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Physical Review Letters

Use of the Relative Phase in a Bichromatic Field Pulse to Control a Quasienergy Gap

Leszek Sirko, S. A. Zelazny, P. M. Koch

Published Jul 5, 2001• 45 citations
Publisher

Abstract

We show experimentally and theoretically how the relative phase in a short, linearly polarized microwave pulse consisting of two phase-locked frequencies is effective for strong-field quantum control of He Rydberg atoms when the frequency ratio p:q is 3:1. It is also effective when p:q = 2:1 but less effective for 3:2. Parameters in our experiment are similar to those investigating quantum control of tightly bound atoms or molecules with ultrashort pulsed lasers.

DOI
10.1103/physrevlett.87.043002

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International Conference Physics and Control•Oct 4, 2006•0 citations
We show experimentally and theoretically how the relative phase in a short, linearly polarized microwave pulse consisting of two phase-locked frequencies is effective for strong-field quantum control of He Rydberg atoms when the frequency ratio p:q is 3:1. It is also effective when p:q = 2:1 but less effective for 3:2. Parameters in our experiment are similar to those investigating quantum control of tightly bound atoms or molecules with ultrashort pulsed lasers.
We consider the interaction of atoms with a pulse of a linearly polarized electric field consisting of two phase-locked frequencies whose ratio ω H /ω L is the ratio of arbitrary integers h / l , with h > l . If the electric amplitudes vary in time, they do so with the same slow envelope. The relative phase can be used as a control parameter via variation of the phase ϕ H of ω H or ϕ L of ω L . We derive the physically important ranges of relative phase for total-yield processes as a function of h : l ; they depend on whether h , l are both odd or only one is odd. We tabulate a variety of relevant phase-dependent results for all h : l from 2:1 through 8:7. We use calculations and experimental data for helium and hydrogen Rydberg atoms driven by a bichromatic microwave field to confirm the physically important ranges of ϕ H and ϕ L for a few h : l ratios. Two experimental examples taken from the literature for the interactions of atoms with sub-picosecond, bichromatic laser pulses also confirm our conclusions.
A numerical method is presented to treat atoms in strong time-dependent electric fields. The method is applied to calculate ionization probabilities of H Rydberg atoms in strong monochromatic and bichromatic microwave fields. Recent experimental data on the microwave ionization of H Rydberg atoms are well reproduced. Ionization probabilities for microwave field parameters not yet covered experimentally are predicted. We propose to use the setup of existing two-frequency waveguide experiments to reveal the structure of the quasi-energy spectrum of microwave-driven Rydberg atoms. In analogy to dressed-state spectroscopy of atoms in strong laser fields, the quasi-energies of a periodically driven quantum system are mapped out by sweeping the frequency of a second (weak) additional rf probe field.
An experiment on Ramsey interferometry of the 37S 1/2 → 37P 1/2 microwave transition in sodium Rydberg atoms has been performed. Interaction of Rydberg atoms with a cw microwave radiation was effectively controlled by a pulse of weak (<1 V cm −1 ) electric field, that manipulated the transition frequency near 70 050 MHz. The pulse detuned the microwave radiation from exact resonance, and induced additional phases to the wavefunctions of Rydberg states due to the quadratic Stark shifts. As a result, the Ramsey fringes were observable both on scanning the frequency of the microwave field and on scanning the strength of the electric field pulse. The experiment confirmed that this Stark-switching technique provides a fast and effective control of the atom–light interactions, and preserves the atomic coherence. Possible applications of this technique to experiments on quantum computers are discussed.
The four-wave mixing produced with two ultrashort phase-locked !-3! laser pulses propagating coherently in a two-level system in the infrared spectral region is shown to depend on the pulses relative phase. The Maxwell-Bloch equations are solved beyond the rotating-wave approximation to account for field frequencies which are largely detuned from the atomic resonance. The relative phase dominating the efficiency of the coupling to the 5! anti-Stokes Raman component is determined by sign of the total ac Stark shift induced in the system, in such a way that the phase influence disappears precisely where the ac Stark effect due to both pulses is compensated. This fundamental quantum interference effect can be the basis for nonlinear ultrafast optical spectroscopy techniques. Phenomena arising from the coherent control of nonlinear interactions are of importance in fields as diverse as optoelectronics and materials research, in high harmonic generation, in photoionization or molecular dissociation, and in biological applications such as spectroscopy and imaging, among others [1, 2, 3, 4, 5, 6, 7]. Optical quantum coherent control is based on the fact that the phases of interfering transition amplitudes in light-matter interactions can be controlled through the optical phase of coherent light sources that drive the interaction, in such a way that the transition rates to final states and the dynamics at various stages of the process can be modified [1]. In a recent paper [8], a theoretical investigation on the quantum coherent control of the optical transient four-wave mixing of two intense phase-locked femtosecond laser pulses of central angular frequencies ω and 3ω propagating in a two-level atom (TLA) was reported. It was shown how the nonlinear (χ (3) ) coupling to the antiStokes Raman field at frequency 5ω depends critically on the initial relative phase φ of the propagating pulses. In Ref. [8], the study was centered to intense pulses in the visible and ultraviolet spectral regions, with frequencies at resonance or lower than the atomic transition. The phenomena observed in [8], however, can be scaled to various laser and material parameters. In the infrared spectral range, for instance, experiments on ultrafast molecular dynamics are frequently performed by help of twocolor pump probe nonlinear spectroscopy techniques. In this type of studies, due to the high intensities inherent to ultrashort (subpicosecond) pulses, nonlinear effects such as stimulated Raman processes may become important and are often utilized as a complementary tool to gain information [9]. In this Letter, we address the conditions for quantum coherent control of transient four-wave mixing interactions with two phase-locked ω-3ω femtosecond laser pulses in the mid-IR spectral region. Our purpose is to reveal the basic physics for a strict two-level medium and to this end the Maxwell-Bloch TLA will be considered. We will study pulses with a duration of 300 fs (with a w 5w
We have observed the phase dependence of microwave above-threshold ionization (ATI) of Rydberg potassium atoms at a microwave intensity of 3\ifmmode\times\else\texttimes\fi{}104{10}^{4}104 W ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$. By using 5-ps pulses derived from a mode-locked tunable dye laser to create the initial Rydberg state, and phase locking the microwave field to a high harmonic of the mode-locking frequency, we are able to excite the atom at a specific phase of the microwave field. Measurement of the ejected electrons' energy as a function of the initial Rydberg state and the phase of the microwave field show that it is the phase of the field at which the electron becomes free of the atom that determines its kinetic energy. The energy dependence is described by a simple, classical theory that reveals the relationship between the so-called ``quiver'' and ``drift'' terms in the electron energy previously observed in ATI experiments at higher frequencies.
The paper is devoted to the theoretical investigation of the phase control of atomic photo-excitation in discrete energy spectrum under the action of bichromatic laser field with the frequency ratio 1:2 in the presence of stationary electric field. The calculations are made for the case of alkali atoms. It is shown that the phase modulation of the photo-excitation strongly depends upon the electric field strength and the ratio between the intensities of the monochromatic components of the radiation. The optimal range of parameters for the effect observation is determined.