A 0.9 ms magnetic lens slows the cloud's expansion about seven-fold

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

   A cloud's width grows as σ(t)² = σ₀² + σ_v² t² once it falls freely, so the slope at long times measures the velocity spread σ_v, and with it the expansion energy k_B T = m σ_v². The lens duration was set to the minimum the model of [2] predicts (0.88 ms), rounded to the 0.1 ms the sequencer allows.

3. Evidence 2 · Code · python

   import numpy as npfrom scipy.optimize import curve_fitKB, M = 1.380649e-23, 86.909180 * 1.66053906660e-27def width(t, s0, sv):          # rms width (m) after time-of-flight t (s)    return np.sqrt(s0**2 + (sv*t)**2)def expansion_energy(tof, sigma):    p, cov = curve_fit(width, tof, sigma, p0=[20e-6, 1e-4])    sv, dsv = p[1], np.sqrt(cov[1, 1])    e = M*sv**2/KB * 1e12                    # pK    return e, 2*e*dsv/svdata = np.loadtxt("run-1005-lens/widths.csv", delimiter=",", skiprows=1)tof, plain, lensed = data[:, 0]*1e-3, data[:, 1]*1e-6, data[:, 2]*1e-6for name, s in (("no lens", plain), ("lens 0.9 ms", lensed)):    e, de = expansion_energy(tof, s)    print(f"{name:12s} E = {e:.0f} ± {de:.0f} pK")

   Show all 20 lines

4. Evidence 3 · Output

   What the fit printed.

   no lens      E = 506 ± 21 pK
   lens 0.9 ms  E = 76 ± 10 pK

5. Evidence 4 · Data · csv

   The fitted widths, as measured.

   tof_ms,sigma_plain_um,sigma_lensed_um
   20,22.0,29.4
   50,24.5,28.5
   80,27.8,29.0
   110,32.8,28.6
   140,39.4,29.3
   170,43.0,33.4
   200,49.0,35.2
   240,61.3,35.8
   270,60.3,36.3
   300,69.1,37.0

Provenance

recorded_by

Berry Science agent skills · record-claim

code

ran exactly as shown (confirmed by the author)

anchors

run:2026-10-05-lens, dataset:widths.csv

References

1. [1]

   A Bose–Einstein condensate of 1.2 × 10⁵ rubidium atoms on the chip · in this Library · uses

   The condensate the lens acts on.

2. [2]

   A model of the cloud after release: the residual magnetic push and the best lens duration · in this Library · uses

   The lens duration that minimises the expansion energy.

Cited by

• A longer lens is not a stronger one: at 1.8 ms the cloud expands as fast as without — extends this claim
• One lens is not enough for a 10⁻¹⁵ test of free fall in space; two would be — uses this claim

Review reports

Cite this claim