diff --git a/scripts/simulations/002_calibration_demonstration.py b/scripts/simulations/002_calibration_demonstration.py
new file mode 100644
index 0000000..81989fe
--- /dev/null
+++ b/scripts/simulations/002_calibration_demonstration.py
@@ -0,0 +1,426 @@
+"""A demonstration of the ringdown spectroscopy protocol."""
+
+from rabifun.system import *
+from rabifun.plots import *
+from rabifun.utilities import *
+from ringfit.utils import WelfordAggregator
+from rabifun.analysis import *
+import multiprocessing
+import copy
+
+
+def solve_shot(
+    params: Params, t: np.ndarray, t_before: np.ndarray, t_after: np.ndarray
+):
+    """A worker function to solve for the time evolution in separate processes.
+
+    :param params: The parameters of the system.
+    :param t: The time axis.
+    :param t_before: The time axis before the EOM is switched off.
+    :param t_after: The time axis after the EOM is switched off.
+    """
+
+    solution = solve(t, params)
+    amps = solution.y[::, len(t_before) - 1 :]
+
+    return t_after, amps
+
+
+def make_shots(
+    params: Params,
+    total_lifetimes: float,
+    eom_range: tuple[float, float],
+    eom_steps: int,
+    num_freq: int = 1,
+    randomize_off_time: bool = True,
+):
+    """Generate a series of shots with varying EOM frequencies.
+
+    The implementation here slightly varies the off time of the laser
+    so as to introduce some random relative phases of the modes.
+
+    :param params: The parameters of the system.
+    :param total_lifetimes: The total time of the experiment in
+        lifetimes.
+    :param eom_range: The range of EOM frequencies in units of
+        :any:`params.Ω`.
+    :param eom_steps: The number of steps in the EOM frequency range.
+    :param num_freq: The number of frequencies to drive.  If a number
+        greater than 1 is given, the EOM will be driven at multiple
+        frequencies where the highest frequency is the base frequency
+        plus an consecutive integer multiples of :any:`params.Ω`.
+    :param randomize_off_time: Whether to randomize the off time of the
+        laser.  This is useful to introduce some random relative phases
+        for the modes.
+    """
+
+    solutions = []
+    shot_params = []
+
+    rng = np.random.default_rng(seed=0)
+    off_time = params.laser_off_time or 0
+    analyze_time = params.lifetimes(total_lifetimes) - off_time
+    t_after = time_axis(params, total_time=analyze_time, resolution=0.01)
+
+    for step in range(eom_steps):
+        base = params.Ω * (
+            eom_range[0] + (eom_range[1] - eom_range[0]) * step / eom_steps
+        )
+
+        current_params = copy.deepcopy(params)
+        current_params.drive_override = (
+            base + params.Ω * np.arange(num_freq),
+            np.ones(num_freq),
+        )
+
+        current_params.drive_phases = rng.uniform(0, 2 * np.pi, size=num_freq)
+        off_time += rng.normal(0, 0.1 * off_time) if randomize_off_time else 0
+
+        current_params.laser_off_time = None  # off_time
+        current_params.drive_off_time = off_time
+
+        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((current_params, t, t_before, t_after))
+
+    pool = multiprocessing.Pool()
+    solutions = pool.starmap(solve_shot, shot_params)
+    return solutions
+
+
+def process_shots(
+    params: Params,
+    solutions: list[tuple[np.ndarray, np.ndarray]],
+    noise_amplitude: float,
+    num_freq: int,
+):
+    """
+    Calculates the normalized average Fourier power spectrum of a
+    series of experimental (simulated) shots.
+
+    :param params: The parameters of the system.
+    :param solutions: A list of solutions to process returned by
+        :any:`solve_shot`.
+    :param noise_amplitude: The amplitude of the noise to add to the
+        signal.
+
+        The amplitude is normalized by 2/η which is roughly the steady
+        state signal amplitude if a bath mode is excited resonantly by
+        a unit-strength input.
+
+    :param num_freq: The number of frequencies to drive.  See
+        :any:`make_shots` for details.
