Potassium tune-out-wavelength measurement using atom interferometry and a multipass optical cavity

The longest tune-out wavelength for potassium atoms, ${\lambda }_{\mathrm{zero}}=768.9701\left(4\right)$ nm, was measured using an atom interferometer with a large irradiance gradient supported in a multipass optical cavity. Systematic errors in ${\lambda }_{\mathrm{zero}}$ measurements that arise from laser light, Doppler shifts, and the Earth's rotation are described. The ratio of oscillator strengths for the potassium $D2$ and $D1$ lines inferred from this ${\lambda }_{\mathrm{zero}}$ measurement is $\rho =f_{D2}/f_{D1}=2.0066\left(11\right)$, and the ratio of line strengths is $R=S_{D2}/S_{D1}=1.9977\left(11\right)$.

Figure 1

(a) Top-view schematic of atom interferometer paths passing through a multipass optical optical cavity. (b) Side-view schematic of the plane-plane optical multipass cavity aligned so atoms interact with multiple passes of the laser beam. The deviation from parallel is exaggerated to show how the laser beam folds back at different angles.

Figure 2

Enhanced slope for phase vs wavelength data due to multipass cavity. The slope for ${\varphi }_{\text{multi}}$ is $d\varphi /d\lambda =1.9$ mrad/pm with $v=2900$ m/s atoms (solid line and solid circles). A smaller slope of 0.76 mrad/pm was observed for a single-pass experiment (${\varphi }_{\text{single}}$) with $v=1600$ m/s atoms (dashed line and open circles).

Figure 3

Decoherence spectroscopy data (solid red circles) showing contrast vs laser wavelength. Theoretical curves are shown in solid blue for no Doppler shift and dashed blue for a $-0.21$-pm Doppler shift. The best-fit model indicates that a $+0.21$-pm shift should be added to our ${\lambda }_{\mathrm{zero}}$ measurements due to Doppler shifts in the MPC [29].

Figure 4

Power spectrum output from our tapered amplifier. The broadband spectrum (open blue circles) was observed with 1000 times more acquisition time while using a dark fringe from an etalon to suppress the monochromatic component of the spectrum, as described in this paper. A spectrum with the monochromatic light tuned to a bright fringe of the etalon is shown with solid red circles.

Figure 5

Error in ${\lambda }_{\mathrm{zero}}$ due to broadband light. (a) Spectra of $\alpha \left(\omega \right)$ and $P_{\text{broad}}$ vs wavelength used in Eq. (14) to calculate ${\varphi }_{\text{BB}}$. Two different $P_{\text{broad}}$ spectra indicate how temperature-tuning the tapered amplifier laser adjusts the peak wavelength ${\lambda }_{\text{BB}}$ of the broadband light. $P_{\text{broad}}$ and $\alpha \left(\omega \right)$ are scaled in order to be viewed conveniently on the same graph. (b) Resulting error ($\delta {\lambda }_{\mathrm{zero}}$) as a function of the broadband peak wavelength ${\lambda }_{\text{BB}}$.

Figure 6

${\lambda }_{\mathrm{zero}}$ measurement as a function of optical polarization and magnetic field orientation. Data with circularly polarized laser light are from [22] and were taken with $v\approx 1600$ m/s atom beams. Data with linearly polarized light were take with $v\approx 2900$ m/s atom beams. Open red squares show measurements with the laser beam on the right side of the interferometer and solid blue circles show measurements on the left side.

Figure 7

Determination of ${\lambda }_{\mathrm{zero}}$ from the average $\frac{1}{2}({\lambda }_{\mathrm{zero},\mathrm{lab}}^{\text{right}}+{\lambda }_{\mathrm{zero},\mathrm{lab}}^{\text{left}})$. Only statistical error bars of two times the standard error of the mean are shown. Systematic corrections total 0.3 pm, and systematic uncertainties totaling 0.3 pm are later added before a final result is presented for ${\lambda }_{\mathrm{zero}}$.

Figure 8

(a) Phase data for the laser shining on the right path of the interferometer. Each file contains 5 s of data. Laser light from the tapered amplifier was chopped on or off in between every file. Light-on data are shown in solid red circles; light-off data are shown in open black circles. After 24 files the seed laser wavelength was automatically changed. (b) Phase data from (a) vs laser wavelength. Corrections for the net Doppler shift and broadband laser light have not been applied to the shown data in (a) and (b).

Figure 9

Comparison of measured and calculated values for the longest ${\lambda }_{\mathrm{zero}}$ for potassium. Calculations are shown in solid red circles. Calculations that assume $R=2$ or ${\alpha }_{\text{r}}=0$ are shown with open red circles. The result from lifetime measurements is shown with solid green triangles. Measurements made with atom interferometry are shown with solid blue squares.

Figure 10

Theoretical calculations shown with solid circles, and experimental measurements shown with open circles, of $\rho$, the ratio of oscillator strengths (top), and $R$, the ratio of line strengths (bottom): MBPT refers to many-body perturbation theory and the number in parentheses refers to the order [45]. RMBPT refers to relativistic MBPT [37]. DF refers to Dirac-Fock basis orbitals [37]. SD refers to the single-double all order method [37]. RCICP refers to the relativistic configuration interaction plus core polarization approach [12]. CICP refers to the configuration interaction plus core polarization method [12]. DHF refers to the Dirac-Hartree-Fock method [39]. CCSD refers to the singles-doubles coupled-cluster method [39]. BGLS refers to beam-gas-laser spectroscopy measurements [40]. AIFM refers to atom interferometry measurements. BEC IFM refers to interferometry measurements made with Bose-Einstein condensates [3]. Photo assoc. spec. refers to photoassociation spectroscopy [47, 67, 68]. Abs. spec. refers to absorption spectroscopy [47].