--- title: "Atom Interferometer Gravimeter Interactive Lab | Sandbox Physics" description: "How can three laser pulses measure gravity with falling atoms? Three laser pulses split each atom's wave, steer the two halves and recombine them." canonical_url: "https://sandboxphysics.com/labs/atom-interferometer-gravimeter/" language: "en" page_type: "lab" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/labs/atom-interferometer-gravimeter/" last_modified: "2026-10-27" --- Q008 · Split / recombine / count # Atom Interferometer Gravimeter **How can three laser pulses measure gravity with falling atoms?** Three laser pulses split each atom's wave, steer the two halves and recombine them. Gravity adds a phase that grows with the square of the time between pulses: double the time and the phase grows fourfold. Scanning the last pulse's phase and fitting the output counts reads it off. Longer waits raise the sensitivity but make it harder to tell which fringe you are on. Split an atomic matter wave, steer the two parts back together and recombine them. Scan the phase of the last laser pulse, fit the recorded counts, and see why a longer wait between pulses makes the measurement more sensitive but also more ambiguous. > Interactive simulation: open this page in a web browser to change the parameters and run the model. The model is an ideal short-pulse Raman interferometer in uniform gravity, with independent phase noise and the same detection loss for both outputs. Only the one-dimensional paths of the wave-packet centers are computed. The Lab makes no accuracy claim about finite pulses, vibration, wavefront errors or gravity gradients. 02 / Count at this setting ## Which internal state returns? Model reference Initial state · A 0 Transferred state · B 0 Not detected 0 Latest 60 trials at this setting. Blue: A · amber: B · grey: missed. Each trial starts with a fresh particle. Fraction in A · detected trials $\text{—}$ Pointwise 95% Wilson interval. Misses are retained in the raw records; the fraction conditions on detection. $\text{—}$ 03 / Read the fringe ## Gravity adds a phase, and the fringe moves. Fraction in A versus scan setting $\phi_L/\pi$ Blue points: recorded counts. Thin lines: Wilson intervals. Amber: model. Dashed blue: a fixed-period harmonic fit to the records. Click the chart to choose a setting. Estimated from the records $\text{—}$ Equivalent gravity above reference $\text{—}$ This is only one value from a periodic family of solutions. A single fringe cannot pick the absolute branch. $\text{—}$ At least eight settings with ten detections each are needed. An unresolved fringe gives no phase estimate. The errors come from a conservative variance bound and a local approximation; they do not describe instrument accuracy. 04 / Connect the paths to the phase ## Three pulses bring the two branches back together. $\text{—}$ Time runs to the right; height runs upward. Both centers move on the same vertical axis in the apparatus. Their separation is enlarged 12 times around their mean; the readout reports the actual separation. Dotted lines mark the three pulses. The first pulse splits, the middle pulse exchanges momenta, and the last recombines. State-selective detection counts the two internal outputs at one collection region. 05 / Save the evidence ## Save a sample, change one setting, then compare. Up to eight frozen samples. Saving freezes the run; the next acquisition starts a new run. Export includes active and saved trials with all preparation settings. Model, conventions & sources $$ P_A=\tfrac12[1+C_0e^{-\sigma_\phi^2/2}\cos\Delta\phi],\quad P_B=1-P_A $$ $$ \Delta\phi=k_{\rm eff}(g-g_c)T^2+\phi_L $$ Gravity and the effective wavevector are positive downward. The atoms are nominal rubidium-87 at a wavelength of 780 nm; the effective wavevector is twice the optical one, and the reference gravity is 9.81 metres per second squared. The launch velocity brings the atoms back near the starting height after the sequence. Gravity is uniform, the pulses are ideal and instantaneous, and the phase noise is independent and Gaussian. Finite pulse duration, correlated vibration, gradients and wavefront errors are left out. [McGuirk et al. · 2001](https://arxiv.org/abs/physics/0105088) Noise is averaged analytically before independent binary sampling. Detection loss is equal for both states and is recorded without a hidden outcome. The harmonic regression fixes the known period; it does not measure that period. It is unconstrained and descriptive, so finite samples can give fitted contrast above one. Physics tutorial ## Atom Interferometer Gravimeter **Background** A phase you can control shows up as a difference in counts between the two outputs. **Why it matters** A single count is random. A scan over many atoms traces out a fringe that you can reproduce. Start with the essentials - **Focus question**: How can three flashes of light measure a fall? - **One-sentence intuition**: Compare settings, keep the raw counts and fit only the counts you recorded. ### Core mathematical model #### Phase set by the fall $$ \Delta\phi=(k_{\rm eff}g-\alpha)T^2+\phi_3 $$ Downward acceleration and the effective wavevector count as positive. The chirp term is an angular-frequency chirp: the effective wavevector times the chirp acceleration, which is the reference value plus an offset. #### Recoil speed and largest separation $$ v_r=\hbar k_{\rm eff}/m,\qquad d_{\max}=v_rT $$ The first pulse adds a recoil kick, the middle pulse swaps it between the branches, and the last pulse brings the two centers together again. The branches separate vertically in the apparatus. #### Gravity spacing between equivalent fringes $$ \Delta g_{\rm period}=\frac{2\pi}{k_{\rm eff}T^2} $$ The fit returns one gravity offset, but shifting it by any whole number of these intervals fits equally well. Picking the right fringe takes extra information. #### Second difference of the laser phase $$ \phi_L(0)-2\phi_L(T)+\phi_L(2T)=(k_{\rm eff}g-\alpha)T^2 $$ With uniform acceleration and instantaneous pulses, the constant term and the initial-velocity term cancel. Real vibration, finite pulse length and wavefront effects are left out. #### Detector loss and phase noise $$ C=C_0e^{-\sigma_\phi^2/2},\quad P_{\varnothing}=1-\eta $$ Independent Gaussian phase noise is averaged analytically. Loss that is equal for both outputs reduces the number of detected atoms, not the visibility among those detected. ### Common difficulties #### A path is not a trajectory **Typical misconception** The colored lines show which way each detected atom went. **Better mental model** They show the coherent branches of the wave or the centers of the wave packets. Nothing records which path an atom took. #### A small fit error is not real accuracy **Typical misconception** A small fit error proves the real instrument is accurate. **Better mental model** The quoted uncertainty is only the statistical error within this model. Apparatus effects the model leaves out, and the ambiguity, are still there. ### Run the experiment 1. 01 #### Predict Try the first two presets and predict which exit gains counts. **What to observe:** A preset only sets the conditions; it does not record any data. 2. 02 #### Measure Detect once, then collect 200 trials. Scan all 21 positions. **What to observe:** Missed atoms stay in the record. The output frequency and its pointwise Wilson interval use only the detected atoms. 3. 03 #### Compare Save the scan, change coherence or pulse spacing, and scan again. Export both runs. **What to observe:** When the contrast is low, no phase estimate is given. A longer pulse spacing narrows the gravity ambiguity interval. Physical conclusion Keep three things apart: the model's reference curve, what you measured and the phase ambiguity that remains. Quantum & fields · Starter path ## Start from a single measurement Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference. [Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/) 1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/) 2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/) 3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/) 4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/) 5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/) 6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/) [View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)