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We solve numerically the one-dimensional Schrodinger equation with a model potential for the case of excitation by two commensurate (the fundamental and third harmonic) intense laser fields and find a strong dependence of the atomic evolution and high-harmonic generation on the relative phase between the two fields. Our method employs the Kramers-Henneberger frame to exploit the insights gained from emphasizing the wave-packet dynamics of an electron oscillating under the influence of the strong laser fields.PACS number(s): 32.80.WrThe excitation of an atom by a very strong laser field continues to attract attention from experimentalists and theorists [1,2]. The application of a single laser frequency has led to the discovery of above-threshold ionization [3] (ATI), high-harmonic generation [4], and the ejection of electrons by very strong fields in a tunneling process [5]. Recently, attention has been focused on the issue of stabilization [1,2,6] and suppression of ionization in strong fields. Theoretical concepts such as the production of dressed wave packets [7], the use of the KramersHenneberger frame [8] to describe strongly perturbed atomic electrons, the adoption of Floquet methods [9], and the use of computationally intensive numerical methods [10] have all contributed to our understanding of strong-field atomic physics. Often, one-dimensional models [11,12] have proved useful in developing theoretical insights which retain their utility in fully threedimensional (and therefore more complicated) models [13].When an atom is excited by two distinct frequencies, phenomena related to the phase-dependent modification of the electronic motion are produced [14]. Early work on two-color excitation of atoms by the fundamental and second harmonic of a laser field demonstrated how ATI and ionization yields can be significantly changed by phase-dependent interactions [15,16], suggesting that a form of "coherent control" [17] over the multiphoton dynamics is possible. In the present paper, we extend these considerations of two-color excitation to the intense-field stabilization regime in which the ponderomotive quiver motion dominates the dynamics. We address the problem of two-color excitation by a fundamental and its third harmonic: For such a choice of frequencies, there is direct competition between the two fields to access nearresonant states [18,19] so that phase dependence is expected to be significant even at modest intensities. At higher intensities the tunneling followed by a quiver picture of ionization and high-harmonic generation [20 -22] can be modified in a phase-dependent way by such a cornbination of frequencies. These interfere to enhance or diminish that part of the quiver close to the nucleus, as we shall show.The nonperturbative results we present here have been where the effect of the laser electric field is contained in a(t)= (elm-) f A (r)dr, which is the classical displacement of the electron in the electric field. The "Rochester potential, " in atomic units [11],is used as it is continuous...

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