Quantum Critical Metrology

Interference is fundamental to wave dynamics and quantum mechanics. The quantum wave properties of particles are exploited in metrology using atom interferometers, allowing for high-precision inertia measurements [1, 2]. Furthermore, the state-of-the-art time standard is based on an interferometric technique known as Ramsey spectroscopy. However, the precision of an interferometer is limited by classical statistics owing to the finite number of atoms used to deduce the quantity of interest [3]. Here we show experimentally that the classical precision limit can be surpassed using nonlinear atom interferometry with a Bose-Einstein condensate. Controlled interactions between the atoms lead to non-classical entangled states within the interferometer; this represents an alternative approach to the use of non-classical input states [4-8]. Extending quantum interferometry [9] to the regime of large atom number, we find that phase sensitivity is enhanced by 15 per cent relative to that in an ideal classical measurement. Our nonlinear atomic beam splitter follows the "one-axis-twisting" scheme [10] and implements interaction control using a narrow Feshbach resonance. We perform noise tomography of the quantum state within the interferometer and detect coherent spin squeezing with a squeezing factor of -8.2dB [11-15]. The results provide information on the many-particle quantum state, and imply the entanglement of 170 atoms [16]. Show more

Atom chips provide a versatile `quantum laboratory on a microchip' for experiments with ultracold atomic gases. They have been used in experiments on diverse topics such as low-dimensional quantum gases, cavity quantum electrodynamics, atom-surface interactions, and chip-based atomic clocks and interferometers. A severe limitation of atom chips, however, is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. Such techniques enable chip-based studies of entangled many-body systems and are a key prerequisite for atom chip applications in quantum simulations, quantum information processing, and quantum metrology. Here we report experiments where we generate multi-particle entanglement on an atom chip by controlling elastic collisional interactions with a state-dependent potential. We employ this technique to generate spin-squeezed states of a two-component Bose-Einstein condensate and show that they are useful for quantum metrology. The observed 3.7 dB reduction in spin noise combined with the spin coherence imply four-partite entanglement between the condensate atoms and could be used to improve an interferometric measurement by 2.5 dB over the standard quantum limit. Our data show good agreement with a dynamical multi-mode simulation and allow us to reconstruct the Wigner function of the spin-squeezed condensate. The techniques demonstrated here could be directly applied in chip-based atomic clocks which are currently being set up. Show more