diff --git a/poetry.lock b/poetry.lock
index f9a3298..6cfb1fc 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -22,6 +22,23 @@ files = [
     {file = "appnope-0.1.4.tar.gz", hash = "sha256:1de3860566df9caf38f01f86f65e0e13e379af54f9e4bee1e66b48f2efffd1ee"},
 ]
 
+[[package]]
+name = "asteval"
+version = "1.0.2"
+description = "Safe, minimalistic evaluator of python expression using ast module"
+optional = false
+python-versions = ">=3.8"
+files = [
+    {file = "asteval-1.0.2-py3-none-any.whl", hash = "sha256:2ece3179809185598d054289e089b8e7706c1a5afa5f7e7c236b3cdae0cf8290"},
+    {file = "asteval-1.0.2.tar.gz", hash = "sha256:00e27d9dc565858056d04ebf741f9db4dc4ba319ac3517d094b1608e7f73fa6a"},
+]
+
+[package.extras]
+all = ["asteval[dev,doc,test]"]
+dev = ["build", "twine"]
+doc = ["Sphinx"]
+test = ["coverage", "pytest", "pytest-cov"]
+
 [[package]]
 name = "asttokens"
 version = "2.4.1"
@@ -42,63 +59,78 @@ test = ["astroid (>=1,<2)", "astroid (>=2,<4)", "pytest"]
 
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 name = "cffi"
-version = "1.16.0"
+version = "1.17.0"
 description = "Foreign Function Interface for Python calling C code."
 optional = false
 python-versions = ">=3.8"
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 [package.dependencies]
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 description = "An implementation of the Debug Adapter Protocol for Python"
 optional = false
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 ]
 
 [[package]]
@@ -266,6 +298,21 @@ files = [
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 ]
 
+[[package]]
+name = "dill"
+version = "0.3.8"
+description = "serialize all of Python"
+optional = false
+python-versions = ">=3.8"
+files = [
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+
+[package.extras]
+graph = ["objgraph (>=1.7.2)"]
+profile = ["gprof2dot (>=2022.7.29)"]
+
 [[package]]
 name = "executing"
 version = "2.0.1"
@@ -282,53 +329,53 @@ tests = ["asttokens (>=2.1.0)", "coverage", "coverage-enable-subprocess", "ipyth
 
 [[package]]
 name = "fonttools"
-version = "4.51.0"
+version = "4.53.1"
 description = "Tools to manipulate font files"
 optional = false
 python-versions = ">=3.8"
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 [package.extras]
@@ -362,13 +409,13 @@ ipython = {version = ">=7.31.1", markers = "python_version >= \"3.11\""}
 
 [[package]]
 name = "ipykernel"
-version = "6.29.4"
+version = "6.29.5"
 description = "IPython Kernel for Jupyter"
 optional = false
 python-versions = ">=3.8"
 files = [
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 [package.dependencies]
@@ -395,13 +442,13 @@ test = ["flaky", "ipyparallel", "pre-commit", "pytest (>=7.0)", "pytest-asyncio
 
 [[package]]
 name = "ipython"
-version = "8.24.0"
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 [package.dependencies]
@@ -419,7 +466,7 @@ typing-extensions = {version = ">=4.6", markers = "python_version < \"3.12\""}
 [package.extras]
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 kernel = ["ipykernel"]
 matplotlib = ["matplotlib"]
 nbconvert = ["nbconvert"]
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 notebook = ["ipywidgets", "notebook"]
 parallel = ["ipyparallel"]
 qtconsole = ["qtconsole"]
-test = ["pickleshare", "pytest", "pytest-asyncio (<0.22)", "testpath"]
+test = ["packaging", "pickleshare", "pytest", "pytest-asyncio (<0.22)", "testpath"]
 test-extra = ["curio", "ipython[test]", "matplotlib (!=3.2.0)", "nbformat", "numpy (>=1.23)", "pandas", "trio"]
 
 [[package]]
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 [[package]]
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 python-versions = ">=3.8"
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 [package.dependencies]
@@ -469,7 +516,7 @@ traitlets = ">=5.3"
 
 [package.extras]
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+test = ["coverage", "ipykernel (>=6.14)", "mypy", "paramiko", "pre-commit", "pytest (<8.2.0)", "pytest-cov", "pytest-jupyter[client] (>=0.4.1)", "pytest-timeout"]
 
 [[package]]
 name = "jupyter-console"
@@ -628,41 +675,66 @@ files = [
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 ]
 
