Quantum signatures of chaos in a kicked top

 

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Chaudhury, S., Smith, A., Anderson, B. E., Ghose, S., Jessen, P. S.

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
 

Chaotic behaviour is ubiquitous and plays an important part in most fields of science. In classical physics, chaos is characterized by hypersensitivity of the time evolution of a system to initial conditions. Quantum mechanics does not permit a similar definition owing in part to the uncertainty principle, and in part to the Schrodinger equation, which preserves the overlap between quantum states. This fundamental disconnect poses a challenge to quantum classical correspondence, and has motivated a long-standing search for quantum signatures of classical chaos. Here we present the experimental realization of a common paradigm for quantum chaos, the quantum kicked top and the observation directly in quantum phase space of dynamics that have a chaotic classical counterpart. Our system is based on the combined electronic and nuclear spin of a single atom and is therefore deep in the quantum regime; nevertheless, we find good correspondence between the quantum dynamics and classical phase space structures. Because chaos is inherently a dynamical phenomenon, special significance attaches to dynamical signatures such as sensitivity to perturbation, or the generation of entropy and entanglement, for which only indirect evidence has been available. We observe clear differences in the sensitivity to perturbation in chaotic versus regular, non-chaotic regimes, and present experimental evidence for dynamical entanglement as a signature of chaos.
 

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Constructing general unitary maps from state preparations

 

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Merkel, Seth T., Brennen, Gavin, Jessen, Poul S., Deutsch, Ivan H.
 

We present an efficient algorithm for generating unitary maps on a d-dimensional Hilbert space from a time-dependent Hamiltonian through a combination of stochastic searches and geometric construction. The protocol is based on the eigendecomposition of the map. A unitary matrix can be implemented by sequentially mapping each eigenvector to a fiducial state, imprinting the eigenphase on that state, and mapping it back to the eigenvector. This requires the design of only d state-to-state maps generated by control wave forms that are efficiently found by a gradient search with computational resources that scale polynomially in d. In contrast, the complexity of a stochastic search for a single wave form that simultaneously acts as desired on all eigenvectors scales exponentially in d. We extend this construction to design maps on an n-dimensional subspace of the Hilbert space using only n stochastic searches. Additionally, we show how these techniques can be used to control atomic spins in the ground-electronic hyperfine manifold of alkali metal atoms in order to implement general qudit logic gates as well to perform a simple form of error correction on an embedded qubit.
 

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Microwave Control of Atomic Motion in Optical Lattices

 

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Leonid Forster, Michal Karski, Jai-Min Choi, Andreas Steffen, Wolfgang Alt, Dieter Meschede, Artur Widera, Enrique Montano, Jae Hoon Lee, Worawarong Rakreungdet, Poul S. Jessen
 

We control the quantum mechanical motion of neutral atoms in an optical lattice by driving microwave transitions between spin states whose trapping potentials are spatially offset. Control of this offset with nanometer precision allows for adjustment of the coupling strength between different motional states, analogous to an adjustable effective Lamb-Dicke factor. This is used both for efficient one-dimensional sideband cooling of individual atoms to a vibrational ground state population of 97 percent, and to drive coherent Rabi oscillation between arbitrary pairs of vibrational states. We further show that microwaves can drive well resolved transitions between motional states in maximally offset, shallow lattices, and thus in principle allow for coherent control of long range quantum transport.
 

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