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Physical Review A

Decoherence and decay of motional quantum states of a trapped atom coupled to engineered reservoirs

Q. A. Turchette, Christopher J. Myatt, B. E. King, Charles A. Sackett, D. Kielpinski, Wayne M. Itano, Christopher R. Monroe, D. J. Wineland

Published Oct 16, 2000• 285 citations

Abstract

We present results from an experimental study of the decoherence and decay of quantum states of a trapped atomic ion's harmonic motion interacting with several types of engineered reservoirs. We experimentally simulate three types of reservoirs: a high-temperature amplitude reservoir, a zero-temperature amplitude reservoir, and a high-temperature phase reservoir. Interaction with these environments causes the ion's motional state to decay or heat, and in the case of superposition states, to lose coherence. We report measurements of the decoherence of superpositions of coherent states and two-Fock-state superpositions into these reservoirs, as well as the decay and heating of Fock states. We confirm the theoretically well-known scaling laws that predict that the decoherence rate of superposition states scales with the square of the ``size'' of the state.

DOI: 10.1103/physreva.62.053807

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We investigate high frequency motional states of trapped atomic ions. Trapped ions in rf traps are confined by an approximate harmonic potential and exhibit quantum motional states that mediate essential techniques in quantum computing, simulation, networking, and precision measurement. However, motional state decoherence mechanisms, heating and dephasing, are broadly limiting: reduced two-qubit gate fidelities; lower fidelity and lifetime of highly nonclassical bosonic states; long laser cooling times; and large recoil heating rates. These also challenge the scalability of increasingly sophisticated protocols. We propose high motional frequency ion trapping as an operating regime that addresses these challenges and reshapes the design landscape for quantum information experiments and quantum control techniques. We report an experimentally motivated investigation of realizing this high-frequency regime and discuss the consequences for laser cooling, motional state coherence, fidelity and lifetime of nonclassical bosonic states, and scalability of experimental runtimes. We report clear design trajectories for ion traps to reach high motional frequency, a new limiting mechanism for laser cooling at these high frequencies, and more than an order-of-magnitude speedup in experimental duty cycles with larger speed ups possible for quantum error correction protocols. Taken together, high motional frequency ion trapping has broad implications for the future of quantum information experiments.

We report the creation of thermal, Fock, coherent, and squeezed states of motion of a harmonically bound

{}^{9}{\mathrm{Be}}^{+}

ion. The last three states are coherently prepared from an ion which has been initially laser cooled to the zero point of motion. The ion is trapped in the regime where the coupling between its motional and internal states, due to applied (classical) radiation, can be described by a Jaynes-Cummings-type interaction. With this coupling, the evolution of the internal atomic state provides a signature of the number state distribution of the motion.

We investigate the dynamics of two trapped ions interacting with a common thermal reservoir, focusing on how cross-correlated dissipation influences heating, steady-state behavior, and parameter sensitivity. Starting from a microscopic system--reservoir model, we derive the corresponding Heisenberg--Langevin equations and show that reservoir-induced correlations generate collective decay channels and, when the cross-damping rate matches the local damping, a decoherence-free normal mode that preserves memory of the initial excitations. Using the Fisher information associated with motional population measurements, we identify the parameter regimes in which cross-damping enhances the estimability of both system and reservoir properties. For nonclassical initial states, we also show that reservoir-mediated correlations can generate or maintain entanglement, with the strongest effects occurring near the decoherence-free condition.