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RESULTS: make some nice demos

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This commit is contained in:
Valentin Boettcher 2024-05-31 12:24:24 -04:00
parent 8e66d5b4ff
commit 27bcba8287
13 changed files with 796 additions and 109 deletions
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2
.gitignore vendored
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@ -10,3 +10,5 @@ devenv.local.nix
data
__pycache__
*.pkl

38
fitting_ringdown.org
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@ -1,38 +1,10 @@
:PROPERTIES:
:ID: d7630955-6ca9-4de7-9770-2d50d4847bcd
:END:
#+title: Fitting Ringdown
#+title: Python Code for the Fibre Loop Experiment
* Fitting transients
- one can solve the equation of motion for when a mode is in the
steady state and the laser is suddenly switched. one obtains a
decaying oscillation which can be fitted to the data.
- this works ok, when the system /was/ in the steady state before the jump
- see [[file:scripts/transients_without_amplification.py]]
- we obtain \(γ\approx\SI{2.2}{\kilo\hertz}\) but this can vary a lot
- the detuning frequency seems to be completely off
This is the code for the experimental side of [[id:bbd22b2d-4fcd-4ea9-9db7-8d599511a815][Simulation of Open
Systems with Fiber Loops]].
* Failure of the steady state
On the right peak on can see that there might be something fish going
on. This is ~data/24_05_24/nice_transient2~.
[[file:figures/non_steady.png]]
* Weird Oscillations :ATTACH:
- when turning on the amp while the laser is running we get some
oscillations at \(\sim \SI{40}{\kilo\hertz}\) which is a period of
\(\SI{25}{\micro\second}\). this is 500 times roundrip time :(). I
thought it might be a wave packet traveling around the loop, i.e
multiple modes together...
[[attachment:osci_closeup.png][osci_closeup.png]]
[[attachment:osci_far.png][osci_far.png]]
[[attachment:cleaned.png][cleaned.png]]
- it isn't close to the fsr though...
- fitting a sine to that gives pretty much the same, as does an fft
[[attachment:cleaned_fit.png][cleaned_fit.png]]
- it is pretty constant over all steps in [[file:data/09_05_24/Nicely_hybridised_2 2024,05,09, 15h57min00sec/][data]] as can be ascertained
from [[file:scripts/weird_oscillations.py][this script]]
- these are also present w/o the amp cutout!
[[attachment:osci_without.png][osci_without.png]]
It contains some analysis code which is discussed in separate notes
and a partial re-implementation of the [[id:c45097d2-2599-426d-82db-6ecfb5207151][Julia Code Project for the Non-Markovian Quantum Walk in Fiber Loops]].

114
scripts/experiments/004_full_nm_walk_tests.py
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@ -1,49 +1,105 @@
from rabifun.system import *
from rabifun.plots import *
from rabifun.utilities import *
import itertools
# %% interactive
def test_collective_mode_rabi():
"""This is couples to a linear combination of bathe modes in stead of to a single one, but the result is pretty much the same."""
ω_c = 0.1 / 2
params = Params(
def make_params(ω_c=0.1, N=10):
return Params(
η=0.5,
Ω=13,
δ=1 / 4,
ω_c=ω_c,
g_0=ω_c / 5,
laser_detuning=0,
ω_c=ω_c,
N=2,
N_couplings=2,
N=2 * N + 2,
N_couplings=N,
measurement_detuning=0,
α=0.1,
α=0,
rwa=False,
flat_energies=True,
flat_energies=False,
correct_lamb_shift=True,
laser_off_time=0,
)
params.laser_off_time = params.lifetimes(10)
# params.initial_state = make_zero_intial_state(params)
# params.initial_state[1] = 1
t = time_axis(params, 10, 0.01)
# solution = solve(t, params)
# print(RuntimeParams(params))
# signal = output_signal(t, solution.y, params)
def decay_rwa_analysis():
"""This is couples to a linear combination of bathe modes in stead of to a single one, but the result is pretty much the same."""
