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Results in Physics

High-order correction calculation for survival of Rydberg atoms in intense laser fields

Jiajia Zha, Zhihao Qin, Jiayi Yan, Na Cao, Qi Wei, Pingxiao Wang

Published Feb 6, 2021• 4 citations
Publisher

Abstract

Using a method based on the Magnus expansion, the survival of Rydberg atoms in intense laser fields is studied. Usually, for atoms in intense laser fields, effects beyond the electric dipole approximation need to be considered. In the past few years, researchers have primarily paid attention to the nondipole effects induced by the electric quadrupole term of the optical field. The quadrupole term plays a more important role than the electric dipole term in the calculation of the survival probability of Rydberg atoms in intense laser fields even though the magnitude of the former is smaller than that of the latter in terms of the multipole expansion of the optical vector potential. Meanwhile, the effects of higher-order corrections beyond the quadrupole term remain ambiguous. In this paper, we confirm that corrections containing higher-order terms, except for the quadrupole term, can be neglected in the calculation of the transitions of Rydberg atoms in external fields. We then use the second-order time evolution operator containing the quadrupole term to study the scaling law of the transition probability of Rydberg He in laser fields with different parameters.

DOI
10.1016/j.rinp.2020.103594

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Using a method based on the Magnus expansion, the survival of Rydberg atoms in intense laser fields is studied. Usually, for atoms in intense laser fields, effects beyond the electric dipole approximation need to be considered. In the past few years, researchers have primarily paid attention to the nondipole effects induced by the electric quadrupole term of the optical field. The quadrupole term plays a more important role than the electric dipole term in the calculation of the survival probability of Rydberg atoms in intense laser fields even though the magnitude of the former is smaller than that of the latter in terms of the multipole expansion of the optical vector potential. Meanwhile, the effects of higher-order corrections beyond the quadrupole term remain ambiguous. In this paper, we confirm that corrections containing higher-order terms, except for the quadrupole term, can be neglected in the calculation of the transitions of Rydberg atoms in external fields. We then use the second-order time evolution operator containing the quadrupole term to study the scaling law of the transition probability of Rydberg He in laser fields with different parameters.
We consider the interaction of Rydberg atoms with strong infrared laser pulses using an approach based on the Magnus expansion of the time evolution operator. First-order corrections beyond the electric dipole approximation are also included in the theory. We illustrate the dynamics of the interaction at the parameters of the experiment [Eichmann et al., Phys. Rev. Lett. 110, 203002 (2013)]. It emerges that the depletion of Rydberg atoms in this regime comes predominantly from the nondipole effects.
Currently, the Magnus expansion method is widely used in studying Rydberg atoms in intense laser fields. In these studies, pulse lengths are usually set as an integer multiple of wavelength, at the same time, the initial phase of the laser pulse are usually set as zero, i.e. , without considering the effect of the initial phase in the calculation. However, this will result in some items multiplied by zero. Then, contributions from these items will be lost. Herein, we investigated the effects of the non-integer-cycle pulse and laser initial phase in the calculation of the transition probability of Rydberg atoms in intense laser fields. Our calculation result shows that these effects are trivial when the nondipole approximation is adopted. In dipole approximation i.e. , when the wavelength of the laser field exceeds the characteristic size of atomic or molecular orbitals, these effects are trivial only in the case of a long pulse duration and a large principal quantum number, however in the case of ultrashort laser pulses, these effects are obvious.
We treat the interaction of an atom with a short intense few-cycle laser pulse by the use of the Magnus expansion of the time-evolution operator. Terms of the Magnus expansion up to the third order in the pulse duration are evaluated explicitly, and expressions for the transition probability between atomic eigenstates are given. The transition operators up to this order are particularly simple, involving only momentum and position shifts arising from the laser field alone. The connection to other existing approaches is established. For a variety of generic short-pulse forms the results of the Magnus approximation are in excellent agreement with time-dependent transition probabilities obtained from accurate ab initio numerical calculations. However, the limitation of the Magnus expansion for pulses having both vanishing momentum and position shifts is demonstrated also.
The quadrupole interaction between the Rydberg electronic states of a Rydberg ion and the radio frequency electric field of the ion trap is analyzed. Such a coupling is negligible for the lowest energy levels of a trapped ion but it is important for a trapped Rydberg ion due to its large electric quadrupole moment. This coupling cannot be neglected by the standard rotating-wave approximation because it is comparable to the frequency of the trapping electric field. We investigate the effect of the quadrupole coupling by performing a suitable effective representation of the Hamiltonian. For a single ion we show that in this effective picture the quadrupole interaction is replaced by rescaled laser intensities and additional Stark shifts of the Rydberg levels. Hence this detrimental quadrupole coupling can be efficiently compensated by an appropriate increase of the Rabi frequencies. Moreover, we consider the strong dipole-dipole interaction between a pair of Rydberg ions in the presence of the quadrupole coupling. In the effective representation we observe reducing of the dipole-dipole coupling as well as additional spin-spin interaction.
Abstract The strong interaction between individual Rydberg atoms provides a powerful tool exploited in an ever-growing range of applications in quantum information science, quantum simulation and ultracold chemistry. One hallmark of the Rydberg interaction is that both its strength and angular dependence can be fine-tuned with great flexibility by choosing appropriate Rydberg states and applying external electric and magnetic fields. More and more experiments are probing this interaction at short atomic distances or with such high precision that perturbative calculations as well as restrictions to the leading dipole–dipole interaction term are no longer sufficient. In this tutorial, we review all relevant aspects of the full calculation of Rydberg interaction potentials. We discuss the derivation of the interaction Hamiltonian from the electrostatic multipole expansion, numerical and analytical methods for calculating the required electric multipole moments and the inclusion of electromagnetic fields with arbitrary direction. We focus specifically on symmetry arguments and selection rules, which greatly reduce the size of the Hamiltonian matrix, enabling the direct diagonalization of the Hamiltonian up to higher multipole orders on a desktop computer. Finally, we present example calculations showing the relevance of the full interaction calculation to current experiments. Our software for calculating Rydberg potentials including all features discussed in this tutorial is available as open source.
Manipulation of cold atoms by lasers has so far been studied solely within the framework of the conventional dipole approximation, and the atom-light interaction has been treated using low order perturbation theory. Laser control of atomic motions has been ascribed exclusively to the corresponding light-induced dipole forces. In this work, we present a general theory to derive the potential experienced by an atom in a monochromatic laser field in a context analogous to the Born-Oppenheimer approximation for molecules in the field-free case. The formulation goes beyond the dipole approximation and gives rise to the field-atom coupling potential terms which so far have not been taken into consideration in theoretical or experimental studies. Contrary to conventional approaches, our method is based upon the many electron Floquet theory and remains valid also for high intensity laser fields (i.e., for a strongly nonperturbative atom-light interaction). As an illustration of the developed theory, we investigate the trapping of cold atoms in optical lattices. We find that for some atoms for specific laser parameters, despite the absence of the dipole force, the laser trapping is still possible due to the electric quadrupole forces. Namely, we show that by using realistic laser parameters one can form a quadrupole optical lattice which is sufficiently strong to trap Ca and Na atoms.