Dynamical localization in the microwave interaction of Rydberg atoms: The influence of noise

Abstract

We present experimental and theoretical results on highly excited Rydberg atoms passing through a waveguide. The waveguide is excited in a coherent mode with a superimposed component of technically generated noise. In the theoretical part of the paper we derive and solve a master equation for a Rydberg atom driven by a monochromatic coherent microwave field in the presence of noise. We show that a Rydberg atom subjected to a mixture of coherent modes and noise fields exhibits four dynamical regimes: (i) diffusive broadening, (ii) localization, (iii) destruction of coherence and localization, and (iv) relaxation to equilibrium. The four regimes are passed one after the other as a function of irradiation time. They occur on different time scales and are thus temporally well separated from each other. The theory is checked by an experiment on the time dependence of the population distribution of highly excited rubidium Rydberg atoms initially prepared in a unique and well-defined Rydberg state and irradiated by a strong microwave field. The localization regime, characterized by a "freezing" of the width of the wave packet with respect to the Rydberg levels, has been observed. The addition of a small noise component was shown to lead to delocalization after times inversely proportional to the noise power, as predicted by our theory. PACS number(s): 32.80. Rm, 05.45. +b,

Non-dispersive wave packets in periodically driven quantum systems

“…The microwave ionization of atomic Rydberg states was thus identified as an experimental testing ground for quantum transport under the conditions of classically mixed regular chaotic dynamics, where the transport was simply measured by the experimentally observed ionization yield, or -with some additional experimental effort -by the time dependent redistribution of the atomic population over the bound states [198][199][200][201]. Depending on the precise value of the scaled frequency ω 0 -the ratio of the microwave frequency ω to the Kepler frequency Ω Kepler of the initially excited Rydberg atom, eq.…”

“…Hence, state of the art experiments are "blind" for the details of the atomic excitation process on the way to ionization, and therefore not suitable for the unambiguous identification of individual eigenstates of the atom in the field, notably of non-dispersive wave-packets. The case is getting worse with additional complications which are unavoidable in a real experiment, such as the unprecise definition of the initial state the atoms are prepared in [133,137,[209][210][211][212][213][214][215][216], the experimental uncertainty on the envelope of the amplitude of the driving field experienced by the atoms as they enter the interaction region with the microwave (typically a microwave cavity or wave guide) [200,211,217], stray electric fields due to contact potentials in the interaction region, and finally uncontrolled noise sources which may affect the coherence effects involved in the quantum mechanical transport process [218]. On the other hand, independent experiments on the microwave ionization of Rydberg states of atomic hydrogen [132,137], as well as on hydrogenic initial states of lithium [217], did indeed provide hard evidence for the relative stability of the atom against ionization when driven by a resonant field of scaled frequency ω 0 ≃ 1.0.…”

Population Trapping in Extremely Highly Excited States in Microwave Ionization

“…Of particular interest for this work, it was observed long ago in classical calculations that the Rydberg atom could be left in very high lying states by a microwave pulse [5][6][7]. More recently there have been extensive calculations of the final state distributions subsequent to a microwave pulse [8][9][10][11]. At low microwave fields the final state population is found to fall off roughly exponentially with the change in n of the final state from the initial state, and experiments have confirmed these predictions [8,9].…”

The dissipative quantum Duffing oscillator: A comparison of Floquet-based approaches

“…Because the bath consists of infinite degrees of freedom we assume the effects of the interaction with the DO system on the bath to dissipate away quickly, such that the bath remains in thermal equilibrium for all times t. We wish to obtain an equation of motion for the reduced density operator ρ DO (t) = tr BρDO+B (t). Following [38,39,40,41,42,43] a Born-Markov approximation is applied and a Floquet-Markov master equation for the reduced density operator expressed in the Floquet basis of the DO is derived:…”