# f, (_, ax) = plot_simulation_result(
# make_figure(), t, signal, params, window=(params.lifetimes(5), t[-1])
# )
# # ax.axvline(params.laser_off_time)
# plot_rabi_sidebands(ax, params)
ω_c = 0.1
fig = make_figure()
ax = fig.subplots()
Ns = [1, 4] # [5, 10, 20]
sol_nonrwa, sol_nonrwa, *_ = plot_rwa_vs_real_amplitudes(ax, t, params)
ax.axvline(params.laser_off_time, color="black", linestyle="--")
fig = make_figure("decay_test")
ax_ns = fig.subplots(len(Ns), 2)
print(sol_nonrwa.y[2][-1] / sol_nonrwa.y[3][-1])
runtime = RuntimeParams(params)
print(runtime.drive_amplitudes[0] / runtime.drive_amplitudes[1])
have_legend = False
results = {}
param_dict = {}
for i, N in enumerate(Ns):
params = make_params(ω_c=ω_c, N=N)
params.laser_off_time = params.lifetimes(0)
params.initial_state = make_zero_intial_state(params)
params.initial_state[1] = 1
a_site = a_site_indices(params)[1]
ax_real, ax_corrected = ax_ns[i]
t = time_axis(params, recurrence_time(params) * 1.1 / params.lifetimes(1), 0.1)
for α in [0, 2]:
params.α = α
sol_nonrwa, sol_rwa = solve_nonrwa_rwa(t, params)
results[(N, α, True)] = sol_rwa
results[(N, α, False)] = sol_nonrwa
param_dict[(N, α)] = params
for correct, rwa in itertools.product([True, False], [True, False]):
sol = sol_rwa if rwa else sol_nonrwa
ax = ax_corrected if correct else ax_real
y = sol.y
if correct:
y = correct_for_decay(sol, params)
ax.plot(
sol.t,
np.abs(y[a_site]) ** 2,
label=f"{'rwa' if rwa else ''} α={α}",
linestyle="--" if rwa else "-",
alpha=0.5 if rwa else 1,
color=f"C{α}",
)
ax_real.set_title(f"Real, N={N}")
ax_corrected.set_title(f"Decay Removed, N={N}")
for ax in [ax_real, ax_corrected]:
if not have_legend:
ax.legend()
have_legend = True
ax.set_xlabel("t [1/Ω]")
ax.set_ylabel("Population")
ax.set_ylim(0, 1)
ax.set_xlim(0, t[-1])
ax.axvline(recurrence_time(params), color="black", linestyle="--")
fig.tight_layout()
fig.suptitle(
f"Decay test for η={params.η}MHz, Ω={params.Ω}MHz, δ/Ω={params.δ}, ω_c/Ω={params.ω_c}"
)
save_figure(fig, "decay_test", extra_meta=dict(params=param_dict, Ns=Ns))
quick_save_pickle(
dict(results=results, params=param_dict, Ns=Ns),
"decay_test",
param_dict=param_dict,
)
# %% make all figures
decay_rwa_analysis()

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scripts/experiments/figs/001_decay_test.pdf.meta.yaml Normal file
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@ -0,0 +1,108 @@
change_id: snsvmqorzwxnvuvwsrsxqqmukqyspwkw
commit_id: 8c5536ad27086daddb7a7e83aae06271b764fff5
description: 'RESULTS: make some nice demos'
extra_meta:
Ns:
- 1
- 4
params:
? !!python/tuple
- 1
- 0
: &id001 !!python/object:rabifun.system.Params
N: 4
N_couplings: 1
correct_lamb_shift: true
drive_off_time: null
dynamic_detunting: &id002 !!python/tuple
- 0
- 0
flat_energies: false
g_0: 0.03333333333333333
initial_state: !!python/object/apply:numpy.core.multiarray._reconstruct
args:
- &id003 !!python/name:numpy.ndarray ''
- !!python/tuple
- 0
- !!binary |
Yg==
state: !!python/tuple
- 1
- !!python/tuple
- 6
- &id004 !!python/object/apply:numpy.dtype
args:
- c16
- false
- true
state: !!python/tuple
- 3
- <
- null
- null
- null
- -1
- -1
- 0
- false
- !!binary |
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAPA/AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
