Speaker: Mario Napolitano, ICFO, Barcelona, Spain

Title: Interaction-based nonlinear quantum metrology with a cold atomic ensemble

Abstract:

The research in quantum metrology during the last decades was mainly focused in developing and demonstrating the importance of quantum correlations among particles, i.e., entanglement or squeezing, for enhanced measurement sensitivity. However, such resources are very fragile and sometimes they cannot be used. A debate rose up in the last years about a possible different strategy making use of direct interactions between probing particles. The theory of this different approach for a nonlinear quantum metrology, in particular phase estimation in nonlinear interferometry, was developed by the group of Carlton M. Caves in the University of New Mexico [1]. 

In this talk I will present our theoretical and experimental investigation which led to the first demonstration of quantum-noise-limited measurement by nonlinear interferometry, or from another perspective, quantum-noise-limited interaction-based measurement. 

We proposed to implement the Caves group's ideas using a polarization-based quantum interface between propagating light pulses and cold rubidium-87 atoms trapped in an optical dipole trap. To evaluate this proposal we develop two theoretical approaches, which I will describe in the talk. First, an extension of the collective quantum variables approach, often employed to describe quantum interfaces and atomic spin ensembles, to nonlinear optical processes. This results in an effective Hamiltonian containing nonlinear terms of the form described by the Caves group, and demonstrates a qualitative equivalence of the two schemes [2]. The second approach uses the Maxwell-Bloch equations to describe nonlinear propagation of pulses through an atomic spin ensemble, including inhomogeneities and relaxation effects. This latter method makes quantitative predictions about optical rotation signals under realistic experimental conditions [3].

Then I will move on the implementation of the proposal in the lab. I will present the existing trapping and probing system, focusing on the characteristics that make it suitable for shot-noise-limited and projection-noise-limited atomic spin measurements. I will then describe adaptations to use the apparatus with shorter, higher-intensity pulses as required for nonlinear measurements, as well as characterization of the photodetection system under these modified conditions. Calibration of the nonlinear polarization rotation versus probe laser detuning allows us to produce a nearly pure nonlinear rotation signal.

Finally, experimental results will be presented showing shot-noise-limited nonlinear rotation signals over three orders of magnitude in photon number N [4]. The results are consistent with our theoretical models and confirm a major prediction of the Caves group's work, in that a two-photon interaction gives a scaling for the measurement sensitivity as N^{-3/2}.

A brief discussion relates this experimental observation to theoretical discussions of the “Heiseinberg limit” of quantum metrology, and possible further applications of nonlinear measurement techniques.

[1] Boixo, et al., PRL 98, 090401 (2007)
[2] Napolitano & Mitchell, New J. Phys. 12, 093016 (2010)
[3] Supp. Info of Napolitano, et al., Nature 471, 486-489 (2011)
[4] Napolitano, et al., Nature 471, 486-489 (2011)