+[[package]]
+name = "lmfit"
+version = "1.3.2"
+description = "Least-Squares Minimization with Bounds and Constraints"
+optional = false
+python-versions = ">=3.8"
+files = [
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+]
+
+[package.dependencies]
+asteval = ">=1.0"
+dill = ">=0.3.4"
+numpy = ">=1.19"
+scipy = ">=1.6"
+uncertainties = ">=3.2.2"
+
+[package.extras]
+all = ["lmfit[dev,doc,test]"]
+dev = ["build", "check-wheel-contents", "flake8-pyproject", "pre-commit", "twine"]
+doc = ["Pillow", "Sphinx", "cairosvg", "corner", "emcee (>=3.0.0)", "ipykernel", "jupyter-sphinx (>=0.2.4)", "matplotlib", "numdifftools", "numexpr", "pandas", "pycairo", "sphinx-gallery (>=0.10)", "sphinxcontrib-svg2pdfconverter", "sympy"]
+test = ["coverage", "flaky", "pytest", "pytest-cov"]
+
 [[package]]
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+version = "3.9.1.post1"
 description = "Python plotting package"
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 python-versions = ">=3.9"
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 ]
 
 [package.dependencies]
@@ -670,12 +742,15 @@ contourpy = ">=1.0.1"
 cycler = ">=0.10"
 fonttools = ">=4.22.0"
 kiwisolver = ">=1.3.1"
-numpy = ">=1.21"
+numpy = ">=1.23"
 packaging = ">=20.0"
 pillow = ">=8"
 pyparsing = ">=2.3.1"
 python-dateutil = ">=2.7"
 
+[package.extras]
+dev = ["meson-python (>=0.13.1)", "numpy (>=1.25)", "pybind11 (>=2.6)", "setuptools (>=64)", "setuptools_scm (>=7)"]
+
 [[package]]
 name = "matplotlib-inline"
 version = "0.1.7"
@@ -721,58 +796,67 @@ test = ["pytest (>=7.2)", "pytest-cov (>=4.0)"]
 
 [[package]]
 name = "numpy"
-version = "1.26.4"
+version = "2.0.1"
 description = "Fundamental package for array computing in Python"
 optional = false
 python-versions = ">=3.9"
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 [package.extras]
-docs = ["furo", "olefile", "sphinx (>=2.4)", "sphinx-copybutton", "sphinx-inline-tabs", "sphinx-removed-in", "sphinxext-opengraph"]
+docs = ["furo", "olefile", "sphinx (>=7.3)", "sphinx-copybutton", "sphinx-inline-tabs", "sphinxext-opengraph"]
 fpx = ["olefile"]
 mic = ["olefile"]
 tests = ["check-manifest", "coverage", "defusedxml", "markdown2", "olefile", "packaging", "pyroma", "pytest", "pytest-cov", "pytest-timeout"]
@@ -892,13 +987,13 @@ xmp = ["defusedxml"]
 
 [[package]]
 name = "platformdirs"
-version = "4.2.1"
+version = "4.2.2"
 description = "A small Python package for determining appropriate platform-specific dirs, e.g. a `user data dir`."
 optional = false
 python-versions = ">=3.8"
 files = [
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 ]
 
 [package.extras]
@@ -908,13 +1003,13 @@ type = ["mypy (>=1.8)"]
 
 [[package]]
 name = "prompt-toolkit"
-version = "3.0.43"
+version = "3.0.47"
 description = "Library for building powerful interactive command lines in Python"
 optional = false
 python-versions = ">=3.7.0"
 files = [
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 ]
 
 [package.dependencies]
@@ -922,27 +1017,28 @@ wcwidth = "*"
 
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+version = "6.0.0"
 description = "Cross-platform lib for process and system monitoring in Python."
 optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*, !=3.5.*"
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 ]
 
 [package.extras]
@@ -950,19 +1046,19 @@ test = ["enum34", "ipaddress", "mock", "pywin32", "wmi"]
 
 [[package]]
 name = "ptpython"
-version = "3.0.26"
+version = "3.0.29"
 description = "Python REPL build on top of prompt_toolkit"
 optional = false
 python-versions = ">=3.7"
 files = [
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 ]
 
 [package.dependencies]
 appdirs = "*"
 jedi = ">=0.16.0"
-prompt-toolkit = ">=3.0.34,<3.1.0"
+prompt-toolkit = ">=3.0.43,<3.1.0"
 pygments = "*"
 
 [package.extras]
@@ -982,13 +1078,13 @@ files = [
 
 [[package]]
 name = "pure-eval"
-version = "0.2.2"
+version = "0.2.3"
 description = "Safely evaluate AST nodes without side effects"
 optional = false
 python-versions = "*"
 files = [
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 ]
 
 [package.extras]
@@ -1072,159 +1168,182 @@ files = [
 
 [[package]]
 name = "pyyaml"
-version = "6.0.1"
+version = "6.0.2"
 description = "YAML parser and emitter for Python"
 optional = false
-python-versions = ">=3.6"
+python-versions = ">=3.8"
 files = [
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 [[package]]
 name = "six"
@@ -1304,22 +1423,22 @@ tests = ["cython", "littleutils", "pygments", "pytest", "typeguard"]
 
