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Density matrix detection

In the usual preparatioii-evohition-detection paradigm, neither the preparation nor the detection depend on the details of the Hamiltonian, except hi special cases. Starthig from equilibrium, a hard pulse gives a density matrix that is just proportional to F. The detector picks up only the unweighted sum of the spin operators,... [Pg.2101]

The observable NMR signal s(t), detected in the quadrature mode, is related to the density matrix p t) at time t as follows ... [Pg.127]

Nuclear spin relaxation is considered here using a semi-classical approach, i.e., the relaxing spin system is treated quantum mechanically, while the thermal bath or lattice is treated classically. Relaxation is a process by which a spin system is restored to its equilibrium state, and the return to equilibrium can be monitored by its relaxation rates, which determine how the NMR signals detected from the spin system evolve as a function of time. The Redfield relaxation theory36 based on a density matrix formalism can provide... [Pg.73]

The necessary summations reflect the fact that no complete information exists with respect to these magnetic quantum numbers statistically significant information can be derived from initial states with all quantum numbers M-, represented with equal probability, l/(2Jj + 1), the detection of final states with quantum numbers Mf being independent of the actual Mf value, and the summations over Mj and Mf taking care of all possible combinations of matrix elements leading from Mj to Mf substates. The appropriate formalism for such statistical information is that of density matrices. In the special representation in which the basic states for defining the density matrix coincide with the actual states of the ensemble, one obtains forms for the density matrices which are easy to interpret the density matrix attached to the initial, randomly oriented state has the following... [Pg.340]

In the final state the property of the detector is important. Since the relevant density matrix depends upon this detection efficiency, it is called the efficiency matrix < f>. In the present example the detection efficiency is independent of Mf, and one gets... [Pg.341]

The explanation of this phenomenon is clearly visible from the calculation based on the simulation of average density matrix. In this case, Equation (10) can be solved analytically. The detected frequencies and the linewidth of the signals are given by the real and the imaginary part of the following expression 106... [Pg.194]

At time point t (in the rth time slice, meaning t° l < f < t(n), the density matrix can be calculated from // l according to Equation (43), and so the detected signal at time point t is given as ... [Pg.202]

Further propagation should be calculated from this matrix. The detected signal can be calculated from the transformed density matrix as ... [Pg.204]

Figure 11 Simulation of the fid of a spin set. (A) Individual density matrix is calculated at each exchange point. (B) Eigencoherence representation of the density matrix is propagated from the beginning of the time slice for each detection point. Figure 11 Simulation of the fid of a spin set. (A) Individual density matrix is calculated at each exchange point. (B) Eigencoherence representation of the density matrix is propagated from the beginning of the time slice for each detection point.
After that conversion precessions restart with the frequencies of the new conformer (E).This interpretation of the vector model shown in Figure 14 describes the evaluation of the elements of the density matrix only but not the detected signal. The FID is calculated from the actual elements of the eigenfunction representation of the density matrix (that is the (t) vector) as ... [Pg.210]

Applying this approach to Eq. (19), the density matrix Eq. (17), during the detection period, has the form... [Pg.335]

In order to evaluate Eq. (39) we need some detailed knowledge of the density matrix p(t). This operator will contain information about the prior evolution in the applied magnetic field gradients as well as contain information about the relaxation processes and the NMR free precession spectrum. In order to handle this complexity it is very helpful to separate the prior evolution domain from the detection domain. [Pg.337]

We now turn to a quantitative examination of the feasibility of conditional Fock state generation using our preparation and retrieval technique. For applications in long-distance quantum communication, the quality of the atomic state preparation is the most important quantity. Assuming perfect atom-photon correlations in the write Raman processes, we can find the density matrix p for the number of atomic spin-wave excitations conditioned on the detection of ns Stokes photons. Here we consider only the spin-wave modes correlated with our detection mode. For example, in the absence of losses and background, the conditional atomic density matrix is simply p(ns) = ns)(ns. Loss on the Stokes channel (characterized by transmission coefficient a.s) leads to a statistical mixture of spin-wave excitations,... [Pg.74]

In MQMAS the isotropic component of the phase accumulated by the detectable elements of the density matrix at the echo (or antiecho) position is governed by both MQ and SQ evolution periods. The angular frequency of the spectral line in Fi of each quadrupolar site may be conveniently expressed as... [Pg.116]

By using the density-matrix formalism for calculation of the detected signal, the evolution of the double-quantum part p2Q of the density matrix during the double-quantum space-encoding period t is needed as an intermediate result [Gun2, Gotl],... [Pg.348]

