Abstract
We describe nonlinear quantum atom–light interfaces and nonlinear quantum metrology in the collective continuous variable formalism. We develop a nonlinear effective Hamiltonian in terms of spin and polarization collective variables and show that model Hamiltonians of interest for nonlinear quantum metrology can be produced in 87Rb ensembles. With these Hamiltonians, metrologically relevant atomic properties, e.g. the collective spin, can be measured better than the 'Heisenberg limit' ∝1/N, where N is the number of photons. In contrast to other proposed nonlinear metrology systems, the atom–light interface allows both linear and nonlinear estimation of the same atomic quantities.
GENERAL SCIENTIFIC SUMMARY Introduction and background. Intrinsic quantum noise limits the sensitivity of any measurement. The standard quantum limit comes from the use of N uncorrelated probe particles in estimating some parameter of interest and scales as 1/N1/2. Quantum entanglement amongst the probe particles, allows one to move towards the less restrictive Heisenberg limit, with sensitivity scaling as 1/N. Another, complementary, approach is exploiting nonlinear interactions between the probe particles. In such a nonlinear measurement the sensitivity improves faster than 1/N even without entanglement. Here we investigate metrologically useful nonlinearities within a polarization-based atom-light interface, where probing photons are used to estimate the spin polarization of a cold atomic ensemble.
Main results. We generalise the formalisms of continuous variables to describe nonlinearities in atom-light interaction at the quantum level. In this way, we derive a Hamiltonian including several tuneable couplings which can be used for nonlinear metrology. We identify terms that should lead to a measurement sensitivity scaling as 1/N3/2 in a realistic experiment. A special feature of the particular implementation we investigate is that it permits an easy swap between linear and nonlinear regimes of probing, a useful thing for comparison and characterization.
Wider implications. Nonlinear quantum metrology of atomic spins has direct applications to magnetometry and atomic clocks. More generally, this 'proof of principle' that nonlinear metrology with a scaling faster than 1/N can be demonstrated with a reasonable simple system should prompt further investigation into other realisable experimental systems which could, in principle, outperform quantum-limited linear measurements.