+    """
+
+    rng = np.random.default_rng(seed=0)
+
+    noise_amplitude /= params.η * np.pi
+
+    aggregate = None
+    for t, amps in solutions:
+        signal = output_signal(t, amps, params)
+        signal += rng.normal(scale=noise_amplitude, size=len(signal))
+        window = (0, t[-1])
+
+        freq, fft = fourier_transform(
+            t,
+            signal,
+            low_cutoff=0.3 * params.Ω,
+            high_cutoff=params.Ω * (1 + num_freq),
+            window=window,
+        )
+
+        power = np.abs(fft) ** 2
+
+        # ugly hack because shape is hard to predict
+        if aggregate is None:
+            aggregate = WelfordAggregator(power)
+        else:
+            aggregate.update(power)
+
+    assert aggregate is not None  # appease pyright
+
+    max_power = np.max(aggregate.mean)
+    return (freq, aggregate.mean / max_power, aggregate.ensemble_std / max_power)
+
+
+def process_and_plot_results(
+    params: Params,
+    ax: plt.Axes,
+    freq: np.ndarray,
+    average_power_spectrum: np.ndarray,
+    σ_power_spectrum: np.ndarray,
+    annotate: bool = True,
+):
+    """
+    Fits the ringdown spectrum and plots the results.
+
+    :param params: The parameters of the system.
+    :param ax: The axis to plot on.
+    :param freq: The frequency array.
+    :param average_power_spectrum: The average power spectrum obtained from :any:`process_shots`.
+    :param σ_power_spectrum: The standard deviation of the power
+        spectrum.
+    :param annotate: Whether to annotate the plot with peak and mode positions.
+    """
+
+    ringdown_params = RingdownParams(
+        fω_shift=params.measurement_detuning,
+        mode_window=(params.N, params.N),
+        fΩ_guess=params.Ω,
+        fδ_guess=params.Ω * params.δ,
+        η_guess=0.5,
+        absolute_low_cutoff=0.3 * params.Ω,
+    )
+
+    peak_info = find_peaks(
+        freq,
+        average_power_spectrum,
+        ringdown_params,
+        prominence=0.05,
+        height=0.1,
+        σ_power=σ_power_spectrum,
+    )
+
+    peak_info = refine_peaks(peak_info, ringdown_params, height_cutoff=0.05)
+
+    plot_spectrum_and_peak_info(ax, peak_info, annotate=annotate)
+
+    if peak_info.lm_result is not None:
+        fine_freq = np.linspace(freq.min(), freq.max(), 5000)
+        fine_fit = peak_info.lm_result.eval(ω=fine_freq)
+        ax.plot(
+            fine_freq,
+            fine_fit - peak_info.noise_floor,
+            color="C3",
+            zorder=-100,
+            label="Fit",
+        )
+        ax.set_ylim(-0.1, max(1, fine_fit.max() * 1.1))
+
+    ax.set_xlabel("Frequency (MHz)")
+    ax.legend()
+
+    if annotate:
+        annotate_ringodown_mode_positions(params, ax)
+
+
+def generate_data(
+    Ω=13,
+    η=0.2,
+    g_0=0.5,
+    η_factor=5,
+    noise_amplitude=0.3,
+    laser_detuning=0,
+    laser_on_mode=0,
+    N=10,
+    eom_ranges=(0.5, 2.5),
+    eom_steps=20,
+    excitation_lifetimes=2,
+    measurement_lifetimes=4,
+    num_freq=3,
+    extra_title="",
+    save: str | None = None,
+    randomize_off_time: bool = True,
+):
+    """Simulate and plot the ringdown spectroscopy protocol.
+
+    The idea is to have the laser on ``laser_on_mode`` and to sweep
+    the EOM frequency over a range of values given in ``eom_ranges``
+    in ``eom_steps`` steps.  For each step, the laser and EOM are
+    inputting into the system for a time given by
+    ``excitation_lifetimes``.  Then, the ringdown signal is collected
+    for a time given by ``measurement_lifetimes``.  (Lifetime units
+    are given by ``η``.) The resulting power spectra are averaged and
+    then fitted.
+
+    :param Ω: The FSR of the system.
+    :param η: The decay rate of the system.