laser_detuning: 0
laser_off_time: 0.0
measurement_detuning: 0
rwa: false
"\u03A9": 13
"\u03B1": 2
"\u03B4": 0.25
"\u03B7": 0.5
"\u03C9_c": 0.1
? !!python/tuple
- 1
- 2
: *id001
? !!python/tuple
- 4
- 0
: &id005 !!python/object:rabifun.system.Params
N: 10
N_couplings: 4
correct_lamb_shift: true
drive_off_time: null
dynamic_detunting: *id002
flat_energies: false
g_0: 0.03333333333333333
initial_state: !!python/object/apply:numpy.core.multiarray._reconstruct
args:
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- !!python/tuple
- 0
- !!binary |
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state: !!python/tuple
- 1
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- 12
- *id004
- false
- !!binary |
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laser_detuning: 0
laser_off_time: 0.0
measurement_detuning: 0
rwa: false
"\u03A9": 13
"\u03B1": 2
"\u03B4": 0.25
"\u03B7": 0.5
"\u03C9_c": 0.1
? !!python/tuple
- 4
- 2
: *id005
name: 001_decay_test
refers_to: ./figs/001_decay_test.pdf
source: scripts/simulations/001_full_system_rwa_analysis.py

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scripts/simulations/001_full_system_rwa_analysis.py Normal file
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@ -0,0 +1,121 @@
from rabifun.system import *
from rabifun.plots import *
from rabifun.utilities import *
import itertools
# %% interactive
def make_params(ω_c=0.1 / 2, N=10, gbar=1 / 3):
"""
Make a set of parameters for the system with the current
best-known settings.
"""
return Params(
η=0.5,
Ω=13,
δ=1 / 4,
ω_c=ω_c,
g_0=ω_c * gbar,
laser_detuning=0,
N=2 * N + 2,
N_couplings=N,
measurement_detuning=0,
α=0,
rwa=False,
flat_energies=False,
correct_lamb_shift=True,
laser_off_time=0,
)
def decay_rwa_analysis():
"""
Plot the population of the A site for different values of N and α,
with and without the RWA.
The parameters are chosen corresponding to the current best-known
values from the experiment.
The cutoff frequency is chosen to be 0.05Ω (which is the strongest
that still kinda works.).
Surprisingly the whole thing works for a gbar = 1/3 instead of 1/5
and with much fewer modes.
"""
ω_c = 0.05
Ns = [5, 10, 20]
gbar = 1 / 3
fig = make_figure("decay_test", figsize=(15, len(Ns) * 3))
ax_ns = fig.subplots(len(Ns), 2)
have_legend = False
results = {}
param_dict = {}
for i, N in enumerate(Ns):
params = make_params(ω_c=ω_c, N=N, gbar=gbar)
params.laser_off_time = params.lifetimes(0)
params.initial_state = make_zero_intial_state(params)
params.initial_state[1] = 1
a_site = a_site_indices(params)[1]
ax_real, ax_corrected = ax_ns[i]
t = time_axis(params, recurrence_time(params) * 1.1 / params.lifetimes(1), 0.1)
for α in [0, 2]:
params.α = α
sol_nonrwa, sol_rwa = solve_nonrwa_rwa(t, params)
results[(N, α, True)] = sol_rwa
results[(N, α, False)] = sol_nonrwa
param_dict[(N, α)] = params
for correct, rwa in itertools.product([True, False], [True, False]):
sol = sol_rwa if rwa else sol_nonrwa
ax = ax_corrected if correct else ax_real
y = sol.y
if correct:
y = correct_for_decay(sol, params)
ax.plot(
sol.t,
np.abs(y[a_site]) ** 2,
label=f"{'rwa' if rwa else ''} α={α}",
linestyle="--" if rwa else "-",
alpha=0.5 if rwa else 1,
color=f"C{α}",
)
ax_real.set_title(f"Real, N={N}")
ax_corrected.set_title(f"Decay Removed, N={N}")
