Figure 1

Schematic of the in-trap recombination with a well-defined relative phase. (a) The phase-coherent condensates were prepared using a radio frequency induced double-well potential on an atom chip [21]. The splitting was done within 75 ms by ramping up the rf frequency from 140 to 225 kHz. During the hold time, the relative phase of two independent condensates evolved with time at $\sim 500\mathrm{Hz}$. After a variable time, the double-well potential was deformed into a single well and the two trapped condensates were merged by decreasing the rf frequency by 33 kHz over a variable “recombination time.” The condensates started to spill over the barrier after $\le 10\%$ of the recombination time or $\sim 3\mathrm{kHz}$ decrease of the rf frequency. (b),(c) The merged matter-wave functions are shown for the cases of an adiabatic merger of noninteracting condensates and for a sudden merger of interacting condensates.Reuse & Permissions

Figure 2

Phase-sensitive recombination of two separate condensates. (a) The relative phase of two split condensates was monitored for various hold time after splitting by suddenly releasing the two condensates and observing interference fringes. For the independent condensates (solid circle), the evolution rate of the relative phase was determined from the linear fit to be $\sim 500\mathrm{Hz}$. For the weakly coupled condensates (open square), the relative phase did not evolve. At 0 ms hold time, the relative phase was set to zero for both cases. (b) For the same range of delay times as in (a), the condensate atom loss after in-trap recombination was determined. The relative phase ($x$ axis) was obtained from interference patterns as in (a). The merging time was 5 ms. (c) The matter-wave interference patterns (after 9 ms time of flight) and absorption images of merged clouds (after 8 ms time of flight) show the correlation between phase shift and absorption signal. The field of view is $260\times 200\mu \mathrm{m}$ and $160\times 240\mu \mathrm{m}$ for matter-wave interferences and merged clouds, respectively.Reuse & Permissions

Figure 3

Oscillations of condensate atom loss after recombination reflecting the coherent phase evolution. The condensate atom loss was monitored during a variable hold time for the two split condensates whose relative phase evolved at $\sim 500\mathrm{Hz}$. The merging was done for different values of the recombination time: 100 (a), 10 (b), 5 (c), and 1 ms (d). The dotted lines are sinusoidal curves fitted with fixed frequency $\sim 500\mathrm{Hz}$. The reproducible phase shift for the 5 and 10 ms data occurred during the recombination process. The data points represent the average of 6 measurements.Reuse & Permissions

Figure 4

Recombination time and atom loss. (a) The amplitude of atom loss oscillations was determined for various recombination times. (b) Assuming that minimum atom loss occurs at 0-relative phase of the two condensates, relative phases were obtained from the fitted atom loss oscillations in Fig. 3.Reuse & Permissions