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add negative uncoupled modes too

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fix a_shift issues
This commit is contained in:
Valentin Boettcher 2024-06-04 09:35:24 -04:00
parent d5e74d718e
commit 589a370515
7 changed files with 144 additions and 329 deletions
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72
scripts/experiments/005_mean_displacement_semi_analytic.py
View file

@ -38,16 +38,22 @@ def characteristic_poly(g: np.ndarray, ε: np.ndarray, η_A: float = 0):
return poly
def hamiltonian(g: np.ndarray, ε: np.ndarray, η_A: float = 0):
H = np.diag([-1j * η_A, *ε])
def hamiltonian(g: np.ndarray, ε: np.ndarray, ε_A: float = 0, η_A: float = 0):
H = np.diag([ε_A - 1j * η_A, *ε])
H[0, 1:] = g
H[1:, 0] = np.conj(g)
return H
def a_site_population(t, ω, coeff):
def a_site_population(t, ω, coeff, lower_cutoff=0):
return (
np.abs(np.sum(coeff[None, :] * np.exp(-1j * ω[None, :] * t[:, None]), axis=1))
np.abs(
np.sum(
coeff[None, lower_cutoff:]
* np.exp(-1j * ω[None, lower_cutoff:] * t[:, None]),
axis=1,
)
)
** 2
)
@ -64,7 +70,7 @@ def make_params(ω_c=0.1 / 2, N=10, gbar=1 / 3):
ω_c=ω_c,
g_0=ω_c * gbar,
laser_detuning=0,
N=2 * N + 2,
N=N,
N_couplings=N,
measurement_detuning=0,
α=0,
@ -76,29 +82,53 @@ def make_params(ω_c=0.1 / 2, N=10, gbar=1 / 3):
def test():
params = make_params(N=10, gbar=1 / 3)
params = make_params(N=20, gbar=1 / 4)
params.flat_energies = False
params.α = 0.0
params.correct_lamb_shift = True
params.α = 0
params.correct_lamb_shift = 1
runtime = RuntimeParams(params)
t = time_axis(params, recurrences=1.5)
g = runtime.g / 2
t = time_axis(params, recurrences=1.1)
g = runtime.g
ε = runtime.bath_ε
H = hamiltonian(g, ε.real, 0 * params.η / 2)
ω = np.linalg.eigvals(H)
M = np.linalg.eig(H).eigenvectors
H = hamiltonian(g, ε.real, ε_A=runtime.a_shift, η_A=0 * params.η / 2)
print(runtime.a_shift - ε[-1])
eig = np.linalg.eig(H)
ω = eig.eigenvalues
idx = np.argsort(ω.real)
ω = ω[idx]
M = np.linalg.eig(H).eigenvectors[:, idx]
Minv = np.linalg.inv(M)
v0 = Minv[:, 0]
coeff = M[0, :] * v0.T
coeff = M[0, :] * Minv[:, 0]
f = make_figure()
U_A = np.abs(1 / (1 + np.sum((g / (ω[0] - ε.real)) ** 2))) ** 2
U_A_coeff = np.max(np.abs(coeff**2))
print(np.argmax(np.abs(coeff**2)))
print(coeff)
ax_t, ax_e = f.subplots(1, 2)
ax_t.plot(t, a_site_population(t, ω, coeff, 0))
# ax_t.plot(t, U_A_coeff + .1 * np.sin(ω[0].real * t))
ax_t.set_ylim(0, 1.01)
ax_t.set_xlabel("Time [1/Ω]")
ax_t.set_ylabel(r"$ρ_A$")
# coeff /= np.abs(np.sum(coeff))
# coeff = coefficients(ω, g, ε)
# print((np.abs(1 / (1 + np.sum((g / ε) ** 2)))))
ax_t.axhline(U_A, color="green", linestyle="-.")
print(U_A)
ax_t.axhline(U_A_coeff, color="red", linestyle="--")
plt.cla()
plt.plot(t, a_site_population(t, ω, coeff))
plt.ylim(0, 1)
return ω
for ω_ in ω:
ax_e.axvline(ω_.real, color="blue", alpha=0.5)
ax_e.axvline(min(ω.real), color="black", linestyle="--")
ax_e.axvline(max(ω.real), color="black", linestyle="--")
ax_e.axvline(max(ε.real), color="green", linestyle="--")
ax_e.set_xlabel("Energy")

