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-.:... --,,",. :c.j I i '- [ > restartiwith(linalg): Warning, the protected names norm and trace have been redefined and unprotected > rot1:=matrix([[k*eo/sqrt(delta"2+k"2*eo"2),0,-delta/sqrt(delta"2+k "2*EO"2)], [0,1,0], [Delta/sqrt(Delta"2+k"2*EO"2),0,k*EO/sqrt(Delta" 2+k"2*EO"2)]])i keo "k2m2 rot I := 0 1 0 t:!. 2.m2 0 0 t:!. -2-k2.m2 keo 2-m2 > rot2:=matrix([[1,0,0], [O,cos(Omega*t),-sin(Omega*t)], [0, sin (Omega* t),cos(omega*t)]])i 0 0 rot2 : cos(.q t) -sin(.q t) 0 sin(.q t) cos(.q t) > rot3:=matrix([[k*eo/sqrt(delta"2+k"2*eo"2),0,delta/sqrt(delta"2+k" 2*EO"2)], [0,1,0], [-Oelta/sqrt(Delta"2+k"2*EO"2),0,k*EO/sqrt(Delta" 2+k"2*EO"2)]])i keo 22.m2 0 t:!. 2-k2m2 rot3 := 0 1 0 t:!. keo -0 2k2-m2 2m 2 > bloch:=rot3.rot2.rot1i k2 E02 t:!. 2 cos(.qt) t:!..sin(.q. t) k EO t:!. t:!. cos(.q. t)k EO + -+ t:!. 2 + k2 E02 t:!. 2 + k2 E02 2k2-m2 t:!. 2 + k2 E02 t:!. 2 + k2 E02 t:!. sin(.q t) k EO sin(.q. t) bloch.-- 22-m2 cos(.q. t).-2 - t:!. +k 2 EO 2 22.m2 L.l A 2+ k2 E0 2 k EO t:!. t:!. cos(.q t)k EO k EO sin(.q. t) t:!.2 k2 E02 cos(.q t) -t:!. 2 + k2 E02 + t:!. 2 + k2 E02 22-EO2 t:!. 2 + k2 E02 + t:!. 2 + k2 E02 > subs(delta=o,bloch)i \cj 'To? f'\."""'- ;i-., L- f 1 r- /\J-' :l(iaj. T' k 't- r at1.- "'" -Q"(.i, IA.. (.Jt pf'j- oj, '1J:lt 'Ic.4113- c- () I

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E(t) 11:/2 11: 0 t1 t )- 2 1/3 t 4 w T2*d) v Initial ground ---'-"" state population u w 11: pulse R u

-- -: > pi2pulse:=matrix([[1,-alpha,-alpha],[alpha,0,1], [-alpha,l,o]]); 1 ked ked > init :=Vector [column] ([0,0, -1] ); pi2pulse:= -0 ked 1 -keij" -1 0 init : : -1 ] > dephase:=matrix([[cos(delta*t21),-sin(delta*t21),0], [sin(delta*t21 ),cos(delta*t21),o], [0,0,1]]); > cos( t21) -sin( t21) 0 dephase:= sin(t21) cos( t21) 0 0 0 1 > pipulse:=matrix([[1,0,-2*alpha], [0,-1,0], [-2*alpha,0,-1]]); 1 0-2 - ked pipulse := 0-1 0-2- 0-1 ked > rephase:=matrix([[cos(delta*t43),-sin(delta*t43),0], [sin(delta*t43 ), cas (Delta*t43), 0], [0,0,1]]) ; [COS( t43) -sin( 143) 0 ] rephase:= sin( t43) cos( t43) 0 0 0 1 > phecho:=rephase.pipulse.dephase.pi2pulse.init; phecho := [(Cos( t43)cos( t21)+sin( t43) sin( t21)) ked + cos( t43) sin( t21) -sin( t43) co.( t21) ] [ (-{:os( t43) sin( t21)+sin( t43)cos( t21)), ked + sin( t43) sin( t21) + cos( t43) cos( t21) ] l [-2 2 cos( t21) -2 sin( t21) k2 E02 ked, [ > \ ]

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