Quantum metrology with Bose-Einstein condensates

The ability to make ultra-precise measurements is fundamentally important to science as it allows theories to be tested and refined. Interferometers offer unrivalled
measurement precision and therefore form the basis of many metrology schemes. Research has shown that by using quantum states as inputs to interferometers, precisions better than anything possible classically can be achieved. Nevertheless, these states are difficult to produce and fragile to particle losses. Consequently, classical
inputs, which are extremely robust, are used in experiments. Here, however, we propose experimentally accessible schemes to make quantum-limited measurements, in
particular rotation measurements using Bose-Einstein condensates, that are robust to losses.

We begin by describing how, by loading a Bose-Einstein condensate into an optical ring lattice, multiport beam splitters are created through a simple raising and lowering of potential barriers between sites. We then use these ‘splitters’ to create an atomic gyroscope. We demonstrate how to create several quantum states
in the gyroscope, all capable of making rotation measurements. Whilst NOON states afford best precision in idealised set-ups, we find they are outperformed by
‘bat’ states for modest loss rates.

However, bat states are not ideal as they are outperformed by classical states for large losses. A second gyroscope scheme is therefore developed. Using multiple momentum modes, rather than just two, we show quantum-limited precisions can be reached using states that have similar robustness to classical states.

The final section focuses on the precision of linear interferometers. Recent work[1, 2] has calculated the theoretical optimum initial states for two-mode lossy interferometers. Here we present an experimental way to produce initial states that afford similar precisions to this optimum. We also consider lossy multimode interferometry and demonstrate a potential advantage over two-mode systems. It is thought with further investigation other advantages will be found.