High-Resolution Atom Interferometers with Suppressed Diffraction Phases

We experimentally and theoretically study the diffraction phase of large-momentum transfer beam splitters in atom interferometers based on Bragg diffraction. We null the diffraction phase and increase the sensitivity of the interferometer by combining Bragg diffraction with Bloch oscillations. We demonstrate agreement between experiment and theory, and a 1500-fold reduction of the diffraction phase, limited by measurement noise. In addition to reduced systematic effects, our interferometer has high contrast with up to $4.4\times {10}^6$ radians of phase difference, and a resolution in the fine structure constant of $\delta \alpha /\alpha =0.25\mathrm{ppb}$ in 25 h of integration time.

Figure 1

(a) Trajectories of our simultaneous conjugate interferometers with Bloch oscillations. Gravity has been neglected. The wiggly lines indicate laser pulses driving Bragg diffraction; the shaded area marked “BO” represents the Bloch oscillations. (b) Strong suppression of the beam splitter phase shift in radians as a function of the number $N$ of Bloch oscillations for Bragg diffraction orders of $n=1-8$ ($n=2$ lies outside the scale at ${\tilde{\mathrm{\Phi }}}_0\sim -0.6$). The inset shows an enlarged part for large Bloch oscillation numbers $N$.

Figure 2

Reduced diffraction phase shift in radians calculated for a pair of interferometers as a function of the detuning $\delta /{\omega }_r$ from the Bragg resonance. The solid lines indicate the phase without Bloch oscillations, $N=0$, the dashed lines with $N=16$. The nominal pulse duration is $\tau =0.2/{\omega }_r$, with the pulse peak intensity adjusted so as to provide 50% diffraction efficiency. The Gaussian pulses are truncated at $1/40$ of their peak amplitude.

Figure 3

(a) Suppression of the beam splitter phase for $n=4$. The open symbols show the measured recoil frequency $f_r={\omega }_r/2\pi$ without Bloch oscillations with Rabi frequencies ${\widehat{\mathrm{\Omega }}}_R=90$ (diamonds) and 100 a.u. (triangles), where 100 a.u. results in a 50% beam splitter. Least-squares fits determine the diffraction phase as ${\mathrm{\Phi }}_0=0.482(21)\mathrm{mrad}$ and ${\mathrm{\Phi }}_0=-0.403(7)\mathrm{mrad}$, respectively; shaded areas represent the $1-\sigma$ fit error. Closed symbols are measured at ${\widehat{\mathrm{\Omega }}}_R=100\mathrm{a}.\mathrm{u}.$ with $N=16$ Bloch oscillations, showing suppression of ${\mathrm{\Phi }}_0$ to 0.0012(8) mrad. (b) Reduced diffraction phase measured (symbols) and calculated (lines) as a function of the two-photon detuning $\delta$. (c) Contrast $C(T)$ of the interferometer as a function of the pulse separation time $T$ with $n=5,N=16$ along with a linear fit. As a measure of the expected sensitivity, we also plot the product $CT$.

Figure 4

Data covering 25.3 h taken with $T=80\mathrm{ms}$, $n=4$, and $N=25$ using feedback to null diffraction phases. Shown is the measured recoil frequency $8(n+N){\omega }_r$ relative to its average of approximately $2\pi \times 479\mathrm{kHz}$. The inset shows how the measured diffraction phase is zeroed exponentially upon activating the feedback.