Interference effects in the multiphoton ionization of sodium

Volume averaging effect in nonlinear processes of focused laser fields

We report theoretical derivations and experimental results on the volume averaging effect of nonlinear processes in focused laser fields. This effect is considered detrimental in revealing the intensity dependence of a nonlinear process, caused by the intensity variation across the sampled volume of a focused laser. Following the treatment in the literature, we prove that if the signal dependence can be expressed as a simple power function of the laser intensity and if the detection region encompasses effectively the whole volume, volume average does not affect the final conclusion on the derived exponent. However, to reveal the detailed saturation effect of a multi-photon process, intensity selective scans involving spatial filters and displacement of the laser focus (z-scan) are required. Moreover, to fully capture the dependence of the signal on the variation of the laser intensity, the degree of spatial discrimination and the corresponding range of the z-scan need to be modeled carefully. Limitations in the dynamic range of the detector or the laser power, however, can thwart the desired scan range, resulting in erroneous fitting exponents. Using our nanosecond laser with a non-ideal Gaussian beam profile based on multiphoton ionization of argon atoms from a collimated molecular beam and from ambient argon gas, we report experimental measurements of the beam waist and Rayleigh range and compare the experimental intensity dependence of Ar⁺ with theoretical values. Agreements between theory and experiment are remarkable.

Intensity-dependent angular distribution of low-energy electrons generated by intense high-frequency laser pulse

By solving the three-dimensional time-dependent Schrödinger equation, we investigate the angular distributions of the low-energy electrons when an intense high-frequency laser pulse is applied to the hydrogen atom. Our numerical results show that the angular distributions of the low-energy electrons which generated by the nonadiabatic transitions sensitively depend on the laser intensity. The angular distributions evolve from a two-lobe to a four-lobe structure as the laser intensity increases. By analyzing nonadiabatic process in the Kramers-Henneberger frame, we illustrate that this phenomenon is attributed to the intensity-dependent adiabatic evolution of the ground state wavefunction. When the laser intensity further increases, the pathway of nonadiabatic transition from the ground state to the excited state and then to the continuum states is non-negligible, which results in the ring-like structure in the photoelectron momentum distribution. The angular distributions of the low-energy electrons provide a way to monitor the evolution of the electron wavefunction in the intense high frequency laser fields.

Dynamic interference as signature of atomic stabilization

We study the ionization of atoms by very intense linearly polarized pulse with moderately high frequency by numerically solving the time-dependent Schrödinger equation (TDSE). In this regime, the photon energy exceeds the ionization potential allowing for one-photon ionization which is, however, strongly influenced by strong nonlinear photon-atom interactions. We find that the onset of atomic stabilization can be monitored by the appearance of a dynamic interference pattern in the photoelectron spectrum.

Electron Dynamics Driven by Light-Pulse Derivatives

We demonstrate that ultrashort pulses carry the possibility for a new regime of light-matter interaction with nonadiabatic electron processes sensitive to the envelope derivative of the light pulse. A standard single pulse with its two peaks in the derivative separated by the width of the pulse acts in this regime like a traditional double pulse. The two ensuing nonadiabatic ionization bursts have slightly different ionization amplitudes. This difference is due to the redistribution of continuum electron energy during the bursts, negligible in standard photoionization. A time-dependent close-coupling approach based on cycle-averaged potentials in the Kramers-Henneberger reference frame permits a detailed understanding of light-pulse derivative-driven electron dynamics.

Essential Conditions for Dynamic Interference

We develop general quantitative criteria for dynamic interference, a manifestation of a double-slit interference in time which should be realizable with brilliant state-of-the-art high-frequency laser sources. Our analysis reveals that the observation of dynamic interference hinges upon maximizing the difference between the dynamic polarization of the initial bound and the final continuum states of the electron during the light pulse while keeping depletion of the initial state small. These two properties, Stark shift and depletion, can be determined from electronic structure calculations avoiding expensive propagation in time. Confirmed by numerical results, we predict that this is impossible for the hydrogen ground state but feasible for excited states; this has been exemplified for the case of the hydrogen 2p state.

