Amplified Quantum Dynamics and Enhanced Parameter Sensitivity via Coherent Feedback in Collective Atomic Spin Systems

Bradley A. Chase and JM Geremia
Department of Physics and Astronomy, The University of New Mexico, Albuquerque NM 87131 USA

Abstract. We consider the effective dynamics obtained by double-passing a far-detuned laser probe through a large atomic spin system. The net result of the atom-field interaction is a type of coherent positive feedback that amplifies the values of selected spin observables. An effective equation of motion for the atomic system is presented, and an approximate 2-parameter model of the dynamics is developed that should provide a viable approach to modeling even the extremely large spin systems, with N>>1 atoms, encountered under typical laboratory conditions.

Combining the nonlinear dynamics that result from the positive feedback with continuous observation of the atomic spin offers an improvement in quantum parameter estimation. We explore the possibility of reaching the Heisenberg uncertainty scaling in atomic magnetometry without the need for any appreciable spin-squeezing by analyzing our system via the quantum Cramer-Rao inequality. Finally, we develop a realistic quantum parameter estimator for atomic magnetometry that is based on a two-parameter family of Gaussian states and investigate the performance of this estimator through numerical simulations. In doing so, we identify several issues, such as numerical convergence and the reudction of estimator bias, that must be addressed when incorporating our parameter estimation methods into an actual laboratory setting.

Funded by: National Science Foundation (PHY-0639994).

Downloads

Resources for the paper include the source document draft history, graphics files, data files, and simulation code used to produce the paper. The code makes extensive use of the C++ SDE Integrator classes written by Brad Chase as well as a number of specialized classes for the implementation of Gaussian manifold projection filters and particle filter parameter estimators. The zipfile linked below is self-contained, and provides relative path addressing in Matlab such that files can be executed from whatever location they are unpacked. If pre-compiled mex libraries are not provided for your platform, you will require a functioning c++ compiler and license support for the Matlab compiler. Instructions and helper routines for building library objects can be found in the source code directories.

Please follow these links to download the available items in tar-gzip format:

• [LaTeX Source and Figure Files] (4M tar.gz file with RevTeX source and pdf and eps figure files)
• [Simulation Code and Data Files] (83.4 MB tar.gz file with Matlab, mex and C++ source, including pre-compiled mex libraries for 32-bit windows, 64-bit windows, Intel Mac and PowerPC Mac architectures)

We have also provided access to some of the notes we generated during this research project, to provide a glimpse into the project as it progressed. The following archive includes derivations in the form of Mathematica notebooks and laTeX files describing those derivations.

• [Project Notes and Derivations] (tar.gz file containing laTeX source and .nb notebooks)

DISCLAIMER: these notes catalog the path we took toward the results presented in the paper, and therefore also include the history of mistakes and corrections that occurred in the research project. The notes may include some typographical errors, they are not published material, so please keep that in mind when reading them.