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arXiv:atom-ph/9603002

Quantum Reservoir Engineering

J. F. Poyatos, J. I. Cirac, P. Zoller

Published Mar 15, 1996• 2 citations
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Abstract

We show how to design different couplings between a single ion trapped in a harmonic potential and an environment. This will provide the basis for the experimental study of the process of decoherence in a quantum system. The coupling is due to the absorption of a laser photon and subsequent spontaneous emission. The variation of the laser frequencies and intensities allows one to ``engineer'' the coupling and select the master equation describing the motion of the ion.

DOI
10.48550/arxiv.atom-ph/9603002

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We show how to design different couplings between a single ion trapped in a harmonic potential and an environment. This will provide the basis for the experimental study of the process of decoherence in a quantum system. The coupling is due to the absorption of a laser photon and subsequent spontaneous emission. The variation of the laser frequencies and intensities allows one to ``engineer'' the coupling and select the master equation describing the motion of the ion.
Known as an engineered reservoir due to fluctuations in trap parameter, a classical source of quantum decoherence is considered for a single trapped ion theoretically. For simplicity it is assumed that the fluctuations involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. Our results show that the decoherence rate depends on the vibrational quantum number in different ways corresponding to the vibrational excitation sideband used there. Besides, this source of decoherence also leads to occurrence of dissipation in the ion system.
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.
Coherent states are the only quantum states that recover the harmonic oscillator classical motion. However, rather than being deduced as the classical limit of the theory, coherent states were introduced into physics in a different context and then found to have properties that we can identify with our familiar classical experience. If classicality is really brought about by decoherence, coherent states should emerge naturally as the unique privileged states selected by the interaction with the environment. This is shown explicitly here, for the field in a single-mode cavity with ordinary one-photon losses, by calculating them directly as the only pure state solutions of the master equation at zero temperature.
Summary form only given, as follows. The ability to create and completely characterize a variety of fundamental quantum states has long been sought after in the laboratory since it brings to the forefront issues involving the relationship between quantum and classical physics. The interaction of a trapped atom with classical laser light constitutes a simple and well-isolated quantum system that makes experiments along these lines possible. The motion of an ion trapped in a rf-trap can be described as a quantum harmonic oscillator. If the ion is driven by a classical light field, several interactions similar to and beyond the simple Jaynes-Cummings coupling can be realized. These couplings allow for precisely controlled engineering and measurement of quantum states. We create states having both classical and nonclassical character including thermal, number, coherent, squeezed, and Schrodinger cat states. The motional quantum state is fully reconstructed with use of two novel schemes that determine the density matrix in the number state basis and the Wigner function. Our techniques allow well-controlled experiments on decoherence and related phenomena on the quantum-classical borderline.