Quantum Many-Body Effects in Matter-Wave Breathers
Professor Vladimir A. Yurovsky
School of Chemistry, Tel Aviv University, Israel
Breather is a non-linear superposition of two solitons with the 3:1 mass ratio and zero relative
velocity. This exact solution of a one-dimensional (1D) Gross-Pitaevskii equation (GPE) oscillates without decay and can be formed by the four-fold quench of the attractive interaction strength from a fundamental soliton. The quantum counterpart of the 1D GPE, a system of 1D atoms in a flat potential with zero-range interactions (the Lieb-Liniger-McGuire model) has exact Bethe-ansatz solutions.
Solutions of such kind are applied here to the analyses of the quench in a quantum system. Exact analytic expressions for transition probabilities, obtained with computer algebra for up to N=20 atoms, demonstrate the formation of two-soliton states with arbitrary relative velocities. The velocity distribution width is scaled as √N, leading to a dissociation of breathers in √N periods . This is a robust quantum many-body effect, while the dissociation of mean-field breathers is forbidden by integrability of the 1D GPE. The scaling law agrees with the results of a truncated Wigner simulation  even for N=104.
The Bethe-ansatz solutions are also used here for the fidelity calculation. The dephasing due to the spread of the relative kinetic energy of the constituent solitons leads to decay of the fidelity oscillation amplitude by one-half in the course of ~2.5 breather periods.
In real experiments, a quasi-1D gas can be realized with atoms trapped in a 3D elongated trap. The effect of axial trap potential is analyzed here with relation to the current experiments at Rice University.
1. V.A. Yurovsky, B.A. Malomed, R.G. Hulet and M. Olshanii, Phys. Rev. Lett. 119, 220401 (2017).
2. B. Opanchuk and P.D. Drummond, Phys. Rev. A 96, 053628 (2017).
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