Coherent control of atomic excitation using off-resonant strong few-cycle pulses

Abstract

We study the dynamics of a two-level system driven by an off-resonance few-cycle pulse which has a phase jump φ at t = t 0 , in contrast to many-cycle pulses, under the nonrotating-wave approximation (NRWA). We give a closed form analytical solution for the evolution of the probability amplitude |C a (t)| for the upper level. Using the appropriate pulse parameters like the phase jump φ, jump time t 0 , pulse width τ , frequency ν, and Rabi frequency 0 the population transfer after the pulse is gone can be optimized and, for the pulse considered here, an enhancement factor of 10 6 -10 8 was obtained. Of current interest is the interaction between strong broadband electromagnetic fields and atoms, especially laser radiation that is tuned far from resonance. Short pulses can excite coherence on high-frequency transitions that may be used for efficient generation of extreme ultraviolet (XUV) radiation [4][5][6]. Shaped pulses can enhance transient population of excited states [7] or create optimal coherence in two-level systems (TLSs) [8]. Recently, we have found an analytical solution describing the dynamics of a two-level atom under the action of laser radiation with an arbitrary pulse shape and polarization [9]. Furthermore, we have studied two mechanisms of atomic excitation: multiphoton excitation, and breaking of adiabaticity [4], and we have shown [10] that the latter can be more efficient.The interaction of such ultrashort pulses with a two-level atom under the rotating-wave approximation does not give us the complete picture since the variation of the atomic polarization and population within the optical cycle is not slow. Thus, we should not neglect the contribution of the counter-rotating terms in the Hamiltonian while studying few-cycle-pulse interactions with atomic systems [11][12][13][14][15][16][17][18]. On the other hand, if the fields are not too strong and the variation of the atomic polarization and population within the optical cycle is slow, the rotating-wave approximation (RWA) appears to be a good approximation.In this brief report, we study the interaction of few-cycle pulses (in contrast to many-cycle pulses [19][20][21]) with a TLS. These pulses have a phase jump φ at t = t 0 . Thus, they can be characterized by the parameters peak Rabi frequency 0 , pulse width τ , carrier frequency ν, phase jump φ, and jump moment t 0 along with the pulse envelope (which we have considered Gaussian for the numerical simulation, see Fig. 1). We present an analytical solution for this problem. Using the appropriate characterizing parameters, the population transfer can be optimized and, for the pulse considered here, enhancement by a factor of 10 6 -10 8 was obtained [see Fig. 5(b)]. The equation of motion for the probability amplitudes for the states |a and |b of a two-level atom (TLA) interacting with a classical field is given as [22]wherehω is the energy difference between two levels, ℘ is the atomic dipole moment, E(t) = E(t)cos(νt). In the RWA we let cos(νt)e ±iωt → e ±i t /2, where = ω − ν [23] is t...

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