Interacting Atomic Interferometry for Rotation Sensing Approaching the Heisenberg Limit

Atom interferometers provide exquisite measurements of the properties of noninertial frames. While atomic interactions are typically detrimental to good sensing, efforts to harness entanglement to improve sensitivity remain tantalizing. Here we explore the role of interactions in an analogy between atomic gyroscopes and SQUIDs, motivated by recent experiments realizing ring-shaped traps for ultracold atoms. We explore the one-dimensional limit of these ring systems with a moving weak barrier, such as that provided by a blue-detuned laser beam. In this limit, we employ Luttinger liquid theory and find an analogy with the superconducting phase-slip qubit, in which the topological charge associated with persistent currents can be put into superposition. In particular, we find that strongly interacting atoms in such a system could be used for precision rotation sensing. We compare the performance of this new sensor to an equivalent noninteracting atom interferometer, and find improvements in sensitivity and bandwidth beyond the atomic shot-noise limit.

Figure 1

A cartoon of the system. Atoms are trapped in a 1D ring of length $L$ with a blue-detuned laser crossing at a single point, $x_b(t)$. In the atom frame, the barrier rotates through the ring at a rate combining the laboratory frame rotation [${\omega }_{\text{frame}}=(2\pi v_{\text{frame}}/L)$] and the externally controlled stirring rate [${\omega }_{\mathrm{stir}}=(2\pi v_{\mathrm{stir}}/L)$].

Figure 2

(a) The energy spectrum for the perturbed current states, lower (upper) represents the ground (excited) state. The weak barrier creates avoided crossings at rotation $\omega =(n+1/2){\omega }_0$, $n\in \mathbb{Z}$. The arrows represent the proposed “$\pi /2$ pulse”: the system is adiabatically driven to the avoided crossing (single arrow) and diabatically returned $\omega =0$ (double arrow). (b) A cartoon of the proposed Ramsey sequence. The sequence consists of two $\pi /2$ pulses with an observation time ${\tau }_{\mathrm{obs}}$ in between.

Figure 3

(a) The sensitivity of our proposed gyroscope (solid) plotted on a log-log scale as a function of atom number. The dashed (dotted) line represents the sensitivity for a noiseless Luttinger (atom interferometer) system with an observation time of ${\tau }_{\mathrm{comp}}=0.838\mathrm{s}$. (b) Solid (dashed) lines: The single-shot sensitivity for the noisy Luttinger (atom interferometer) system for different observation times, $\tau$, as a function of atom number.