Observation of Broadband Time-Dependent Rabi Shifting in Microplasmas Ryan Compton, Alex Filin, Dmitri A. Romanov, and Robert J. Levis Center for Advanced Photonics Research, Departments of Chemistry and Physics, Temple University, Philadelphia, Pennsylvania 19122, USA (Received 6 July 2009; published 10 November 2009) Coherent broadband radiation in the form of Rabi sidebands is observed when a ps probe laser propagates through a weakly ionized, electronically excited microplasma generated in the focus of an intense pump beam. The sidebands arise from the interaction of the probe beam with pairs of excited states of a constituent neutral atom via the probe-induced Rabi oscillation. Sideband shifting of >90 meV from the probe carrier frequency results in an effective bandwidth of 200 meV. The sidebands are controlled by the intensity and temporal profile of the probe pulse; with amplitude and shift in agreement with the predictions of a time-dependent generalized Rabi cycling model. DOI: 10.1103/PhysRevLett.103.205001 PACS numbers: 52.38.r The Rabi oscillation [1] is a central paradigm in modern optics and is manifest in both the spectral and temporal domains when the cycling period is less than the character- istic decoherence time of the system. Recent implementa- tion of Rabi oscillations include the manipulation of qubits, quantum dots, and excitonic state population [2–6]. Low temperatures must be used (  10 K) to suppress damping in each of the condensed phase experiments. We show here giant Rabi shifting (100 meV) in a laser-induced micro- plasma where dephasing might be expected to limit all coherent processes. The Rabi sidebands occur simulta- neously on multiple atomic transitions producing a coher- ent and tunable radiation source, and we present a time- dependent generalized Rabi cycling model to interpret the phenomena. The giant Rabi shift creates sufficient band- width to support 20 fs temporal features and is generated from a much longer ( 1 ps) driving pulse. Finally, the ratios of multiple excited state transition dipole moments can be measured simultaneously using the effect. Rabi oscillations are manifest in the frequency domain as sidebands on a carrier frequency, ! c . This work dem- onstrates that an intense laser with time-dependent electric field amplitude, A 0 ðtÞ, interacting with a two-level system will result in the generation of red- and blue-shifted side- bands at frequencies ! c   0 ðtÞ and ! c þ  0 ðtÞ, where  0 ðtÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 þ  2 ðtÞ p is the time-dependent generalized Rabi frequency, ðtÞ¼ M 10 A 0 ðtÞ=@ is the time-dependent Rabi frequency, and M 10 is the transition dipole moment. The time-dependent case is most easily visualized by the transitions in a dressed-state scheme in which the bare atomic states are split by  0 ðtÞ, as shown in Fig. 1. A pulse with carrier frequency ! c , blue detuned from the resonant frequency by , results in a dynamic Rabi shift that gen- erates two new sidebands. The Rabi shift reaches a maxi- mum,  0 max , at the maximum of the electric field (t ¼  0 ). The instantaneous frequency of the Rabi-shifted pulses generated at  0  t and  0 þ t is identical for a Gaussian temporal profile [ 0 ð 0  tÞ¼  0 ð 0 þ tÞ], suggesting the ability to produce temporally chirped pulses, as will be discussed later. In previous measure- ments, the laser inducing the Rabi oscillation has been self-modulated, generating nanosecond duration sidebands in Na vapor at 3:5 meV [7,8]. Thin GaAs films [9,10] have also been used to demonstrate Rabi shifting on the order of the carrier frequency in the optical regime using a carrier-envelope phase stabilized femtosecond pulse. Rabi sidebands are generally difficult to observe due to damping (dephasing and spontaneous emission) mecha- nisms, which eliminate coherence. For electronic transi- tions arising from the excitation of ground-state atoms and molecules this difficulty is due in part to the rapid T 1 damping. Note that when a substantial degree of excited electronic states are populated in an atom, low-energy transitions (1–2 eV) are available for Rabi cycling. We accomplish this electronic excitation using a partially ion- FIG. 1 (color). A dynamic dressed-state energy level scheme for a two-level system, where levels 0 and 1 are the ground and excited bare atomic states, respectively. A pulse with carrier frequency ! c (green waveform), detuned from the resonant frequency by , results in a time-dependent Rabi shift that generates two new dynamic sidebands at ! c   0 ðtÞ (blue and red waveforms). PRL 103, 205001 (2009) PHYSICAL REVIEW LETTERS week ending 13 NOVEMBER 2009 0031-9007= 09=103(20)=205001(4) 205001-1 Ó 2009 The American Physical Society