Spin squeezing and precision probing with light and samples of atoms in the Gaussian description (12 pages)

Vivi Petersen, Lars Bojer Madsen

Lars Bojer Madsen, Klaus Mølmer

We consider an ensemble of trapped atoms interacting with a continuous-wave laser field. For sufficiently polarized atoms and for a polarized light field, we may approximate the nonclassical components of the collective spin angular momentum operator for the atoms and the Stokes vectors of the field by effective position and momentum variables for which we assume a Gaussian state. Within this approximation, we present a theory for the squeezing of the atomic spin by polarization rotation measurements on the probe light. We derive analytical expressions for the squeezing with and without inclusion of the noise effects introduced by atomic decay and by photon absorption. The theory is readily adapted to the case of inhomogeneous light-atom coupling [A. Kuzmich and T.A.B. Kennedy, Phys. Rev. Lett. 92, 030407 (2004)]. As a special case, we show how to formulate the theory for an optically thick sample by slicing the gas into pieces, each having only small photon absorption probability. Our analysis of a realistic probing and measurement scheme shows that it is the maximally squeezed component of the atomic gas that determines the accuracy of the measurement.

Elizaveta P. Yukalova, Vyacheslav I. Yukalov

Ilija K. Nikolov, Adrian Del Maestro, Chandrasekhar Ramanathan +1 more

Vivi Petersen, Lars Bojer Madsen, Klaus Mølmer

We present a theory for the estimation of a scalar or a vector magnetic field by its influence on an ensemble of trapped spin-polarized atoms. The atoms interact off resonantly with a continuous laser field, and the measurement of the polarization rotation of the probe light, induced by the dispersive atom-light coupling, leads to spin squeezing of the atomic sample which enables an estimate of the magnetic field that is more precise than that expected from standard counting statistics. For polarized light and polarized atoms, a description of the non classical components of the collective spin angular momentum for the atoms and the collective Stokes vectors of the light field in terms of effective Gaussian position and momentum variables is practically exact. The Gaussian formalism describes the dynamics of the system very effectively and accounts explicitly for the back action on the atoms due to measurement and for the estimate of the magnetic field. Multicomponent magnetic fields are estimated by the measurement of suitably chosen atomic observables and precision and efficiency is gained by dividing the atomic gas in two or more samples which are entangled by the dispersive atom-light interaction.

Klaus Mølmer, Lars Bojer Madsen

We present a theory for the estimation of a classical magnetic field by an atomic sample with a Gaussian distribution of collective spin components. By incorporating the magnetic field and the probing laser field as quantum variables with Gaussian distributions on equal footing with the atoms, we obtain a very versatile description which is readily adapted to include probing with squeezed light, dissipation, and loss and additional measurement capabilities on the atomic system.