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CH_4_state_vector.f95
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!! gfortran CH_4_state_vector.f95 -o CH_4 -lfftw3
!! just for test
module para
implicit none
complex*8 :: imag = sqrt((-1.0,0.0))
real*8 :: pi = 4.0 * atan(1.0)
integer :: i , j, p, q
!!!!! Unit of frequency is 10^14 HZ !!!!!!!
! the atomic energy level frequencies
real(8) :: w_a = 5.0D+00, &
w_b = 0.4596D+00, &
w_c = 0.0D+00, &
w_d = 0.9051D+00
! the laser frequeny
real(8) :: nu_pu = 2.8176D+00, &
nu_st = 2.3580D+00, &
nu_pr = 2.8176D+00, &
nu_dr = 0.4455D+00 !44.55D+00
real(8) :: om_pu = 0.01D+00, &
om_st = 0.01D+00, &
om_pr = 0.01D+00
real(kind = 8) om_dr
!!!!!! Unit of time is 10^(-14) second !!!!!!
! the pulse parameters
real(8) :: tau_pu=2000.0D+00, &
tau_st=2000.0D+00, &
tau_pr=2000.0D+00
real(8) :: t0_pu=5000.0D+00, &
t0_st=5000.0D+00, &
t0_pr=8000.0D+00
end module para
program main
!*****************************************************************************80
!
implicit none
write ( *, '(a)' ) ' '
write ( *, '(a)' ) 'RK4_method for FORTRAN90 version'
call rk4vec_test ( )
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' Normal end of execution.'
write ( *, '(a)' ) ' '
stop
end program main
subroutine rk4vec_test ( )
use para
!*****************************************************************************80
!
implicit none
integer ( kind = 4 ), parameter :: n = 4
integer ( kind = 8 ) step_number
real ( kind = 8 ), parameter :: dt = 0.01D+00
real ( kind = 8 ) t0
real ( kind = 8 ) t1
real ( kind = 8 ), parameter :: tmax = 18000.0D+00
complex ( kind = 8 ) u0(n)
complex ( kind = 8 ) u1(n)
real*8 :: fre, fre_min = 3.272, fre_max =3.284
integer*4 index_ini, index_final, data_number
integer ierr_1, ierr_2, ierr_3, ierr_4, ierr_5
complex(8), dimension(:), allocatable :: rho_ab_time, rho_ab_freq
integer ( kind = 4 ), parameter :: fftw_estimate = 128
integer ( kind = 4 ), parameter :: fftw_forward = -1
integer*8 plan
write ( *, '(a)' ) ' '
write ( *, '(a)' ) ' RK4VEC takes a Runge Kutta step for a vector ODE.'
write ( *, '(a)' ) ' '
step_number = int(tmax/dt)
write(*, *) "the Total_Number Time_Step Time_END"
write(*, '(2x,i12,4x, g14.6, 2x, g14.6)') step_number, dt, tmax
!!---------- delete the previse data ------------------------------
open(1, file='data_abs.txt', status='unknown', iostat=ierr_1)
if ( ierr_1 .eq. 0) then
! file opened successfully, delete
close(1, status='delete')
endif
open(2, file='om_dr.txt', status='unknown', iostat=ierr_2)
if ( ierr_2 .eq. 0) then
! file opened successfully, delete
close(2, status='delete')
endif
open(3, file='fre_apt.csv', status='unknown', iostat=ierr_3)
if ( ierr_3 .eq. 0) then
! file opened successfully, delete
close(3, status='delete')
endif
!! ------------- find the index which gives the frequency region we care about!
index_ini = 0
do i = 1, step_number
fre = 2.0 * pi * i/tmax
if (fre < fre_min) then
! ----- mark the initial index of frequency
index_ini = index_ini + 1
Cycle
else if (fre > fre_min .AND. fre < fre_max) then
Cycle
else
! ----- mark the initial index of frequency
index_final = i
EXIT
end if
end do
write (*, *) "Number of data :", index_final - index_ini - 1
allocate(rho_ab_time(step_number))
allocate(rho_ab_freq(step_number))
!open (unit = 4, file = 'data_abs.txt', ACTION="write")
open (unit = 7, file = 'fre_apt.csv', ACTION="write")
open (unit = 6, file = 'om_dr.txt', ACTION="write")
do p = 0, 80, 1
om_dr = p * 0.0001D+00
!write( * , *) "The Driving flied", om_dr
write( 6 , *) om_dr
t0 = 0.0D+00
u0(1) = (0.0D+00, 0.0D+00)
u0(2) = (0.0D+00, 0.0D+00)
u0(3) = (1.0D+00, 0.0D+00)
u0(4) = (0.0D+00, 0.0D+00)
do i = 1 , step_number
!write(*, *) i
! ----------- store the offdignal data to FFTW, which give the frequency information
rho_ab_time(i) = real(u0(1) * u0(3))
!write ( 4, * ) t0, abs(u0(1))**2, abs(u0(2))**2, abs(u0(3))**2, abs(u0(4))**2, real(rho_ab_time(i))
t1 = t0 + dt
call rk4vec ( t0, n, u0, dt, rk4vec_test_f, u1 )
!
