in the IP response with the spatial variation over the surface of the IP was found, when irradiated by the homogeneous field of X-rays or neutrons and deviations were dominated by the incident radiation statistics (1). 

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... 

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