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arXiv:2309.12205 · Physical Review Research

Dynamically assisted tunneling in the Floquet picture

Daniil Ryndyk, Christian Kohlfürst, Friedemann Queißer, Ralf Schützhold

Published Apr 16, 2024• 10 citations
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Abstract

We study how tunneling through a potential barrier V ( x ) can be enhanced by an additional harmonically oscillating electric field E ( t ) = E 0 cos ( ω t ) or a similar oscillating force. To this end, we transform into the Kramers-Henneberger frame and calculate the coupled Floquet channels numerically. We find distinct signatures of resonances when the incident energy E equals the driving frequency ω = E , which clearly shows the breakdown of the time-averaged potential approximation in this regime. As a simple model for experimental applications (e.g., in solid-state physics), we study the rectangular potential, which can also be benchmarked with respect to analytical results. Finally, we consider the truncated Coulomb potential relevant for nuclear fusion. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.023056

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We study how tunneling through a potential barrier V ( x ) can be enhanced by an additional harmonically oscillating electric field E ( t ) = E 0 cos ( ω t ) or a similar oscillating force. To this end, we transform into the Kramers-Henneberger frame and calculate the coupled Floquet channels numerically. We find distinct signatures of resonances when the incident energy E equals the driving frequency ω = E , which clearly shows the breakdown of the time-averaged potential approximation in this regime. As a simple model for experimental applications (e.g., in solid-state physics), we study the rectangular potential, which can also be benchmarked with respect to analytical results. Finally, we consider the truncated Coulomb potential relevant for nuclear fusion. Published by the American Physical Society 2024
The second-order perturbation theory in the framework of the Kramers-Henneberger oscillating frame representation of the Hamiltonian [H. A. Kramers, Quantum Mechanics (North-Holland, Amsterdam, 1956); W. C. Henneberger, Phys. Rev. Lett. 21, 838 (1968)] is used to study the tunneling process in a periodically driven double-well potential. The eigenstates of the Floquet Hamiltonian are efficiently approximated when a field frequency is larger than a classical frequency of the time-averaged Hamiltonian. The conditions for coherent enhancement and suppression of tunneling are obtained when the standard perturbation theory fails. It is shown that the enhancement and suppression of tunneling is due to field-induced coupling between states of a one-period averaged effective potential.
Since the early days of quantum mechanics, tunneling has been recognized as one of the hallmarks of the wave character of microscopic physics. The possibility of a quantum particle to penetrate an energetic barrier represents certainly one of the most spectacular implications of quantum theory and has led to various applications in nuclear, atomic, and molecular physics as well as in mesoscopic science. Typical scenarios in which tunneling manifests are the escape route of a quantum particle from a quasibounded region, the transition between two or more symmetry-related, but classically disconnected wells (which we shall focus on in the following), as well as scattering or transport through potential barriers. The spectrum of scenarios becomes even richer when the concept of tunneling is generalized to any kind of classically forbidden transitions in phase space, that is, to transitions that are not necessarily inhibited by static potential barriers but by some other constraints of the underlying classical dynamics (such as integrals of motion). Such “dynamical tunneling” processes arise frequently in molecular systems [1] and were realized with cold atoms propagating in periodically modulated optical lattices [2-4]. Moreover, the electromagnetic analog of dynamical tunneling was also obtained with microwaves in billiards [5].
We study the enhancement of tunneling through a potential barrier V(x)V(x)V(x) by a time-dependent electric field with special emphasis on pulse-shaped vector potentials such as ${A}_{x}(t)={A}_{0}/{cosh}^{2}(\ensuremath{\omega}t)$. In addition to the known effects of preacceleration and potential deformation already present in the adiabatic regime, as well as energy mixing in analogy to the Franz-Keldysh effect in the nonadiabatic (impulse) regime, the pulse Ax(t){A}_{x}(t)Ax​(t) can enhance tunneling by ``pushing'' part of the wave function out of the rear end of the barrier. Aside from the natural applications in condensed matter and atomic physics, these findings could be relevant for nuclear fusion, where pulses Ax(t){A}_{x}(t)Ax​(t) with $\ensuremath{\omega}=1\phantom{\rule{0.28em}{0ex}}\mathrm{keV}$ and peak field strengths of 1016V/m{10}^{16}\phantom{\rule{0.28em}{0ex}}\mathrm{V}/\mathrm{m}1016V/m might enhance tunneling rates significantly.
At sufficiently low temperatures, the reaction rates in solids are controlled by quantum rather than by thermal fluctuations. We solve the Schrödinger equation for a Gaussian wave packet in a nonstationary harmonic oscillator and derive simple analytical expressions for the increase of its mean energy and dispersion with time induced by time-periodic modulation. Applying these expressions to the modified Kramers theory, we demonstrate a strong increase of the rate of escape out of a time-periodic potential well at a constant height of the potential barrier, when the driving frequency of the well position equals its eigenfrequency, or when the driving frequency of the well width exceeds its eigenfrequency by a factor of ∼2. Physical realization of the time-periodic driving modes can be induced by localized anharmonic vibrations (LAVs), a.k.a. discrete breathers, in which the amplitude of atomic oscillations greatly exceeds the amplitude of zero-point oscillations. At low temperatures LAVs can be excited by external triggering (such as irradiation by fast particles or by a laser), which can result in strong catalytic effects due to amplification of the Kramers rate. Numerical solution of Schrodinger equation for time-periodic double well potential is obtained, which agrees qualitatively with modified Kramers rate theory. Application of the present theory to low-energy nuclear reactions is discussed.
Periodically driven quantum systems provide a powerful route to engineer novel states of matter by controlling their effective Hamiltonians through external fields. However, most treatments are usually simplified by considering the high-frequency limit, and do not account for the processes taking place in the transient regime during the onset of the drive. In this work, we introduce a time and momentum resolved tunneling spectroscopy protocol to probe the instantaneous energy spectrum of Floquet-driven systems beyond the high-frequency regime, capturing both emergent effects and non-adiabatic phenomena without requiring explicit reconstruction of the full time-dependent Green's function. We benchmark the method on driven non-interacting fermionic models, and then generalize the approach to strongly correlated systems with the aid of time-dependent density matrix renormalization group techniques. We also provide a microscopic description to the emergence of in-gap states under resonant driving, and briefly explore its finite temperature analog.
Time-averaged trapping potentials have played an important role in the development of the field of ultracold atoms. Despite their widespread application, there is not yet a complete understanding of when a system can be considered time-averaged. Here we use Floquet theory to analyze the lowest energy state of time-periodic trapping potentials, and characterize the transition from a localized state in a slowly moving trap to a delocalized state in a rapidly oscillating time-averaged potential. We investigate how the driving parameters affect the density and phase of the Floquet ground state, and provide a quantitative measure of the degree to which they can be considered time-averaged. We study a number of simple representative systems, and comment on the features affecting the experimental realization of time-averaged trapping potentials.