Dynamics of Macroscopic Wave Packet Passing through Double Slits: Role of Gravity and Nonlinearity

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Using the nonlinear Schrödinger equation (Gross–Pitaevskii equation), the dynamics of a macroscopic wave packet for Bose–Einstein condensates falling through double slits is analyzed. This problem is identified with a search for the fate of a soliton showing a head-on collision with a hard-walled obstacle of finite size. We explore the splitting of the wave packet and its reorganization to form an interference pattern. Particular attention is paid to the role of gravity (g) and repulsive nonlinearity (u0) in the fringe pattern. The peak-to-peak distance in the fringe pattern and the number of interference peaks are found to be proportional to g−1⁄2 and u01⁄2g1⁄4, respectively. We suggest a way of designing an experiment under controlled gravity and nonlinearity.

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