Absolute Polarization Measurement Using a Vector Light Shift

We have measured the vector light shift due to a cavity built-up optical lattice by using a variation of the Hanle effect with trapped Cs atoms, where the time-evolving population of all magnetic sublevels is measured in situ. The measurement is linearly sensitive to the electric field of the nonlinearly polarized light, which allows unprecedented sensitivity to absolute linear polarization quality, to the level of ${10}^{-10}$ in fractional intensity. Our approach to measuring and improving linear polarization can be applied to electron electric dipole moment searches, optical lattice clocks, magnetometery, and quantum computing.

Figure 1

Schematic of the experimental setup (not to scale). Laser-cooled atoms are trapped in two parallel 1D optical lattices made in 2-m-long build-up cavities, separated by 1 cm. The 1064 nm input cavity beam polarizations are cleaned up by GLPs. Each cavity contains two low-birefringence vacuum windows and a pair of Brewster plates for cavity locking and polarization purification. The 90° cavity-folding mirror is necessitated by geometric constraints.

Figure 2

Population evolution for all seven $F=3$ Zeeman sublevels during a Larmor precession cycle in an effective magnetic field of $100\mu \mathrm{G}$. Spins are prepared in $\mathbf{y}$ and measured in $\mathbf{x}$. The lines are theoretical predictions without dephasing (which is quantified later in the Letter). Each set of seven points is from a single atom ensemble. The standard deviation of $\pm 0.05$ in fractional population is dominated by fluctuations in the background from scattered trapping light. Imperfect background substraction due to these fluctuations can lead to an inference of negative populations. These fluctuations can be avoided in future measurements with an additional 1064 nm filter.

Figure 3

Measured spin precession for two different trap depths: $U_0=k_B\times 100\mu \mathrm{K}$ (red circles) and $U_0=k_B\times 50\mu \mathrm{K}$ (blue squares). For illustrative purposes, ${\omega }_U$ is made much larger than ${\omega }_B$ for this measurement. The atoms are prepared in state $|3,+3⟩$ along $\mathbf{y}$, are allowed to spin precess along $\mathbf{z}$, and are then measured along $\mathbf{y}$. Lowering the trap depth by half decreases the precession frequency by a factor of 2. Points on the two curves are taken alternately to minimize any effect of small ${\omega }_B$ drifts. Numerical fitting (solid lines) to Eq. (5) implies a vector light shift of $792\pm 30\mathrm{Hz}$ for a $100\mu \mathrm{K}$ trap depth.

Figure 4

Measured spin precession at two different lattice depths in the (a) $+X$ and (b) $-X$ lattices. All cavity elements are aligned for optimum linear polarization. The atoms are prepared in $|3,+3⟩$ along $\mathbf{y}$, spin precess along $\mathbf{z}$ due to a combination of ${\omega }_B$ and ${\omega }_U$, and are finally measured along $\mathbf{x}$. Numerical fitting (solid lines) to Eq. (6) implies vector light shifts of $-13.9\pm 0.5\mathrm{Hz}$ ($+X$) and $12.3\pm 0.4\mathrm{Hz}$ ($-X$) for a $100\mu \mathrm{K}$ trap depth. The signs are different because the residual circular polarizations of the two lattices have opposite handedness.