Semi-classical formula for quantum tunneling in asymmetric double-well potentials
arXiv:1205.0366 · doi:10.1103/PhysRevA.86.012106
Abstract
Despite quantum tunneling has been studied since the advent of quantum mechanics, the literature appears to contain no simple (textbook) formula for tunneling in generic asymmetric double-well potentials. In the regime of strong localization, we derive an succinct analytical formula based on the WKB semi-classical approach. Two different examples of asymmetric potentials are discussed: when the two localized levels are degenerate or not. For the first case, we also discuss a time-dependent problem showing quantum Zeno effect.
(9 pages, 7 figures)
References in corpus (13)
- Quantum Computing
- Quantum state engineering with Josephson-junction devices
- Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
- Coupled quantum dots as quantum gates
- Coherent Quantum Dynamics of a Superconducting Flux Qubit
- Fluxonium: single Cooper pair circuit free of charge offsets
- Decoherence in Josephson Qubits from Junction Resonances
- Nonlinear Self-Trapping of Matter Waves in Periodic Potentials
- Relaxation and frequency shifts induced by quasiparticles in superconducting qubits
- Observation of quantum oscillations between a Josephson phase qubit and a microscopic resonator using fast readout
- Tunnel splittings for one dimensional potential wells revisited
- Optical Weak Link between Two Spatially Separate Bose-Einstein Condensates
- Macroscopic tunnel splittings in superconducting phase qubits
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