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noninteracting1DSpinsRampOn.py
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noninteracting1DSpinsRampOn.py
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# -*- coding: utf-8 -*-
"""
Created on Wed Jul 06 10:23:49 2016
@author: dng5
"""
import numpy as np
import matplotlib.pyplot as plt
from scipy import linalg as sLA
import time
hbar = 1.0545718e-34 # reduced Planck constant m^2 kg/s
mRb =1.44467e-25 #mass of rubidium in kg
lambdaR = 790e-9 # Raman wavelength in m
lambdaL = 1.064e-6 #lattice wavelength in m
Erecoil = (2.0*np.pi*hbar)**2.0/(2.0*mRb*lambdaL**2.0) #recoil energy
a=-40*np.pi
b=40*np.pi
alpha=1.0e-6
xSteps=1024
latticeRampOnt=0.03 # in seconds
ramanRampOnt=0.02 # in seconds
omegaMax=0.5
delta0=0.0
deltaN=0.0
phi=0.8*2.0*np.pi
epsilon=0.048
Vmax=6.0
x0max=-1964.0
xHopt=10.0e-6 # in seconds
phi=4.0/3.0
tMax=0.090 # in seconds
tstep=0.1 # in recoils
def params(t, Vmax, omegaMax, x0Max, delta0):
latticeRampOntr=latticeRampOnt*Erecoil/hbar
ramanRampOntr=ramanRampOnt*Erecoil/hbar
xHoptr=xHopt*Erecoil/hbar
if t<latticeRampOntr:
omega=0.0
x0=0.0
V0=Vmax*t/latticeRampOntr
updating=True
delta=delta0+deltaN*np.sin(2.0*np.pi*t*hbar/Erecoil+phi)
elif t<latticeRampOntr+ramanRampOntr:
omega=omegaMax*(t-latticeRampOntr)/ramanRampOntr
V0=Vmax
x0=0
delta=delta0+deltaN*np.sin(2.0*np.pi*t*hbar/Erecoil+phi)
updating=True
elif t< latticeRampOntr+ramanRampOntr+xHoptr:
V0=Vmax
omega=omegaMax
x0=x0Max*(t-latticeRampOntr-ramanRampOntr)/xHoptr
delta=delta0+deltaN*np.sin(2.0*np.pi*t*hbar/Erecoil+phi)
updating=True
else:
V0=Vmax
omega=omegaMax
x0=x0Max
delta=delta0+deltaN*np.sin(2.0*np.pi*t*hbar/Erecoil+phi)
if deltaN==0.0:
updating=False
else:
updating=True
return V0,omega,x0,delta,updating
def Vho(x,alpha=1.0,x0=0.0):
return alpha*((x-x0)**2.0)
def vLatHo(x,V0=6.0,alpha=0.00015,x0=0.0):
return (V0/1.0)*(np.sin(x))**2.0+Vho(x,alpha=alpha,x0=x0)
def Fx(S):
F=np.zeros((2*S+1,2*S+1))
for i in range(2*S+1):
for j in range(2*S+1):
if np.abs(i-j)==1:
F[i,j]=(1.0/2.0)*np.sqrt(S*(S+1)-(i-S)*(j-S))
return F
def vRaman(x,omega=1.0,delta=0.0,epsilon=0.048,phi=4.0/3.0):
x=np.array(x)
s=1
v=v=np.einsum('i,jk->ijk',omega*np.exp(1.0j*2.0*phi*x),Fx(s)*np.sqrt(2.0)/2.0)
v=np.array([np.triu(v[i])+np.conjugate(np.triu(v[i],1)).transpose() for i in range(x.size)])
v+=np.array([np.diag([epsilon+delta,0.0,epsilon-delta])]*x.size)
