def test_fn_list_td_corr():
"""
correlation: comparing TLS emission correlations (fn-list td format)
"""
# calculate emission zero-delay second order correlation, g2(0), for TLS
# with following parameters:
# gamma = 1, omega = 2, tp = 0.5
# Then: g2(0)~0.57
sm = destroy(2)
args = {"t_off": 1, "tp": 0.5}
H = [[2 * (sm+sm.dag()),
lambda t, args: np.exp(-(t-args["t_off"])**2 / (2*args["tp"]**2))]]
tlist = linspace(0, 5, 50)
corr = correlation_3op_2t(H, fock(2, 0), tlist, tlist, [sm],
sm.dag(), sm.dag() * sm, sm, args=args)
# integrate w/ 2D trapezoidal rule
dt = (tlist[-1]-tlist[0]) / (np.shape(tlist)[0]-1)
s1 = corr[0, 0] + corr[-1, 0] + corr[0, -1] + corr[-1, -1]
s2 = sum(corr[1:-1, 0]) + sum(corr[1:-1, -1]) + \
sum(corr[0, 1:-1]) + sum(corr[-1, 1:-1])
s3 = sum(corr[1:-1, 1:-1])
exp_n_in = np.trapz(
mesolve(
H, fock(2, 0), tlist, [sm], [sm.dag()*sm], args=args
).expect[0], tlist
)
# factor of 2 from negative time correlations
g20 = abs(
sum(0.5*dt**2*(s1 + 2*s2 + 4*s3)) / exp_n_in**2
)
assert_(abs(g20-0.57) < 1e-1)
def test_np_list_td_corr():
"""
correlation: comparing TLS emission corr. (np-list td format)
"""
# both H and c_ops are time-dependent
# calculate emission zero-delay second order correlation, g2[0], for TLS
# with following parameters:
# gamma = 1, omega = 2, tp = 0.5
# Then: g2(0)~0.85
sm = destroy(2)
t_off = 1
tp = 0.5
tlist = np.linspace(0, 5, 50)
H = [[2 * (sm + sm.dag()), np.exp(-(tlist - t_off)**2 / (2 * tp**2))]]
c_ops = [
sm, [sm.dag() * sm * 2,
np.exp(-(tlist - t_off)**2 / (2 * tp**2))]
]
corr = correlation_3op_2t(H, fock(2, 0), tlist, tlist, [sm], sm.dag(),
sm.dag() * sm, sm)
# integrate w/ 2D trapezoidal rule
dt = (tlist[-1] - tlist[0]) / (np.shape(tlist)[0] - 1)
s1 = corr[0, 0] + corr[-1, 0] + corr[0, -1] + corr[-1, -1]
s2 = sum(corr[1:-1, 0]) + sum(corr[1:-1, -1]) + \
sum(corr[0, 1:-1]) + sum(corr[-1, 1:-1])
s3 = sum(corr[1:-1, 1:-1])
exp_n_in = np.trapz(
mesolve(H, fock(2, 0), tlist, c_ops, [sm.dag() * sm]).expect[0], tlist)
# factor of 2 from negative time correlations
g20 = abs(sum(0.5 * dt**2 * (s1 + 2 * s2 + 4 * s3)) / exp_n_in**2)
assert_(abs(g20 - 0.85) < 1e-2)
def test_H_str_list_td_corr():
"""
correlation: comparing TLS emission corr., H td (str-list td format)
"""
# calculate emission zero-delay second order correlation, g2[0], for TLS
# with following parameters:
# gamma = 1, omega = 2, tp = 0.5
# Then: g2(0)~0.57
sm = destroy(2)
args = {"t_off": 1, "tp": 0.5}
H = [[2 * (sm + sm.dag()), "exp(-(t-t_off)**2 / (2*tp**2))"]]
tlist = np.linspace(0, 5, 50)
corr = correlation_3op_2t(H,
fock(2, 0),
tlist,
tlist, [sm],
sm.dag(),
sm.dag() * sm,
sm,
args=args)
# integrate w/ 2D trapezoidal rule
dt = (tlist[-1] - tlist[0]) / (np.shape(tlist)[0] - 1)
s1 = corr[0, 0] + corr[-1, 0] + corr[0, -1] + corr[-1, -1]
s2 = sum(corr[1:-1, 0]) + sum(corr[1:-1, -1]) + \
sum(corr[0, 1:-1]) + sum(corr[-1, 1:-1])
s3 = sum(corr[1:-1, 1:-1])
exp_n_in = np.trapz(
mesolve(H, fock(2, 0), tlist, [sm], [sm.dag() * sm],
args=args).expect[0], tlist)
# factor of 2 from negative time correlations
g20 = abs(sum(0.5 * dt**2 * (s1 + 2 * s2 + 4 * s3)) / exp_n_in**2)
assert_(abs(g20 - 0.59) < 1e-2)
def _2ls_g2_0(H, c_ops):
sp = qutip.sigmap()
start = qutip.basis(2, 0)
times = _2ls_times
correlation = qutip.correlation_3op_2t(H, start, times, times, [sp],
sp.dag(), sp.dag()*sp, sp,
args=_2ls_args)
n_expectation = qutip.mesolve(H, start, times, [sp] + c_ops,
e_ops=[qutip.num(2)],
args=_2ls_args).expect[0]
integral_correlation = _trapz_2d(np.real(correlation), times)
integral_n_expectation = np.trapz(n_expectation, times)
