Spectral density quantum limits

In optical domain, preamplifier is no more an utopia and is in actual use in fiber communication. However quantum physics prohibits the noiseless cloning of photons an amplifier must have a spectral density of noise greater than 1 photon/spatial mode (a "spatial mode" corresponds to a geometrical extent of A /4). Most likely, an optical heterodyne detector will be limited by the photon noise of the local oscillator and optical preamplifier will not increase the detectivity of the system. 

An analytical theory of the outer-sphere PRE for slowly rotating systems with an arbitrary electron spin quantum number S, appropriate at the limit of low field, has been proposed by Kruk et al. (144). The theory deals with the case of axial as well as rhombic static ZFS. In analogy to the inner sphere case (95), the PRE for the low field limit could be expressed in terms of the electron spin spectral densities s ... 

Here we apply the LAND-map approach to compute of the time dependent average population difference, A t) = az t)), between the spin states of a spin-boson model. Here az = [ 1)(1 — 2)(2 ]. Within the limits of linear response theory, this model describes the dissipative dynamics of a two level system coupled to an environment [59,63-65]. The environment is represented by an infinite set of harmonic oscillators, linearly coupled to the quantum subsystem. The characteristics of the system-bath coupling are completely described by the spectral density J(w). In the following, we shall restrict ourselves to the case of an Ohmic spectral density... 

An important achievement of the early theories was the derivation of the exact quantum mechanical expression for the ET rate in the Fermi Golden Rule limit in the linear response regime by Kubo and Toyozawa [4b], Levich and co-workers [20a] and by Ovchinnikov and Ovchinnikova [21], in terms of the dielectric spectral density of the solvent and intramolecular vibrational modes of donor and acceptor complexes. The solvent model was improved to take into account time and space correlation of the polarization fluctuations [20,21]. The importance of high-frequency intramolecular vibrations was fully recognized by Dogonadze and Kuznetsov [22], Efrima and Bixon [23], and by Jortner and co-workers [24,25] and Ulstrup [26]. It was shown that the main role of quantum modes is to effectively reduce the activation energy and thus to increase the reaction rate in the inverted... 

An alternative way to obtain the spectral density is by numerical simulation. It is possible, at least in principle, to include the intramolecular modes in this case, although it is rarely done [198]. A standard approach [33-36,41] utilizes molecular dynamics (MD) trajectories to compute the classical real time correlation function of the reaction coordinate from which the spectral density is calculated by the cosine transformation [classical limit of Eq. (9.3)]. The correspondence between the quantum and the classical densities of states via J(co) is a key for the evaluation of the quantum rate constant, that is, one can use the quantum expression for /Cj2 with the classically computed J(co). This is true only for a purely harmonic system [199]. Real solvent modes are anharmonic, although the response may well be linear. The spectral density of the harmonic system is temperature independent. For real nonlinear systems, J co) can strongly depend on temperature [200]. Thus, in a classical simulation one cannot assess equilibrium quantum populations correctly, which may result in serious errors in the computed high-frequency part of the spectrum. Song and Marcus [37] compared the results of several simulations for water available at that time in the literature [34,201] with experimental data [190]. The comparison was not in favor of those simulations. In particular, they failed to predict... 

Due to intrinsic computational complexity of quantum and even semiclassical calculations only the simplest models of bath relaxation are usually employed, namely, the Debye and Ohmic models, as discussed in Section II.A.2. It should be emphasized that these models fail to reproduce Marcus s energy gap dependence in the inverted region. For example, the Debye model predicts in the Golden Rule limit that fei2 (AG-l- ,) for AG — [21]. The Ohmic model gives minus fifth power. This illustrates the importance of the cutoff function for the spectral density. 

HgCdTe photodiode performance for the most part depends on high quantum efficiency and low dark current density (83,84) as expressed by equations 23 and 25. Typical values of at 77 K ate shown as a function of cutoff wavelength in Figure 16 (70). HgCdTe diodes sensitive out to a wavelength of 10.5 p.m have shown ideal diffusion current limitation down to 50 K. Values of have exceeded 1 x 10 . Spectral sensitivities for... 

This sensitivity value has to be considered as an upper limit for monoquantum processes without amplification because restrictive factors such as radiationless decays of the excited state A, emission processes such as fluorescence and phosphorescence, degradation reactions and spectral Interference have to be taken Into account for each chemical system, limiting In several ways the value of the Imaging quantum yield. A rather similar calculation made by Jackson (1) In the case of photochro-mlc systems gives a limiting sensitivity value of 7 x 10 ergs/cm for an optical density of 2 at 330 nm. 

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