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

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 reduction of estimator bias, that must be addressed when incorporating our parameter estimation methods into an actual laboratory setting.

28 Pages with 6 Figures. Please visit http://qmc.phys.unm.edu to download C++ class files, mex/Matlab source code, and data files used to generate all simulation data and figures in this paper as well as precompiled mex libraries for the Windows x64 and intel Mac platforms

References in corpus (20)

• Long-distance quantum communication with atomic ensembles and linear optics
• Resonant nonlinear magneto-optical effects in atoms
• Generalized Limits for Single-Parameter Quantum Estimation
• Continuous quantum error correction via quantum feedback control
• Spin squeezing via quantum feedback
• Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry
• Three-dimensional theory for interaction between atomic ensembles and free-space light
• Capture and release of a conditional state of a cavity QED system by quantum feedback
• Continuous Weak Measurement and Nonlinear Dynamics in a Cold Spin Ensemble
• Risk-Sensitive Optimal Control of Quantum Systems
• Tensor polarizability and dispersive quantum measurement of multilevel atoms
• Collective processes of an ensemble of spin-1/2 particles
• Efficient quantum memory and entanglement between light and an atomic ensemble using magnetic fields
• Quantum limited measurements of atomic scattering properties
• Single shot parameter estimation via continuous quantum measurement
• Polarization squeezing by optical Faraday rotation
• Magnetometry via a double-pass continuous quantum measurement of atomic spin
• Derivation of Maxwell-Bloch-type equations by projection of quantum models
• A quantum stochastic calculus approach to modeling double-pass atom-field coupling
• Scattering of polarized laser light by an atomic gas in free space: a QSDE approach