# Factor of two from negative time correlations.
return 2 * integral_correlation / integral_n_expectation**2
def compute_two_ph_corr(
obj: floquet_analysis.FloquetAnalyzer,
num_periods: int,
inp_freqs: np.ndarray,
inp_amp: float) -> np.ndarray:
# Get the time lists.
init_times = np.arange(obj.num_dt) * obj.dt
delays = np.arange(obj.num_dt * (num_periods - 1)) * obj.dt
# Get the qutip operators.
two_ph_corrs = []
for freq in inp_freqs:
H, L = obj._system.get_qutip_operators(freq, inp_amp)
psi_init_as_list = []
for dim in H[0].dims[0]:
psi_init_as_list.append(qutip.basis(dim))
psi_init = qutip.tensor(psi_init_as_list)
two_ph_corrs.append(qutip.correlation_3op_2t(
H, psi_init, init_times, delays, [L], L, L, L))
return two_ph_corrs
def test_H_fn_td_corr():
"""
correlation: comparing TLS emission corr., H td (fn td format)
"""
# calculate emission zero-delay second order correlation, g2[0], for TLS
# with following parameters:
# gamma = 1, omega = 2, tp = 0.5
# Then: g2(0)~0.57
sm = destroy(2)
def H_func(t, args):
return 2 * args["H0"] * np.exp(-2 * (t - 1)**2)
tlist = linspace(0, 5, 50)
corr = correlation_3op_2t(H_func,
fock(2, 0),
tlist,
tlist, [sm],
sm.dag(),
sm.dag() * sm,
sm,
args={"H0": sm + sm.dag()})
# integrate w/ 2D trapezoidal rule
dt = (tlist[-1] - tlist[0]) / (np.shape(tlist)[0] - 1)
s1 = corr[0, 0] + corr[-1, 0] + corr[0, -1] + corr[-1, -1]
s2 = sum(corr[1:-1, 0]) + sum(corr[1:-1, -1]) +\
sum(corr[0, 1:-1]) + sum(corr[-1, 1:-1])
s3 = sum(corr[1:-1, 1:-1])
exp_n_in = trapz(
mesolve(H_func,
fock(2, 0),
tlist, [sm], [sm.dag() * sm],
args={
"H0": sm + sm.dag()
}).expect[0], tlist)
# factor of 2 from negative time correlations
g20 = abs(sum(0.5 * dt**2 * (s1 + 2 * s2 + 4 * s3)) / exp_n_in**2)
assert_(abs(g20 - 0.59) < 1e-2)
def test_H_np_list_td_corr():
"""
correlation: comparing TLS emission corr., H td (np-list td format)
"""
#from qutip.rhs_generate import rhs_clear
#rhs_clear()
# calculate emission zero-delay second order correlation, g2[0], for TLS
# with following parameters:
# gamma = 1, omega = 2, tp = 0.5
# Then: g2(0)~0.57
sm = destroy(2)
tp = 0.5
t_off = 1
tlist = np.linspace(0, 5, 50)
H = [[2 * (sm + sm.dag()), np.exp(-(tlist - t_off) ** 2 / (2 * tp ** 2))]]
corr = correlation_3op_2t(H, fock(2, 0), tlist, tlist, [sm],
sm.dag(), sm.dag() * sm, sm)
# integrate w/ 2D trapezoidal rule
dt = (tlist[-1] - tlist[0]) / (np.shape(tlist)[0] - 1)
s1 = corr[0, 0] + corr[-1, 0] + corr[0, -1] + corr[-1, -1]