return v
def getEigenHam2(a,b,xSteps,V,omega=1.0,delta=0.0,epsilon=0.048,phi=4.0/3.0,*args,**kwargs):
s=1
xgrid=np.linspace(a,b,xSteps)
# print '1. Xgrid:' +str(xgrid.shape)
eigE=np.zeros((xgrid.size,2*s+1),dtype=complex)
eigV=np.zeros((xgrid.size,2*s+1,2*s+1),dtype=complex)
eigVdagger=np.zeros((xgrid.size,2*s+1,2*s+1),dtype=complex)
for i,x in enumerate(xgrid):
Vgrid=np.diag(np.array([V(x,*args,**kwargs)]*(2*s+1)))
Vspin=vRaman(x,omega=omega,delta=delta,epsilon=epsilon,phi=phi)
Vtot=Vgrid+Vspin
eigE[i],eigV[i]=sLA.eigh(Vtot)
eigVdagger[i]=np.conj(eigV[i]).transpose()
return eigE,eigV,eigVdagger
def getEigenHam3(a,b,xSteps,V,omega=1.0,delta=0.0,epsilon=0.048,phi=4.0/3.0,*args,**kwargs):
s=1
xgrid=np.linspace(a,b,xSteps)
# print '1. Xgrid:' +str(xgrid.shape)
eigE=np.zeros((xgrid.size,2*s+1),dtype=complex)
eigV=np.zeros((xgrid.size,2*s+1,2*s+1),dtype=complex)
eigVdagger=np.zeros((xgrid.size,2*s+1,2*s+1),dtype=complex)
Vgrid=np.array([np.diag([V(xgrid,*args,**kwargs)[i]]*3) for i in range(xgrid.size)])
Vspin=vRaman(xgrid,omega=omega,delta=delta,epsilon=epsilon,phi=phi)
Vtot=Vgrid+Vspin
eigE,eigV=np.linalg.eig(Vtot)
eigVdagger=np.swapaxes(np.conj(eigV),1,2)
return eigE,eigV,eigVdagger
def splitStepPropagatorEigB2(psi,dt,a,b,eigE,eigV,eigVdagger):
xgrid=np.linspace(a,b,psi.shape[0])
U=np.exp(-1.0j*eigE*dt/2.0)
psi1=U*psi
psi1=np.einsum('ijk,ik->ij',eigV,psi1)
kgrid=np.fft.fftfreq(xgrid.size,d=((b-a)/xgrid.size/(2.0*np.pi)))
fft1=np.fft.fft(psi1.transpose())
psi2=np.exp(-1.0j*dt*(kgrid**2.0))*fft1
fft2=np.fft.ifft(psi2).transpose()
psi3=np.einsum('ijk,ik->ij',eigVdagger,fft2)
psi3=U*psi3
return psi3
def splitStepPropagatorUncoupledSpins(psi,V,dt,a,b,*args,**kwargs):
xgrid=np.linspace(a,b,psi.shape[0])
Vgrid=V(xgrid,*args,**kwargs)
U=np.array([np.exp(-1.0j*Vgrid*dt/2.0)]*3).transpose()
psi1=U*psi
kgrid=np.fft.fftfreq(xgrid.size,d=((b-a)/xgrid.size/(2.0*np.pi)))
psi2=np.exp(-1.0j*dt*(kgrid**2.0))*np.fft.fft(psi1.transpose())
psi3=U*np.fft.ifft(psi2).transpose()
return psi3
def propagateInTime(psi0,V,a,b,tf,dt,omegaMax=1.0,delta0=0.0,epsilon=0.048,phi=4.0/3.0,x0max=0.0,Vmax=6.0,**kwargs):
xgrid=np.linspace(a,b,psi0.shape[0])
dx=(b-a)/(psi0.shape[0])
tgrid=np.arange(dt,tf,dt)
fracM=np.zeros(tgrid.size)
frac0=np.zeros(tgrid.size)
fracP=np.zeros(tgrid.size)
com0=np.zeros(tgrid.size)
for ind,t in enumerate(tgrid):
psiMag=psi0*np.conj(psi0)
fracM[ind]=dx*np.sum(psiMag[:,2])
