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AIP conference proceedings

Conventional and anomalous quantum Rabi oscillations in graphene

Enamullah Enamullah, Vipin Kumar, Upendra Kumar, Girish S. Setlur

Published Jan 1, 2014• 0 citations
Publisher

Abstract

We study the non linear response of graphene in presence of quantum field in two different regimes. Far from resonance, using our new technique asymptotic rotating wave approximation (ARWA), we obtained that the matter field interaction leads to the slow oscillations like conventional Rabi oscillations observed in conventional semiconductors using well known rotating wave approximation (RWA). The Rabi frequency obtained in both the regimes.

DOI
10.1063/1.4872586

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We study the non linear response of graphene in presence of quantum field in two different regimes. Far from resonance, using our new technique asymptotic rotating wave approximation (ARWA), we obtained that the matter field interaction leads to the slow oscillations like conventional Rabi oscillations observed in conventional semiconductors using well known rotating wave approximation (RWA). The Rabi frequency obtained in both the regimes.
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Graphene has been theoretically shown to exhibit anomalous Rabi oscillations (AROs) far from resonance in addition to conventional Rabi oscillations close to resonance (classical light frequency matches particle-hole frequency). The ARO has been attributed to the pseudospin degree of freedom that is unique to graphene-like systems. In this work, we show the same phenomenon also occurs in the single-photon limit or even in a vacuum. This is to be expected for conventional Rabi oscillations; however, the prediction that AROs also occur in the single-photon situation means that this notion of ARO is robust and not an artifact of approximations. We also study collapse and revival of both conventional and AROs in response to a coherent radiation field and extract the collapse and revival times in both cases.
We have investigated vacuum Rabi oscillation of an atom coupled with single-mode cavity field exactly, and compared the results with that of the Jaynes–Cummings (J–C) model. The results show that for resonant case, there is no Rabi oscillation for an atom. For small detuning and weak coupling case, the probability for the atom in excited state oscillates against time with different frequencies and amplitudes from that of the J-C model. It exhibits that the counter-rotating wave interaction could significantly effect the dynamic behaviour of the atom, even under the condition in which the RWA is considered to be justified.
We study the interaction of an ac electric field with a semiconductor quantum well by using the effective nonlinear Bloch equations. Only the first two electron subbands in the well are considered. We apply the rotating wave approximation and derive analytical solutions for the Bloch equations for two different values of the detuning. At exact resonance we find a critical value of the Rabi frequency around which the dynamics of the system changes abruptly. Above this critical value one obtains electron oscillations with complete inversion in the two-subband system, while below this value we obtain electron oscillations without complete inversion and with the majority of the electron population on average in the lower subband. We also present numerical calculations for a specific quantum well structure and assess the limits of validity of the analytical results.
We considered the semiclassical Rabi model, that is, a two-level system interacting with a single-mode, classical field. In resonance and for an arbitrary initial state of the system, we obtained a simple, approximate, and analytic solution that takes into account the counterrotating terms and that is accurate as long as the Rabi frequency is smaller than or equal to 1/2 (1/4) of the angular frequency of the field and 1 (10) Rabi oscillations are considered. In addition, the approximate solution has the same level of complexity as that obtained with the rotating-wave-approximation (RWA) and allows one to describe the evolution of the Bloch vector of the system in terms of a \textit{slow-precessional} and a \textit{fast-nutational} motion similar to that of a symmetric top with one point fixed. Finally, the approximate solution also leads to a simple criterion that allows one to determine the accuracy of the solution in the RWA.