The Journal of Physical Chemistry Letters

Nonadiabatic Couplings Can Speed Up Quantum Tunneling Transition Path Times

Tom Rivlin, Eli Pollak

Published Nov 7, 2022• 4 citations

Abstract

Quantum tunneling is known to play an important role in the dynamics of systems with nonadiabatic couplings. However, until recently, the time-domain properties of nonadiabatic scattering have been severely under-explored. Using numerically exact quantum methods, we study the impact that nonadiabatic couplings have on the time it takes to tunnel through a barrier. We find that the Wigner phase time is the appropriate measure to use when determining the tunneling flight time also when considering nonadiabatic systems. The central result of the present study is that in an avoided crossing system in one dimension, the nonadiabatic couplings speed up the tunneling event, relative to the adiabatic case in which all nonadiabatic coupling is ignored. This has implications for both the study of quantum tunneling times and for the field of nonadiabatic scattering and chemistry.

DOI: 10.1021/acs.jpclett.2c03008

Related papers

Chapter 12. The Tunnelling Flight Time

Eli Pollak

How much time does it take for a particle to tunnel through a barrier? This question continues to baffle up to this very day, one of the reasons being the non-existence of an energy–time commutator analogous to the position–momentum commutation relation. Instead of worrying about the definition of an operator one may consider time as a parameter in the time-dependent Schrödinger equation and study the time evolution of a wavepacket appropriately scattered on a potential barrier. Using this approach, one may formally define a tunnelling flight time that may be measured in a time-of-flight experiment. The resulting tunnelling flight time either vanishes or is very small. The implications of this observation with respect to recent hydrogen and helium atom attosecond photoionization experiments are discussed. The vanishing or small flight time does not contradict the finite time measured in Larmor clock experiments, where the tunnelling particle affects an external degree of freedom whose dynamics induced by the tunnelling may be interpreted in terms of a time scale. Flight times are also relevant to quantum reflection where coherences due to resonance scattering are not well accounted for by Wigner's phase time delay.

RSC theoretical and computational chemistry seriesJan 1, 20201 citation

Tunneling Flight Time, Chemistry, and Special Relativity

Jakob Petersen, Eli Pollak

Attosecond ionization experiments have not resolved the question "What is the tunneling time?". Different definitions of tunneling time lead to different results. Second, a zero tunneling time for a material particle suggests that the nonrelativistic theory includes speeds greater than the speed of light. Chemical reactions, occurring via tunneling, should then not be considered in terms of a nonrelativistic quantum theory calling into question quantum dynamics computations on tunneling reactions. To answer these questions, we define a new experimentally measurable paradigm, the tunneling flight time, and show that it vanishes for scattering through an Eckart or a square barrier, irrespective of barrier length or height, generalizing the Hartman effect. We explain why this result does not lead to experimental measurement of speeds greater than the speed of light. We show that this tunneling is an incoherent process by comparing a classical Wigner theory with exact quantum mechanical computations.

The Journal of Physical Chemistry LettersAug 9, 201727 citations

Instantaneous Tunneling Flight Time for Wavepacket Transmission through Asymmetric Barriers

Jakob Petersen, Eli Pollak

The time it takes a particle to tunnel through the asymmetric Eckart barrier potential is investigated using Gaussian wavepackets, where the barrier serves as a model for the potential along a chemical reaction coordinate. We have previously shown that the, in principle experimentally measurable, tunneling flight time, which determines the time taken by the transmitted particle to traverse the barrier, vanishes for symmetric potentials like the Eckart and square barrier [ Petersen , J. ; Pollak , E. J. Phys. Chem. Lett. 2017 , 9 , 4017 ]. Here we show that the same result is obtained for the asymmetric Eckart barrier potential, and therefore, the zero tunneling flight time seems to be a general result for one-dimensional time-independent potentials. The wavepacket dynamics is simulated using both an exact quantum mechanical method and a classical Wigner prescription. The excellent agreement between the two methods shows that quantum coherences are not important in pure one-dimensional tunneling and reinforces the conclusion that the tunneling flight time vanishes.

The Journal of Physical Chemistry AMar 20, 201814 citations

Experimental investigation of tunneling times using Bose-Einstein condensates

D. Ciampini, O. Morsch, E. Arimondo

The time it takes a quantum system to complete a tunneling event (which in the case of cross-barrier tunneling can be viewed as the time spent in a classically forbidden area) is related to the time required for a state to evolve to an orthogonal state, and an observation, i.e., a quantum mechanical projection on a particular basis, is required to distinguish one state from another. We have performed time-resolved measurements of Landau-Zener tunneling of Bose-Einstein condensates in accelerated optical lattices, clearly resolving the steplike time dependence of the band populations. The use of different protocols enabled us to access the tunneling probability, in two different bases, namely, the adiabatic basis and the diabatic basis. The adiabatic basis corresponds to the eigenstates of the lattice, and the diabatic one to the free-particle momentum eigenstates. Our findings pave the way towards more quantitative studies of the tunneling time for LZ transitions, which are of current interest in the context of optimal quantum control and the quantum speed limit.

arXiv:1102.1666Journal of Physics Conference SeriesJul 8, 20111 citation

Time distributions for classically unallowed processes of a two-level system: Nonadiabatic tunneling and above-barrier reflection

Randall S. Dumont

Channel-specific transit time distributions for a two-level model system exhibiting simple avoided crossing are computed and interpreted in terms of a general semiclassical analysis which expresses wave packet evolution in terms of sums over complex trajectories. Novel effects observed include “quantum speedup” (the Hartman effect), for tunneling, and “quantum slowdown” for above-barrier reflection. Nonadiabatic effects are found to appear only at times for which their exponentially small amplitude is comparable or greater than the amplitude of adiabatic contributions. This is in accord with the semiclassical treatment provided. Nonadiabatic effects include, most notably, the appearance of slowly leaking resonances in the excited level potential energy well.

The Journal of Chemical PhysicsMay 9, 20025 citations

Dynamical norm method for nonadiabatic macroscopic quantum tunneling

N. Takigawa, K. Hagino, M. Abe

We present a method for macroscopic quantum tunneling, named dynamical norm method, which works over a very wide range of situations between the adiabatic and the sudden limits. We examine the validity of the method by studying the effects of linear oscillator coupling on the tunneling rate through an Eckart barrier. We then apply the method to discussing the effects of a nuclear intrinsic excitation on fission. This method shows that the adiabaticity of the tunneling process is governed not only by the relative time scale of the tunneling degree of freedom and of environmental degrees of freedom, but also by the properties of the coupling between them. We also show that the dynamical norm factor which represents nonadiabatic effects in our method is closely related to the dissipation factor in the Caldeira-Leggett theory for dissipative quantum tunneling.

Physical Review CJan 1, 199524 citations