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AIP conference proceedings

Rabi oscillations in trilayer graphene

Enamullah Enamullah, Vipin Kumar, Girish S. Setlur

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We study the nonlinear optical phenomenon, Rabi oscillations in trilayer graphene in presence of an optical field in two different regime - close to resonance and far from resonance. Close to resonance means when the incident optical frequency is nearly equal to transition frequency. We find the Rabi frequency in both the regime - near to resonance conventional Rabi frequency (CRF) is obtained by an approximation well known as rotating wave approximation (RWA). Far from resonance, anomalous Rabi frequency (ARF), unique to grapheme, is obtained using an alternative of RWA called asymptotic RWA (ARWA), introduced by us for single layer graphene. The existence of anomalous Rabi oscillation (ARO) is attributable to a peculiar property of graphene, namely, pseudo spin.

DOI
10.1063/1.4810227

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We study the nonlinear optical phenomenon, Rabi oscillations in trilayer graphene in presence of an optical field in two different regime - close to resonance and far from resonance. Close to resonance means when the incident optical frequency is nearly equal to transition frequency. We find the Rabi frequency in both the regime - near to resonance conventional Rabi frequency (CRF) is obtained by an approximation well known as rotating wave approximation (RWA). Far from resonance, anomalous Rabi frequency (ARF), unique to grapheme, is obtained using an alternative of RWA called asymptotic RWA (ARWA), introduced by us for single layer graphene. The existence of anomalous Rabi oscillation (ARO) is attributable to a peculiar property of graphene, namely, pseudo spin.
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.
In this work, we study the well-known phenomenon of the Bloch–Siegert shift, paying special attention to the change in the resonance condition of anomalous Rabi oscillations that are peculiar to graphene. The inclusion of frequency doubling (counter-rotating terms) in the conventional rotating wave approximation leads to a rather small shift in the resonance condition which forms the conventional Bloch–Siegert shift. In case of anomalous Rabi oscillations, however, band anisotropy caused by the inclusion of next-nearest neighbor hopping together with frequency doubling or the Rashba effect leads to a Bloch–Siegert shift which is quite substantial (in percentage terms, actually infinite), lending credence to the claim that the anomalous Rabi oscillation is sensitive to qualitative changes in the low energy band structure of graphene and as such is a useful indicator of the chiral massless Dirac fermion nature of quasiparticles in graphene.
One of the simplest models involving the atom-field interaction is the coupling of a single two-level atom with single-mode optical field. Under the rotating wave approximation, this problem is reduced to a form that can be solved exactly. But the approximation is only valid when the two levels are resonant or nearly resonant with the applied electromagnetic radiation. Here we present an analytical solution without the rotating wave approximation and applicable to general atom-field interaction far away from the resonance. We find that there exists remarkable influence of the initial phase of optical field on the Rabi oscillations and Rabi splitting, and this issue cannot be explored in the context of the rotating wave approximation. Due to the retention of the counter-rotating terms, higher-order harmonic appears during the Rabi splitting. The analytical solution suggests a way to regulate and control the quantum dynamics of a two-level atom and allows for exploring more essential features of the atom-field interaction.
We study the pump-probe optical response and the third-order self-Kerr nonlinearity of a localized exciton coupled to a suspended monolayer Z-shaped graphene nanoribbon nanoresonator, while it is strongly pumped by a near-resonant electromagnetic field. We derive the quantum Langevin equations that govern the dynamics of the electron population and after expanding the physical quantities involved in a third-order series with respect to the probe field Rabi frequency, we obtain a set of density matrix differential equations. Analytical expressions for the effective linear optical susceptibility and the four-wave mixing coefficient are derived, while the third-order optical susceptibility is calculated numerically. We investigate the modification of the characteristics of the spectra related to these effects for different values of the pump field Rabi frequency, within and outside the bistability region. In the low pump field intensity regime, we detect on the spectra two doublets of resonances with quite different widths, while, in the high pump field intensity regime, the spectral profiles come as a consequence of superimposing a doublet of sharp resonances on the corresponding optical response exhibited by an uncoupled two-level system. This work may find applications in the creation of nonlinear nanophotonic devices for ultrafast optical switching and ultra-sensitive optical sensing.
Summary form only given. Illuminating a semiconductor with a constant light intensity can lead to a periodic oscillation of the inversion, a phenomenon which is known as Rabi flopping. Using pulsed excitation, Rabi flopping has been observed on semiconductors and exhibited periods in the range from 100 fs to 1 ps. Hughes (Phys. Rev. Lett. vol. 81, p. 3363, 1998) theoretically investigated the question of what happens when the light intensity becomes so high that the period of one Rabi oscillation becomes comparable with that of only one cycle of light, 2.7 fs for the band edge of GaAs, and predicted a new phenomenon: carrier-wave Rabi flopping. During a carrier-wave Rabi oscillation, the optical polarization becomes strongly distorted, which can lead to a double-peak structure (the Fourier-transform of the Rabi oscillation) in the third-harmonic (3/spl omega/) spectra. This characteristic shape is quite different from the well-known off-resonant third-harmonic generation. Importantly, resonant effects contain information on the dynamics of electronic resonances-potentially on the timescale of a single optical cycle. It is clear that, under these conditions, the usual envelope approximation breaks down, i.e. both the rotating wave approximation (RWA) as well as the slowly varying envelope approximation (SVEA) must not be used. This paper investigates carrier-wave Rabi flopping experimentally.