Figure 1

(a) Chip geometry. We use dc currents superposed with a static homogeneous field ${\mathbf{B}}_{\mathbf{0}}=(B_x,B_y,B_z)=(15,8,0)\mathrm{G}$. To first approximation, the potential can be understood as follows: The field of $I_0=100\mathrm{mA}$ combines with ${\mathbf{B}}_{\mathbf{0}}$ to create harmonic confinement in the $xy$ plane. The minimum is located at a distance $z_0={\mu }_0{I}_0/2\pi B_y$ from the $I_0$ wire and the field in the minimum is $B_x$. This minimum is modified by $I_1=2.0\mathrm{mA}$ and $I_2$, whose fields are predominantly along $x$ on the trap axis. For $z_0\gtrsim d$, the two $I_1$ wires together provide harmonic confinement along $x$. $I_2$, of opposite polarity, creates the barrier of adjustable height and also determines the spacing between the two resulting wells. (b) Profile of the trapping potential along the splitting axis $x$, for $I_2=0\mathrm{mA}$ (cooling trap, dashed line) and $I_2=2.4\mathrm{mA}$ (solid line). The $x$ axis is the same as in (a). (c) Barrier height $V_b$ (top), trap frequencies ($f_x,f_y,f_z$) (center), and position $x_0$ of the right minimum (bottom) as functions of the current $I_2$. Lines, numerical calculation based on current configuration; blue circles, measured frequencies $f_x$.Reuse & Permissions

Figure 2

First experiment. Fluctuations of the atom number difference as a function of splitting time ${\tau }_r$ for a BEC with $N=1300$. Red squares, measured ${\xi }^2$; dotted line, dynamical TMM simulation. Upper inset: $E_C$ (dashed line) and $E_J$ (solid line) from numerical 3D Gross-Pitaevskii equation solution for 1300 atoms using the full calculated potential. Lower inset: Degradation of the number squeezing under the influence of heating. The BEC is held for a variable time ${\tau }_h$ before splitting; ${\tau }_r=50\mathrm{ms}$ is constant.Reuse & Permissions

Figure 3

Second experiment. (a) Effect of the temperature on ${\xi }^2$. We vary the final frequency ${\nu }_f$ of the evaporative cooling ramp before splitting the cloud using a 50 ms linear current ramp. Typical absorption images are shown in the inset of (a). Red squares, ${\xi }^2$; open green circles, fringe noise. (Estimation of the ${\xi }^2$ we expect to measure when the actual fluctuations are binomial—the estimate is obtained by analyzing a region of the image that does not contain atoms.) (b) Total atom number $N$ (red diamonds) and condensed fraction $N_0/N$ prior to splitting (blue circles).Reuse & Permissions

Figure 4

Classical field simulations (open symbols and dotted lines) and modified TMM (full symbols and full lines). Dark gray (blue) lines and triangles, $N=6000$; light gray (red) lines and circles, $N=17000$. The trapping potential is harmonic transversally ($f_{y,z}=1120,1473\mathrm{Hz}$), and quartic along $x$ with $V_b/h=2.69\mathrm{kHz}$ and $x_0=3.8\mu \mathrm{m}$. The longitudinal oscillation frequency within each well is $f_x=411\mathrm{Hz}$. The temperature unit in the figure is the ideal gas transition temperature in the harmonic potential prior to splitting $T_c^{\mathrm{harm}}$ ($N=6000$: $T_c^{\mathrm{harm}}=0.89\mu \mathrm{K}$; $N=17000$: $T_c^{\mathrm{harm}}=1.25\mu \mathrm{K}$). Inset: Fraction of the population in the two lowest energy modes $N_{2m}$, extracted from the classical field simulations.Reuse & Permissions