frac0[ind]=dx*np.sum(psiMag[:,1])
fracP[ind]=dx*np.sum(psiMag[:,0])
com0[ind]=np.sum(xgrid*(psiMag[:,1]+psiMag[:,0]+psiMag[:,2])*dx)
V0,omega,x0,delta,updating=params(t,Vmax,omegaMax,x0max,delta0)
change=0
if omega==0.0:
psi0=splitStepPropagatorUncoupledSpins(psi0,V,dt,a,b,V0=V0,x0=x0,**kwargs)
elif updating:
eigE,eigV,eigVdagger=getEigenHam3(a,b,psi0.shape[0],V,omega=omega,delta=delta,epsilon=epsilon,phi=phi,x0=x0,V0=V0,**kwargs)
psi0eigB=np.einsum('ijk,ik->ij',eigVdagger,psi0)
psi0eigB=splitStepPropagatorEigB2(psi0eigB,dt,a,b,eigE,eigV,eigVdagger)
psi0=np.einsum('ijk,ik->ij',eigV,psi0eigB)
else:
if change==0:
eigE,eigV,eigVdagger=getEigenHam3(a,b,psi0.shape[0],V,omega=omega,delta=delta,epsilon=epsilon,phi=phi,x0=x0,V0=V0,**kwargs)
change+=1
psi0eigB=np.einsum('ijk,ik->ij',eigVdagger,psi0)
psi0eigB=splitStepPropagatorEigB2(psi0eigB,dt,a,b,eigE,eigV,eigVdagger)
psi0=np.einsum('ijk,ik->ij',eigV,psi0eigB)
return fracM,frac0,fracP,com0,tgrid,psi0
xgrid=np.linspace(a,b,xSteps)
kgrid=np.fft.fftfreq(xgrid.size,d=((b-a)/xgrid.size/(2.0*np.pi)))
dx=xgrid[1]-xgrid[0]
psiAn=np.exp(-np.sqrt(alpha)*xgrid**2.0/2.0)
psiAn=psiAn/np.sqrt(np.dot(psiAn,np.conj(psiAn)*dx))
Vgrid=vLatHo(xgrid,alpha=alpha)
psi0=np.swapaxes(np.array([np.zeros(psiAn.size),psiAn,np.zeros(psiAn.size)],dtype=complex),0,1)
#fig2=plt.figure()
#pan2=fig2.add_subplot(1,1,1)
#pan2.plot(xgrid,Vgrid)
Vgrid=vLatHo(xgrid, alpha=alpha,x0=19640,V0=0.0)
print np.gradient(Vgrid)[xSteps/2.0]/(xgrid[1]-xgrid[0])
s=1
t1=time.clock()
fracM,frac0,fracP,com0,tgrid,psiOut=propagateInTime(psi0,vLatHo,a,b,tMax*Erecoil/hbar,tstep,omegaMax=omegaMax,delta0=delta0,epsilon=epsilon,phi=phi,alpha=alpha,Vmax=Vmax,x0max=x0max)
t2=time.clock()
print 'Time propagation completed in %f seconds' %(t2-t1)
psiOut=psiOut.reshape(xgrid.size,2*s+1).transpose()
#
#deltaList = np.arange(-0.15,0.15,0.003)
#fracMofD=np.zeros(deltaList.size)
#frac0ofD=np.zeros(deltaList.size)
#fracPofD=np.zeros(deltaList.size)
#
#
#for ind,delta in enumerate(deltaList):
#
# t1=time.clock()
# fracM,frac0,fracP,com0,tgrid,psiOut=propagateInTime(psi0,vLatHo,a,b,tMax*Erecoil/hbar,tstep,omegaMax=omegaMax,delta0=delta0,epsilon=epsilon,phi=4.0/3.0,alpha=alpha,Vmax=Vmax,x0max=x0max)
# fracMofD[ind]=fracM[-1]
# frac0ofD[ind]=frac0[-1]
# fracPofD[ind]=fracP[-1]
# t2=time.clock()
# print 'Time propagation completed in %f seconds for index %i' %(t2-t1,ind)
# psiOut=psiOut.reshape(xgrid.size,2*s+1).transpose()
#
#
#fig1=plt.figure()
