Milena Grifoni

DRIVEN QUANTUM TUNNELING

Abstract A contemporary review on the behavior of driven tunneling in quantum systems is presented. Diverse phenomena, such as control of tunneling, higher harmonic generation, manipulation of the population dynamics and the interplay between the driven tunneling dynamics and dissipative effects are discussed. In the presence of strong driving fields or ultrafast processes, well-established approximations such as perturbation theory or the rotating wave approximation have to be abandoned. A variety of tools suitable for tackling the quantum dynamics of explicitly time-dependent Schrodinger equations are introduced. On the other hand, a real-time path integral approach to the dynamics of a tunneling particle embedded in a thermal environment turns out to be a powerful method to treat in a rigorous and systematic way the combined effects of dissipation and driving. A selection of applications taken from the fields of chemistry and physics are discussed, that relate to the control of chemical dynamics and quantum transport processes, and which all involve driven tunneling events.

Driven tunneling dynamics: Bloch-Redfield theory versus path-integral approach

In the regime of weak bath coupling and low temperature we demonstrate numerically for the spin-boson dynamics the equivalence between two widely used but seemingly different roads of approximation, namely, the path-integral approach and the Bloch-Redfield theory. The excellent agreement between these two methods is corroborated by an efficient analytical high-frequency approach: it well approximates the decay of quantum coherence via a series of damped coherent oscillations. Moreover, a suitably tuned control field can selectively enhance or suppress quantum coherence.

DISSIPATIVE TUNNELING WITH PERIODIC POLYCHROMATIC DRIVING: EXACT RESULTS AND TRACTABLE APPROXIMATIONS

Abstract We investigate the long-time dynamics in dissipative two-level-systems (TLS) when driven by — monochromatic or pulse-shaped — periodic fields. The environmental influence is investigated within the noninteracting-blip approximation (NIBA), while no restrictions are assumed on the driving force. With the focus being on electron-transfer (ET) reactions in condensed media, we consider a continuous Ohmic spectrum for the bath modes. The asymptotic dynamics exhibits always the periodicity of the external force. The induced oscillations show a smooth periodic behavior which becomes richer, if, for example, multiphoton resonances occur. For monochromatic driving, the oscillatory multiresonance pattern becomes gradually smoothed out when the temperature, and/or the Ohmic strength are sufficiently high. It may persist, however, for pulse-shaped driving. Exact NIBA analytical and/or numerical solutions, for both the Ohmic transfer rate and for the driven dynamics, are used to determine the validity range of the short-time approximation for the bath correlation functions. The latter is frequently employed to investigate the ET dynamics. Our analysis shows that the short-time approximation may give qualitative incorrect results at low temperatures.

Dissipative tunneling control by elliptically polarized fields

The tunneling dynamics of a dissipative two-level system that is strongly driven by elliptically polarized electric fields is investigated. The dissipative dynamics is governed within the noninteracting-blip-approximation for the stochastic forces by a generalized master equation (GME). With the focus being on viscous friction, we compare exact numerical solutions of the GME with analytical approximations to both the transient and the asymptotic, long-time periodic dynamics. Novel phenomena are identified: These are a selective control on localization (or, as well, on delocalization) of the tunneling dynamics, or the inversion of an initially induced localization by a static bias via multiphoton-assisted tunneling. These effects can be selectively tuned as a function of the eccentricity parameter p=Ey/Ex of corresponding field amplitudes. In particular, the case of a circularly polarized driving field with p=±1 yields a dramatic enhancement of the relaxation rate at resonances, when an integer multiple of...

Adiabatically rocked quantum ratchets

We investigate quantum Brownian motion in adiabatically rocked ratchet systems. Above a cross-over temperature Tc tunneling events are rare; yet they already substantially enhance the classical particle current. Below Tc, quantum tunneling prevails and the classical predictions grossly underestimate the transport. Upon approaching T=0 the quantum current exhibits a tunneling induced reversal, and tends to a finite limit.

Decoherence and preparation effects in mesoscopic systems

We study the problem of preparing and operating with a dissipative two-state system in the presence of an external driving field. We derive an exact master equation for the populations and we show that the initial preparation strongly affects the transient dynamics in the underdamped regime and that an appropriately tuned external a.c.-field can slow down decoherence. We finally discuss the connection with the problem of controlling the dynamics of a CJ Qubit.

COMMENT ON TRANSIENT DYNAMICS OF OHMIC DISSIPATIVE TWO-LEVEL SYSTEMS DRIVEN BY DC-AC FIELDS BY WANG AND ZHAO

Abstract Recent results on the dynamics of a two-state system driven by dc-ac fields are discussed. We show that the approximation put forward in the work by Wang and Zhao [Phys. Lett. A 217 (1996) 232] gives qualitative incorrect results for the dynamics when effects of the dc field in the presence or absence of the ac field are considered.