+    :param g_0: The coupling strength of the system in units of
+        :any:`Ω`.  Note that the effective coupling strength between
+        the ``A`` site and the bath modes is reduced by a factor of
+        :math:`\sqrt{2}`.
+
+    :param η_factor: The factor by which the decay rate of the A site
+        is greater.
+    :param noise_amplitude: The amplitude of the noise to add to the
+        signal.  See :any:`process_shots` for details.
+    :param laser_detuning: The detuning of the laser from the the mode
+        it is exciting.
+    :param laser_on_mode: The mode that the laser is exciting.
+    :param N: The number of bath modes.
+    :param eom_ranges: The range of EOM frequencies in units of
+        :any:`Ω`.
+    :param eom_steps: The number of steps in the EOM frequency range.
+    :param excitation_lifetimes: The time the EOM is driving the
+        system.
+    :param measurement_lifetimes: The time the system is left to ring
+        down.
+
+        Note that the laser is not turned off during the ringdown.
+
+    :param num_freq: The number of frequencies to drive.  See
+        :any:`make_shots` for details.
+    :param extra_title: A string to add to the title of the plot.
+    :param save: The filename to save the figure to.  If None,
+        the figure is not saved.
+    :param randomize_off_time: Whether to randomize the off time of the
+        laser.  See :any:`make_shots` for details.
+
+    :returns: The figure containing the plot.
+    """
+
+    final_laser_detuning = laser_detuning + (
+        0 if laser_on_mode == 0 else (laser_on_mode - 1 / 4) * Ω
+    )
+
+    params = Params(
+        η=η,
+        η_hybrid=η_factor * η,
+        Ω=Ω,
+        δ=1 / 4,
+        ω_c=0.1,
+        g_0=g_0 * num_freq,  # as it would be normalized otherwise
+        laser_detuning=final_laser_detuning,
+        N=N,
+        N_couplings=N,
+        measurement_detuning=0,
+        α=0,
+        rwa=False,
+        flat_energies=False,
+        correct_lamb_shift=0,
+        laser_off_time=None,
+        small_loop_detuning=0,
+        drive_override=(np.array([]), np.array([])),
+    )
+
+    params.laser_off_time = params.lifetimes(excitation_lifetimes)
+    params.drive_off_time = params.lifetimes(excitation_lifetimes)
+
+    solutions = make_shots(
+        params,
+        excitation_lifetimes + measurement_lifetimes,
+        eom_ranges,
+        eom_steps,
+        num_freq,
+        randomize_off_time=randomize_off_time,
+    )
+
+    freq, average_power_spectrum, σ_power_spectrum = process_shots(
+        params,
+        solutions,
+        noise_amplitude,
+        num_freq,
+    )
+
+    fig = make_figure(extra_title, figsize=(12, 6))
+    fig.clear()
+    ax = fig.subplots()
+
+    process_and_plot_results(params, ax, freq, average_power_spectrum, σ_power_spectrum)
+    ax.text(
+        0.01,
+        0.95,
+        f"""$Ω/2π = {params.Ω}$MHz
+$η/2π = {params.η}MHz$
+$g_0 = {params.g_0}Ω$
+$N = {params.N}$
+noise = ${noise_amplitude * 2}$
+$η_A = {η_factor}η$
+EOM range = {eom_ranges[0]:.2f}Ω to {eom_ranges[1]:.2f}Ω
+EOM steps = {eom_steps}
+excitation time = {excitation_lifetimes} lifetimes
+measurement time = {measurement_lifetimes} lifetimes
+on mode = {laser_on_mode}
+laser detuning = {laser_detuning}
+num freq = {num_freq}
+total time = {(excitation_lifetimes + measurement_lifetimes) * eom_steps / (params.η * 1e6)}s