#pan1=fig1.add_subplot(1,1,1)
#pan1.plot(deltaList,fracPofD,'b-', label='mF=+1')
#pan1.plot(deltaList,frac0ofD,'g-', label='mF=0')
#pan1.plot(deltaList,fracMofD,'r-', label='mF=-1')
#pan1.set_xlabel('Detuning')
#pan1.set_title(r'$\Omega$=%.2f,V=%.2f,$\delta$=%.3f,$\alpha$=%.0f e-6,$x_0$=%.0f,'%(omegaMax,Vmax,delta,alpha*1e6,x0max)+'\n'+ r'$t_{latramp}$=%.3f,$t_{ramanramp}$=%.3f,xSteps=%.0f,tstep=' %(latticeRampOnt,ramanRampOnt,xSteps)+str(np.round(tstep*1e6*hbar/Erecoil,3)))
#fig=plt.figure()
#pan=fig.add_subplot(1,1,1)
#pan.plot(xgrid,psiOut[0]*np.conj(psiOut[0]),'b-', label='mF=+1')
#pan.plot(xgrid,psiOut[1]*np.conj(psiOut[1]),'g-', label='mF=0')
#pan.plot(xgrid,psiOut[2]*np.conj(psiOut[2]),'r-', label='mF=-1')
#pan.plot(xgrid, psiAn*np.conj(psiAn),'k-')
#fig.show()
#
#psiFFt=np.fft.fft(psiOut)
#fig=plt.figure()
#pan=fig.add_subplot(1,1,1)
#pan.plot(kgrid,psiFFt[0]*np.conj(psiFFt[0]),'bo', label='mF=+1')
#pan.plot(kgrid,psiFFt[1]*np.conj(psiFFt[1]),'go', label='mF=0')
#pan.plot(kgrid,psiFFt[2]*np.conj(psiFFt[2]),'ro', label='mF=-1')
##
#dataFile=np.load('..\\Raman\\29Jun2016_files_37-146.npz')
#imbal=dataFile['imbalArray']
#signalGood=dataFile['signalGood']
#cutoff=0.35
#fieldGoodArray=((imbal<cutoff) & signalGood)
#fractionP=dataFile['fractionP'][fieldGoodArray]
#fraction0=dataFile['fraction0'][fieldGoodArray]
#fractionM=dataFile['fractionM'][fieldGoodArray]
#time=dataFile['tlist'][fieldGoodArray]+(latticeRampOnt+ramanRampOnt)*hbar/Erecoil
fig1=plt.figure()
pan1=fig1.add_subplot(1,1,1)
pan1.plot(tgrid*hbar*1e3/Erecoil,fracP,'b-', label='mF=+1')
pan1.plot(tgrid*hbar*1e3/Erecoil,frac0,'g-', label='mF=0')
pan1.plot(tgrid*hbar*1e3/Erecoil,fracM,'r-', label='mF=-1')
pan1.set_title(r'$\Omega$=%.2f,V=%.2f,$\delta_0$=%.3f,$\delta_N$=%.3f,$\phi$=%.3f,$\alpha$=%.0f e-6,$x_0$=%.0f,'%(omegaMax,Vmax,delta0,deltaN,phi,alpha*1e6,x0max)+'\n'+ r'$t_{latramp}$=%.3f,$t_{ramanramp}$=%.3f,xSteps=%.0f,tstep=' %(latticeRampOnt,ramanRampOnt,xSteps)+str(np.round(tstep*1e6*hbar/Erecoil,3)))
pan1.set_xlim(latticeRampOnt*1e3+ramanRampOnt*1e3,tMax*1e3)
#pan1.plot(time*1.0e3,fractionP,'bo', label=r'$m_F$=+1')
#pan1.plot(time*1.0e3,fraction0,'go', label=r'$m_F$=0')
#pan1.plot(time*1.0e3,fractionM,'ro', label=r'$m_F$=-1')
#
#fig2=plt.figure()
#pan2=fig2.add_subplot(1,1,1)
#pan2.plot(tgrid*hbar*1e3/Erecoil,com0,'b-')