s2 = sum(corr[1:-1, 0]) + sum(corr[1:-1, -1]) + \
sum(corr[0, 1:-1]) + sum(corr[-1, 1:-1])
s3 = sum(corr[1:-1, 1:-1])
exp_n_in = np.trapz(
mesolve(
H, fock(2, 0), tlist, [sm], [sm.dag() * sm]
).expect[0], tlist
)
# factor of 2 from negative time correlations
g20 = abs(
sum(0.5 * dt ** 2 * (s1 + 2 * s2 + 4 * s3)) / exp_n_in ** 2
)
assert_(abs(g20 - 0.59) < 1e-2)
def test_fn_td_corr():
"""
correlation: comparing TLS emission correlations (fn td format)
"""
# calculate emission zero-delay second order correlation, g2(0), for TLS
# with following parameters:
# gamma = 1, omega = 2, tp = 0.5
# Then: g2(0)~0.57
sm = destroy(2)
def H_func(t, args):
return 2 * args["H0"] * np.exp(-2 * (t-1)**2)
tlist = linspace(0, 5, 50)
corr = correlation_3op_2t(H_func, fock(2, 0), tlist, tlist,
[sm], sm.dag(), sm.dag() * sm, sm,
args={"H0": sm+sm.dag()})
# integrate w/ 2D trapezoidal rule
dt = (tlist[-1]-tlist[0]) / (np.shape(tlist)[0]-1)
s1 = corr[0, 0] + corr[-1, 0] + corr[0, -1] + corr[-1, -1]
s2 = sum(corr[1:-1, 0]) + sum(corr[1:-1, -1]) +\
sum(corr[0, 1:-1]) + sum(corr[-1, 1:-1])
s3 = sum(corr[1:-1, 1:-1])
exp_n_in = trapz(
mesolve(
H_func, fock(2, 0), tlist, [sm], [sm.dag()*sm],
args={"H0": sm+sm.dag()}
).expect[0], tlist
)
# factor of 2 from negative time correlations
g20 = abs(
sum(0.5*dt**2*(s1 + 2*s2 + 4*s3)) / exp_n_in**2
)
assert_(abs(g20-0.57) < 1e-1)
def test_str_list_td_corr():
"""
correlation: comparing TLS emission corr. (str-list td format)
"""
# both H and c_ops are time-dependent
# calculate emission zero-delay second order correlation, g2[0], for TLS
# with following parameters:
# gamma = 1, omega = 2, tp = 0.5
# Then: g2(0)~0.85
sm = destroy(2)
args = {"t_off": 1, "tp": 0.5}
tlist = np.linspace(0, 5, 50)
H = [[2 * (sm + sm.dag()), "exp(-(t-t_off)**2 / (2*tp**2))"]]
c_ops = [sm, [sm.dag() * sm * 2, "exp(-(t-t_off)**2 / (2*tp**2))"]]
corr = correlation_3op_2t(H, fock(2, 0), tlist, tlist, [sm],
sm.dag(), sm.dag() * sm, sm, args=args)
# integrate w/ 2D trapezoidal rule
dt = (tlist[-1] - tlist[0]) / (np.shape(tlist)[0] - 1)
s1 = corr[0, 0] + corr[-1, 0] + corr[0, -1] + corr[-1, -1]
s2 = sum(corr[1:-1, 0]) + sum(corr[1:-1, -1]) + \
sum(corr[0, 1:-1]) + sum(corr[-1, 1:-1])
s3 = sum(corr[1:-1, 1:-1])
exp_n_in = np.trapz(
mesolve(
H, fock(2, 0), tlist, c_ops, [sm.dag() * sm], args=args
).expect[0], tlist
)
# factor of 2 from negative time correlations
g20 = abs(
sum(0.5 * dt ** 2 * (s1 + 2 * s2 + 4 * s3)) / exp_n_in ** 2
)
assert_(abs(g20 - 0.85) < 1e-2)
