Dynamical polarizability of atoms in arbitrary light fields: general theory and application to cesium (1211.2673v2)

Abstract: We present a systematic derivation of the dynamical polarizability and the ac Stark shift of the ground and excited states of atoms interacting with a far-off-resonance light field of arbitrary polarization. We calculate the scalar, vector, and tensor polarizabilities of atomic cesium using resonance wavelengths and reduced matrix elements for a large number of transitions. We analyze the properties of the fictitious magnetic field produced by the vector polarizability in conjunction with the ellipticity of the polarization of the light field.

• The paper introduces a comprehensive formalism to compute cesium atoms' dynamical polarizability across arbitrary light fields, incorporating scalar, vector, and tensor components.
• It employs precise computations to derive ac Stark shifts and identifies magic wavelengths at approximately 686.3 nm and 935.2 nm for optimal atomic control.
• The study highlights significant vector polarizability effects, paving the way for novel experimental setups in quantum information processing and optical trapping.

Dynamical Polarizability of Atoms in Arbitrary Light Fields

The paper presents a thorough formalism for calculating the dynamical polarizability of atomic states, considering interactions with light fields of arbitrary polarization. The focus is on cesium atoms, and the investigation includes the derivation of expressions for the ac Stark shift and the scalar, vector, and tensor components of atomic polarizability. This work is pivotal for theoretical predictions and experimental setups in atomic, molecular, and optical physics, notably in quantum information processing and atomic trapping using far-off-resonance light fields.

Overview of the Theory

The authors detail a systematic approach to determining the dynamical polarizability of atoms, integrating the effects of far-off-resonance light fields. The framework considers scalar, vector, and tensor polarizabilities, which are pertinent for understanding the ac Stark shift experienced by both ground and excited atomic states. This is essential for scenarios where light-induced energy level shifts are influenced by the intensity and polarization of an external optical field.

In deriving the dynamical polarizabilities, the authors deploy resonance wavelengths and reduced matrix elements to compute polarizabilities for numerous transitions. The quantified scalar, vector, and tensor polarizabilities are given in atomic units (a.u.). The paper also explores how vector polarizability contributes to a fictitious magnetic field, a noteworthy element for experimental configurations involving pseudo-magnetic effects due to light-atom interactions.

Computational and Numerical Analysis

Numerical results are presented for cesium atoms, covering a broad range of light wavelengths. The scalar polarizability is calculated for the cesium ground state $6S_{1/2}$, with an approximate static value of 398.9 a.u., consistent with other high-precision theoretical and experimental studies. The analysis includes identifying magic wavelengths, where the shifts for ground and excited states are identical, simplifying atomic manipulation in optical traps. Two such magic wavelengths are highlighted: a blue-detuned magic wavelength at ≈686.3 nm and a red-detuned one at ≈935.2 nm.

Importantly, numerical data reveal that vector polarizability can be substantial, indicating significant vector Stark shifts under non-linear polarizations. This reinforces the necessity for precise polarization alignment in experimental setups to correctly control atomic states.

Implications and Future Prospects

This research has significant implications for quantum information science, especially in areas like quantum memories and optical lattices, where control over atomic states is crucial. The detailed calculations for different polarization components aid in designing experiments that exploit specific characteristics of atom-light interactions.

The nuanced investigation into vector light shifts as a consequence of fictitious magnetic fields opens avenues for novel applications that could utilize these pseudo-magnetic effects for manipulating atomic spin states without external magnetic fields.

Future advancements may involve extending these calculations to more complex atomic species or incorporating the results into large-scale computational models for better simulation of quantum systems. Additionally, incorporating relativistic corrections or exploring interactions in even more exotic polarization scenarios could further deepen the understanding of atom-light interaction dynamics.

Conclusion

The paper rigorously examines the dynamical polarizability of cesium atoms in arbitrary light fields, providing substantial theoretical and numerical data essential for practical applications in quantum technologies. By offering a comprehensive set of theoretical tools and clarifying the underlying physics of light-induced atomic behavior, the paper contributes significantly to the fundamental and applied optics field.