10
scripts/simulations/001_full_system_rwa_analysis.py
View file

@ -43,9 +43,9 @@ def decay_rwa_analysis():
and with much fewer modes.
"""
ω_c = 0.05
Ns = [5, 10, 20]
gbar = 1 / 3 / 2
ω_c = 0.1 / 2
Ns = [1, 5]
gbar = 1 / 4
fig = make_figure("decay_test", figsize=(15, len(Ns) * 3))
ax_ns = fig.subplots(len(Ns), 2)
@ -56,7 +56,7 @@ def decay_rwa_analysis():
param_dict = {}
for i, N in enumerate(Ns):
params = make_params(ω_c=ω_c, N=N, gbar=gbar)
params = make_params(ω_c=ω_c, N=N, gbar=gbar, compensate=1)
params.laser_off_time = 0
params.initial_state = make_zero_intial_state(params)
params.initial_state[1] = 1
@ -67,7 +67,7 @@ def decay_rwa_analysis():
t = time_axis(params, recurrences=1.1, resolution=0.1)
for α in np.linspace(0, 2, 5):
for α in np.linspace(0, 2, 3):
params.α = α
sol_nonrwa, sol_rwa = solve_nonrwa_rwa(t, params)

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scripts/simulations/figs/001_decay_test.pdf
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154
scripts/simulations/figs/001_decay_test.pdf.meta.yaml
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@ -1,14 +1,13 @@
change_id: wykwpsvmtrzvwtunotxnzokztpyrnsrx
commit_id: 94f23ecee30914b5163f14fd5af637a8777b42cc
change_id: zqvmrwsoxvtmtutmpnkonxuntmvxpnou
commit_id: fa7a31938c77430505d38b5a0415ff0666a1fc6c
description: ''
extra_meta:
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params:
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@ -27,15 +26,15 @@ extra_meta:
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N: 12
N_couplings: 5
correct_lamb_shift: 2
N: 4
N_couplings: 1
correct_lamb_shift: 1
drive_off_time: null
dynamic_detunting: &id003 !!python/tuple
- 0
- 0
flat_energies: false
g_0: 0.008333333333333333
g_0: 0.0125
initial_state: !!python/object/apply:numpy.core.multiarray._reconstruct
args:
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@ -46,7 +45,7 @@ extra_meta:
state: !!python/tuple
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drive_off_time: null
dynamic_detunting: *id003
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g_0: 0.008333333333333333
g_0: 0.0125
initial_state: !!python/object/apply:numpy.core.multiarray._reconstruct
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function: decay_rwa_analysis
name: 001_decay_test
refers_to: ./figs/001_decay_test.pdf

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scripts/simulations/figs/001_decay_test.png
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151
scripts/simulations/outputs/001_decay_test.pkl.meta.yaml
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@ -1,10 +1,10 @@
change_id: wykwpsvmtrzvwtunotxnzokztpyrnsrx
commit_id: e4399f86a81e8dc0fbbe24226b948db60bd83807
change_id: zqvmrwsoxvtmtutmpnkonxuntmvxpnou
commit_id: 7372777c2aeb7f97f97d5e754b4bfde3a6244232
description: ''
function: decay_rwa_analysis
param_dict:
? !!python/tuple
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@ -23,15 +23,15 @@ param_dict:
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N: 12
N_couplings: 5
correct_lamb_shift: 2
N: 4
N_couplings: 1
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drive_off_time: null
dynamic_detunting: &id003 !!python/tuple
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flat_energies: false
g_0: 0.008333333333333333
g_0: 0.0125
initial_state: !!python/object/apply:numpy.core.multiarray._reconstruct
args:
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@ -42,7 +42,7 @@ param_dict:
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drive_off_time: null
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rwa: false
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refers_to: outputs/001_decay_test.pkl
source: scripts/simulations/001_full_system_rwa_analysis.py

