Beating the classical precision limit with spin-1 Dicke states of more than 10,000 atoms

Abstract

Interferometry is a paradigm for most precision measurements. Using N uncorrelated particles, the achievable precision for a two-mode (two-path) interferometer is bounded by the standard quantum limit (SQL), [Formula: see text], due to the discrete (quanta) nature of individual measurements. Despite being a challenging benchmark, the two-mode SQL has been approached in a number of systems, including the Laser Interferometer Gravitational-Wave Observatory and today's best atomic clocks. For multimode interferometry, the SQL becomes [Formula: see text] using modes. Higher precision can also be achieved using entangled particles such that quantum noises from individual particles cancel out. In this work, we demonstrate an interferometric precision of [Formula: see text] dB beyond the three-mode SQL, using balanced spin-1 (three-mode) Dicke states containing thousands of entangled atoms. The input quantum states are deterministically generated by controlled quantum phase transition and exhibit close to ideal quality. Our work shines light on the pursuit of quantum metrology beyond SQL.

Molecular interferometers: effects of Pauli principle on entangled-enhanced precision measurements

“…We found that condensate depletion reduces the odd/even discrete structure of the typical U-shaped particle distribution that arise when measuring the different numbers of particles populating both modes. Such an odd/ even fluctuation reduction is very similar to that caused by particle losses [5,6,8]. Condensate depletion also renders the standard deviation of the interfering mBECs to be smaller, as compared with the one given by the ideal BECs interference of bosonic atoms.…”

“…Even though fermions co-tunnel as pairs in the BEC regime through the simple dynamics induced by the Hamiltonian (7), it is not clear that there is a well defined operator dynamic describing the interference processes (8). This is because couplings between modes 1 and 2 are neglected by Pauli principle when two fermion-pairs occupy the same internal state j of the modes.…”

“…states with two orthogonal modes populated by the same number of particles, have been produced with both, photons [4,5] and ultracold bosonic atoms [6][7][8]. However, entangled-enhanced precision measurements of the resulting interference phase have been performed only in the case of ultracold bosonic atoms [6,8]. This is mainly because current twin photon beams experiments have much higher particle losses than experiments with twin matter waves.…”

Multi-parameter estimation with multi-mode Ramsey interferometry

“…, although more generally the state preparation can start from any Zeeman sublevels to reach the same final probability amplitude distribution of the optimal state. Such multi-parameter estimation scheme can be useful when atoms are subjected to different sources of phase shifts simultaneously, as for example, with spin-1 87 Rb atoms dressed by near-resonant microwaves while under a static magnetic field [47,48], or spin-9/2 87 Sr atoms placed in an optical lattice with polarization dependent light shifts, and collisions with background or non-condensed atoms.…”

“…When detection noise is present, we numerically simulate the estimation process of the two parameters q q , 1 2 { } using 10 4 three-mode (spin-1) atoms with a detection resolution (noise) of 14 atoms (typical numbers achievable in cold-atom experiments [47,48]). For each pair of {θ 1 , θ 2 }, we first compute the probability of detecting an atom in the output mode…”