Localization or tunneling in asymmetric double-well potentials

Abstract

An asymmetric double-well potential is considered, assuming that the wells are parabolic around the minima. The WKB wave function of a given energy is constructed inside the barrier between the wells. By matching the WKB function to the exact wave functions of the parabolic wells on both sides of the barrier, for two almost degenerate states, we find a quantization condition for the energy levels which reproduces the known energy splitting formula between the two states. For the other low-lying non-degenerate states, we show that the eigenfunction should be primarily localized in one of the wells with negligible magnitude in the other. Using Dekker's method [Physica 146A (1987) 375], the present analysis generalizes earlier results for weakly biased double-well potentials to systems with arbitrary asymmetry.

References in corpus (2)

• Charge insensitive qubit design derived from the Cooper pair box
• Semi-classical formula for quantum tunneling in asymmetric double-well potentials

Cited by in corpus (6)

• Analytic description of inversion vibrational mode for ammonia molecule
• Instanton theory of tunnelling in molecules with asymmetric isotopic substitutions
• Oscillatory states of quantum Kapitza pendulum
• Two-level systems and harmonic excitations in a mean-field anharmonic quantum glass
• Quantum signatures and semiclassical limitations in the transmission of Fock states
• Dynamical system analysis of quantum tunneling in an asymmetric double-well potential