86
src/rabifun/system.py
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@ -1,3 +1,4 @@
from pdb import run
import numpy as np
import matplotlib.pyplot as plt
from dataclasses import dataclass
@ -70,8 +71,8 @@ class Params:
if self.N_couplings > self.N:
raise ValueError("N_couplings must be less than or equal to N.")
if self.initial_state and len(self.initial_state) != self.N + 2:
raise ValueError("Initial state must have length N + 2.")
if self.initial_state and len(self.initial_state) != 2 * self.N + 2:
raise ValueError("Initial state must have length 2N + 2.")
def periods(self, n: float):
"""
@ -100,37 +101,45 @@ class RuntimeParams:
"""Secondary Parameters that are required to run the simulation."""
def __init__(self, params: Params):
bath = np.arange(1, params.N + 1)
freqs = (
2
* np.pi
* params.Ω
* np.concatenate([[-1 * params.δ, params.δ], np.arange(1, params.N + 1)])
* np.concatenate([[-1 * params.δ, params.δ], bath, -bath])
)
decay_rates = -1j * np.repeat(params.η / 2, params.N + 2)
decay_rates = -1j * np.repeat(params.η / 2, 2 * params.N + 2)
Ωs = freqs + decay_rates
self.drive_frequencies, self.detunings, self.g = (
self.drive_frequencies, self.detunings, self.g, a_shift = (
drive_frequencies_and_amplitudes(params)
) # linear frequencies!
self.g *= 2 * np.pi
self.Ωs = Ωs
self.bath_ε = 2 * np.pi * self.detunings - 1j * params.η / 2
self.ε = (
2
* np.pi
* np.concatenate(
[
[0, 0],
[-a_shift, a_shift],
self.detunings,
np.zeros(params.N - params.N_couplings),
-self.detunings,
np.zeros(params.N - params.N_couplings),
]
)
+ decay_rates
)
self.bath_ε = 2 * np.pi * self.detunings - 1j * params.η / 2
self.a_shift = 2 * np.pi * a_shift
self.detuned_Ωs = freqs - self.ε.real
self.RWA_H = np.zeros((2 * params.N + 2, 2 * params.N + 2), np.complex128)
self.RWA_H[1, 2 : 2 + params.N_couplings] = self.g
self.RWA_H[2 : 2 + params.N_couplings, 1] = np.conj(self.g)
self.detuning_matrix = self.detuned_Ωs[:, None] - self.detuned_Ωs[None, :]
def __repr__(self):
return f"{self.__class__.__name__}(Ωs={self.Ωs}, drive_frequencies={self.drive_frequencies}, drive_amplitudes={self.g})"
@ -164,7 +173,7 @@ def time_axis(
return np.arange(0, tmax, resolution * np.pi / (params.Ω * params.N))
def eom_drive(t, x, ds, ωs, rwa, detuned_Ωs):
def eom_drive(t, x, ds, ωs, det_matrix):
"""The electrooptical modulation drive.
:param t: time
@ -173,22 +182,14 @@ def eom_drive(t, x, ds, ωs, rwa, detuned_Ωs):
:param ωs: linear drive frequencies
"""
if rwa:
coupled_indices = 2 + len(ds)
det_matrix = np.zeros((len(x), len(x)))
det_matrix[1, 2:coupled_indices] = ds
det_matrix[2:coupled_indices, 1] = ds
driven_x = det_matrix @ x
else:
det_matrix = detuned_Ωs[:, None] - detuned_Ωs[None, :]
# test = abs(det_matrix.copy())
# test[test < 1e-10] = np.inf
# print(np.min(test))
# print(np.argmin(test, keepdims=True))
# test = abs(det_matrix.copy())
# test[test < 1e-10] = np.inf
# print(np.min(test))
# print(np.argmin(test, keepdims=True))
det_matrix = np.exp(-1j * det_matrix * t)
det_matrix = np.exp(-1j * det_matrix * t)
driven_x = np.sum(2 * ds * np.sin(2 * np.pi * ωs * t)) * (det_matrix @ x)
driven_x = np.sum(2 * ds * np.sin(2 * np.pi * ωs * t)) * (det_matrix @ x)
return driven_x
