Decay of multispin multiple-quantum coherent states in the NMR of a solid and the stabilization of their intensity profile with time

Variations, experimentally observed in [14], in the intensity profiles of multiple-quantum (MQ) coherences in the presence of two special types of perturbations are explained on the basis of the theory, earlier developed by the authors, of the growth of the effective size of correlated clusters (the number of correlated spins) and the relaxation of MQ coherent states [23]. The intensity and the character of perturbation were controlled by the experimenters. It is shown that the observed stabilization of profiles with time is not associated with the stabilization of the cluster size. Quite the contrary, a cluster of correlated spins monotonically grows, while the observed variations in the intensity profile and its stabilization with time are attributed to the dependence of the decay rate of an MQ coherence on its order (its position in the MQ spectrum). The results of the theory are in good agreement with the experimental data.     

Growth and decay of multispin coherent states in a solid

Analytic expressions for the arbitrary-order time-correlation functions (TCFs) describing the dynamics of multispin coherent states observed by multiquantum NMR spectroscopy methods are obtained using the approximation developed here. The expression for higher-order TCFs are obtained for the first time in closed form. In further realization of the approach to describing the high-order TCFs developed here, a consistent dynamic theory can be constructed. This considerably distinguishes the approach proposed here from the model calculations performed earlier [10] on the basis of the modified Anderson theory for qualitative interpretation of some experimental results. Our results are in satisfactory agreement with experimental data.     

On the second moment of the multiquantum NMR spectrum of a solid

New experimental data on the time dependence of an increase in the number of correlated spins under the conditions of the observation of the multiquantum NMR spectrum of a solid are processed on the basis of a microscopic theory for describing the growth of the second moment of multiquantum NMR developed by us earlier. As follows from the theory, the growth is an exponential function of time for crystals with quite diverse structures. The results are discussed on the basis of semiphenomenological models.     

Decay of the mixed states

We study the classical escape from local minima for 2d multi-well Hamiltonian systems, realizing the mixed state. We show that escape from such local minima has a diversity of principally new features, representing an interesting topic for conceptual understanding of chaotic dynamics and applications.     

Second moment of multiple-quantum NMR and a time-dependent growth of the number of multispin correlations in solids

The time evolution of multispin correlations (the growth of the number of correlated spins as a function of time) can be observed directly using the multiple-quantum nuclear magnetic resonance spectroscopy of solids. A quantity related to this number, namely, the second moment 〈n ²(t)〉 of the intensity distribution of coherences of different orders in the multiple-quantum spectrum can be calculated using the theory proposed in this work. An approach to the calculation of the four-spin time correlation function through which this moment is expressed is developed. The main sequences of contributions in the expansion of this function into a time power series are summed using the approximation of a large number of neighbors both for systems with a secular dipole-dipole interaction and for systems with a nonsecular effective interaction. An exponential dependence of 〈n ²(t)〉 is obtained. The value of 〈n ²(t)〉 is additionally calculated using an expansion in terms of orthogonal operators for three model examples corresponding to different limiting realizations of spin systems. It is shown that the results of the microscopic theory at least qualitatively agree with both the results obtained for model examples and experimental results obtained recently for adamantane.     

On the coherent states of a free electron laser

The coherence properties of the Free Electron Laser are examined both in the single mode and multimode case.     

Decay of Rydberg states in the field of a highly charged ion

The quasi-stationary spectrum of highly excited (Rydberg) states in the field of a multiply charged ion is calculated in the asymptotic region. The result is used to obtain the electron transfer cross section, within the decay approximation, for the process.     

