An atom chip interferometer

TL;DR

This work demonstrates a Ramsey-type atom interferometer implemented on an atom chip that uses microwave dressing from two on-chip waveguides to split and recombine a thermal $^{87}$Rb cloud in two internal states. The experiment achieves a maximum spatial separation of $1.2~\mu$m with fringe contrasts around $8\%$, and it introduces a quantitative model for contrast decay that accounts for velocity-induced fringe formation and Bose statistics. By combining state-selective displacement with a Ramsey sequence, the authors map out the dependence of fringe visibility on path separation, temperature, and trap asymmetry, and they identify velocity mismatch as the key limitation. The results indicate that improved pulse sequences and symmetry control could enable larger separations and enhanced sensitivity, moving toward practical, compact, chip-based inertial sensors with potential micro-g-scale acceleration sensitivity.

Abstract

We have realized an interferometer using a thermal cloud of magnetically trapped rubidium 87 atoms on a chip. The interferometer resembles a Ramsey interferometer with a state selective spatial splitting of the two internal states as proposed in [M. Ammar, and al., Phys. Rev. A, 91, 053623]. The splitting is effected by microwave fields from two on-chip waveguides while the atoms remain magnetically trapped. The inferred maximum separation is $1.2\pm 0.1~μ$m. We observe interference fringes with a contrast around 8\% limited by velocity difference of the two interferometer states when we close the interferometer. We devellop a model describing this contrast decay.

Figures (10)

• Figure 1: (Color online) Levels of $^{87}\mathrm{Rb}$. $5^2S_{1/2}$ levels $\left|1,-1\right>=\left|1\right>$ and $\left|2,1\right>=\left|2\right>$ are the states used for the Ramsey interferometer. These two states (displayed in blue and red) are shifted in energy in the presence of microwave fields oscillating at pulsation $\omega_1$ and $\omega_2$, detuned by $\Delta_1$ and $\Delta_2$ from the resonances as shown. $\Omega_1$ and $\Omega_2$ are Rabi frequencies. Transitions in attenuated colors are other possible transitions for microwave dressing.
• Figure 2: (Color online) (a) Picture of the atom chip used in the experiment. The two coplanar waveguides (CPW) are highlighted in blue and red. The z and dimple wires used in the experiment are highlighted respectively in pink and green, as are the two external magnetic bias fields $A_0$ and $A_1$. (b) Vertical slice of the atom chip, at the position of the trap. The z and dimple wires are located in the DC level. The dimple trap is centered between the two waveguides (CPW1 and CPW2).
• Figure 3: (Color online) Displacements (refered as $x^{cm}_i(t_{m}+t_{t})$ in the text) along $x$ (see figure \ref{['fig_AtomChip']}) of polarized states as a function of microwave dressing frequency injected into a single coplanar waveguide: (a) and (c) displacement of state $\left|1,-1\right>$. (b) and (d) displacement of state $\left|2,1\right>$. The microwave power is injected in CPW1 ((a) and (d)) or in CPW2 ((b) and (c)), while the power ramp is unchanged. Each dot corresponds to one preparation of an atomic cloud and hence a different measurement. Solid red lines correspond to a moving average over 5 points. Vertical black lines show the position of the allowed transitions calculated with the Breit-Rabi formula for the magnetic field value at the bottom of the trap. From state $\left|2,1\right>$ there are 2 possible transitions, while there are 3 transitions for state $\left|1,-1\right>$ (see figure \ref{['fig_RbLevel']}).
• Figure 4: (Color online) Simulation of the atom center of mass trajectories $x^{cm}_i(t)$ as a function of the time $t$, see appendix \ref{['Annexe_A_ComputePos']}. In red state $\left|2,1\right>$, in blue state $\left|1,-1\right>$. The solid lines are the trajectories and the shaded area represent the uncertainty computed from a 5% uncertainty on the maximum $\Omega_{i0}$ of the dressing Rabi frequency (see text).
• Figure 5: (Color online) Interference fringes. Population in state $\left|2,1\right>$, $N_{\left|2,1\right>}$, as a function of the detuning $\delta$ between the $\pi/2$ pulse frequency $\omega$ and the transition frequency $\omega_0$ of $\left|1,-1\right> \leftrightarrow \left|2,1\right>$, with a spatial splitting of the two clock states during the interferometry sequences. Blue dots are experimental data and red solid lines are fits. (a) Microwave injected in CPW1 to displace only $\left|1,-1\right>$. (b) Microwave injected in CPW2 to displace only $\left|2,1\right>$. (c) Microwaves injected in both waveguides to displace both states simultaneously in opposite directions.