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Register a new userGeneralized gauge-invariant formulations of the strong-field approximation
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The gauge problem in the so-called strong-field approximation (SFA) describing atomic or molecular systems exposed to intense laser fields is investigated. Introducing a generalized gauge and partitioning of the Hamiltonian it is demonstrated that the S-matrix expansion obtained in the SFA depends on both gauge and partitioning in such a way that two gauges always yield the same S-matrix expansion, if the partitioning is properly chosen.
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We consider the interaction of hydrogen-like atoms with a strong laser field and show that the strong field approximation and all its variants may be grouped into a set of families of approximation schemes. This is done by introducing an ansatz describing the electron wave packet as the sum of the initial state wave function times a phase factor and a function which is the perturbative solution in the Coulomb potential of an inhomogeneous time-dependent Schrodinger equation. It is the phase factor that characterizes a given family. In each of these families, the velocity and length gauge version of the approximation scheme lead to the same results at each order in the Coulomb potential. By contrast, irrespective of the gauge, approximation schemes belonging to different families give different results. Furthermore, this new formulation of the strong field approximations allows us to gain deeper insight into the validity of the strong field approximation schemes. In particular, we address two important questions: the role of the Coulomb potential in the output channel and the convergence of the perturbative series in the Coulomb potential. In all the physical situations we consider here, our results are compared to those obtained by solving numerically the time-dependent Schrodinger equation.
We study photoelectron angular distributions (PADs) near the ionization threshold with a newly developed Coulomb quantum-orbit strong-field approximation (CQSFA) theory. The CQSFA simulations present an excellent agreement with the result from time-dependent Schrodinger equation method. We show that the low-energy fan-shaped structure in the PADs corresponds to a subcycle time-resolved holographic structure and stems from the significant influence of the Coulomb potential on the phase of the forward-scattering electron trajectories, which affects different momenta and scattering angles unequally. For the first time, our work provides a direct explanation of how the fan-shaped structure is formed, based on the quantum interference of direct and forward-scattered orbits.
The strong-field approximation can be and has been applied in both length gauge and velocity gauge with quantitatively conflicting answers. For ionization of negative ions with a ground state of odd parity, the predictions of the two gauges differ qualitatively: in the envelope of the angular-resolved energy spectrum, dips in one gauge correspond to humps in the other. We show that the length-gauge SFA matches the exact numerical solution of the time-dependent Schrodinger equation.
We study the gauge invariance of laser-matter interaction. The velocity gauge where the vector potential is expanded to the $n$-th order with respect to the spatial coordinate, and the length gauge where the electric and magnetic fields are expanded to the $n$-th and $(n-1)$-th orders, respectively, are mutually gauge-transformed, describing the physically equivalent situation. The latter includes up to the electric $2^{n+1}$-pole and magnetic $2^n$-pole interactions as well as two extra terms. The finding serves to develop consistent nonperturbative simulation methods beyond the electric dipole approximation.
The quasistatic limit of the velocity-gauge strong-field approximation describing the ionization rate of atomic or molecular systems exposed to linear polarized laser fields is derived. It is shown that in the low-frequency limit the ionization rate is proportional to the laser frequency, if a Coulombic long-range interaction is present. An expression for the corresponding proportionality coefficient is given. Since neither the saddle-point approximation nor the one of a small kinetic momentum is used in the derivation, the obtained expression represents the exact asymptotic limit. This result is used to propose a Coulomb correction factor. Finally, the applicability of the found asymptotic expression for non-vanishing laser frequencies is investigated.
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