for ax in [ax_real, ax_corrected]:
if not have_legend:
ax.legend()
have_legend = True
ax.set_xlabel("t [1/Ω]")
ax.set_ylabel("Population")
ax.set_ylim(0, 1)
ax.set_xlim(0, t[-1])
ax.axvline(recurrence_time(params), color="black", linestyle="--")
fig.tight_layout()
fig.suptitle(
f"Decay test for η={params.η}MHz, Ω={params.Ω}MHz, δ/Ω={params.δ}, ω_c/Ω={params.ω_c}, g_0/ω_c={params.g_0/params.ω_c:.2f}"
)
save_figure(fig, "001_decay_test", extra_meta=dict(params=param_dict, Ns=Ns))
quick_save_pickle(
dict(results=results, params=param_dict, Ns=Ns),
"001_decay_test",
param_dict=param_dict,
)
# %% make all figures
decay_rwa_analysis()

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scripts/simulations/figs/001_decay_test.pdf.meta.yaml Normal file
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change_id: snsvmqorzwxnvuvwsrsxqqmukqyspwkw
commit_id: 6ec1859dba940a2ada3aefedc5adea2cb436339f
description: 'RESULTS: make some nice demos'
extra_meta:
Ns:
- 5
- 10
- 20
params:
? !!python/tuple
- 5
- 0
: &id001 !!python/object:rabifun.system.Params
N: 12
N_couplings: 5
correct_lamb_shift: true
drive_off_time: null
dynamic_detunting: &id002 !!python/tuple
- 0
- 0
flat_energies: false
g_0: 0.016666666666666666
initial_state: !!python/object/apply:numpy.core.multiarray._reconstruct
args:
- &id003 !!python/name:numpy.ndarray ''
- !!python/tuple
- 0
- !!binary |
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state: !!python/tuple
- 1
- !!python/tuple
- 14
- &id004 !!python/object/apply:numpy.dtype
args:
- c16
- false
- true
state: !!python/tuple
- 3
- <
- null
- null
- null
- -1
- -1
- 0
- false
- !!binary |
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laser_detuning: 0
laser_off_time: 0.0
measurement_detuning: 0
rwa: false
"\u03A9": 13
"\u03B1": 2
"\u03B4": 0.25
"\u03B7": 0.5
"\u03C9_c": 0.05
? !!python/tuple
- 5
- 2
: *id001
? !!python/tuple
- 10
- 0
: &id005 !!python/object:rabifun.system.Params
N: 22
N_couplings: 10
correct_lamb_shift: true
drive_off_time: null
dynamic_detunting: *id002
flat_energies: false
g_0: 0.016666666666666666
initial_state: !!python/object/apply:numpy.core.multiarray._reconstruct
args:
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laser_detuning: 0
laser_off_time: 0.0
measurement_detuning: 0
rwa: false
"\u03A9": 13
"\u03B1": 2
"\u03B4": 0.25
"\u03B7": 0.5
"\u03C9_c": 0.05
? !!python/tuple
- 10
- 2
: *id005
? !!python/tuple
- 20
- 0
: &id006 !!python/object:rabifun.system.Params
N: 42
N_couplings: 20
correct_lamb_shift: true
drive_off_time: null
dynamic_detunting: *id002
flat_energies: false
g_0: 0.016666666666666666
initial_state: !!python/object/apply:numpy.core.multiarray._reconstruct
args:
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laser_detuning: 0
laser_off_time: 0.0
measurement_detuning: 0
rwa: false
"\u03A9": 13
"\u03B1": 2
"\u03B4": 0.25
"\u03B7": 0.5
"\u03C9_c": 0.05
? !!python/tuple
- 20
- 2
: *id006
function: decay_rwa_analysis
name: 001_decay_test
refers_to: ./figs/001_decay_test.pdf
source: scripts/simulations/001_full_system_rwa_analysis.py

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change_id: snsvmqorzwxnvuvwsrsxqqmukqyspwkw
commit_id: 049b547f220987c6bb63165a9a020b20b1c4377b
description: 'RESULTS: make some nice demos'
