The antiphase term 211yl2z can be re-written using the single-element operators Ia und IB 2l12z2=I1y2-ly2B341 (21,=IQ-IB, Ia+IB=1; I@ und IP are called polarization operators The antiphase state 2I1yI2z consists of two separate populations for one half of the molecules in the ensemble spin 1 is in +y coherence(when spin 2 is in the a state), for the other half spin 1 is in -y coherence(with spin 2 in the B state); " spin 1 is in antiphase with respect to spin 2 Such an antiphase state can develop from Iix when spin 1 is J-coupled to spin 2. This leads to a dublet for spin 1, i.e., it splits into two lines with an up- and downfield shift by/2, depending on the spin state of the coupling partner, spin 2. If we wait long enough(/2J), then the frequency difference of J between the dublet lines ( I2a and Iix I2B)has brought them 180 out of phase C"antiphase"), as shown in the vector diagram I,I,sinπJt 1, (L, COsTJt (I1cosπJt IsinπJt) lsinπJt) I,cosπJt This is an oscillation between Iix in-phase coherence and 2lly I2z antiphase coherence. The antiphase component evolves with sin(/y) and then refocusses back to -Iix in-phase coherence(after t=3) Single-element operators In some cases(phase cycling, gradient coherence selection) it is necessary to use operators with a defined coherence order(Eigenstates of coherence order ) Coherence order describes the changes in quantum numbers mz caused by the coherence. A spin-12 system(no coupling) can assume two coherent states: a transition from a(m2+/2)to B(m2-72), i.e., a change(coherence order)of-132 The antiphase term 2I1yI2z can be re-written using the single-element operators Ia und Ib: 2I1yI2z = I1yI2 a - I1yI2 b [3-14] (2Iz = Ia - Ib, Ia + Ib = 1; Ia und Ib are called polarization operators ) The antiphase state 2I1yI2z consists of two separate populations: for one half of the molecules in the ensemble spin 1 is in +y coherence (when spin 2 is in the a state), for the other half spin 1 is in -y coherence (with spin 2 in the b state); "spin 1 is in antiphase with respect to spin 2". Such an antiphase state can develop from I1x when spin 1 is J-coupled to spin 2. This leads to a dublet for spin 1, i.e., it splits into two lines with an up- and downfield shift by J /2, depending on the spin state of the coipling partner, spin 2. If we wait long enough ( 1 /2J ), then the frequency difference of J between the dublet lines (I1x I2a and I1x I2b ) has brought them 180° out of phase ("antiphase"), as shown in the vector diagram. This is an oscillation between I1x in-phase coherence and 2I1y I2z antiphase coherence. The antiphase component evolves with sin(pJt) and then refocusses back to -I1x in-phase coherence (after t= 1 /J ). Single-element operators In some cases (phase cycling, gradient coherence selection) it is necessary to use operators with a defined coherence order (Eigenstates of coherence order). Coherence order describes the changes in quantum numbers mz caused by the coherence. A spin-1 /2 system (no coupling) can assume two coherent states: a transition from a (mz=+1 /2) to b (mz=- 1 /2), i.e., a change (coherence order) of -1