 [[package]]
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+    {file = "tornado-6.4.1-cp38-abi3-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:613bf4ddf5c7a95509218b149b555621497a6cc0d46ac341b30bd9ec19eac7f3"},
+    {file = "tornado-6.4.1-cp38-abi3-musllinux_1_2_aarch64.whl", hash = "sha256:25486eb223babe3eed4b8aecbac33b37e3dd6d776bc730ca14e1bf93888b979f"},
+    {file = "tornado-6.4.1-cp38-abi3-musllinux_1_2_i686.whl", hash = "sha256:454db8a7ecfcf2ff6042dde58404164d969b6f5d58b926da15e6b23817950fc4"},
+    {file = "tornado-6.4.1-cp38-abi3-musllinux_1_2_x86_64.whl", hash = "sha256:a02a08cc7a9314b006f653ce40483b9b3c12cda222d6a46d4ac63bb6c9057698"},
+    {file = "tornado-6.4.1-cp38-abi3-win32.whl", hash = "sha256:d9a566c40b89757c9aa8e6f032bcdb8ca8795d7c1a9762910c722b1635c9de4d"},
+    {file = "tornado-6.4.1-cp38-abi3-win_amd64.whl", hash = "sha256:b24b8982ed444378d7f21d563f4180a2de31ced9d8d84443907a0a64da2072e7"},
+    {file = "tornado-6.4.1.tar.gz", hash = "sha256:92d3ab53183d8c50f8204a51e6f91d18a15d5ef261e84d452800d4ff6fc504e9"},
 ]
 
 [[package]]
@@ -1339,15 +1458,32 @@ test = ["argcomplete (>=3.0.3)", "mypy (>=1.7.0)", "pre-commit", "pytest (>=7.0,
 
 [[package]]
 name = "typing-extensions"
-version = "4.11.0"
+version = "4.12.2"
 description = "Backported and Experimental Type Hints for Python 3.8+"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "typing_extensions-4.11.0-py3-none-any.whl", hash = "sha256:c1f94d72897edaf4ce775bb7558d5b79d8126906a14ea5ed1635921406c0387a"},
-    {file = "typing_extensions-4.11.0.tar.gz", hash = "sha256:83f085bd5ca59c80295fc2a82ab5dac679cbe02b9f33f7d83af68e241bea51b0"},
+    {file = "typing_extensions-4.12.2-py3-none-any.whl", hash = "sha256:04e5ca0351e0f3f85c6853954072df659d0d13fac324d0072316b67d7794700d"},
+    {file = "typing_extensions-4.12.2.tar.gz", hash = "sha256:1a7ead55c7e559dd4dee8856e3a88b41225abfe1ce8df57b7c13915fe121ffb8"},
 ]
 
+[[package]]
+name = "uncertainties"
+version = "3.2.2"
+description = "calculations with values with uncertainties, error propagation"
+optional = false
+python-versions = ">=3.8"
+files = [
+    {file = "uncertainties-3.2.2-py3-none-any.whl", hash = "sha256:fd8543355952f4052786ed4150acaf12e23117bd0f5bd03ea07de466bce646e7"},
+    {file = "uncertainties-3.2.2.tar.gz", hash = "sha256:e62c86fdc64429828229de6ab4e11466f114907e6bd343c077858994cc12e00b"},
+]
+
+[package.extras]
+all = ["uncertainties[arrays,doc,test]"]
+arrays = ["numpy"]
+doc = ["python-docs-theme", "sphinx", "sphinx-copybutton"]
+test = ["pytest", "pytest-cov"]
+
 [[package]]
 name = "wcwidth"
 version = "0.2.13"
@@ -1362,4 +1498,4 @@ files = [
 [metadata]
 lock-version = "2.0"
 python-versions = "^3.11"
-content-hash = "bd710587ab2f126418734d7e1ba12d705d476cf8a8704710e7d16942ebab2455"
+content-hash = "1960c7e9fb8ed8561e5fa43a5ab6a9a1c3f0bbe03ef3c16dadf0b080479db5e6"
diff --git a/pyproject.toml b/pyproject.toml
index e7e5d1c..71dc59e 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -12,6 +12,7 @@ click = "^8.1.7"
 matplotlib = "^3.8.4"
 networkx = "^3.3"
 pyyaml = "^6.0.1"
+lmfit = "^1.3.2"
 
 
 [tool.poetry.group.dev.dependencies]
diff --git a/scripts/experiments/013_step_through.py b/scripts/experiments/013_step_through.py
index a19ed0a..750b254 100644
--- a/scripts/experiments/013_step_through.py
+++ b/scripts/experiments/013_step_through.py
@@ -11,13 +11,24 @@ from scipy.ndimage import rotate
 # %% interactive
 
