On the use of cross polarization in solid-state NMR:1 H spinlock versus adiabatic demagnetization in the rotating frame

Cross polarization(CP)is a widely used solid-state nuclear magnetic resonance(NMR)technique for enhancing the polarization of dilute S spins from much larger polarization of abundant I spins such as 1 H.To achieve such a polarization transfer,the I spin should either be spin-locked or be converted to the dipolar ordered state through adiabatic demagnetization in the rotating frame.In this work,we analyze the spin dynamics of the Hartmann-Hahn CP(HHCP)utilizing the 1 H spin-locking,and the dipolar-order CP(DOCP)having the 1 H adiabatic demagnetization.We further propose an adiabatic demagnetization CP(ADCP)where a constant radio-frequency pulse is applied on the S spin while 1 H is adiabatically demagnetized.Our analyses indicate that ADCP utilizes the adiabatic passage to effectively achieve the polarization transfer from the 1 H to S spins.In addition,the dipolar ordered state generated during the 1 H demagnetization process could also be converted into the observable S polarization through DOCP,further enhancing the polarized signals.It is shown by both static and magic-angle-spinning(MAS)NMR experiments that ADCP has dramatically broadened the CP matching condition over the other CP schemes.Various samples have been used to demonstrate the polarization transfer efficiency of this newly proposed ADCP scheme.

Effects of notches on the order of flux-closure state formation in bi-rings by micromagnetic simulation

The effects of the number and the location of notches on the formation of flux-closure states in bi-rings with fields applied in the x direction （i.e., along the short axis direction of hi-rings） and y direction （i.e., along the long axis direction of bi-rings） are investigated using micromagnetic simulation. For the bi-rings with one notch and the bi-rings with two notches symmetric about y axis, the order of flux-closure state formation in each ring can be controlled. But the flux-closure state forms simultaneously in each ring for the bi-rings with two notches symmetric about x axis. For the bi-rings with two notches that are symmetric neither about x axis nor about y axis, only one ring can form a flux- closure state in the y-direction field and no fluxclosure state can be found in rings in the x-direction field. Therefore, logic states can be defined by controlling the order of flux-closure state formation, which can be utilized in future logic devices.

The squeezing entangled state of two particles with unequal mass

For two unequal-mass particles,we construct the entangled state representation and then derive the corresponding squeezing operator.This squeezing operator has a natural realization in the entangled state representation,which exhibits the intrinsic relation between squeezing and quantum entanglement.This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings.The maximum squeezing occurs when the two particles possess equal mass.When the two particles＇ mass difference becomes large,the component of the two single-mode squeezings becomes dominant.

New optical field operator expansion in number state representation

By virtue of the Weyl ordering method,we find a new formalism of optical field operator expansion in number state representation.Miscellaneous optical fields＇（coherent state,squeezed field,Wigner operator,etc.） new expansions are therefore exhibited.Some new generating functions of special polynomials are derived herewith.

The feedback control of fractional order unified chaotic system

This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.

Measures of imaginarity and quantum state order

Complex numbers are widely used in classical and quantum physics.Further,they play an important role in describing quantum systems and their dynamical behaviors.Herein,we propose several measures of the imaginarity of quantum states based on l1 norm and convex functions in the framework of resource theory.Further,we investigate the quantum state order after a quantum system passes through a real channel.Rigorous proof shows that these proposed measures possess all the desirable properties for a measure of imaginarity.The connection between the measure of imaginarity based on the l1 norm and the measure of imaginarity based on relative entropy is derived.Moreover,we demonstrate that the l1 norm-based and the relative entropy-based measures of imaginarity are of the same order for qubit quantum states.Further we discuss the influences of the bit flip channel,phase damping channel,and amplitude flip channel on single qubit state order.

Dynamics of coherence-induced state ordering under Markovian channels

We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels： amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qnbit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by l1 norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative α-entropies, while the bit flit channel does change for some special cases.