! ---------- Shift the data to prepare for another step.
!
t0 = t1
u0(1:n) = u1(1:n)
end do
call dfftw_plan_dft_1d(plan,step_number,rho_ab_time,rho_ab_freq,fftw_forward,fftw_estimate)
call dfftw_execute_dft(plan,rho_ab_time,rho_ab_freq)
!write(7, *) "------------------------------"
do i = index_ini + 1, index_final - 1
write(7,*) 2.0 * pi * i/tmax, ',' ,abs(rho_ab_freq(i))
end do
call dfftw_destroy_plan(plan)
end do
!close(4)
close(7)
close(6)
return
contains
FUNCTION Omega_pu(t)
real(8) :: Omega_pu, t
!Omega_pu = sin(t)
Omega_pu = om_pu * exp(-(t - t0_pu)*(t - t0_pu)/(2*tau_pu*tau_pu)) * cos(nu_pu*t)
return
END FUNCTION
FUNCTION Omega_st(t)
real(8) :: Omega_st, t
Omega_st = om_st * exp(-(t -t0_st)*(t -t0_st)/(2*tau_st*tau_st)) * cos(nu_st*t)
return
END FUNCTION
FUNCTION Omega_pr(t)
real(8) :: Omega_pr, t
Omega_pr = om_pr * exp(-(t -t0_pr)*(t -t0_pr)/(2*tau_pr*tau_pr)) * cos(nu_pr*t)
return
END FUNCTION
FUNCTION Omega_dr(t)
real (8) :: Omega_dr, t
Omega_dr = om_dr * cos(nu_dr*t)
return
END FUNCTION
subroutine rk4vec_test_f ( t, n, u, uprime )
!*****************************************************************************80
implicit none
integer ( kind = 4 ) n
real ( kind = 8 ) t
real(8) ham(4,4)
real ( kind = 8 ) vector(4)
complex ( kind = 8 ) u(n)
complex ( kind = 8 ) uprime(n)
!write(*, *) Omega_dr(t)
!om_dr = 0.0D+00
!!! ---- please note that the max number of wards is 132.
ham(1,1) = w_a; ham(1,2) = -(Omega_st(t) + Omega_pr(t)); ham(1,3) = -Omega_pu(t); ham(1,4) = 0.0D+00;
ham(2,1) = ham(1,2); ham(2,2) = w_b; ham(2,3) = 0.0D+00; ham(2,4) = -Omega_dr(t);
ham(3,1) = ham(1,3); ham(3,2) = 0.0D+00; ham(3,3) = w_c; ham(3,4) = 0.0D+00;
ham(4,1) = 0.0D+00; ham(4,2) = ham(2,4); ham(4,3) = 0.0D+00; ham(4,4) = w_d;
vector(1) = 1; vector(2) = 1; vector(3) = 1; vector(4) = 1;
uprime = - imag * matmul(ham,u)
return
end subroutine rk4vec_test_f
subroutine rk4vec ( t0, m, u0, dt, f, u )
!*****************************************************************************80
!
!! RK4VEC takes one Runge-Kutta step for a vector ODE.
implicit none
integer ( kind = 4 ) m
real ( kind = 8 ) dt
external f
complex ( kind = 8 ) f0(m)
complex ( kind = 8 ) f1(m)
complex ( kind = 8 ) f2(m)
complex ( kind = 8 ) f3(m)
real ( kind = 8 ) t0
real ( kind = 8 ) t1
real ( kind = 8 ) t2
real ( kind = 8 ) t3
complex ( kind = 8 ) u(m)
complex ( kind = 8 ) u0(m)
complex ( kind = 8 ) u1(m)
complex ( kind = 8 ) u2(m)
complex ( kind = 8 ) u3(m)
!
! Get four sample values of the derivative.
!
call f ( t0, m, u0, f0 )
t1 = t0 + dt / 2.0D+00
u1(1:m) = u0(1:m) + dt * f0(1:m) / 2.0D+00
call f ( t1, m, u1, f1 )
t2 = t0 + dt / 2.0D+00
u2(1:m) = u0(1:m) + dt * f1(1:m) / 2.0D+00
call f ( t2, m, u2, f2 )
t3 = t0 + dt
u3(1:m) = u0(1:m) + dt * f2(1:m)
call f ( t3, m, u3, f3 )
!
! Combine them to estimate the solution U at time T1.
!
u(1:m) = u0(1:m) + ( dt / 6.0D+00 ) * ( &
f0(1:m) &
+ 2.0D+00 * f1(1:m) &
+ 2.0D+00 * f2(1:m) &
+ f3(1:m) )
return
end subroutine rk4vec
end subroutine rk4vec_test