 
-def make_shots(params, total_lifetimes, eom_range, eom_steps):
+def solve_shot(t, params, t_before, t_after):
+    solution = solve(t, params)
+    amps = solution.y[::, len(t_before) - 1 :]
+
+    return t_after, amps
+
+
+def make_shots(params, total_lifetimes, eom_range, eom_steps, σ_modulation_time):
     solutions = []
-    t = time_axis(params, lifetimes=total_lifetimes, resolution=0.01)
+
+    analyze_time = params.lifetimes(total_lifetimes) - params.laser_off_time
+    t_after = time_axis(params, total_time=analyze_time, resolution=0.01)
 
     pool = multiprocessing.Pool()
 
     shot_params = []
+    rng = np.random.default_rng(seed=0)
+
     for step in range(eom_steps):
         current_params = copy.deepcopy(params)
         current_params.drive_override = (
@@ -30,102 +41,111 @@ def make_shots(params, total_lifetimes, eom_range, eom_steps):
             np.array([1.0]),
         )
 
-        shot_params.append((t, current_params))
+        off_time = rng.normal(
+            params.laser_off_time, σ_modulation_time * params.lifetimes(1)
+        )
+        current_params.laser_off_time = off_time
+        current_params.drive_off_time = off_time
+        current_params.total_lifetimes = (off_time + analyze_time) / params.lifetimes(1)
 
-    solutions = pool.starmap(solve, shot_params)
-    return t, solutions
+        t_before = time_axis(params, total_time=off_time, resolution=0.01)
+        t = np.concatenate([t_before[:-1], t_after + t_before[-1]])
+
+        shot_params.append((t, current_params, t_before, t_after))
+
+    solutions = pool.starmap(solve_shot, shot_params)
+    return solutions
 
 
-def process_shots(t, solutions, noise_amplitude, params):
+def process_shots(solutions, noise_amplitude, params):
     average_power_spectrum = None
-    window = (float(params.laser_off_time) or 0, t[-1])
 
     rng = np.random.default_rng(seed=0)
 
     # let us get a measure calibrate the noise strength
-    signal_amp = 0
     signals = []
-    for solution in solutions:
-        signal = output_signal(t, solution.y, params)
-        signals.append(signal)
-        signal_amp += abs(signal).max()
+    for t, amps in solutions:
+        signal = output_signal(t, amps, params)
+        signals.append((t, signal))
 
-    signal_amp /= len(solutions)
-
-    for signal in signals:
-        signal += rng.normal(scale=noise_amplitude * signal_amp, size=len(signal))
+    noise_amplitude *= 2 * 2 * np.pi / params.η
+    for t, signal in signals:
+        signal += rng.normal(scale=noise_amplitude, size=len(signal))
+        window = (0, t[-1])
 
         freq, fft = fourier_transform(
             t,
             signal,
             low_cutoff=0.5 * params.Ω,
-            high_cutoff=params.Ω * (params.N + 1),
+            high_cutoff=params.Ω * 2.5,
             window=window,
         )
 
         power = np.abs(fft) ** 2
+        power = power / power.max()
         if average_power_spectrum is None:
             average_power_spectrum = power
 
         else:
             average_power_spectrum += power
 
-    return freq, (average_power_spectrum / len(solutions))
+    power = average_power_spectrum / len(solutions)
+    power -= np.median(power)
+    power /= power.max()
+
+    return (freq, power)
 
 
-def plot_power_spectrum(ax_spectrum, freq, average_power_spectrum, params):
-    offset = np.median(average_power_spectrum)
+def plot_power_spectrum(
+    ax_spectrum, freq, average_power_spectrum, params, annotate=True
+):
     # ax_spectrum.plot(freq, average_power_spectrum)
-    # runtime = RuntimeParams(params)
-    # lorentz_freqs = np.linspace(freq.min(), freq.max(), 10000)
-    # fake_spectrum = np.zeros_like(lorentz_freqs)
-
-    # for i, peak_freq in enumerate(runtime.Ωs):
-    #     pos = np.abs(
-    #         params.measurement_detuning
-    #         - peak_freq.real / (2 * np.pi)
-    #         + params.δ * params.Ω
-    #         + params.laser_detuning,
-    #     )
-
-    #     ax_spectrum.axvline(
-    #         pos,
-    #         color="red",
-    #         linestyle="--",
-    #         zorder=-100,
-    #     )
-
-    #     amplitude = average_power_spectrum[np.argmin(abs(freq - pos))] - offset
-    #     ax_spectrum.annotate(
-    #         mode_name(i),
-    #         (
-    #             pos + 0.1,
-    #             (amplitude + offset) * (1 if peak_freq.real < 0 else 1.1),
-    #         ),
-    #     )
-
-    #     fake_spectrum += lorentzian(
-    #         lorentz_freqs, amplitude, pos, peak_freq.imag / np.pi
-    #     )
-
-    # ax_spectrum.plot(lorentz_freqs, fake_spectrum + offset)
+    runtime = RuntimeParams(params)
 
     ringdown_params = RingdownParams(
         fω_shift=params.measurement_detuning,
-        mode_window=(5, 5),
+        mode_window=(3, 3),
         fΩ_guess=params.Ω,
         fδ_guess=params.Ω * params.δ,
         η_guess=0.5,
-        absolute_low_cutoff=1,
+        absolute_low_cutoff=8,
     )
 