@ -218,14 +219,16 @@ def make_righthand_side(runtime_params: RuntimeParams, params: Params):
x[2 + params.N_couplings :] = 0
if (params.drive_off_time is None) or (t < params.drive_off_time):
differential += eom_drive(
t,
x,
runtime_params.g,
runtime_params.drive_frequencies,
params.rwa,
runtime_params.detuned_Ωs,
)
if params.rwa:
differential += runtime_params.RWA_H @ x
else:
differential += eom_drive(
t,
x,
runtime_params.g,
runtime_params.drive_frequencies,
runtime_params.detuning_matrix,
)
if (params.laser_off_time is None) or (t < params.laser_off_time):
freqs = laser_frequency(params, t) - runtime_params.detuned_Ωs.real
@ -253,7 +256,7 @@ def make_righthand_side(runtime_params: RuntimeParams, params: Params):
def make_zero_intial_state(params: Params) -> np.ndarray:
"""Make initial state with all zeros."""
return np.zeros(params.N + 2, np.complex128)
return np.zeros(2 * params.N + 2, np.complex128)
def solve(t: np.ndarray, params: Params, **kwargs):
@ -278,7 +281,7 @@ def solve(t: np.ndarray, params: Params, **kwargs):
(np.min(t), np.max(t)),
initial,
vectorized=False,
max_step=2 * np.pi / (params.Ω * params.N),
max_step=np.pi / (params.Ω * params.N),
t_eval=t,
method="DOP853",
atol=1e-7,
@ -326,13 +329,14 @@ def output_signal(t: np.ndarray, amplitudes: np.ndarray, params: Params):
def bath_energies(N_couplings: int, ω_c: float) -> np.ndarray:
"""Return the energies (drive detunings) of the bath modes."""
return np.arange(1, N_couplings + 1) * ω_c / N_couplings
return (np.arange(1, N_couplings + 1) - 1 / 2) * ω_c / N_couplings
def ohmic_spectral_density(ω: np.ndarray, α: float) -> np.ndarray:
"""The unnormalized spectral density of an Ohmic bath."""
return ω**α
ω = np.concatenate([[0], ω])
return np.diff(ω ** (α + 1))
def lamb_shift(amplitudes, Δs):
@ -341,7 +345,7 @@ def lamb_shift(amplitudes, Δs):
def drive_frequencies_and_amplitudes(
params: Params,
) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
) -> tuple[np.ndarray, np.ndarray, np.ndarray, float]:
"""
Return the linear frequencies and amplitudes of the drives based
on the ``params``.
@ -362,12 +366,12 @@ def drive_frequencies_and_amplitudes(
amplitudes /= np.sum(amplitudes)
amplitudes = params.Ω * params.g_0 * np.sqrt(amplitudes)
# FIXME: this is twice too big
a_shift = 0
if not params.flat_energies and params.correct_lamb_shift:
Δs -= np.sum(amplitudes**2 / Δs) * params.correct_lamb_shift**2
a_shift = np.sum(amplitudes**2 / Δs) * params.correct_lamb_shift**2
ωs = ((np.arange(1, params.N_couplings + 1) - params.δ) * params.Ω) - Δs
return ωs, Δs, amplitudes
ωs = ((np.arange(1, params.N_couplings + 1) - params.δ) * params.Ω) - (Δs - a_shift)
return ωs, Δs, amplitudes, a_shift
def mode_name(mode: int):
@ -392,7 +396,7 @@ def coupled_bath_mode_indices(params: Params):
def uncoupled_bath_mode_indices(params: Params):
"""Return the indices of the bath modes that not coupled to the A site."""
return np.arange(2 + params.N_couplings, 2 + params.N)
return np.arange(2 + params.N_couplings, 2 + 2 * params.N)
def uncoupled_mode_indices(params: Params):
@ -411,7 +415,7 @@ def coupled_mode_indices(params: Params):
def dimension(params: Params):
"""Return the dimension of the system."""
return params.N + 2
return 2 * params.N + 2
def recurrence_time(params: Params):