Strongly Enhanced Spin Squeezing via Quantum Control

 

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Collin M. Trail, Poul S. Jessen, and Ivan H. Deutsch

Center for Quantum Information and Control (CQuIC) and Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico, USA, CQuIC and College of Optical Sciences and Department of Physics, University of Arizona, Tuscon, Arizona, USA
 

We describe a new approach to spin squeezing based on a double-pass Faraday interaction between an optical probe and an optically dense atomic sample. A quantum eraser is used to remove residual spin- probe entanglement, thereby realizing a single-axis twisting unitary map on the collective spin. This interaction can be phase matched, resulting in exponential enhancement of squeezing as a function of optical density for times short compared to the decoherence time. In practice the scaling and peak squeezing depends on decoherence, technical loss, and noise. Including these imperfections, our model indicates that ~10 dB of squeezing should be achievable with laboratory parameters.
 

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Coherent control of atomic transport in spinor optical lattices

 

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Brian E. Mischuck, Poul S. Jessen, Ivan H. Deutsch
 

Coherent transport of atoms trapped in an optical lattice can be controlled by microwave-induced spin flips that correlate with site-to-site hopping. We study the controllability of homogeneous one-dimensional systems of noninteracting atoms in the absence of site addressability. Given these restrictions, we construct a deterministic protocol to map an initially localized Wannier state to a wave packet that that is coherently distributed over n sites. This is extended to analytic solutions for arbitrary unitary maps given homogenous systems and in the presence of time-dependent uni- form forces. Such control is important for applications in quantum information processing such as quantum computing and quantum simulations of condensed matter phenomena.
 

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Quantum control and measurement of atomic spins in polarization spectroscopy

 

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Ivan H. Deutsch, Poul S. Jessen
 

Quantum control and measurement are two sides of the same coin. To affect a dynamical map, well-designed time-dependent control fields must be applied to the system of interest. To read out the quantum state, information about the system must be transferred to a probe field. We study a particular example of this dual action in the context of quantum control and measurement of atomic spins through the light-shift interaction with an off-resonant optical probe. By introducing an irreducible tensor decomposition, we identify the coupling of the Stokes vector of the light field with moments of the atomic spin state. This shows how polarization spectroscopy can be used for continuous weak measurement of atomic observables that evolve as a function of time. Simultaneously, the state-dependent light shift induced by the probe field can drive nonlinear dynamics of the spin, and can be used to generate arbitrary unitary transformations on the atoms. We revisit the derivation of the master equation in order to give a unified description of spin dynamics in the presence of both nonlinear dynamics and photon scattering. Based on this formalism, we review applications to quantum control, including the design of state-to-state mappings, and quantum-state reconstruction via continuous weak measurement on a dynamically controlled ensemble.
 

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