Coherent Phase Control Research Articles

Dc Field-Induced, Phase and Polarization Control of Interference between One- and Two-Photon Ionization Amplitudes

We demonstrate that a weak, static electric field enables nearly complete coherent phase control of the total ionization yield in a two-color ionization process using fundamental and second-harmonic radiation. The static electric field induces a dipole-forbidden resonance in the two-photon transition amplitude so that the final photoelectron states are identical to those in a single photon transition. We demonstrate also a phase controllable circular dichroism effect in the total photoelectron yield. Experimental realization of this process using alkali metal atoms is discussed.

X-ray photoionization in the presence of a bichromatic laser field

X-ray photoionization of hydrogen in the presence of a bichromatic laser field is considered. The expressions for the $T$ matrix and the cross sections for the laser-assisted x-ray photoionization are presented. The initial state is the laser-field-dressed hydrogen-atom ground state, while the final state is the improved Coulomb-Volkov wave. The gauge consistency is ensured by working in the $\mathbf{r}\ensuremath{\cdot}\mathbf{E}$ gauge. It turns out that the matrix elements (the explicit form of which is given in the Appendix) are much simpler in this case. This enables one to consider the symmetry properties of the $T$ matrix and the cross sections analytically. It was shown that the symmetry $(\ensuremath{\varphi}+\ensuremath{\pi},\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta})\ensuremath{\leftrightarrow}(\ensuremath{\varphi},\ensuremath{\theta})$, where $\ensuremath{\varphi}$ is the relative phase between the laser-field components and $\ensuremath{\theta}$ is the polar angle of the outgoing electron, is exact in our case. In addition to this, there are approximate symmetries $\ensuremath{\varphi}\ensuremath{\leftrightarrow}\ensuremath{-}\ensuremath{\varphi}$ and $\ensuremath{\varphi}\ensuremath{\leftrightarrow}\ensuremath{\varphi}+\ensuremath{\pi}$. All these symmetries, as well as the behavior of the differential and total cross sections as functions of $\ensuremath{\varphi}$, $\ensuremath{\theta}$, and the number of exchanged photons, are analyzed in numerous examples. The results presented show the possibility of the coherent phase control of the laser-assisted x-ray photoionization process. It was also shown that in the monochromatic case our model gives results that are in good agreement with the results of previous work.

Electron-atom ionizing collisions in the presence of a bichromatic laser field

A theory of electron-atom ionizing collisions in the presence of a bichromatic laser field is developed. The incident and scattered electron of high energy is described by Volkov states, the atomic ground state is dressed by the laser field to first order in the electric-field strength, and the atomic continuum state that corresponds to the ejected slow electron is dressed by the laser field to all orders in the field strength, but in an approximate way. It is shown that the dressing of these continuum states is mainly responsible for the different effects that a bichromatic laser field introduces into this process. These effects are more pronounced compared to similar effects recently observed in an analysis of the target dressing in free-free transitions in a bichromatic laser field. The possibility of the coherent phase control is analyzed and it is shown that the triple differential cross section (TDCS) can be changed by almost one order of magnitude by changing the relative phase between the two laser field components. The TDCS as a function of the relative phase, the number of absorbed (emitted) photons, and the laser electric-field strength shows a specific behavior that is mainly determined by the properties of the generalized Bessel functions appearing in our results. It is also shown that these effects are particularly pronounced for rather small scattering angles of the fast electron.

Higher harmonic generation at metal surfaces by powerful bichromatic laser fields

We generalize our recent model calculations on the generation of higher harmonics at metal surfaces by a powerful femtosecond laser pulse [Phys. Rev. A 54, 3245 (1996)] for the case in which a bichromatic field of frequencies \ensuremath{\omega} and 2\ensuremath{\omega} is applied, where both components are out of phase by an angle \ensuremath{\varphi}, and we discuss the coherent phase control of the harmonic generation process, relating our results to those obtained for harmonic generation by shining a bichromatic laser field on atoms.

Coherent control over the photodissociation of CH3I

Coherent phase control of the photodissociation of CH3I has been achieved by quantum mechanical interference between competing paths. The control was accomplished by exciting the parent molecules with three UV photons of frequency ω1 and one VUV photon of frequency ω3=3ω1. Varying the phase difference between the two laser beams resulted in a modulation of the I+ and CH+3 signals, without affecting the parent ion signal. We propose a mechanism in which control occurs over the photodissociation step to produce CH3+I*, followed by ionization of the neutral fragments by additional UV photons.

Phase-dependent on- and off-shell effects in reflection of electrons from an impenetrable potential wall in a bichromatic laser field

We consider the reflection of electrons by an infinitely high potential wall in the presence of a bichromatic laser field having two components of frequency omega and 2 omega . Both components are out of phase by an angle phi . We evaluate the induced and inverse bremsstrahlung for this elementary scattering process and we discuss the coherent phase-control of the non-linear currents j(n; phi ) of electron reflection. If E0 is the initial electron energy and h(cross) omega the photon energy, two specific cases will be of interest: (a) E0>>h(cross) omega and (b) E0>or approximately=h(cross) omega , where in the latter case off-shell effects are particularly relevant. We shall relate our findings to the corresponding scattering of electrons by a hard sphere in a bichromatic field.

Coherent phase control of free-free transitions in bichromatic laser fields

We consider the coherent phase control of the nonlinear cross sections of induced and inverse bremsstrahlung in a powerful bichromatic laser field. The two field components have frequencies r omega and s omega , where r and s are small positive integers, and the relative phase phi of both components can be changed arbitrarily. Amending our earlier work on this problem (Varro and Ehlotzky, 1993) we show that for the ratios r:s=1:2, 1:3 and 2:3 the phase-dependent changes of the free-free cross sections are quite appreciable, whereas for increasing values of s the phase dependence gradually disappears, assuming both field components have the same intensity. If, however, the intensity of the harmonic field component is considerably increased, phase dependent effects again show up even for larger values of s.

Coherent phase control of the photoionization of H2S

Coherent phase control was demonstrated for a bound-to-continuum transition of a polyatomic molecule. Three UV photons of frequency ω1 and one vacuum ultraviolet (VUV) photon of frequency ω3=3ω1 simultaneously excited H2S above its ionization threshold. The parent ion, H2S+, and fragment ions, HS+ and S+, produced by absorption of additional photons, were observed. All three ion signals were modulated as the phase difference between the light fields was varied.

The use of coherent phase control of multiphoton ionization to measure the refractive indices of H2 and Ar between 1100 and 1150 Å

We have used the method of coherent phase modulation, first proposed by Brumer and Shapiro for controlling the rates of chemical reactions, to measure the refractive index of a gas in the vacuum ultraviolet. In these experiments we populated a Rydberg state of HCl or CO by simultaneous absorption of one VUV photon and three UV photons. Molecular ions were generated by absorption of an additional UV photon and detected with a time-of-flight mass spectrometer. The phase difference for the UV and VUV beams was altered by passing them through a cell containing either H2 or Ar. By varying the pressure in the cell we could control this phase difference and thereby modulate the ion signal. From the modulation frequency of the signal it was possible to determine the difference between the refractive indices of the gas at the UV and VUV wavelengths. Using reliable refractive indices in the UV, we extracted from our data values for the VUV indices. These values are in quantitative agreement with a calculation that uses dipole oscillator strengths constructed using constrained oscillator strength methods, taking into account the dispersion resulting from individual rotational transitions. The experimental method can be used very close to an optical transition of the refractive medium, provided that the refractive index does not vary appreciably across the bandwidth of the VUV laser.