A Bose–Einstein condensate of 1.2 × 10⁵ rubidium atoms on the chip

Conventions

units.lab v1

Lengths in mm or µm, times in ms or s, accelerations in mm/s²; z points away from the chip surface. Expansion energies as k_B·T in pK, with k_B T = m σ_v². · units

Evidence

1. Evidence 1 · Reasoning · markdown

   The image is summed along one axis and fitted with the two-part profile of a partly condensed cloud: an inverted parabola for the condensate, a Gaussian for the thermal atoms. Each part's area, divided by the resonant cross-section, is an atom number. The condensed fraction follows from the two.

2. Evidence 2 · Code · python

   The fit, as it ran on the camera frame.

   import numpy as npfrom scipy.optimize import curve_fitPIXEL = 4.0e-6                         # m per pixel, object planeSIGMA0 = 3 * 780.241e-9**2 / (2*np.pi)  # resonant cross-section, m^2def bimodal(x, a_bec, r_tf, a_th, s_th, x0, off):    u = np.clip(1 - ((x - x0) / r_tf)**2, 0, None)    return a_bec*u**2 + a_th*np.exp(-(x - x0)**2 / (2*s_th**2)) + offod = np.load("run-0929-17/od_tof20ms.npy")   # optical density imageprofile = od.sum(axis=0)                      # integrate along zx = np.arange(profile.size, dtype=float)p, cov = curve_fit(bimodal, x, profile, p0=[60, 18, 10, 28, x.size/2, 0])err = np.sqrt(np.diag(cov))def atoms(area):   # integrated OD -> atom number    return area * PIXEL**2 / SIGMA0n_bec = atoms(p[0] * p[1] * 16/15)           # ∫(1-u²)² du = 16/15 r_tfn_th = atoms(p[2] * p[3] * np.sqrt(2*np.pi))print(f"N_BEC = {n_bec:.3e}  N_th = {n_th:.3e}  "      f"fraction = {n_bec/(n_bec+n_th):.3f}")print(f"relative uncertainty of N_BEC: fit {np.hypot(err[0]/p[0], err[1]/p[1]):.4f}, "      f"with 5 % calibration {np.hypot(np.hypot(err[0]/p[0], err[1]/p[1]), 0.05):.3f}")

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3. Evidence 3 · Parameters · yaml

   evaporation: 1.6 s, final RF 3.62 MHztime_of_flight: 20 msimaging: resonant, σ⁺, 50 µspixel_size: 4.0 µm (object plane)camera_frame: run-0929-17/od_tof20ms.npy

4. Evidence 4 · Output

   What the fit printed.

   fit: a_bec = 113.22 ± 0.29, r_tf = 17.97 ± 0.03 px, a_th = 11.56 ± 0.43, s_th = 26.49 ± 1.61 px
   N_BEC = 1.194e+05  N_th = 4.225e+04  fraction = 0.739
   relative uncertainty of N_BEC: fit 0.0030, with 5 % calibration 0.050

Provenance

recorded_by

Berry Science agent skills · record-claim

code

ran exactly as shown (confirmed by the author)

anchors

run:2026-09-29-17, dataset:od_tof20ms

Cited by

• A 0.9 ms magnetic lens slows the cloud's expansion about seven-fold — uses this claim

Review reports

Cite this claim