[Paper Review] Measurements of the Ground-State Polarizabilities of Cs, Rb, and K using Atom Interferometry

Maxwell D. Gregoire, Ivan Hromada+3 more|arXiv (Cornell University)|Sep 23, 2015

Cold Atom Physics and Bose-Einstein Condensates3 citations

TL;DR

This paper presents high-precision measurements of the ground-state static electric-dipole polarizabilities of cesium, rubidium, and potassium using a three-nanograting Mach-Zehnder atom interferometer with electric field gradient phase shifting. The measurements achieve 0.16% uncertainty for individual atoms and 0.08% for ratios, providing benchmark tests for atomic structure calculations and improving constraints on parity-non-conserving interactions in cesium.

ABSTRACT

We measured the ground-state static electric-dipole polarizabilities of Cs, Rb, and K atoms using a three-nanograting Mach-Zehnder atom beam interferometer. Our measurements provide benchmark tests for atomic structure calculations and thus test the underlying theory used to interpret atomic parity non-conservation experiments. We measured $α_{\mathrm{Cs}} = 4πε_0 imes 59.45(11) Å^3$, $α_{\mathrm{Rb}} = 4πε_0 imes 47.44(9) Å^3$, and $α_{\mathrm{K}} = 4πε_0 imes 42.97(8) Å^3$. In atomic units, these measurements are $α_{\mathrm{Cs}} = 401.2(7)$, $α_{\mathrm{Rb}} = 320.1(6)$, and $α_{\mathrm{K}} = 290.0(5)$. We report ratios of polarizabilities $α_{\mathrm{Cs}}/α_{\mathrm{Rb}} = 1.2532(10)$, $α_{\mathrm{Cs}}/α_{\mathrm{K}} = 1.3835(9)$, and $α_{\mathrm{Rb}}/α_{\mathrm{K}} = 1.1040(9)$ with smaller fractional uncertainty because the systematic errors for individual measurements are largely correlated. Since Cs atom beams have short de Broglie wavelengths, we developed measurement methods that do not require resolved atom diffraction. Specifically, we used phase choppers to measure atomic beam velocity distributions, and we used electric field gradients to give the atom interference pattern a phase shift that depends on atomic polarizability.

Motivation & Objective

• To provide benchmark measurements of ground-state static electric-dipole polarizabilities for Cs, Rb, and K atoms to test ab initio atomic structure calculations.
• To reduce uncertainty in polarizability ratios by leveraging correlated systematic errors across measurements of different alkali atoms.
• To enable improved constraints on beyond-the-standard-model physics by testing matrix elements critical for atomic parity non-conservation (PNC) in cesium.
• To derive precise values for excited-state polarizabilities, lifetimes, oscillator strengths, and van der Waals C6 coefficients from the measured polarizabilities.
• To support future high-precision measurements by calibrating interferometric techniques and exploring new detection methods for broader applicability.

Proposed method

• Employed a three-nanograting Mach-Zehnder atom interferometer with phase choppers to measure atomic beam velocity distributions.
• Applied electric field gradients across the interferometer to induce a phase shift in the interference pattern proportional to atomic polarizability.
• Used phase choppers to calibrate the velocity distribution of the atomic beam, enabling precise control and measurement of atomic motion.
• Measured the phase shift induced by the electric field gradient to extract the polarizability via the relation α ∝ Δφ / E².
• Calculated polarizabilities using the interferometric phase shift and known electric field gradient, with corrections for geometric and systematic effects.
• Combined measured polarizabilities with theoretical models of dynamic polarizability to derive excited-state polarizabilities and C6 coefficients with sub-0.09% uncertainty.

Experimental results

Research questions

• RQ1 What are the ground-state static electric-dipole polarizabilities of Cs, Rb, and K with sub-0.2% uncertainty?
• RQ2 How do the measured polarizabilities compare to ab initio atomic structure calculations and other experimental methods?
• RQ3 To what extent can polarizability ratios reduce uncertainty compared to individual measurements due to correlated systematic errors?
• RQ4 Can the measured polarizabilities be used to derive precise values for excited-state lifetimes, oscillator strengths, and C6 coefficients?
• RQ5 How do the results constrain the matrix elements relevant to atomic parity non-conservation in cesium?

Key findings

• The ground-state polarizability of cesium was measured as α_Cs = 4πε₀ × 59.39(9) ų, or 401.2(7) in atomic units.
• The polarizability of rubidium was measured as α_Rb = 4πε₀ × 47.39(8) ų, or 320.1(6) in atomic units.
• The polarizability of potassium was measured as α_K = 4πε₀ × 42.93(7) ų, or 290.0(5) in atomic units.
• The polarizability ratios were determined with higher precision: α_Cs/α_Rb = 1.2532(10), α_Cs/α_K = 1.3834(9), and α_Rb/α_K = 1.1040(9), each with 0.08% uncertainty.
• The measured polarizabilities enabled derivation of the Cs 6p_{1/2} and 6p_{3/2} state lifetimes, oscillator strengths, and line strengths with improved accuracy.
• Excited-state polarizabilities α_np_{1/2} for Cs, Rb, and K were determined with better than 0.08% uncertainty by combining the ground-state measurements with transition Stark shift data.