function: decay_rwa_analysis
param_dict:
? !!python/tuple
- 5
- 0
: &id001 !!python/object:rabifun.system.Params
N: 12
N_couplings: 5
correct_lamb_shift: true
drive_off_time: null
dynamic_detunting: &id002 !!python/tuple
- 0
- 0
flat_energies: false
g_0: 0.016666666666666666
initial_state: !!python/object/apply:numpy.core.multiarray._reconstruct
args:
- &id003 !!python/name:numpy.ndarray ''
- !!python/tuple
- 0
- !!binary |
Yg==
state: !!python/tuple
- 1
- !!python/tuple
- 14
- &id004 !!python/object/apply:numpy.dtype
args:
- c16
- false
- true
state: !!python/tuple
- 3
- <
- null
- null
- null
- -1
- -1
- 0
- false
- !!binary |
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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA=
laser_detuning: 0
laser_off_time: 0.0
measurement_detuning: 0
rwa: false
"\u03A9": 13
"\u03B1": 2
"\u03B4": 0.25
"\u03B7": 0.5
"\u03C9_c": 0.05
? !!python/tuple
- 5
- 2
: *id001
? !!python/tuple
- 10
- 0
: &id005 !!python/object:rabifun.system.Params
N: 22
N_couplings: 10
correct_lamb_shift: true
drive_off_time: null
dynamic_detunting: *id002
flat_energies: false
g_0: 0.016666666666666666
initial_state: !!python/object/apply:numpy.core.multiarray._reconstruct
args:
- *id003
- !!python/tuple
- 0
- !!binary |
Yg==
state: !!python/tuple
- 1
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- false
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laser_detuning: 0
laser_off_time: 0.0
measurement_detuning: 0
rwa: false
"\u03A9": 13
"\u03B1": 2
"\u03B4": 0.25
"\u03B7": 0.5
"\u03C9_c": 0.05
? !!python/tuple
- 10
- 2
: *id005
? !!python/tuple
- 20
- 0
: &id006 !!python/object:rabifun.system.Params
N: 42
N_couplings: 20
correct_lamb_shift: true
drive_off_time: null
dynamic_detunting: *id002
flat_energies: false
g_0: 0.016666666666666666
initial_state: !!python/object/apply:numpy.core.multiarray._reconstruct
args:
- *id003
- !!python/tuple
- 0
- !!binary |
Yg==
state: !!python/tuple
- 1
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laser_detuning: 0
laser_off_time: 0.0
measurement_detuning: 0
rwa: false
"\u03A9": 13
"\u03B1": 2
"\u03B4": 0.25
"\u03B7": 0.5
"\u03C9_c": 0.05
? !!python/tuple
- 20
- 2
: *id006
refers_to: outputs/001_decay_test.pkl
source: scripts/simulations/001_full_system_rwa_analysis.py

24
src/plot_utils.py
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@ -6,11 +6,23 @@ import yaml
import inspect
import subprocess
import pathlib
import sys
P = ParamSpec("P")
R = TypeVar("R")
def noop_if_interactive(f):
@wraps(f)
def wrapped(*args, **kwargs):
if hasattr(sys, "ps1"):
return
return f(*args, **kwargs)
return wrapped
def make_figure(fig_name: str = "interactive", *args, **kwargs):
fig = plt.figure(fig_name, *args, **kwargs)
fig.clf()
@ -94,19 +106,21 @@ def write_meta(path, **kwargs):
.strip()
)
frame = inspect.stack()[1]
frame = inspect.stack()[3]
module = inspect.getmodule(frame[0])
filename = str(
pathlib.Path(module.__file__).relative_to(project_dir) # type: ignore
if module
else "<unknown>"
)
function = frame.function
outpath = f"{path}.meta.yaml"
with open(outpath, "w") as f:
yaml.dump(
dict(
source=filename,
function=function,
change_id=change_id,
commit_id=commit_id,
description=description.strip(),
@ -119,19 +133,21 @@ def write_meta(path, **kwargs):