+randomize off time = {'yes' if randomize_off_time else 'no'} """,
+        transform=ax.transAxes,
+        ha="left",
+        va="top",
+        size=10,
+        bbox=dict(boxstyle="round", facecolor="wheat", alpha=0.9),
+    )
+    ax.set_title(extra_title)
+
+    fig.tight_layout()
+
+    save_figure(fig, f"002_{save}")
+    quick_save_pickle(
+        locals(),
+        f"002_{save}",
+    )
+
+    return fig
+
+
+# %% save
+if __name__ == "__main__":
+    generate_data(
+        g_0=0.5,
+        η_factor=5,
+        noise_amplitude=0.3,
+        N=5,
+        eom_ranges=(0.7, 0.9),
+        eom_steps=100,
+        laser_detuning=0,
+        laser_on_mode=0,
+        excitation_lifetimes=2,
+        measurement_lifetimes=4,
+        num_freq=4,
+        randomize_off_time=True,
+        extra_title="Laser on A site",
+        save="001_laser_on_A",
+    )
+
+    fig = generate_data(
+        g_0=0.5,
+        η_factor=5,
+        noise_amplitude=0.3,
+        N=5,
+        eom_ranges=(1.2, 1.3),
+        eom_steps=200,
+        laser_detuning=0,
+        laser_on_mode=-1,
+        excitation_lifetimes=2,
+        measurement_lifetimes=4,
+        num_freq=1,
+        extra_title="Laser on Bath Mode",
+        randomize_off_time=True,
+        save="002_laser_on_bath",
+    )
+
+    fig = generate_data(
+        g_0=0.3,
+        η_factor=5,
+        noise_amplitude=0.0,
+        N=5,
+        eom_ranges=(1.2, 1.3),
+        eom_steps=100,
+        laser_detuning=0,
+        laser_on_mode=-1,
+        excitation_lifetimes=2,
+        measurement_lifetimes=4,
+        num_freq=1,
+        randomize_off_time=False,
+        extra_title="Laser on Bath Mode, No randomized off-time.",
+        save="003_laser_on_bath_no_random",
+    )
+
+    fig = generate_data(
+        g_0=0.3,
+        η_factor=5,
+        noise_amplitude=0.0,
+        N=5,
+        eom_ranges=(1.2, 1.3),
+        eom_steps=100,
+        laser_detuning=0,
+        laser_on_mode=-1,
+        excitation_lifetimes=2,
+        measurement_lifetimes=4,
+        num_freq=1,
+        randomize_off_time=True,
+        extra_title="Laser on Bath Mode, Randomized off-time.",
+        save="004_laser_on_bath_random",
+    )
diff --git a/scripts/simulations/figs/002_001_laser_on_A.pdf b/scripts/simulations/figs/002_001_laser_on_A.pdf
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+change_id: nnyqrroulxpmtpxksrmpyoozouxtluur
+commit_id: bc45229f9e8466056fd4d5143f87e739dd3785ae
+description: 'RESULT: calibration simulation'
+extra_meta: null
+function: generate_data
+function_args:
+  N: 5
+  eom_ranges: !!python/tuple
+  - 0.7
+  - 0.9
+  eom_steps: 100
+  excitation_lifetimes: 2
+  extra_title: Laser on A site
+  g_0: 0.5
+  laser_detuning: 0
+  laser_on_mode: 0
+  measurement_lifetimes: 4
+  noise_amplitude: 0.3
+  num_freq: 4
+  randomize_off_time: true
+  save: 001_laser_on_A
+  Ω: 13
+  η: 0.2
+  η_factor: 5
+name: 002_001_laser_on_A
+refers_to: ./figs/002_001_laser_on_A.pdf
+source: scripts/simulations/002_calibration_demonstration.py
diff --git a/scripts/simulations/figs/002_001_laser_on_A.png b/scripts/simulations/figs/002_001_laser_on_A.png
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diff --git a/scripts/simulations/figs/002_002_laser_on_bath.pdf b/scripts/simulations/figs/002_002_laser_on_bath.pdf
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+++ b/scripts/simulations/figs/002_002_laser_on_bath.pdf.meta.yaml
