Quantum Metrology with a Scanning Probe Atom Interferometer

We use a small Bose-Einstein condensate on an atom chip as an interferometric scanning probe to map out a microwave field near the chip surface with a few micrometers resolution. With the use of entanglement between the atoms, our interferometer overcomes the standard quantum limit of interferometry by 4 dB and maintains enhanced performance for interrogation times up to 10 ms. This corresponds to a microwave magnetic field sensitivity of $77\mathrm{pT}/\sqrt{\mathrm{Hz}}$ in a probe volume of $20\mu {\mathrm{m}}^3$. Quantum metrology with entangled atoms is useful in measurements with high spatial resolution, since the atom number in the probe volume is limited by collisional loss. High-resolution measurements of microwave near fields, as demonstrated here, are important for the development of integrated microwave circuits for quantum information processing and applications in communication technology.

Figure 1

Experimental setup. Central region of the atom chip showing the atomic probe (blue, size to scale) and the scanning trajectory we use (between 40 and $16\mu \mathrm{m}$ from the chip surface). The probe is used to measure the magnetic near-field potential generated by an on-chip microwave guide (microwave currents indicated by arrows). A simulation of the potential is shown in red and yellow.

Figure 2

Scanning probe interferometer operating below the SQL. (a) Experimental sequence, showing Rabi (red) and on-chip microwave (blue) pulses and the trap position (purple). Spheres 1–6 show the Wigner function [39] of the collective spin state at various stages of the experiment, simulated for $N=200\mathrm{atoms}$. (b) Measured phase shift $⟨\Delta \phi ⟩$ induced by a microwave near-field pulse as a function of the atom-surface distance, compared to the simulated potential (dotted line, see also Fig. 1). (c) Measured performance of the interferometer, expressed as squeezing factor ${\xi }^2$. Each data point (based on 240 measurements) has a statistical uncertainty of $\pm 0.4\mathrm{dB}$, shown as an error bar on the lower left point. The experiment was repeated up to 5 times at each position.

Figure 3

Interferometer performance. Observed phase noise in a Ramsey interferometer with squeezed (blue diamonds) and coherent (red circles) input states for varying interrogation times $T_R$. Dashed lines model constant performance of ${\xi }^2=-4\mathrm{dB}$ (squeezed state) and $+0.2\mathrm{dB}$ (coherent state), plus technical noise due to shot-to-shot frequency fluctuations. Each data point is the result of 240 measurements, and error bars indicate statistical uncertainty. Inset: typical squeezed-state Ramsey fringe measurements for $T_R=5\mathrm{ms}$ (points) and fitted sine (line) yielding a contrast of $C=(98.1\pm 0.2)\%$.