print(f"Metadata written to {outpath}")
def save_figure(fig, name, *args, **kwargs):
@noop_if_interactive
def save_figure(fig, name, extra_meta=None, *args, **kwargs):
dir = pathlib.Path(f"./figs/")
dir.mkdir(exist_ok=True)
fig.tight_layout()
write_meta(f"./figs/{name}.pdf", name=name)
write_meta(f"./figs/{name}.pdf", name=name, extra_meta=extra_meta)
plt.savefig(f"./figs/{name}.pdf", *args, **kwargs)
plt.savefig(f"./figs/{name}.png", *args, dpi=600, **kwargs)
print(f"Figure saved as {name}.pdf")
print(f"Figure saved as ./figs/{name}.pdf")
@noop_if_interactive
def quick_save_pickle(obj, name, **kwargs):
"""Quickly save an object to a pickle file with metadata."""
import pickle

59
src/rabifun/plots.py
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@ -1,5 +1,13 @@
from plot_utils import *
from .system import Params, RuntimeParams, solve, coupled_mode_indices, mode_name
from .system import (
Params,
RuntimeParams,
solve,
coupled_mode_indices,
mode_name,
uncoupled_mode_indices,
correct_for_decay,
)
from .analysis import fourier_transform
import matplotlib.pyplot as plt
import numpy as np
@ -114,7 +122,15 @@ def clone_color_or_default(lines: dict, mode: int):
return line.get_color()
def plot_rotating_modes(ax, solution, params, plot_uncoupled=False, clone_colors=None):
def plot_rotating_modes(
ax,
solution,
params,
plot_uncoupled=False,
clone_colors=None,
only_A_site=False,
correct_for_decay=False,
):
"""Plot the amplitude of the modes in the rotating frame.
:param ax: The axis to plot on.
@ -123,63 +139,74 @@ def plot_rotating_modes(ax, solution, params, plot_uncoupled=False, clone_colors
:param plot_uncoupled: Whether to plot the uncoupled modes.
:param clone_colors: A dictionary of lines indexed by mode index
from which to clone colors from.
:param only_A_site: Whether to plot only the A site modes.
:param correct_for_decay: Whether to correct for decay by
multiplying with an exponential.
"""
lines = dict()
if clone_colors is None:
clone_colors = dict()
for mode in coupled_mode_indices(params):
h = solution.y
if correct_for_decay:
h = correct_for_decay(solution, params)
for mode in [1] if only_A_site else coupled_mode_indices(params):
lines[mode] = ax.plot(
solution.t,
np.abs(solution.y[mode]),
np.abs(h[mode]),
label=mode_name(mode) + (" (rwa)" if params.rwa else ""),
color=clone_color_or_default(clone_colors, mode),
linestyle="dashdot" if params.rwa else "-",
)[0]
if plot_uncoupled:
if plot_uncoupled and not only_A_site:
for mode in uncoupled_mode_indices(params):
lines[mode] = ax.plot(
solution.t,
np.abs(solution.y[mode]),
np.abs(h[mode]),
label=mode_name(mode) + (" (rwa)" if params.rwa else ""),
color=clone_color_or_default(clone_colors, mode),
linestyle="dotted" if params.rwa else "--",
)[0]
ax.legend()
# ax.legend()
ax.set_xlabel("Time (1/Ω)")
ax.set_ylabel("Amplitude")
ax.set_title("Mode Amplitudes in the Rotating Frame")
ax.set_title(
"Mode Amplitudes in the Rotating Frame"
+ (" (corrected)" if correct_for_decay else "")
)
return lines
def plot_rwa_vs_real_amplitudes(ax, t, params, **kwargs):
def plot_rwa_vs_real_amplitudes(ax, solution_no_rwa, solution_rwa, params, **kwargs):
"""Plot the amplitudes of the modes of the system ``params`` in
the rotating frame with and without the RWA onto ``ax``.
