Tunneling and energy splitting in an asymmetric double-well potential

Abstract

An asymmetric double-well potential is considered, assuming that the minima of the wells are quadratic with a frequency $\omega$ and the difference of the minima is close to a multiple of $\hslash \omega$. A WKB wave function is constructed on both sides of the local maximum between the wells, by matching the WKB function to the exact wave functions near the classical turning points. The continuities of the wave function and its first derivative at the local maximum then give the energy-level splitting formula, which not only reproduces the instanton result for a symmetric potential, but also elucidates the appearance of resonances of tunneling in the asymmetric potential.

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• Condensate splitting in an asymmetric double well for atom chip based sensors
• Ultracold Bosons in a Tilted Multi-level Double-Well Potential
• Momentum distribution of a Fermi gas of atoms in the BCS-BEC crossover
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• Two-level systems and harmonic excitations in a mean-field anharmonic quantum glass
• Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation
• Hallmarks of tunneling dynamics with broken reflective symmetry
• Modelling assisted tunneling on the Bloch sphere using the Quantum Composer
• Dynamical system analysis of quantum tunneling in an asymmetric double-well potential