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Optics Letters

Ultrafast Rabi flopping in a three-level energy ladder

Jongseok Lim, Kanghee Lee, Jaewook Ahn

Published Aug 6, 2012• 11 citations
Publisher

Abstract

We demonstrate Rabi oscillation of a resonant two-photon transition in a three-level ladder-type quantum system of gaseous rubidium atoms induced by a single femtosecond laser pulse. For this, we shape the flat-top spatial profile of the laser pulse and perform the ultrafast population cycling of the atoms as a function of pulse energy. The experimental result confirms that the Rabi frequency of the transition from a ground state to a final state depends linearly on the pulse area, although the transition is a two-photon process.

DOI
10.1364/ol.37.003378

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We demonstrate Rabi oscillation of a resonant two-photon transition in a three-level ladder-type quantum system of gaseous rubidium atoms induced by a single femtosecond laser pulse. For this, we shape the flat-top spatial profile of the laser pulse and perform the ultrafast population cycling of the atoms as a function of pulse energy. The experimental result confirms that the Rabi frequency of the transition from a ground state to a final state depends linearly on the pulse area, although the transition is a two-photon process.
The interactions of sub-cycle and single-cycle pulses with two- or three-level quantum systems are studied, respectively. For the two-level quantum system, two cases in which the carrier frequency of pulses is in resonance and far from resonance with the atom are analysed. The ultrafast complete population transfer can be obtained. The sub-cycle pulse with a far off-resonant carrier frequency is found to be more suitable for the population transfer. The relation between the area of pulses and population transfer is clarified in the sub-cycle and single-cycle domain. For the Lambda-type three-level quantum system, more than 90% of population transfer can be achieved from one level to another. The scheme is insensitive to the variation of the laser parameters such as the peak Rabi frequency and the carrier frequency for both two- and three-level quantum systems.
We consider the Rabi oscillation of an atom ensemble of Gaussian spatial distribution interacting with ultrafast laser pulses. Based on an analytical model calculation, we show that its dephasing dynamics is solely governed by the size ratio between the atom ensemble and the laser beam, and that every oscillation peak of the inhomogeneously broadened Rabi flopping falls on the homogeneous Rabi oscillation curve. The results are verified experimentally with a cold rubidium vapor in a magneto-optical trap. As a robust means to achieve higher-fidelity population inversion of the atom ensemble, we demonstrate a spin-echo type R(x)(π/2)R(y)(π)R(x)(π/2) composite interaction as well.
We study the dynamics of three-level $\ensuremath{\Lambda}$-type atoms driven by a coherent train of short, nonoverlapping laser pulses. We derive analytical nonperturbative expressions for the density matrix by approximating the pulses by a $\ensuremath{\delta}$ function. We demonstrate that, depending on the train parameters, several scenarios of system dynamics can be realized. We show the possibility of driving Raman transitions between the two ground states of the $\ensuremath{\Lambda}$ system, avoiding populating excited states by using pulses with effective area equal to $2\ensuremath{\pi}$. The number of $2\ensuremath{\pi}$ pulses needed to transfer the entire population from one ground state to another depends on the ratio between the Rabi frequencies of two allowed transitions. In the case of equal Rabi frequencies, the system can be transferred from one ground state to another with a single $2\ensuremath{\pi}$ pulse. When the total pulse area differs from $2\ensuremath{\pi}$ and the two-photon resonance condition is fulfilled, the system evolves into a ``dark'' state and becomes transparent to subsequent pulses. The third possible scenario is the quasi-steady-state regime when neither the total single-pulse area is equal to $2\ensuremath{\pi}$ nor is the two-photon resonance condition fulfilled. In this regime the radiative-decay-induced drop in the population following a given pulse is fully restored by the subsequent pulse. We derive an analytical expression for the density matrix in the quasi-steady-state regime. We analyze the dependence of the postpulse excited-state population in the quasi-steady-state regime on the train parameters. We find the optimal values for the train parameters corresponding to the maximum of the excited-state population. The maximum of the excited-state population in the steady-state regime is reached at an effective single-pulse area equal to $\ensuremath{\pi}$ and is equal to 2/32/32/3 in the limiting case when its radiative lifetime is much shorter than the pulse repetition period.
Rabi oscillations of quantum population are known to occur in two-level systems driven by spectrally narrow laser fields. In this work we study Rabi oscillations induced by shaped broadband femtosecond laser pulses. Due to the broad spectral width of the driving field, the oscillations are initiated between a ground state and a coherent superposition of excited states, or a ``wave packet,'' rather than a single excited state. Our experiments reveal an intricate dependence of the wave-packet phase on the intensity of the laser field. We confirm numerically that the effect is associated with the strong-field nature of the interaction and provide a qualitative picture by invoking a simple theoretical model.
We study the Rabi flopping of the population between the ground and excited 2p states of the hydrogen atom, induced by intense short laser pulses of different shapes and of carrier frequency ω=0.375 a.u. which resonantly couples the two states, and manifestations of this dynamics in the energy spectra of photoelectrons produced in the subsequent ionization of the atom from the excited state. It is found that, for Gaussian, half-Gaussian and rectangular pulses, characterized by the same pulse area, the final populations take the same values and the spectra consist of similar patterns having the same number of peaks and approximately the same separation between the prominent edge (Autler–Townes) peaks. The additional analysis in terms of dressed states showed that the mechanism of formation of multiple-peak structures during the photoionization process is the same regardless of the pulse shape. These facts disprove the hypothesis proposed in earlier studies with Gaussian pulse, that the multiple-peak pattern appears due to dynamic interference of the photoelectrons emitted with a time delay at the rising and falling sides of the pulse, since the hypothesis is not applicable to either a half-Gaussian pulse that has no rising part or a rectangular pulse whose intensity is constant.
We present a comprehensive theoretical and computational study on harmonic generation (HG) of Li atoms in one- and two-photon Rabi-flopping regimes where the population transfer from the ground 2s2s2s state to the excited 2p2p2p, 3s3s3s, and 3d3d3d states is substantial. Our all-electron approach is based on the time-dependent density-functional theory and takes into account the polarization of the core and the dynamic response of the electrons to the laser field. We show that the population oscillations in the time domain with the Rabi frequency $\mathrm{\ensuremath{\Omega}}$ are reflected in the fine structure of the HG spectra in the frequency domain on the scale of $2\mathrm{\ensuremath{\Omega}}$. Our results also manifest that even finer structures of the harmonic peaks on the smaller frequency scale originate from the pulse-shape-related interference effects. These features are clearly seen in one-photon Rabi-flopping regime between the 2s2s2s and 2p2p2p states. The pattern in the HG spectra becomes more complex in the two-photon Rabi-flopping regime involving 3s3s3s and 3d3d3d states. Our findings can be used for developing coherent control methods for HG in the Rabi-flopping regime.