@@ -0,0 +1,27 @@
+change_id: nnyqrroulxpmtpxksrmpyoozouxtluur
+commit_id: 79069d5f978fcd3e48fa401aad6dbcfcf2d8f917
+description: 'RESULT: calibration simulation'
+extra_meta: null
+function: generate_data
+function_args:
+  N: 5
+  eom_ranges: !!python/tuple
+  - 1.2
+  - 1.3
+  eom_steps: 200
+  excitation_lifetimes: 2
+  extra_title: Laser on Bath Mode
+  g_0: 0.5
+  laser_detuning: 0
+  laser_on_mode: -1
+  measurement_lifetimes: 4
+  noise_amplitude: 0.3
+  num_freq: 1
+  randomize_off_time: true
+  save: 002_laser_on_bath
+  Ω: 13
+  η: 0.2
+  η_factor: 5
+name: 002_002_laser_on_bath
+refers_to: ./figs/002_002_laser_on_bath.pdf
+source: scripts/simulations/002_calibration_demonstration.py
diff --git a/scripts/simulations/figs/002_002_laser_on_bath.png b/scripts/simulations/figs/002_002_laser_on_bath.png
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+++ b/scripts/simulations/figs/002_003_laser_on_bath_no_random.pdf.meta.yaml
@@ -0,0 +1,27 @@
+change_id: nnyqrroulxpmtpxksrmpyoozouxtluur
+commit_id: ec06ea8db6bf543984fa0cf3b39843c05044e654
+description: 'RESULT: calibration simulation'
+extra_meta: null
+function: generate_data
+function_args:
+  N: 5
+  eom_ranges: !!python/tuple
+  - 1.2
+  - 1.3
+  eom_steps: 100
+  excitation_lifetimes: 2
+  extra_title: Laser on Bath Mode, No randomized off-time.
+  g_0: 0.3
+  laser_detuning: 0
+  laser_on_mode: -1
+  measurement_lifetimes: 4
+  noise_amplitude: 0.0
+  num_freq: 1
+  randomize_off_time: false
+  save: 003_laser_on_bath_no_random
+  Ω: 13
+  η: 0.2
+  η_factor: 5
+name: 002_003_laser_on_bath_no_random
+refers_to: ./figs/002_003_laser_on_bath_no_random.pdf
+source: scripts/simulations/002_calibration_demonstration.py
diff --git a/scripts/simulations/figs/002_003_laser_on_bath_no_random.png b/scripts/simulations/figs/002_003_laser_on_bath_no_random.png
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+++ b/scripts/simulations/figs/002_004_laser_on_bath_random.pdf.meta.yaml
@@ -0,0 +1,27 @@
+change_id: nnyqrroulxpmtpxksrmpyoozouxtluur
+commit_id: 7d0e9be06057bfe7332a83bf4997b15565a4f832
+description: 'RESULT: calibration simulation'
+extra_meta: null
+function: generate_data
+function_args:
+  N: 5
+  eom_ranges: !!python/tuple
+  - 1.2
+  - 1.3
+  eom_steps: 100
+  excitation_lifetimes: 2
+  extra_title: Laser on Bath Mode, Randomized off-time.
+  g_0: 0.3
+  laser_detuning: 0
+  laser_on_mode: -1
+  measurement_lifetimes: 4
+  noise_amplitude: 0.0
+  num_freq: 1
+  randomize_off_time: true
+  save: 004_laser_on_bath_random
+  Ω: 13
+  η: 0.2
+  η_factor: 5
+name: 002_004_laser_on_bath_random
+refers_to: ./figs/002_004_laser_on_bath_random.pdf
+source: scripts/simulations/002_calibration_demonstration.py
diff --git a/scripts/simulations/figs/002_004_laser_on_bath_random.png b/scripts/simulations/figs/002_004_laser_on_bath_random.png
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diff --git a/scripts/simulations/outputs/002_001_laser_on_A.pkl.meta.yaml b/scripts/simulations/outputs/002_001_laser_on_A.pkl.meta.yaml
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index 0000000..9c292d3
--- /dev/null
+++ b/scripts/simulations/outputs/002_001_laser_on_A.pkl.meta.yaml
@@ -0,0 +1,7 @@
+change_id: nnyqrroulxpmtpxksrmpyoozouxtluur
+commit_id: f9eaf01d1e1c5b0925d718c69a7f84e0e14ce875
+description: 'RESULT: calibration simulation'
+function: generate_data