The keyword arguments are passed to :any:`plot_rotating_modes`.
:param ax: The axis to plot on.
:param t: The time axis.
:param non_rwa: The solution without the rwa.
:param rwa: The solution with the rwa.
:param params: The system parameters.
:param kwargs: Additional keyword arguments to pass to
:any:`plot_rotating_modes`.
:returns: A tuple of the solutions without and with the rwa and
the dictionaries of the lines plotted indexed by mode
index.
:returns: A tuple of the line dictionaries for the non-rwa and rwa solutions.
"""
original_rwa = params.rwa
params.rwa = False
solution_no_rwa = solve(t, params)
no_rwa_lines = plot_rotating_modes(ax, solution_no_rwa, params, **kwargs)
params.rwa = True
solution_rwa = solve(t, params)
rwa_lines = plot_rotating_modes(
ax, solution_rwa, params, **kwargs, clone_colors=no_rwa_lines
)
return solution_no_rwa, solution_rwa, no_rwa_lines, rwa_lines
params.rwa = original_rwa
return no_rwa_lines, rwa_lines

113
src/rabifun/system.py
View file

@ -18,13 +18,13 @@ class Params:
complement of modes.
"""
Ω: float = 1
Ω: float = 13
"""Free spectral range of the system in *frequency units*."""
δ: float = 1 / 4
"""Mode splitting in units of :any:`Ω`."""
η: float = 0.1
η: float = 0.5
"""Decay rate :math:`\eta/2` of the system in angular frequency units."""
g_0: float = 0.01
@ -61,6 +61,10 @@ class Params:
"""Whether to use a flat distribution of bath energies."""
initial_state: np.ndarray | None = None
"""The initial state of the system."""
correct_lamb_shift: bool = True
"""Whether to correct for the Lamb shift by tweaking the detuning."""
def __post_init__(self):
if self.N_couplings > self.N:
@ -81,7 +85,7 @@ class Params:
Returns the number of lifetimes of the system that correspond to
`n` cycles.
"""
return n / self.η
return 2 * n / self.η
@property
def rabi_splitting(self):
@ -102,9 +106,14 @@ class RuntimeParams:
* params.Ω
* np.concatenate([[-1 * params.δ, params.δ], np.arange(1, params.N + 1)])
)
decay_rates = -1j * np.repeat(params.η / 2, params.N + 2)
Ωs = freqs + decay_rates
self.drive_frequencies, self.detunings, self.drive_amplitudes = (
drive_frequencies_and_amplitudes(params)
) # linear frequencies!
self.Ωs = Ωs
self.diag_energies = (
2
@ -112,17 +121,14 @@ class RuntimeParams:
* np.concatenate(
[
[0, 0],
drive_detunings(params),
self.detunings,
np.zeros(params.N - params.N_couplings),
]
)
+ decay_rates
)
self.detuned_Ωs = freqs - self.diag_energies.real
self.drive_frequencies, self.drive_amplitudes = (
drive_frequencies_and_amplitudes(params)
)
self.detuned_Ωs = freqs - self.diag_energies.real
def __repr__(self):
return f"{self.__class__.__name__}(Ωs={self.Ωs}, drive_frequencies={self.drive_frequencies}, drive_amplitudes={self.drive_amplitudes})"
@ -154,14 +160,22 @@ def eom_drive(t, x, ds, ωs, rwa, detuned_Ωs):
:param ωs: linear drive frequencies
"""
ds = 2 * np.pi * ds
if rwa:
coupled_indices = 2 + len(ds)
det_matrix = np.zeros((len(x), len(x)))
det_matrix[1, 2:] = ds / 2
det_matrix[2:, 1] = ds / 2
det_matrix[1, 2:coupled_indices] = ds / 2
det_matrix[2:coupled_indices, 1] = ds / 2
driven_x = det_matrix @ x
else:
freqs = np.exp(-1j * detuned_Ωs * t)
det_matrix = np.outer(np.conj(freqs), freqs)
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))
det_matrix = np.exp(-1j * det_matrix * t)
driven_x = np.sum(ds * np.sin(2 * np.pi * ωs * t)) * (det_matrix @ x)
return driven_x
@ -283,8 +297,12 @@ def output_signal(t: np.ndarray, amplitudes: np.ndarray, params: Params):
Calculate the output signal when mixing with laser light of
frequency `laser_detuning`.
