In this article we have considered the effect of a magnetic field, the Zeeman effect, nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) on nuclei with spin S ½ looked.Then energy levels, transition frequencies and the energy spectra for the nuclear spins have specified.After using the group definition SU(2), SU(3), SU(4), SU(N) OR SU(2S+1), In quantum mechanics and quantum computation the range nuclear energy levels sin to one qubit, qutrit and qudit assign.We have defined the quantum states.
We report a detailed study of the longitudinal relaxation of several coherent states on the nuclear-magnetic-resonance (NMR) two-qubit quadrupole system,
23Na (spin 3/2) in a lyotropic liquid-crystal system at room temperature. Relaxation of pseudopure states, simulated pseudo-Bell states and Hadamard states were investigated. The coherence of superposition states was verified by applying the respective quantum ``reading'' operators and comparing the recovered state with the original one. The degree of recovery varies between $\ensuremath{\approx}70%$ and $\ensuremath{\approx}100%,$ depending on the time length of the gate, as compared to relaxation times. Spin-lattice relaxation results follow a recently proposed multiexponential model that includes mixed magnetic dipolar and electric quadrupolar interactions. Relaxation curves are governed by initial conditions, and from the experimental curves individual transition rates are derived. The transverse relaxation time constant
T2 is found not to depend on the initial distribution of populations. This is a systematic study of relaxation in the context of NMR quantum computing.
Nuclear-magnetic-resonance gyroscopes that detect rotation as a shift in the precession frequency of nuclear spins have attracted a lot of attention. Under a feedback-generated drive, the precession frequency in the steady state is supposed to be dependent only on the angular momentum and an applied magnetic field. However, nuclei with spins larger than 1/2 experience electric quadrupole interaction with electric-field gradients at the cell walls. This quadrupole interaction shifts the precession frequencies of the nuclear spins, which brings inaccuracy to the rotation measurement as the quadrupole interaction constant
Cq is difficult to precisely measure. In this paper, the effects of quadrupole interaction on nuclear-magnetic-resonance gyroscopes are theoretically studied. We find that, when the constant
Cq is small compared to the characteristic decay rate of the system, which is the case in most gyroscopes for practical use, as the strength of the feedback-driving field increases, the quadrupole shift monotonically decreases, regardless of the system parameters in including
Cq. Furthermore, the larger driving amplitude can reduce the quadrupole shift's fluctuation caused by fluctuations of the system parameters, and, thus, it can reduce systematic errors resulted from the quadrupole interaction. In the large-
Cq regime, more than one precession frequency exists, and the nuclear spins may precess with a single frequency or multifrequencies depending on initial conditions. In this regime with large driving amplitudes, the nuclear spin can restore the single-frequency precession. These results are obtained by solving an effective master equation of the nuclear spins in a rotating frame from which both the steady-state solutions and the dynamics of the system are shown.