The enormous improvement in the nuclear spin polarization achievable by these optical approaches has great potential to impact conventional NMR smdies in a variety of ways. Besides simply increasing the detection sensitivity of NMR, the enhanced nuclear spin polarization may be useful for obtaining enhanced spectral selectivity (e.g., for some spatial, structural, or dynamical feature of a sample) enhanced contrast and resolution in MRI and improved density matrix purity (e.g., for NMR quantum computation). Finally, it is worth noting that the optical fields used in some of these methods can be gated, thereby permitting time-resolved studies that would not be possible with conventional NMR approaches. [Pg.303]

Figure 26. Experimental scheme of two-dimensional NMR spectroscopy, (a) The general scheme of two-dimensional spectroscopy. Here, t, and become two variables of two-dimensional response signals. H and are the Hamiltonians during t, and tj periods, Figure 26. Experimental scheme of two-dimensional NMR spectroscopy, (a) The general scheme of two-dimensional spectroscopy. Here, t, and become two variables of two-dimensional response signals. H and are the Hamiltonians during t, and tj periods, <t(0) is the initial density matrix after the preparation and R represents a mixing operator, (b) One realization of two-dimensional NMR spectroscopy which elucidates the spin connectibility of coupled nuclei called two-dimensional correlated NMR spectroscopy. Here, the first 90° pulse is used to prepare the initial magnetization (or initial density matrix) and the second pulse is applied to mix two transitions (precession frequencies) evolved during the two successive time periods, the evolution period and the detection period (from [73]).
The two-photon correlations stored in the pure TPE state can be measured by detecting fluctuations of the fluorescence field emitted by the atomic system. Squeezing in the fluorescence field is proportional to the squeezing in the atomic dipole operators (squeezing in the atomic spins) which, on the other hand, can be found from the steady-state solutions for the density matrix elements. [Pg.263]

This result is now applied to calculating which elements of the density matrix actually contribute to the detectable signal. Assuming quadrature detection, the detectable magnetization is proportional to (Ix + zTy), which according to equation (18) is Tr (er(Ix + zly)). Using equation (12) it is simple to show that... [Pg.218]

Equation (19) shows that only single-quantum transitions are detectable as transverse magnetization. In order to detect the ia and —ia triple-quantum terms they must be moved into the single-quantum elements of the density matrix. This is the formation of the final 7r/2y pulse. The density matrix after this pulse is... [Pg.226]

Figure 4. PEELS line scan of the craze bands observed in BCB-MI. A sharp transition in density is detected at the boundaries between the dilatation bands and the matrix. The slight increase in density at the center region of the bands may result from the stretched molecules inside the dilatation bands partially snapping back after unloading. Figure 4. PEELS line scan of the craze bands observed in BCB-MI. A sharp transition in density is detected at the boundaries between the dilatation bands and the matrix. The slight increase in density at the center region of the bands may result from the stretched molecules inside the dilatation bands partially snapping back after unloading.
The detection of NMR signals is based on the perturbation of spin systems that obey the laws of quantum mechanics. The effect of a single hard pulse or a selective pulse on an individual spin or the basic understanding of relaxation can be illustrated using a classical approach based on the Bloch equations. However as soon as scalar coupling and coherence transfer processes become part of the pulse sequence this simple approach is invalid and fails. Consequently most pulse experiments and techniques cannot be described satisfactorily using a classical or even semi-classical description and it is necessary to use the density matrix approach to describe the quantum physics of nuclear spins. The density matrix is the basis of the more practicable product operator formalism. [Pg.22]

The hyperfine properties can thus be computed once the unpaired ground state spin density matrix Pa-/3 is obtained. In solution, where the anisotropic terms are averaged due to molecular tumbling, only isotropic couplings are detectable, and their values are given by the relation Aiso = (l/3)lr T. In a solid, however, the anisotropic effects are observable. It should be noted that although the calculation of the isotropic hf couplings require the spin-density to be evaluated at the position of the nucleus only, the... [Pg.314]

The microwave detected MODR scheme closely resembles pulsed nuclear magnetic resonance (Hahn, 1950), optical coherent transients by Stark switching (Brewer and Shoemaker, 1971) and laser frequency switching (Brewer and Genack, 1976). The on-resonance microwave radiation field, ojq = ( 2 — Ei)/H, creates an oscillating bulk electric dipole polarization (off-diagonal element of the density matrix, pi2(t)). The oscillation is at u>o u>r, where ojr is the (Mj-dependent) Rabi frequency,... [Pg.435]


See other pages where Density matrix detection is mentioned: [Pg.292]    [Pg.70]    [Pg.422]    [Pg.201]    [Pg.202]    [Pg.202]    [Pg.250]    [Pg.287]    [Pg.436]    [Pg.190]    [Pg.153]    [Pg.8]    [Pg.98]    [Pg.46]    [Pg.443]    [Pg.162]    [Pg.170]    [Pg.166]    [Pg.2]    [Pg.435]   
See also in sourсe #XX -- [ Pg.639 ]




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