Statistical mechanics of Floquet systems: the pervasive problem of near degeneracies

The statistical mechanics of periodically driven ("Floquet") systems in contact with a heat bath exhibits some radical differences from the traditional statistical mechanics of undriven systems. In Floquet systems all quasienergies can be placed in a finite frequency interval, and the number of near degeneracies in this interval grows without limit as the dimension N of the Hilbert space increases. This leads to pathologies, including drastic changes in the Floquet states, as N increases. In earlier work these difficulties were put aside by fixing N, while taking the coupling to the bath to be smaller than any quasienergy difference. This led to a simple explicit theory for the reduced density matrix, but with some major differences from the usual time independent statistical mechanics. We show that, for weak but finite coupling between system and heat bath, the accuracy of a calculation within the truncated Hilbert space spanned by the N lowest energy eigenstates of the undriven system is limited, as N increases indefinitely, only by the usual neglect of bath memory effects within the Born and Markov approximations. As we seek higher accuracy by increasing N, we inevitably encounter quasienergy differences smaller than the system-bath coupling. We therefore derive the steady state reduced density matrix without restriction on the size of quasienergy splittings. In general, it is no longer diagonal in the Floquet states. We analyze, in particular, the behavior near a weakly avoided crossing, where quasienergy near degeneracies routinely appear. The explicit form of our results for the denisty matrix gives a consistent prescription for the statistical mechanics for many periodically driven systems with N infinite, in spite of the Floquet state pathologies.Comment: 31 pages, 3 figure

Ac Stark Effects and Harmonic Generation in Periodic Potentials

The ac Stark effect can shift initially nonresonant minibands in semiconductor superlattices into multiphoton resonances. This effect can result in strongly enhanced generation of a particular desired harmonic of the driving laser frequency, at isolated values of the amplitude.Comment: RevTeX, 10 pages (4 figures available on request), Preprint UCSBTH-93-2

Trion Species-Resolved Quantum Beats in MoSe2

Monolayer photonic materials offer a tremendous potential for on-chip optoelectronic devices. Their realization requires knowledge of optical coherence properties of excitons and trions that have so far been limited to nonlinear optical experiments carried out with strongly inhomogenously broadened material. Here we employ h-BN encapsulated and electrically gated MoSe2 to reveal coherence properties of trion-species directly in the linear optical response. Autocorrelation measurements reveal long dephasing times up to T2=1.16+-0.05 ps for positively charged excitons. Gate dependent measurements provide evidence that the positively-charged trion forms via spatially localized hole states making this trion less prone to dephasing in the presence of elevated hole carrier concentrations. Quantum beat signatures demonstrate coherent coupling between excitons and trions that have a dephasing time up to 0.6 ps, a two-fold increase over those in previous reports. A key merit of the prolonged exciton/trion coherences is that they were achieved in a linear optical experiment, and thus are directly relevant to applications in nanolasers, coherent control, and on-chip quantum information processing requiring long photon coherence.Comment: 21 pages, 6 figures, 2 SOI figure