"""
runtime = RuntimeParams(params)
rotating = amplitudes * np.exp(-1j * runtime.detuned_Ωs * t)
return (
np.sum(amplitudes, axis=0)
np.sum(rotating, axis=0)
* np.exp(
1j
* (laser_frequency(params, t) + 2 * np.pi * params.measurement_detuning)
@ -305,24 +323,24 @@ def ohmic_spectral_density(ω: np.ndarray, α: float) -> np.ndarray:
return ω**α
def drive_detunings(params: Params) -> np.ndarray:
"""Return the drive detunings of the bath modes in frequency units."""
def lamb_shift(amplitudes, Δs):
return np.sum(amplitudes**2 / Δs)
def drive_frequencies_and_amplitudes(
params: Params,
) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
"""
Return the linear frequencies and amplitudes of the drives based
on the ``params``.
"""
if params.flat_energies:
Δs = np.repeat(params.ω_c, params.N_couplings)
else:
Δs = bath_energies(params.N_couplings, params.ω_c)
return Δs * params.Ω
def drive_frequencies_and_amplitudes(params: Params) -> tuple[np.ndarray, np.ndarray]:
"""
Return the linear frequencies and amplitudes of the drives based
on the ``params``.
"""
Δs = drive_detunings(params)
Δs *= params.Ω
amplitudes = ohmic_spectral_density(
bath_energies(params.N_couplings, 1),
@ -330,10 +348,13 @@ def drive_frequencies_and_amplitudes(params: Params) -> tuple[np.ndarray, np.nda
)
amplitudes /= np.sum(amplitudes)
amplitudes = 2 * np.pi * params.Ω * params.g_0 * np.sqrt(amplitudes)
amplitudes = params.Ω * params.g_0 * np.sqrt(amplitudes)
if not params.flat_energies and params.correct_lamb_shift:
Δs -= np.sum(amplitudes**2 / Δs)
ωs = ((np.arange(1, params.N_couplings + 1) - params.δ) * params.Ω) - Δs
return ωs, amplitudes
return ωs, Δs, amplitudes
def mode_name(mode: int):
@ -378,3 +399,41 @@ def coupled_mode_indices(params: Params):
def dimension(params: Params):
"""Return the dimension of the system."""
return params.N + 2
def recurrence_time(params: Params):
"""Return the recurrence time of the system."""
return params.N_couplings / (params.Ω * params.ω_c)
def solve_nonrwa_rwa(t: np.ndarray, params: Params, **kwargs):
"""
Solve the system in the non-RWA and RWA cases and return the results.
The keyword arguments are passed to :any:`solve`.
:param t: time array
:param params: system parameters
:returns: non-RWA and RWA solutions
"""
initial_rwa = params.rwa
params.rwa = False
nonrwa = solve(t, params, **kwargs)
rwa_params = params
rwa_params.rwa = True
rwa = solve(t, rwa_params, **kwargs)
params.rwa = initial_rwa
return nonrwa, rwa
def correct_for_decay(solution, params):
"""Correct the ``solution`` for decay.
:param solution: The solution from :any:`solve_ivp` to correct.
:param params: The system parameters
:returns: The corrected solution amplitudes.
"""
return solution.y * np.exp(params.η / 2 * solution.t[None, :])