Ramsey-Bordé Matter-Wave Interferometry for Laser Frequency Stabilization at ${10}^{-16}$ Frequency Instability and Below

We demonstrate Ramsey-Bordé (RB) atom interferometry for high performance laser stabilization with fractional frequency instability $<2\times {10}^{-16}$ for timescales between 10 and 1000s. The RB spectroscopy laser interrogates two counterpropagating ${}^{40}\mathrm{Ca}$ beams on the ${{}^{1}S}_0-{}^3{P}_1$ transition at 657 nm, yielding 1.6 kHz linewidth interference fringes. Fluorescence detection of the excited state population is performed on the ($4s4p$) ${}^3{P}_1-(4p^2)$ ${}^3{P}_0$ transition at 431 nm. Minimal thermal shielding and no vibration isolation are used. These stability results surpass performance from other thermal atomic or molecular systems by 1 to 2 orders of magnitude, and further improvements look feasible.

Figure 1

Relevant electronic levels and transitions of neutral ${}^{40}\mathrm{Ca}$. Also shown is the quantum trajectory of a calcium atom passing through the RB interferometer. The atom undergoes four laser interactions with phase ${\varphi }_i$, which repeatedly split the atomic momentum state. Two possible closed trajectories exist (filled areas), creating matter-wave interference. The ${{}^{3}P}_1-{}^3{P}_0$ transition is then rapidly cycled, and the scattered 431 nm photons collected.

Figure 2

Typical RB fringes for a range of frequency sweeps. (a) MHz scale Doppler profile of one atomic beam response, with accompanying measure of fringe contrast. (b) Midrange sweep displaying two RB fringe components from a single atomic beam. (c) Simultaneous fine sweep across the RB fringes from both counterpropagating atomic beams. Dashed lines indicate extrema feature frequencies, and points 1 to 4 indicate four locking frequency locations.

Figure 3

Experimental setup. (a) Both 862 nm (later frequency doubled to 431 nm) and 657 nm lasers are cavity prestabilized. Input optics mounted on the vacuum chamber shape and deliver the light. The vacuum chamber is partitioned into two blue detection zones ($B1$ and $B2$) and the RB zone. Within vacuum, the interrogation laser is steered by a monolithic glass assembly to intersect the atomic beam at four locations. The distance between beams 1 and 2 (or 3 and 4) is 9 cm, whereas the spacing between beams 2 and 3 is roughly 1 mm. In regions $B1$ and $B2$, exited-state atoms are rapidly cycled while their scatter is focused onto an external detector. Magnetic fields are indicated by black coils. Apertures between zones collimate the atomic beams. AOM: acousto-optic modulator; ECDL: external cavity diode laser. [(b) and (c)] Approximate blue (431 nm) and red (657 nm) laser profiles, respectively, are given relative to the atomic beam dimensions. Typical laser powers are 10 (431 nm) and 25 mW (657 nm), incident on the atoms.

Figure 4

Allan deviations for two calcium-stabilized frequency measurements with $1\sigma$ error bars. The general system performance is well represented by the data set labeled ordinary (red circles), whereas extraordinary (blue triangles) highlights shorter data segments exhibiting exceptional performance, averaging below ${10}^{-16}$. The RB laser prestabilization is shown after a $2\mathrm{Hz}/\mathrm{s}$ drift removal, though this drift is present during calcium system operation. The measured range of frequency instability contributions from detection noise sources falls within the gray region; see the text.