     peak_info = find_peaks(
-        freq, average_power_spectrum, ringdown_params, prominence=0.001
+        freq, average_power_spectrum, ringdown_params, prominence=0.1
     )
-    peak_info = refine_peaks(peak_info, ringdown_params)
+    peak_info, lm_result = refine_peaks(peak_info, ringdown_params, height_cutoff=0.05)
     peak_info.power = average_power_spectrum
-    plot_spectrum_and_peak_info(ax_spectrum, peak_info, ringdown_params, annotate=True)
-    print(peak_info.peak_freqs)
+    plot_spectrum_and_peak_info(
+        ax_spectrum, peak_info, ringdown_params, annotate=annotate
+    )
+    if lm_result is not None:
+        ax_spectrum.plot(freq, lm_result.best_fit, color="red")
+
+    for i, peak_freq in enumerate(runtime.Ωs):
+        pos = np.abs(
+            params.measurement_detuning
+            - peak_freq.real / (2 * np.pi)
+            + params.δ * params.Ω
+            + params.laser_detuning,
+        )
+
+        ax_spectrum.axvline(
+            pos,
+            color="black",
+            alpha=0.5,
+            linestyle="--",
+            zorder=-100,
+        )
+
+        ax_spectrum.axvspan(
+            pos - peak_freq.imag / (2 * np.pi),
+            pos + peak_freq.imag / (2 * np.pi),
+            color="black",
+            alpha=0.05,
+            linestyle="--",
+            zorder=-100,
+        )
 
 
 def generate_data(
@@ -139,6 +159,7 @@ def generate_data(
     small_loop_detuning=0,
     excitation_lifetimes=2,
     measurement_lifetimes=4,
+    σ_modulation_time=0.01,
 ):
     η = 0.2
     Ω = 13
@@ -166,40 +187,75 @@ def generate_data(
     params.laser_off_time = params.lifetimes(excitation_lifetimes)
     params.drive_off_time = params.lifetimes(excitation_lifetimes)
 
-    t, solutions = make_shots(
-        params, excitation_lifetimes + measurement_lifetimes, eom_ranges, eom_steps
+    solutions = make_shots(
+        params,
+        excitation_lifetimes + measurement_lifetimes,
+        eom_ranges,
+        eom_steps,
+        σ_modulation_time,
     )
 
-    _, (sol_on_res) = make_shots(
+    (sol_on_res) = make_shots(
         params,
         excitation_lifetimes + measurement_lifetimes,
         ((1 + params.δ), (1 + params.δ)),
         1,
+        0,
     )
 
-    freq, average_power_spectrum = process_shots(t, solutions, noise_amplitude, params)
-    _, spectrum_on_resonance = process_shots(t, sol_on_res, noise_amplitude, params)
+    (sol_on_res_bath) = make_shots(
+        params,
+        excitation_lifetimes + measurement_lifetimes,
+        ((1), (1)),
+        1,
+        0,
+    )
+
+    freq, average_power_spectrum = process_shots(solutions, noise_amplitude, params)
+    _, spectrum_on_resonance = process_shots(sol_on_res, noise_amplitude, params)
+    _, spectrum_on_resonance_bath = process_shots(
+        sol_on_res_bath, noise_amplitude, params
+    )
 
     fig = make_figure()
     fig.clear()
 
-    ax_multi, ax_single = fig.subplot_mosaic("AA\nBB").values()
-    ax_multi.set_title("Averaged Power Spectrum")
-    ax_single.set_title("Single-shot Power-Spectrum with EOM on resonance")
+    fig.suptitle(f"""
+    Spectroscopy Protocol V2
 
-    for ax in [ax_multi, ax_single]:
-        ax.set_xlabel("Frequency (MHz)")
-        ax.set_ylabel("Power")
-        ax.set_yscale("log")
+    Ω/2π = {params.Ω}MHz, η/2π = {params.η}MHz, g_0 = {params.g_0}Ω, N = {params.N}
+    noise amplitude = {noise_amplitude} * 2/η, η_A = {η_factor} x η, EOM stepped from {eom_ranges[0]:.2f}Ω to {eom_ranges[1]:.2f}Ω in {eom_steps} steps
+    """)
+    ax_multi, ax_single, ax_single_bath = fig.subplot_mosaic("AA\nBC").values()
 
     plot_power_spectrum(ax_multi, freq, average_power_spectrum, params)
-    plot_power_spectrum(ax_single, freq, spectrum_on_resonance, params)
+    plot_power_spectrum(ax_single, freq, spectrum_on_resonance, params, annotate=False)
+    plot_power_spectrum(
+        ax_single_bath, freq, spectrum_on_resonance_bath, params, annotate=False
+    )
 
