Nonlinear atom interferometer surpasses classical precision limit

Abstract

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. 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. 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. Extending quantum interferometry 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 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 -8.2 dB (refs 11-15). The results provide information on the many-particle quantum state, and imply the entanglement of 170 atoms.

Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon

“…The largest entanglement depth verified previously has been 170 out of 2300 atoms for a spin-squeezed state [6], and very recently 13 out of 41 atoms for a non-Gaussian state [13].…”

“…This parameter quantifies how widely shared among the particles an entangled state is. For a state of an ensemble characterized by collective measurements, the entanglement depth depends sensitively on the proximity of the state to the ideal symmetric subspace of all particles.The largest entanglement depth verified previously has been 170 out of 2300 atoms for a spin-squeezed state [6], and very recently 13 out of 41 atoms for a non-Gaussian state [13].Here we generate entanglement in a large atomic ensemble by detecting a single photon that has interacted with the ensemble [20]. An incident vertically polarized photon experiences a weak random polarization rotation associated with the quantum noise of the collective atomic spin.…”

“…Metrologically useful entangled states of large atomic ensembles have been experimentally realized [1][2][3][4][5][6][7][8][9][10], but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions [11,12], and very recently in large atomic ensembles [13][14][15].…”

“…Entanglement can be verified in a variety of ways, with one of the strictest criteria being a negative-valued Wigner function [16,17], that necessarily implies that the entangled state has a non-Gaussian wavefunction. To date, the metrologically useful spin-squeezed states [1][2][3][4][5][6][7][8][9][10] have been produced in large ensembles. These states have Gaussian spin distributions and therefore can largely be modeled as systems with a classical source of spin noise, where quantum mechanics enters only to set the amount of Gaussian noise.…”

Quantum Fisher information and spin squeezing in one-axis twisting model

“…Equation (1) shows that a quantum state with the APEP-enhancing must be entangled. Besides entangled states, it has been theoretically and experimentally demonstrated that spin squeezed states (SSSs) can also be used to improve the accuracy of estimation [8,9,10,11,12,13,14,15,16,17,18,19]. The concept of SSSs was first established by Kitagawa and Ueda [9].…”