QUROPE Quantum Information Processing and Communication in Europe

Interferometry with ultracold atoms promises the possibility of ultraprecise and ultrasensitive measurements in many fields of physics, and is the basis of our most precise atomic clocks. Key to a high sensitivity is the possibility to achieve long measurement times and precise readout. Ultracold atoms can be precisely manipulated at the quantum level and can be held for very long times in traps; they would therefore be an ideal setting for interferometry. In this paper, we discuss how the nonlinearities from atom–atom interactions, on the one hand, allow us to efficiently produce squeezed states for enhanced readout and, on the other hand, result in phase diffusion that limits the phase accumulation time. We find that low-dimensional geometries are favorable, with two-dimensional (2D) settings giving the smallest contribution of phase diffusion caused by atom–atom interactions. Even for time sequences generated by optimal control, the achievable minimal detectable interaction energy ΔEmin is of the order of 10−4μ, where μ is the chemical potential of the Bose–Einstein condensate (BEC) in the trap. From these we have to conclude that for more precise measurements with atom interferometers, more sophisticated strategies or turning off the interaction-induced dephasing during the phase accumulation stage, will be necessary.