     runtime = RuntimeParams(params)
-    print(runtime.Ωs.real / (2 * np.pi) - params.laser_detuning)
+    for ax in [ax_multi, ax_single, ax_single_bath]:
+        ax.set_xlabel("Frequency (MHz)")
+        ax.sharex(ax_multi)
+        ax.sharey(ax_multi)
+
+        ax_ticks = ax.twiny()
+        ax_ticks.sharey(ax)
+        ax_ticks.set_xticks(runtime.ringdown_frequencies)
+        ax_ticks.set_xticklabels(
+            [mode_name(i, params.N) for i in range(2 * params.N + 2)]
+        )
+        ax_ticks.plot(freq, np.zeros_like(freq), alpha=0)
+        ax_ticks.set_xlim(ax.get_xlim())
+
+    ax_multi.set_title("Averaged Power Spectrum (sans noise offset)")
+    ax_single.set_title("Single-shot, EOM on A site")
+    ax_single_bath.set_title("Single-shot, EOM on bath mode")
 
     # ax_spectrum.set_yscale(yscale)
 
+    fig.tight_layout()
     return fig
 
 
@@ -208,12 +264,13 @@ if __name__ == "__main__":
     fig = generate_data(
         g_0=1,
         η_factor=5,
-        noise_amplitude=0.25 * 0,
+        noise_amplitude=2e-3,
         N=2,
-        eom_ranges=(1.1, 1.3),
-        eom_steps=20,
+        eom_ranges=(1.1, 1.35),
+        eom_steps=100,
         small_loop_detuning=0,
         laser_detuning=0,
         excitation_lifetimes=2,
-        measurement_lifetimes=20,
+        measurement_lifetimes=30,
+        σ_modulation_time=0.2,
     )
diff --git a/src/plot_utils.py b/src/plot_utils.py
index 07ccce1..5d6822e 100644
--- a/src/plot_utils.py
+++ b/src/plot_utils.py
@@ -7,6 +7,8 @@ import inspect
 import subprocess
 import pathlib
 import sys
+import numpy as np
+
 
 P = ParamSpec("P")
 R = TypeVar("R")
@@ -177,3 +179,51 @@ def quick_load_pickle(name):
 
     with open(path, "rb") as f:
         return pickle.load(f)
+
+
+def scientific_round(val, *err, retprec=False):
+    """Scientifically rounds the values to the given errors."""
+    val, err = np.asarray(val), np.asarray(err)
+    if len(err.shape) == 1:
+        err = np.array([err])
+        err = err.T
+    err = err.T
+
+    if err.size == 1 and val.size > 1:
+        err = np.ones_like(val) * err
+
+    if len(err.shape) == 0:
+        err = np.array([err])
+
+    if val.size == 1 and err.shape[0] > 1:
+        val = np.ones_like(err) * val
+
+    i = np.floor(np.log10(err))
+    first_digit = (err // 10**i).astype(int)
+    prec = (-i + np.ones_like(err) * (first_digit <= 3)).astype(int)
+    prec = np.max(prec, axis=1)
+
+    def smart_round(value, precision):
+        value = np.round(value, precision)
+        if precision <= 0:
+            value = value.astype(int)
+        return value
+
+    if val.size > 1:
+        rounded = np.empty_like(val)
+        rounded_err = np.empty_like(err)
+        for n, (value, error, precision) in enumerate(zip(val, err, prec)):
+            rounded[n] = smart_round(value, precision)
+            rounded_err[n] = smart_round(error, precision)
+
+        if retprec:
+            return rounded, rounded_err, prec
+        else:
+            return rounded, rounded_err
+
+    else:
+        prec = prec[0]
+        if retprec:
+            return (smart_round(val, prec), *smart_round(err, prec)[0], prec)
+        else:
+            return (smart_round(val, prec), *smart_round(err, prec)[0])
diff --git a/src/rabifun/analysis.py b/src/rabifun/analysis.py
index c98a88d..19b65ec 100644
--- a/src/rabifun/analysis.py
+++ b/src/rabifun/analysis.py
@@ -7,6 +7,7 @@ from dataclasses import dataclass
 
 from scipy.optimize import Bounds
 from enum import Enum
+import lmfit
 
 
 def fourier_transform(
@@ -180,8 +181,51 @@ def find_peaks(
     )
 
