Composite-Light-Pulse Technique for High-Precision Atom Interferometry

We realize beam splitters and mirrors for atom waves by employing a sequence of light pulses rather than individual ones. In this way we can tailor atom interferometers with improved sensitivity and accuracy. We demonstrate our method of composite pulses by creating a symmetric matter-wave interferometer which combines the advantages of conventional Bragg- and Raman-type concepts. This feature leads to an interferometer with a high immunity to technical noise allowing us to devise a large-area Sagnac gyroscope yielding a phase shift of 6.5 rad due to the Earth’s rotation. With this device we achieve a rotation rate precision of $120\mathrm{nrad}{\mathrm{s}}^{-1}{\mathrm{Hz}}^{-1/2}$ and determine the Earth’s rotation rate with a relative uncertainty of 1.2%.

Figure 1

Space-time diagram ($x,t$) and the corresponding sensitivity function $g(t)$ defined in Refs. [21, 22] for (a) a conventional Mach-Zehnder interferometer (MZI) with single Raman pulses (red wavy lines) as atom-optical elements [23] and (b) the symmetrized composite-pulse interferometer (SCI) featuring multiple Raman pulses (multiple red wavy lines) for each atom-optical beam splitter and mirror. The single-pulse duration $\tau$ as well as the dark time $t_S$ within a composite pulse is not drawn to scale. The Raman interactions lead to a change of both the electronic state (ground and excited state denoted by solid and dashed lines, respectively) and the kinetic momentum of the wave packet, depending on the direction of the effective photon momentum $\mathbf{k}$ (indicated by black arrows). The contrast of the MZI signal depends crucially on the state preparation. A pure sample of excited-state atoms can be achieved by optical pumping after molasses cooling. As shown in the figure, a specific velocity class of this sample can be selected with the help of a Raman pulse transferring them into the ground state, while the rest of the excited atoms are removed by a resonant blow-away pulse (yellow wavy lines). In contrast, in the SCI the blow-away pulse is not performed until the first two beam-splitter pulses. As indicated by $g(t)$, which expresses the sensitivity to Raman laser phase noise and magnetic field fluctuations, the SCI is insensitive to these noise sources during the free evolution time $T$, while the MZI is most sensitive during the same period.

Figure 2

Interference signals of the MZI (triangles) and the SCI (squares) obtained by scanning the phase ${\mathrm{\Phi }}_{\mathit{L}}$ of the last Raman pulse. Because of an imperfect efficiency of the Raman processes, the larger number of beam-splitter pulses required in the SCI leads to a reduced contrast of 19% in the SCI as compared to the MZI, where it is 36%. From these fringes we also determine the total phase offset which contains the corresponding rotational phase shifts ${\mathrm{\Phi }}_{\mathrm{rot}}^{\mathrm{MZI}}$ and ${\mathrm{\Phi }}_{\mathrm{rot}}^{\mathrm{SCI}}$.

Figure 3

Time series of the sum phases ${\mathrm{\Phi }}_{+}^{\mathrm{MZI}}$ (grey) and ${\mathrm{\Phi }}_{+}^{\mathrm{SCI}}$ (black) expressed in units of a relative rotation rate for a stepwise increasing magnetic offset field (red). The changes in the MZI rotation signal are caused by transients occurring when the magnetic field is changed while the interferometer operates. In contrast, the SCI signal given by the horizontal line is unaffected by these perturbations.

Figure 4

Two-sample standard deviations of the interferometer sum phases ${\mathrm{\Phi }}_{+}^{\mathrm{MZI}}$ (full triangles) and ${\mathrm{\Phi }}_{+}^{\mathrm{SCI}}$ (full squares). Whereas ${\mathrm{\Phi }}_{+}^{\mathrm{MZI}}$ is strongly affected by the phase noise of the Raman laser, ${\mathrm{\Phi }}_{+}^{\mathrm{SCI}}$ is hardly influenced by it. During the measurements we monitor the rotational noise by the differential signal of two seismometers (empty symbols) positioned at the ends of the platform.