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arXiv:1109.4689 · Physical Review A

Strong-field effects in Rabi oscillations between a single state and a superposition of states

Sergey Zhdanovich, J. W. Hepburn, Valery Milner

Published Nov 22, 2011• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.84.053428

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Comment on "Strong-field effects in Rabi oscillations between a single state and a superposition of states"

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In the e-prints arXiv:0909.0984 and 1109.4689 the authors studied the quantum beating in experiments with excitation of potassium atoms by femtosecond laser pulses. Here we propose explanation of physical nature of observed beating and simple experimental test for its verification.

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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.
Rabi oscillations are periodic modulations of populations in two-level systems interacting with a time-varying field. They are ubiquitous in physics with applications in different areas such as photonics, nano-electronics, electron microscopy, and quantum information. While the theory developed by Rabi was intended for fermions in gyrating magnetic fields, Autler and Townes realized that it could also be used to describe coherent light-matter interaction within the rotating wave approximation\cite. Although intense nanometer-wavelength light-sources have been available for more than a decade, Rabi dynamics at such short wavelengths have not been observed directly. Here we show that femtosecond extreme-ultraviolet pulses from a seeded free-electron laser can drive Rabi oscillations between the ground state and an excited state in helium atoms. The measured photoemission signal revealed an Autler-Townes doublet as well as an avoided crossing, phenomena that are both trademarks of quantum optics. Using theoretical analyses that go beyond the strong-field approximation, we found that the ultrafast build-up of the doublet structure follows from a quantum interference effect between resonant and non-resonant photoionization pathways. Given the recent availability of intense attosecond and few-femtosecond extreme-ultraviolet pulses, our results offer opportunities to carry out ultrafast manipulation of coherent processes at short wavelengths using free-electron lasers.
This work presents a theoretical study of two coherent schemes which allow the manipulation of wave packets created in atomic systems by strong ultrashort pulses. Our three-state system is composed of a ground state and two excited states simultaneously excited by the laser pulses. The corresponding dynamics are described in the bright state-dark state formalism where spectacular effects appear. (1) The wave packet created initially by a first pulse can be completely frozen through the action of a second strong pulse. (2) For pulses with a generalized pulse area equal to (2 p +1)2π (p integer), the population is preferentially transferred from the ground state to the dark state whatever the pulse duration. This is in complete disagreement with the physical interpretation valid in the weak field regime where the wave packet created by an ultrashort pulse is localized in the bright state at the end of the pulse. This effect can be revealed with wave packet interference induced by a second identical pulse. A simple analytical model using squared pulses is used to highlight the physical insight. This model is ‘reinforced’ by numerical simulations on the (4s–4p 2 P 1/2,1/3) transitions in potassium atoms excited with Gaussian pulses.
In coherent light-matter interactions the coherent state produced by the light pulse remains coherent during the entire period of observation. One of the well-known examples of such interactions is the Rabi oscillation—a periodic transfer of population in a two-level system induced by an external electromagnetic field. While these oscillations have been studied in light-matter interactions since the discovery of laser itself, most of the studies are limited to long wavelengths, typically ranging from microwave to visible radiation. Here, we discuss how such oscillations can be generated at shorter wavelengths, for example in the extreme ultraviolet domain, using intense femtosecond pulses from seeded free-electron lasers. When a two-level system is undergoing Rabi oscillations, it can be described via an ‘atom + photon’ dressed-state, the properties of which can be further manipulated to study quantum entanglement between massive particles. Our results offer opportunities to employ these intense laser pulses for generating and controlling coherent light-matter interactions across ultrashort timescales.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.