 
+def offset(ω, offset):
+    return offset
+
+
+def filter_peaks(
+    peaks: RingdownPeakData,
+    params: RingdownParams,
+    uncertainty_threshold: float = 0.2,
+    height_cutoff: float = 0.1,
+    to_be_deleted: list = [],
+):
+    deleted_peaks = []
+    for i in reversed(range(len(peaks.peak_freqs))):
+        A, ω0, γ = peaks.lorentz_params[i]
+        Δω0, Δγ = peaks.Δpeak_freqs[i], peaks.Δpeak_widths[i]
+
+        if (
+            i in to_be_deleted
+            or Δω0 > uncertainty_threshold * params.fΩ_guess
+            or A < height_cutoff
+            or A > 1
+            or Δγ > uncertainty_threshold * params.fΩ_guess
+        ):
+            np.delete(peaks.peaks, i)
+            np.delete(peaks.peak_freqs, i)
+            np.delete(peaks.Δpeak_freqs, i)
+            np.delete(peaks.peak_widths, i)
+            np.delete(peaks.Δpeak_widths, i)
+
+            del peaks.lorentz_params[i]
+            deleted_peaks.append(i)
+            continue
+
+    for key, value in peaks.peak_info.items():
+        if isinstance(value, np.ndarray):
+            peaks.peak_info[key] = np.delete(value, deleted_peaks)
+
+    return peaks
+
+
 def refine_peaks(
-    peaks: RingdownPeakData, params: RingdownParams, uncertainty_threshold: float = 0.1
+    peaks: RingdownPeakData,
+    params: RingdownParams,
+    uncertainty_threshold: float = 0.2,
+    height_cutoff: float = 0.1,
 ):
     """
     Refine the peak positions and frequencies by fitting Lorentzians.
@@ -204,8 +248,9 @@ def refine_peaks(
     Δwidths = []
     lorentz_params = []
 
-    window = params.η_guess * 3
+    window = params.η_guess * 1
     deleted_peaks = []
+
     for i, peak_freq in enumerate(peak_freqs):
         mask = (freqs > peak_freq - window) & (freqs < peak_freq + window)
         windowed_freqs = freqs[mask]
@@ -231,7 +276,7 @@ def refine_peaks(
         )
 
         try:
-            popt, pcov = scipy.optimize.curve_fit(
+            scipy_popt, pcov = scipy.optimize.curve_fit(
                 lorentzian,
                 windowed_freqs,
                 windowed_power,
@@ -239,20 +284,28 @@ def refine_peaks(
                 bounds=bounds,
             )
             perr = np.sqrt(np.diag(pcov))
-            popt[0] = popt[0] * scale_power
-            popt[1] = popt[1] * scale_freqs + root_freq
-            popt[2] = popt[2] * scale_freqs
 
-            lorentz_params.append(popt)
+            if (
+                perr[1] * scale_freqs > uncertainty_threshold * params.fΩ_guess
+                or scipy_popt[0] * scale_power / np.max(power) < height_cutoff
+            ):
+                deleted_peaks.append(i)
+                continue
+
+            scipy_popt[0] = scipy_popt[0] * scale_power
+            scipy_popt[1] = scipy_popt[1] * scale_freqs + root_freq
+            scipy_popt[2] = scipy_popt[2] * scale_freqs
+
+            lorentz_params.append(scipy_popt)
 
             if perr[1] > uncertainty_threshold * params.fΩ_guess:
                 deleted_peaks.append(i)
                 continue
 
-            new_freqs.append(popt[1])
+            new_freqs.append(scipy_popt[1])
             Δfreqs.append(perr[1])
 
-            new_widths.append(popt[2])
+            new_widths.append(scipy_popt[2])
             Δwidths.append(perr[2])
         except:
             deleted_peaks.append(i)
@@ -268,10 +321,63 @@ def refine_peaks(
     peaks.Δpeak_widths = np.array(Δwidths)
     peaks.lorentz_params = lorentz_params
 
-    return peaks
+    total_model = None
+    model_params = []
 
+    global_power_scale = 1  # power.max()
+    scaled_power = power / global_power_scale
 
-import matplotlib.pyplot as plt
+    for i, (A, ω0, γ) in enumerate(lorentz_params):
+        model = lmfit.Model(lorentzian, prefix=f"peak_{i}_")
+
+        initial_params = model.make_params(
+            A=dict(value=A / global_power_scale, min=0, max=np.inf),
+            ω0=dict(value=ω0, min=0, max=np.inf),
+            γ=dict(value=γ, min=0, max=np.inf),
+        )
+
+        if total_model is None:
+            total_model = model
+        else:
+            total_model += model
+
+        model_params.append(initial_params)
+
+    aggregate_params = total_model.make_params()
+    for lm_params in model_params:
+        aggregate_params.update(lm_params)
+
+    offset_model = lmfit.Model(offset)
+    aggregate_params.update(offset_model.make_params(offset=0, min=0, max=1))
+    total_model += offset_model
+
+    lm_result = total_model.fit(scaled_power, params=aggregate_params, ω=freqs)
+
+    for i in reversed(range(len(peaks.peak_freqs))):
+        peak_prefix = f"peak_{i}_"
+
+        A, ω0, γ = (
+            lm_result.best_values[peak_prefix + "A"],
+            lm_result.best_values[peak_prefix + "ω0"],
+            lm_result.best_values[peak_prefix + "γ"],
+        )
+
+        ΔA, Δω0, Δγ = (
+            lm_result.params[peak_prefix + "A"].stderr,
+            lm_result.params[peak_prefix + "ω0"].stderr,
+            lm_result.params[peak_prefix + "γ"].stderr,
+        )
+
+        peaks.peak_freqs[i] = ω0
+        peaks.Δpeak_freqs[i] = Δω0
+
+        peaks.peak_widths[i] = γ
+        peaks.Δpeak_widths[i] = Δγ
+
+        peaks.lorentz_params[i] = A, ω0, γ
+
+    peaks = filter_peaks(peaks, params, uncertainty_threshold, height_cutoff)
+    return peaks, lm_result
 