+function_args: {}
+refers_to: outputs/002_001_laser_on_A.pkl
+source: scripts/simulations/002_calibration_demonstration.py
diff --git a/scripts/simulations/outputs/002_002_laser_on_bath.pkl.meta.yaml b/scripts/simulations/outputs/002_002_laser_on_bath.pkl.meta.yaml
new file mode 100644
index 0000000..7d89d92
--- /dev/null
+++ b/scripts/simulations/outputs/002_002_laser_on_bath.pkl.meta.yaml
@@ -0,0 +1,7 @@
+change_id: nnyqrroulxpmtpxksrmpyoozouxtluur
+commit_id: 471ae089658da27f23b939a65b24607786ebd880
+description: 'RESULT: calibration simulation'
+function: generate_data
+function_args: {}
+refers_to: outputs/002_002_laser_on_bath.pkl
+source: scripts/simulations/002_calibration_demonstration.py
diff --git a/scripts/simulations/outputs/002_003_laser_on_bath_no_random.pkl.meta.yaml b/scripts/simulations/outputs/002_003_laser_on_bath_no_random.pkl.meta.yaml
new file mode 100644
index 0000000..77a07b3
--- /dev/null
+++ b/scripts/simulations/outputs/002_003_laser_on_bath_no_random.pkl.meta.yaml
@@ -0,0 +1,7 @@
+change_id: nnyqrroulxpmtpxksrmpyoozouxtluur
+commit_id: 97126fb016e5811d4ba2682ca4371ae561cb3e5b
+description: 'RESULT: calibration simulation'
+function: generate_data
+function_args: {}
+refers_to: outputs/002_003_laser_on_bath_no_random.pkl
+source: scripts/simulations/002_calibration_demonstration.py
diff --git a/scripts/simulations/outputs/002_003_laser_on_bath_random.pkl.meta.yaml b/scripts/simulations/outputs/002_003_laser_on_bath_random.pkl.meta.yaml
new file mode 100644
index 0000000..bb3474d
--- /dev/null
+++ b/scripts/simulations/outputs/002_003_laser_on_bath_random.pkl.meta.yaml
@@ -0,0 +1,7 @@
+change_id: nnyqrroulxpmtpxksrmpyoozouxtluur
+commit_id: df99bc5460c3241dc76a628d40dde8f5c9242ca2
+description: 'RESULT: calibration simulation'
+function: generate_data
+function_args: {}
+refers_to: outputs/002_003_laser_on_bath_random.pkl
+source: scripts/simulations/002_calibration_demonstration.py
diff --git a/scripts/simulations/outputs/002_004_laser_on_bath_random.pkl.meta.yaml b/scripts/simulations/outputs/002_004_laser_on_bath_random.pkl.meta.yaml
new file mode 100644
index 0000000..f3a90f0
--- /dev/null
+++ b/scripts/simulations/outputs/002_004_laser_on_bath_random.pkl.meta.yaml
@@ -0,0 +1,7 @@
+change_id: nnyqrroulxpmtpxksrmpyoozouxtluur
+commit_id: 7a4a4d061cb43345a0984d34b902b485fa956704
+description: 'RESULT: calibration simulation'
+function: generate_data
+function_args: {}
+refers_to: outputs/002_004_laser_on_bath_random.pkl
+source: scripts/simulations/002_calibration_demonstration.py
diff --git a/src/rabifun/plots.py b/src/rabifun/plots.py
index 2fc696f..29f9ca4 100644
--- a/src/rabifun/plots.py
+++ b/src/rabifun/plots.py
@@ -219,6 +219,8 @@ def plot_spectrum_and_peak_info(ax, peaks: RingdownPeakData, annotate=False):
     :param ax: The axis to plot on.
     :param peaks: The peak data.
     :param annotate: Whether to annotate the peaks.
+
+        If ``true`` each peak will be annotated with it's estimated frequency.
     """
 
     ax.clear()
@@ -243,7 +245,8 @@ def plot_spectrum_and_peak_info(ax, peaks: RingdownPeakData, annotate=False):
                 freq,
                 lorentz[0] * 1.1,
                 rf"{i} (${roundfreq}\pm {rounderr}$)",
-                fontsize=20,
+                fontsize=10,
+                clip_on=True,
             )
             t.set_bbox(dict(facecolor="white", alpha=0.8, edgecolor="white"))