Zeeman coherence

The spin state of a paramagnetic system with total spin S wiU lift its (25 + l)-fold degeneracy under the influence of ligand fields (zero-field interaction) and applied fields (Zeeman interaction). The magnetic hyperfine field sensed by the iron nuclei is different for the 25 + 1 spin states in magnitude and direction. Therefore, the absorption pattern of a particular iron nucleus for the incoming synchrotron radiation and consequently, the coherently scattered forward radiation depends on how the electronic states are occupied at a certain temperature. 

Figure 7.2 Schematic representation of coherent oscillations between states 0) and 1) of a qubit. For an electron spin placed in a dc magnetic field, oscillations can be induced via the application of an external radio frequency (rf) pulse resonant with the Zeeman energy. The amplitude 8 of the...

A closely related phenomenon to that described is the observation of quantum beats167-160 in the radiative decay of a set of coherently excited states. Since transitions to the ground state can take place via two or more channels, interference effects may be observed. As an example, in Figure 23 we present the decay curve obtained by Dodd et al.180 for the decay of the coherently excited Zeeman levels of Cd. 

The partial recovery of the quantum phase coherence of nuclear dipoles originates from the non-commutative property of the Zeeman energy with the quantum operator which represents the residual interaction after rotating the spins. This rotation has no effect on the magnetisation dynamics when the residual interaction, hHR, is equal to zero. No... 

So far we have been discussing magnetic (Zeeman) quantum beats taking place at frequencies of coherent sublevel splitting in an external magnetic field. 

The non-diagonal submatrices j j>p and j>j p describe the optical coherences between the magnetic sublevels of the states J" and J. The submatrices j j"P and j>j>p describe the particles on levels J" and J respectively. Their diagonal elements characterize the populations of the respective sublevels M" and M, whilst the non-diagonal elements describe the Zeeman coherences. 

Mlynek, J., Drake, K.H. and Lange W. (1979). Observation of transient and stationary Zeeman coherence by polarization spectroscopy, Proc. IV Intern. Conf. Optical Sciences, Tegemsee.—Berlin Springer, pp. 616-618. 

To maintain thermal stability, hence a condition EB/kBT= In (for) needs to be fulfilled. For z = 10 years storage, 109-10u Hz [28] and ignoring dispersions, i.e. assuming monodisperse particles, this becomes Es/kBT= 40-45. Reversal for isolated, well-decoupled grains to first order can be described by coherent rotation over EB. This simple model, as first discussed by Stoner and Wohlfarth in 1948 [29], considers only intrinsic anisotropy and external field (Zeeman) energy terms. For perpendicular geometry one obtains the following expression ... 

Now let s look at something we do not know the answer to the ideal isotropic mixing Hamiltonian. This is the ideal TOCSY mixing sequence that leads to in-phase to in-phase coherence transfer. The ideal sequence of pulses creates this average environment expressed by the Hamiltonian. The Zeeman Hamiltonian that represents the chemical shifts goes away and we have only the isotropic (i.e., same in all directions) /-coupling Hamiltonian ... 

The major advantage of ultracold trapped hydrogen is that one may be able to achieve a coherence time comparable with the natural lifetime, 122 ms. As described in H-l, [16], The magnetic trapping fields can be reduced to a level where the residual Zeeman shift of the transition is on the order of the natural linewidth of 1.3 Hz. The light-induced shift and the photoionization rate can be reduced to the same level. 

If the ojjtical field that excites atoms or molecules is strong enough, it can create Zeeman coherences not only in the excited state of atoms or molecules, but also in the ground state. In a slightly different context this effect for the first time was studied as an optical pumping of atomic states. 

Figure 9b shows that for small Cq values, the two-component behavior, as predicted by Eq. (13), is readily apparent. With increasing magnitude of Cq, however, the REDOR response is successively attenuated, reflecting the fact that the spins in the outer 3/2> Zeeman states are less and less affected by the n(I) pulses. Note that the simulated curves approach the limiting cases (calculated via Eq. 13) of entirely non-selective irradiation of all the Zeeman states (upper dotted curve) and entirely selective irradiation of the l/2> -l/2> coherence (lower solid curve) of the I-nuclei. Extending now the initial curvature analysis approach discussed above to Fig. 9b, the early parts of these REDOR curves can be approximated by a sum of parabolic functions ... 

Zubairy 2002], allowing for the implementation of //gr-qubit logic gates. For the coherently driven atoms, the order of these nonlinearities is associated with the order of ground state coherence of the atomic Zeeman sublevels. Thus, the detection and characterization of the decoherence rate of high order atomic coherences is of vital practical importance. The article by Yu. P. Malakyan et al. is devoted to the issue of production and detection of the high order atomic coherences. 

We consider the NMOR in coherent atomic media, where the basic mechanism of NMOR is the laser-induced coherence between the Zeeman sublevels of atomic ground state and, hence, the detected NFS is sensitive to the damping rate of atomic coherence. An atomic transition is chosen such that both A- and M-systems are created. Under usual conditions, the contributions of these systems to the Faraday signal cannot be separated, because their manifestations are similar. On the other hand, it is well known that for a given state the highest order atomic coherence is uniquely associated with the atomic polarization moment (PM) of the same order. This means that if we are able to detect the NMOR signal separately from different PM, the corresponding atomic coher-... 

Coherent forward scattering (CFS) atomic spectrometry is a multielement method. The instrumentation required is simple and consists of the same components as a Zeeman AAS system. As the spectra contain only some resonance lines, a spectrometer with just a low spectral resolution is required. The detection limits depend considerably on the primary source and on the atom reservoir used. When using a xenon lamp as the primary source, multielement determinations can be performed but the power of detection will be low as the spectral radiances are low as compared with those of a hollow cathode lamp. By using high-intensity laser sources the intensities of the signals and accordingly the power of detection can be considerably improved. Indeed, both Ip(k) and Iy(k) are proportional to Io(k). When furnaces are used as the atomizers typical detection limits in the case of a xenon arc are Cd 4, Pb 0.9, T11.5, Fe 2.5 and Zn 50 ng [309]. They are considerably higher than in furnace AAS. 

If evolves under a field gradient applied along the z-direction parallel to the static magnetic field, the evolution of spin coherences under the Zeeman interaction leads to changes described by the transformation... 

In order to begin to understand the ideas behind, and information available from experiments probing MQCOH in polymers, let us remind ourselves of the meaning of phase coherence in quantum mechanics. We start with the simplest case, a noninteracting ensemble of spin j systems, and with spin basis functions that are eigen functions of the largest interaction present, the Zeeman Hamiltonian These are I, m) =, ) = a), and, - ) = )3). A spin 2 system will have single particle wavefunction... 

A good introduction to electro- and magneto-optical effects can be found in the book by Harvey on Coherent Light [158]. The main effects and the relationship between them are indicated in table 4.1. Many atoms are readily produced as vapour columns, using standard laboratory methods [159]. The natural mode in which to conduct experiments on unperturbed free atoms is therefore in transmission. As table 4.1 emphasises (the reason is given below), the Faraday effect contains equivalent information to the Zeeman effect in transmission. Actually, what Harvey calls the Zeeman effect in transmission is usually referred to as the inverse Zeeman effect [160], to distinguish it from the Zeeman effect observed in emission.5... 

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