Microwave-Driven Atoms: From Anderson Localization to Einstein’s Photoeffect

Abstract

We study the counterpart of Anderson localization in driven one-electron Rydberg atoms. By changing the initial Rydberg state at fixed microwave frequency and interaction time, we numerically monitor the crossover from Anderson localization to the photo effect in the atomic ionization signal. 32.80.Fb, 05.60.Gg, 05.70.Fh Anderson localization [1,2] is the inhibition of quantum transport due to destructive interference in disordered, static quantum systems. When a Hamiltonian quantum system is periodically driven and its classical counterpart undergoes a transition to chaotic diffusion, an analogous localization phenomenon occurs: destructive interference between many chaotically diffusing trajectories inhibits the transport and localizes the diffusing particle's wave function [3]. Since dynamical chaos rather than static disorder establish Anderson's scenario here, the phenomenon is often labeled dynamical localization.By now, the dynamical variant of Anderson localization (and similar phenomena [4]) was observed in a vast range of physical systems -ranging from cold atoms [5] to photon billiards [6] and atoms [7,8,9,10], and is best understood in the Floquet or dressed state picture, which also allows its formal mapping on Anderson's model [11]. The dressing of the bare system by the driving field photons defines multiphoton transition amplitudes between the initial and the final field-free state, mediated by nearresonantly coupled intermediate states. These amplitudes need be summed up coherently to determine the total transport probability. For destructive interference and thus localization to emerge, a large number of amplitudes is required, what implies that the photon energy be small compared to the energy gap between initial and final state. This is a scenario in perfect contrast to Einstein's photo effect [12], which predicts efficient transport -mediated by one single transition amplitude -for photon energies larger than that energy gap, though the general physical context of a driven quantum system is identical in both cases. Recently, connecting both effects through continuous variation of the experimental parameters has moved into reach for state of the art atomic physics experiments [13], and it is the purpose of the present Letter to (theoretically) establish this connection, and to spell out its characteristic features.Our specific atomic physics scenario is defined by a one electron Rydberg atom under periodic driving by a classical, linearly polarized oscillating electric field of amplitude F and frequency ω, described (in length gauge and atomic units, employing the dipole approximation) by the Hamiltonianwith p and r the electron's momentum and position, respectively. In this system, quantum transport properties are efficiently characterized by the ionization probability P ion (t) after a given atom-field interaction time t, for an atomic initial state |Φ 0 = |n 0 , ℓ 0 , m 0 with well-defined principal and angular momentum quantum numbers n 0 , ℓ 0 and m 0 (the latter one being a constant...

Connecting field ionization to photoionization via 17- and 36-GHz microwave fields

“…In the regime 1 < < 6 the experimental results are in particularly good agreement with the localization model of Jensen [10,11]. The measurements have not, however, tested the range of validity of the localization theory: in particular, how well it works in the photoionization limit, ω > 1/2n 2 or > n/2, where localization theories agree with the perturbation theory result, Fermi's Golden Rule [13].…”

“…In Fig. 4(a) we also show the 10% ionization fields for a 500-ns-long, 17.5-GHz pulse calculated by Schelle et al [13], scaled by a factor of 500 200 ( 17.068 17.5 ) 5/3 . In their calculations they assumed the bound states to be truncated at n = 245, which corresponds to the depression of the limit by a 30-mV/cm field.…”

Eigenmodal analysis of Anderson localization: Applications to photonic lattices and Bose–Einstein condensates

“…The localization concept was proposed in 1958 by P. W. Anderson who explained the absence of diffusion of waves in a disordered medium [1]. It is now recognized that this finding is a general wave phenomenon, which has been experimentally confirmed for the light [2]- [7], electromagnetic (EM) [8], [9] sound [10] and quantum waves [11]- [13] in highly disordered matter. Several approaches have been developed to model and simulate this effect.…”

Dynamical localization of matter waves in optomechanics

“…In this paper, we discuss the dynamical localization of ultra-cold atoms or dilute BEC trapped inside a single mode driven optomechanical cavity with one fixed mirror and the other as a movable mirror. Dynamical localization is an interesting phenomenon in periodically driven nonlinear systems [18][19][20][21][22] and provides quantum mechanical limits on classical diffusion of wave packet. We show that for different modulation regimes the dynamical localization is observed both in position and in momentum space.…”