def vacuum_dm(self):
"""
get initial density matrix for cavity vacuum state
"""
vac = np.zeros(self.n_cav)
vac[0] = 1.
return ket2dm(vac)
def coherent_dm(N, alpha):
"""Density matrix representation of a coherent state.
Constructed via outer product of :func:`qutip.states.coherent`
Parameters
----------
N : int
Number of Fock states in Hilbert space.
alpha : float/complex
Eigenvalue for coherent state.
offset : int (default 0)
The lowest number state that is included in the finite number state
representation of the state.
method : string {'operator', 'analytic'}
Method for generating coherent density matrix.
Returns
-------
dm : qobj
Density matrix representation of coherent state.
Examples
--------
>>> coherent_dm(3,0.25j)
Quantum object: dims = [[3], [3]], \
shape = [3, 3], type = oper, isHerm = True
Qobj data =
[[ 0.93941695+0.j 0.00000000-0.23480733j -0.04216943+0.j ]
[ 0.00000000+0.23480733j 0.05869011+0.j 0.00000000-0.01054025j]
[-0.04216943+0.j 0.00000000+0.01054025j 0.00189294+0.j\
]]
Notes
-----
Select method 'operator' (default) or 'analytic'. With the
'operator' method, the coherent density matrix is generated by displacing
the vacuum state using the displacement operator defined in the
truncated Hilbert space of size 'N'. This method guarantees that the
resulting density matrix is normalized. With 'analytic' method the coherent
density matrix is generated using the analytical formula for the coherent
state coefficients in the Fock basis. This method does not guarantee that
the state is normalized if truncated to a small number of Fock states,
but would in that case give more accurate coefficients.
"""
#if method == "operator":
psi = coherent(N, alpha)
return ket2dm(psi)
#sz += -1j * commutator(sz, H) * dt
f.close()
return ado[:, :, 0]
if __name__ == '__main__':
from lime.phys import pauli
s0, sx, sy, sz = pauli()
H = 2 * np.pi * 0.1 * sx
psi0 = basis(2, 0)
rho0 = ket2dm(psi0)
mesolver = Lindblad_solver(H, c_ops=[0.2 * sx], e_ops=[sz])
Nt = 200
dt = 0.05
L = mesolver.liouvillian()
#result = mesolver.evolve(rho0, dt, Nt=Nt, return_result=True)
#corr = mesolver.correlation_3op_2t(rho0, [sz, sz, sz], dt, Nt, Ntau=Nt)
# from lime.style import subplots
# fig, ax = subplots()
# times = np.arange(Nt) * dt
# ax.imshow(corr.real)
# l = h.to_super() + 1j * c_op.to_linblad(gamma=gamma)
# l = liouvillian(H, c_ops=[gamma*c_op])
# ntrans = 3 * nstates # number of transitions
# eigvals1, U1 = eigs(l, k=ntrans, which='LR')
# eigvals1, U1 = sort(eigvals1, U1)
# print(eigvals1.real)
# omegas = np.linspace(0.1 , 10.5, 200)
from lime.phys import ket2dm
from lime.style import matplot, subplots
rho0 = ket2dm(np.array([1.0, 0.0]))
# rho0.data[0,0] = 1.0
ops = [sx, sx]
# out = correlation_2p_1t(omegas, rho0, ops, L)
# print(eigvecs)
# eigvals2, U2 = eigs(dag(l), k=ntrans, which='LR')
# eigvals2, U2 = sort(eigvals2, U2)
# #idx = np.where(eigvals2.real > 0.2)[0]
# #print(idx)
# norm = [np.vdot(U2[:,n], U1[:,n]) for n in range(ntrans)]
s0, sx, sy, sz = pauli()
# set up the molecule
H0 = 1. / au2ev * 0.5 * (s0 - sz)
H1 = sx.astype(complex)
# def coeff1(t):
# return np.exp(-t**2)*np.cos(1./au2ev * t)
pulse = Pulse(tau=2 / au2fs, omegac=1. / au2ev, delay=0, amplitude=0.05)
# H = [H0.astype(complex), [H1.astype(complex), pulse.field]]
H = H0.astype(complex)
psi0 = basis(2, 0)
rho0 = ket2dm(psi0).astype(complex)
mesolver = Redfield_solver(H, c_ops=[sz.astype(complex)])
Nt = 800
dt = 0.5
result = mesolver.evolve(rho0, dt=dt, Nt=Nt, e_ops=[H1])
#corr = mesolver.correlation_3op_2t(rho0, [sz, sz, sz], dt, Nt, Ntau=Nt)
# print(result.observables)
import proplot as plt
fig, ax = plt.subplots()
times = np.arange(Nt) * dt
ax.plot(times, result.observables[:, 0])
ax.format(ylabel='Coherence')