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Chinese Physics B

Non-linear spectral splitting of Rydberg sodium in external fields

Wei Jia Gao, Haifeng Yang, Hong Cheng, Shanshan Zhang, Danfeng Liu, Hongping Liu

Published Jan 1, 2015• 0 citations
Publisher

Abstract

We have studied highly excited sodium in various electric fields, parallel electric and magnetic fields, with one σ and π photon irradiation, and even in a magnetic field with a complex laser polarization configuration. The σ spectra shows a simple linear Stark effect with the applied electric field, while the π spectra exhibits a strong non-linear dependence on the electric field. The π transitions in parallel fields show a similar behavior to that in a pure electric field but the spectra get more smooth due to the magnetic field. The diamagnetic spectrum with laser polarization angles between 0 and π /2 proves that it can be reproduced by simple linear combination of π and σ components, indicating there is no interference between the π and σ channels. A full quantum calculation considering the quantum defects accounts for all the observations. The quantum defects, especially for the channel n p, play an important role in the spectral profile.

DOI
10.1088/1674-1056/24/1/013202

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We have studied highly excited sodium in various electric fields, parallel electric and magnetic fields, with one σ and π photon irradiation, and even in a magnetic field with a complex laser polarization configuration. The σ spectra shows a simple linear Stark effect with the applied electric field, while the π spectra exhibits a strong non-linear dependence on the electric field. The π transitions in parallel fields show a similar behavior to that in a pure electric field but the spectra get more smooth due to the magnetic field. The diamagnetic spectrum with laser polarization angles between 0 and π /2 proves that it can be reproduced by simple linear combination of π and σ components, indicating there is no interference between the π and σ channels. A full quantum calculation considering the quantum defects accounts for all the observations. The quantum defects, especially for the channel n p, play an important role in the spectral profile.
We report on the experimental spectral observations of barium in parallel electric and magnetic fields. The laser pulse is linearly polarized along or perpendicular to the fields, leading to the states m = 0 and the states m = ±1 populated, respectively, by one photon excitation. By sweeping the electric field, we observe the linear and nonlinear splitting of the diamagnetic spectrum as the electric field increases. The spectral anticrossing is induced by the atomic core effect. The Stark spectrum also shows an obvious nonlinear quadratic behavior when the applied magnetic field varies strongly. All spectra are well explained by the full quantum calculation after taking the quantum defect effects of the channel n s up to n f into account.
We report diamagnetic spectra of sodium atoms observed in a strong magnetic field up to 3 T and compare them with theoretical calculations based on the formulation of an exact quantum-defect theory. We focus on one-photon absorption processes from the ground 3s3s3s state to the excited npnpnp Rydberg states whose magnetic quantum numbers are determined by the polarization of the laser field. The calculations employ BBB-spline basis expansion and the complex spatial coordinate rotation technique, and their results agree well with the observed ones when atomic core effects are appropriately taken into account. When graphed against magnetic field, level anticrossings and core-induced interaction of the npnpnp states provide clear signatures for studying the effects of quantum defect on the diamagnetic spectra.
New results are presented of an experimental investigation of the spectrum of 36 P → 37 P two-photon microwave transition in Rydberg atoms of sodium in a constant electric field. Depending on the conditions of excitation of the initial 36 P state (the constant electric field is switched on either before or after the exciting laser pulse) and polarization of laser radiation, a strong variation is observed of the amplitudes of individual two-photon transitions between the fine-structure Stark components of the 36 P and 37 P states. This effect is an analog of the Paschen-Back effect in a strong magnetic field and is due to the break of L-S coupling and to the variation of the wave functions of Rydberg electrons in an electric field. It is also found that the break of L-S coupling affects considerably the shape of double Stark resonance arising upon intersection of the virtual intermediate level of two-photon transition with the real intermediate 37 S level.
The diamagnetic and Stark shifts of strongly perturbed Rydberg spectra such as those of the alkaline earths are expressed in terms of multichannel---quantum-defect parameters. The theory is applicable when the shifts produced by the external fields are smaller than the neighboring Rydberg separations. It is applied to evaluate the diamagnetic shifts in Ba, an atom in which Rydberg and doubly excited channels are strongly mixed. In such complex spectra, the diamagnetic effect can serve a useful purpose as a tool to disentangle the interacting series. The radial sizes and, therefore, the diamagnetic shifts are quite different for singly and doubly excited states even when they are at the same energy. In fact, for the field strengths considered ($\ensuremath{\simeq}40$ kG), the diamagnetic contribution of the doubly excited configuration is quite negligible. As a result, the observed shift is a direct measure of the amount of singly excited configuration in the state of interest. Exactly similar conclusions apply to Stark shifts. The last part of this paper considers states of very high excitation further up in the spectrum which are no longer in a perturbative regime. Spectra of atoms in a magnetic field have shown equally spaced resonances near the ionization threshold with characteristic spacings. By the consideration of the effects of electric fields which are also often simultaneously present, a criterion is established for the nature of these spacings depending on the relative strengths of the crossed electric and magnetic fields. The spacing seen in any particular experiment is shown to depend on the mass and quantum defect of the atom, the strengths of the external fields, and experimental conditions such as the temperature of the atomic vapor whose absorption spectrum is being studied.
We study the role of laser polarization in the diamagnetic spectrum for the transition from the ground state to the highly excited Rydberg states through a single photon absorption. For simplicity, one usually polarizes the irradiation laser to the selected main quantum axis, which is along the applied external electric or magnetic field. The transition selection rule is simply expressed as m = 0, which corresponds to the π transition. When the polarization is circularly polarized around the main axis, the σ+ or σ- transition occurs, corresponding to the selection rule of m = 1 or m = 1, respectively. A slightly more complex case is that the laser is linearly polarized perpendicular to the main axis. The numerical calculation shows that we can decompose the transition into the sum of σ+ and σ- transitions, it is noted as the σ transition. For the more complex case in which the laser is linearly polarized with an arbitrary angle with respect to the main axis, we have to decompose the polarization into one along the main axis and the other one perpendicular to the main axis. They correspond to π and σ transitions, respectively. We demonstrate that these transitions in the diamagnetic spectrum and the above spectral decomposition well explain the experimentally observed spectra.