Alternative perspective on quantum tunneling and instantons (9 pages)

Daniela Mugnai, Anedio Ranfagni

Yunbo Zhang, H.J.W. Müller-Kirsten

Neil Turok

Frédérik Paradis, H. Kröger, G. Melkonyan +1 more

We present an alternative way to compute and interpret quantum tunneling in a one-dimensional double-well potential. For large transition time we show that the quantum action functional gives an analytical expression for tunneling amplitudes. This has been confirmed by numerical simulations giving relative errors in the order of ${10}^{\ensuremath{-}5}$. In contrast to the classical potential, the quantum potential has a triple well if the classical wells are deep enough. Its minima are located at the positions of extrema of the ground state wave function. The striking feature is that a single trajectory with a double instanton reproduces the tunneling amplitude. This is in contrast to the standard instanton approach, where infinitely many instantons and anti-instantons have to be taken into account. The quantum action functional is valid in the deep quantum regime in contrast to the semiclassical regime where the standard instanton approach holds. We compare both approaches via numerical simulations. While the standard instanton picture describes only the transition between potential minima of equal depth, the quantum action may give rise to instantons also for asymmetric potential minima. Such a case is illustrated by an example.

Masao Hirokawa

Macroscopic quantum tunneling (MQT), a cornerstone of Leggett's program, is deeply linked with instanton physics, yet its experimental verification remains elusive. This Perspective demonstrates that the quantum Rabi model manifests observable, instanton-like effects via quantum simulation. In the MQT regime, qubit-boson interactions drive Polyakov's energy bifurcation, governing tunneling and spontaneous symmetry breaking. Mapping the quantum Rabi model onto an effective double-well potential reveals that while tunneling suppression induces spontaneous symmetry breaking, instanton-like contributions act to restore it. This mechanism enables experimental access to the classical Euclidean action of an effective instanton-like particle, offering a route to probe non-perturbative phenomena.

G. E. Hahne