An extremely robust strong-field control of atomic coherence

We propose and analyze a scheme for adiabatic creation of maximum coherence of 0.5 with a controllable phase between a ground state and the excited state in a model Λ-structured atom using two short laser pulses. One of the pulses has constant carrier frequency quasi-resonant with transition between an initially empty ground and the excite states. The frequency of the second pulse is swept through the resonance with the adjacent transition between the initially populated ground state and the common excited state of the atom. We demonstrate high degree of robustness of the scheme against variation of parameters of the laser radiation in relatively broad region of values. The proposed scheme may find practical applications in the field of multi-photon ionization, high-order harmonics and Raman sideband generation, as well as in nonlinear wave mixing in coherently prepared media.

Strong field multiphoton inversion of a three-level system using shaped ultrafast laser pulses

We demonstrate strong-field population inversion in a three-level system with single and multiphoton coupling between levels using a single shaped ultrafast laser pulse. Our interpretation of the pulse shape dependence illustrates the difference between sequential population transfer and adiabatic rapid passage in three-level systems with multiphoton coupling between levels.

In situ measurement of three-dimensional ion densities in focused femtosecond pulses

We image spatial distributions of Xeq+ ions in the focus of a laser beam of ultrashort, intense pulses in all three dimensions, with a resolution of approximately 3 microm and approximately 12 microm in the two transverse directions. This allows for studying ionization processes without spatially averaging ion yields. Our in situ ion imaging is also useful to analyze focal intensity profiles and to investigate the transverse modal purity of tightly focused beams of complex light. As an example, the intensity profile of a Hermite-Gaussian beam mode HG1,0 recorded with ions is found to be in good agreement with optical images.

Strong-field atomic phase matching

We interpret a learning-control experiment with the goal of optimizing multiphoton population transfer in atomic sodium in the strong-field limit. Despite multiple experimental constraints, a learning algorithm discovers optimal pulses that can be understood in terms of a simple dynamic picture of the atom-field interaction. We show that the shaped pulses counteract the dynamic Stark-induced stimulated emission that would otherwise impede the efficient use of a pi pulse to invert a multiphoton transition.

Disentangling the volume effect through intensity-difference spectra: application to laser-induced dissociation of H2+

An intensity-difference spectrum method is developed to disentangle the intensity volume effect inherent in focused laser beam interaction with gas-phase matter. This method is applicable to a Gaussian beam of constant axial intensity, which keeps the exact contribution from a predetermined intensity range and eliminates the contributions from lower intensities. We apply this method to the angularly resolved kinetic energy release spectrum of laser-induced dissociation of H2+. The difference spectrum at higher intensities is found to be dominated by the bond-softening process, and the distribution shifts to lower energy and becomes narrower with increasing intensity.

Volumetric intensity dependence on the formation of molecular and atomic ions within a high intensity laser focus

The mechanism of atomic and molecular ionization in intense, ultra-short laser fields is a subject which continues to receive considerable attention. An inherent difficulty with techniques involving the tight focus of a laser beam is the continuous distribution of intensities contained within the focus, which can vary over several orders of magnitude. The present study adopts time of flight mass spectrometry coupled with a high intensity (8 x 10(15) Wcm(-2)), ultra-short (20 fs) pulse laser in order to investigate the ionization and dissociation of the aromatic molecule benzene-d1 (C(6)H(5)D) as a function of intensity within a focused laser beam, by scanning the laser focus in the direction of propagation, while detecting ions produced only in a "thin" slice (400 and 800 microm) of the focus. The resultant TOF mass spectra varies significantly, highlighting the dependence on the range of specific intensities accessed and their volumetric weightings on the ionization/dissociation pathways accessed.

Ionization of atoms by the spatial gradient of the pondermotive potential in a focused laser beam

Ionization of atoms by the spatial gradient of the pondermotive potential in a focused laser beam is investigated. Rydberg ions, formed during the interaction of noble gas atoms with an intense laser pulse, are used to probe the gradient field. Rydberg ion species with higher ionization potentials are produced at locations where the gradient field is largest. The measured Rydberg ion yields differ dramatically from estimates that ignore gradient-field ionization, but are in good agreement with predictions that include the effect.