Decay kinetics of metastable states in a disordered linear system

Kolmogorov’s method for describing statistical crystallization is generalized to take into account disorder in the structure and is applied to the calculation of the decay kinetics of metastable states in linear (in the sense of spatial dimensionality) systems. The theory describes the influence of defects on the dynamics of polymers and domain boundaries between phases on substrates, on crystal growth involving the movement of steps over a surface, on the plastic flow of materials due to the motion of dislocations in a Peierls-Nabarro relief, and on the kinetics of other physical systems. Fiz. Tverd. Tela (St. Petersburg) 41, 1988–1993 (November 1999)     

Decay of metastable states in Nd II

The difficulty associated with an accurate determination of transition rates for forbidden lines in lowly ionized heavy elements is illustrated in the case of Nd II. We have investigated the radiative decay of the low-lying metastable levels in Nd⁺ including the two levels K_11/2 and I_13/2. In these two particular cases, using different theoretical approaches, we find that the decay is dominated by the M1 channels but that the E2 contributions are of the same order of magnitude. These levels have also been studied experimentally by lifetime measurements with the heavy ion storage ring CRYRING of Stockholm University. The difficulties encountered when performing such experiments are underlined and discussed.     

Quantum coherent operators: A generalization of coherent states

We introduce a technique to compare different, but related, quantum systems, thereby generalizing the way that coherent states are used to compare quantum systems to classical systems in semiclassical analysis. We then use this technique to estimate the dependence of the free energy of the quantum Heisenberg model on the spin value, and to estimate the relation between the ferromagnetic and antiferromagnetic free energies.Work supported in part by the U.S. National Science Foundation grant PHY-9019433.Work supported in part by the U.S. National Science Foundation grant DMS-9002416.     

Phonon coherent states in transient phenomena

Phonon coherent states (PCS) are shown to be involved in electronic absorption and emission of light and in non radiative decay of molecules in gases and of centers in solids. The relations giving the absorption and emission coefficients and the non radiative decay rate constant are discussed.     

Amplitude-squared squeezing in superposed coherent states

We study amplitude-squared squeezing of the Hermitian operator Z_θ=Z₁ cosθ+Z₂ sin θ, in the most general superposition state , of two coherent states and . Here operators Z_1,2 are defined by , a is annihilation operator, θ is angle, and complex numbers C_1,2 , α, β are arbitrary and only restriction on these is the normalization condition of the state . We define the condition for a state to be amplitude-squared squeezed for the operator Z_θ if squeezing parameter , where N=a⁺a and . We find maximum amplitude-squared squeezing of Z_θ in the superposed coherent state with minimum value 0.3268 of the parameter S for an infinite combinations with α- β= 2.16 exp [±i(π/4) + iθ/2], and with arbitrary values of (α+β) and θ. For this minimum value of squeezing parameter S, the expectation value of photon number can vary from the minimum value 1.0481 to infinity. Variations of the parameter S with different variables at maximum amplitude-squared squeezing are also discussed.     

Generation of superpositions of coherent states on a circle

We propose a simple method to obtain a superposition of coherent states on a circle, including Schr?dinger cat states as a special case, via conditional measurement of the state of three level atoms interacting with a one mode cavity field. In the low amplitude limit, very good approximation of Fock states can also be generated in this way. Received: 8 October 1998 / Accepted: 30 October 1998     

Darboux transformation of the coherent states of a nonrelativistic free particle

Various systems of soliton-potential coherent states have been derived. Measures are found that realize the expansion of a unit operator in terms of projectors on these states. Two different realizations of Hilbert state space are constructed as functions holomorphic throughout the complex plane and with a certain constraint on their increase. Tomsk State University and Tomsk State Pedagogic University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 42, No. 2, pp. 19–25, February, 1999.     

Universal scheme for finite-probability perfect transfer of arbitrary multispin states through spin chains

In combination with the theories of open system and quantum recovering measurement, we propose a quantum state transfer scheme using spin chains by performing two sequential operations: a projective measurement on the spins of ‘environment’ followed by suitably designed quantum recovering measurements on the spins of interest. The scheme allows perfect transfer of arbitrary multispin states through multiple parallel spin chains with finite probability. Our scheme is universal in the sense that it is state-independent and applicable to any model possessing spin–spin interactions. We also present possible methods to implement the required measurements taking into account the current experimental technologies. As applications, we consider two typical models for which the probabilities of perfect state transfer are found to be reasonably high at optimally chosen moments during the time evolution.