Entanglement-enhanced Atom Interferometer with High Spatial Resolution
Authors: Caspar Ockeloen, Roman Schmied, Max F. Riedel, Philipp Treutlein
Affiliation: Department of Physics, University of Basel, Switzerland
Link to Quantum Atom Optics Lab, Treutlein Group >>
Interferometry is the cornerstone of most modern precision measurements. Atom interferometers, making use of the wave-like nature of matter, allow for ultraprecise measurements of gravitation, inertial forces, fundamental constants, electromagnetic fields, and time [1,2]. A well-known application of atom interferometry is found in atomic clocks, which provide the definition of the second. Most current atom interferometers operate with a large number of particles, which provides high precision but limited spatial resolution. Using a small atomic cloud as a scanning probe interferometer would enable new applications in electromagnetic field sensing, surface science, and the search for fundamental short-range interactions .
In an atom interferometer, the external (motional) or internal (spin) state of atoms is coherently split and allowed to follow two different pathways. During the interrogation time T, a phase difference between the paths is accumulated, which depends on the quantity to be measured. When the paths are recombined, the wave-character of the atoms gives rise to an interference pattern, from which the phase can be determined. To measure this interference, the number of atoms in each output state is counted. Here the particle-character of the atoms is revealed, as the measurement process randomly projects the wave function of each atom into a definite state. When operating with an ensemble of N uncorrelated (non-entangled) atoms, the binomial counting statistics limits the phase uncertainty of the interferometer to 1/√N, the standard quantum limit (SQL) of interferometric measurement.
It is possible to overcome the SQL by making use of entanglement between the atoms . Using such quantum correlations, the measurement outcome of each atom can depend on that of the other atoms. If used in a clever way, the phase uncertainty of an interferometer can be reduced below the SQL, in theory down to the ultimate Heisenberg limit of 1/N. Such entanglement-enhanced interferometry is in particular useful in situations where the number of atoms is limited by a physical process and the sensitivity can no longer be improved by simply increasing N. One such scenario is when high spatial resolution is desired. The number of atoms in a small probe volume is fundamentally limited by density-dependent losses due to collisions. As more atoms are added to this volume, the collision rate increases, and eventually any additional atoms are simply lost from the trap before the interferometer sequence has completed. This sets a tight limit on both the phase uncertainty and the maximum interrogation time T.
Fig. 1. Experimental setup. a) Central region of the atom chip showing the atomic probe (blue, size to scale) and the scanning trajectory we use. 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/yellow. b) Photograph of the atom chip, mounted on its ultra-high vacuum chamber.
In a recent paper  we have demonstrated a scanning-probe atom interferometer that overcomes the SQL using entanglement. Our interferometer probe is a Bose-Einstein condensate (BEC) on an atom chip, a micro-fabricated device with current-carrying wires that allow magnetic trapping and accurate positioning of neutral atoms close to the chip surface . A schematic view of the experiment is shown in figure 1. We use N=1400 Rubidium-87 atoms, trapped in a cloud of 1.1 x 1.1 x 4.0 micrometers radius, 16 to 40 micrometers from the surface. Two internal states of the atoms are used as interferometric pathways, and the pathways are split and recombined using two-photon microwave and radio frequency pulses. At the end of the interferometer sequence, we count the atoms in each output state with sensitive absorption imaging, with a precision of about 5 atoms.
We create entanglement between the atoms by making use of collisions naturally present in our system. When two atoms collide, both atoms obtain a phase shift depending on the state of the other atom, thus creating quantum correlations between the two. Normally, the effect of these collisions is negligible in our experiment, as the phase shift due to collisions between atoms in the same state are almost completely canceled out by collisions where each atom is in a different state. We can turn on the effect of collisions by spatially separating the two states, such that collisions between states do not occur. When, after some time, we recombine the two states, collisional phase shifts are effectively turned off during the subsequent interrogation time of the interferometer.
The performance of our interferometer is shown in figure 2, measured at 40 micrometer from the chip surface. It has a sensitivity of 4 dB in variance below to SQL, and improved sensitivity is maintained for up to T = 10 ms of interrogation time, longer than in previous experiments [6,7,8]. We demonstrate the scanning probe interferometer by transporting the entangled atoms between 40 and 16 micrometer from the atom chip surface, and measuring a microwave near field potential at each location. The microwave potential is created by wires on our atom chip, and is also used for generation of the entangled state. As shown in figure 3, our scanning probe interferometer operates on average 2.2 dB below the SQL, demonstrating that the entanglement partially survives being transported close to the chip surface, which takes 20 ms of transport time.
Fig. 2. Interferometer performance operating at a single position for different interrogation times. Plotted is the variance relative to the standard quantum limit (SQL). The entanglement-enhanced interferometer (blue diamonds) operates about 4 dB below the SQL, whereas the non-entangled interferometer (red, coherent state) operates close to the SQL. For T > 10 ms, both experiments are limited by technical noise. The inset shows a typical interference fringe, with a fringe contrast of (98.1 ± 0.2)%.
The scanning probe measurement presented here corresponds to a microwave magnetic field sensitivity of 2.4 µT in a single shot of the experiment (cycle time ~ 11 s). The sensitivity shown in figure 2 corresponds to 23 pT for an interrogation time of 10 ms. This sensitivity is obtained with a probe volume of only 20 µm3. Our interferometer bridges the gap between vapor cell magnetometers, which achieve subfemtotesla sensitivity at the millimeter to centimeter scale [9,10] but do not have the spatial resolution needed to resolve near-field structures on microfabricated devices, and nitrogen vacancy centers in diamond, which are excellent magnetometers at the nanometer scale but currently offer lower precision in the micrometer regime .
Fig. 3. Scanning probe interferometer. a) Phase shift due to the microwave near-field potential measured at different positions. The dashed line is a simulation of the potential. b) Interferometer performance for the same measurement. At all positions, the interferometer operates below the SQL. These measurements were done with an interrogation time of T = 100 µs, during which the microwave near-field was pulsed on for 80 µs.
In conclusion, we have experimentally demonstrated a scanning-probe atom interferometer operating beyond the standard quantum limit, and used it for the measurement of a microwave near-field. High-resolution measurements of microwave near-fields are relevant for the design of new microwave circuits for use in communication technology . This is the first demonstration of entanglement-enhanced atom interferometry with a high spatial resolution scanning probe, and promises further high-resolution sensing and measurement applications.
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