 
 class StepType(Enum):
diff --git a/src/rabifun/plots.py b/src/rabifun/plots.py
index a4a5b2c..aeb807c 100644
--- a/src/rabifun/plots.py
+++ b/src/rabifun/plots.py
@@ -225,24 +225,38 @@ def plot_spectrum_and_peak_info(
     """
 
     ax.clear()
-    ax.plot(peaks.freq, peaks.power, label="FFT Power", color="C0")
     ax.plot(
-        peaks.peak_freqs,
-        peaks.power[peaks.peaks],
-        "x",
-        label="Peaks",
-        color="C2",
+        peaks.freq,
+        peaks.power,
+        label="FFT Power",
+        color="C0",
+        linewidth=0.5,
+        marker="o",
+        markersize=2,
     )
 
-    ax_angle = ax.twinx()
-    ax_angle.clear()
-    ax_angle.set_ylabel("Phase (rad)")
-
     if annotate:
-        for i, (freq, height, lorentz) in enumerate(
-            zip(peaks.peak_freqs, peaks.power[peaks.peaks], peaks.lorentz_params)
+        for i, (freq, Δfreq, lorentz) in enumerate(
+            zip(peaks.peak_freqs, peaks.Δpeak_freqs, peaks.lorentz_params)
         ):
-            ax.annotate(f"{i} ({freq:.2e})", (freq, height))
+            # ax.plot(
+            #     freq,
+            #     max(lorentz[0], 1),
+            #     "x",
+            #     label="Peaks",
+            #     color="C2",
+            # )
+
+            roundfreq, rounderr = scientific_round(freq, Δfreq)
+
+            t = ax.text(
+                freq,
+                lorentz[0],
+                rf"{i} (${roundfreq}\pm {rounderr}$)",
+                fontsize=20,
+            )
+            t.set_bbox(dict(facecolor="white", alpha=1, edgecolor="white"))
+
             ax.plot(
                 peaks.freq,
                 lorentzian(peaks.freq, *lorentz),
@@ -261,4 +275,5 @@ def plot_spectrum_and_peak_info(
         zorder=-10,
         label="Frequency Shift",
     )
+    ax.set_xlim(peaks.freq[0], peaks.freq[-1])
     ax.legend()
diff --git a/src/rabifun/system.py b/src/rabifun/system.py
index c2b378c..cf47ff1 100644
--- a/src/rabifun/system.py
+++ b/src/rabifun/system.py
@@ -136,6 +136,8 @@ class RuntimeParams:
     """Secondary Parameters that are required to run the simulation."""
 
     def __init__(self, params: Params):
+        self.params = params
+
         H_A = np.array(
             [
                 [0, params.δ],
@@ -215,17 +217,34 @@ class RuntimeParams:
         """The mode splitting of the system in *frequency units*."""
         return (self.Ωs[1] - self.Ωs[0]).real / (4 * np.pi)
 
+    @property
+    def ringdown_frequencies(self) -> np.ndarray:
+        """
+        The frequencies that are detectable in the ringdown spectrum.
+        In essence, those are the eigenfrequencies of the system,
+        shifted by laser detuning and measurement detuning.
+        """
+
+        return np.abs(
+            self.params.measurement_detuning
+            - self.Ωs.real / (2 * np.pi)
+            + self.params.δ * self.params.Ω
+            + self.params.laser_detuning
+        )
+
 
 def time_axis(
     params: Params,
     lifetimes: float | None = None,
     recurrences: float | None = None,
+    total_time: float | None = None,
     resolution: float = 1,
 ):
     """Generate a time axis for the simulation.
 
     :param params: system parameters
     :param lifetimes: number of lifetimes to simulate
+    :params total_time: the total timespan to set of the time array
     :param resolution: time resolution
 
         Setting this to `1` will give the time axis just enough
@@ -238,6 +257,8 @@ def time_axis(
         tmax = params.lifetimes(lifetimes)
     elif recurrences is not None:
         tmax = recurrence_time(params) * recurrences
+    elif total_time:
+        tmax = total_time
     else:
         raise ValueError("Either lifetimes or recurrences must be set.")
 
@@ -437,13 +458,18 @@ def drive_frequencies_and_amplitudes(
     return ωs, Δs, amplitudes, a_shift
 
 
-def mode_name(mode: int):
+def mode_name(mode: int, N: int | None = None):
     """Return the name of the mode."""
     if mode == 0:
-        return "anti-A"
+        return r"$\bar{A}$"
     if mode == 1:
         return "A"
 
+    if N:
+        bath_mode = mode - 2
+        if mode >= N:
+            return rf"$\bar{{B}}{bath_mode % N + 1}$"
+
     return f"B{mode - 1}"