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arXiv:quant-ph/9904087 · Physical Review A

Control of decoherence and relaxation by frequency modulation of a heat bath

G. S. Agarwal

Published Dec 14, 1999• 112 citations
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Abstract

We demonstrate, in a very general fashion, the considerable slowing down of decoherence and relaxation by fast frequency modulation of the system-heat--bath coupling. The slowing occurs as the decoherence rates are now determined by the spectral components of bath correlations which are shifted due to fast modulation. We present several examples including the slowing down of the heating of a trapped ion, where the system-bath interaction is not necessarily Markovian.

DOI
10.1103/physreva.61.013809

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We demonstrate, in a very general fashion, the considerable slowing down of decoherence and relaxation by fast frequency modulation of the system-heat--bath coupling. The slowing occurs as the decoherence rates are now determined by the spectral components of bath correlations which are shifted due to fast modulation. We present several examples including the slowing down of the heating of a trapped ion, where the system-bath interaction is not necessarily Markovian.
The effect of a number of mechanisms designed to suppress decoherence in open quantum systems are studied with respect to their effectiveness at slowing down the loss of entanglement. The effect of photonic band-gap materials and frequency modulation of the system-bath coupling are along expected lines in this regard. However, other control schemes, like resonance fluorescence, achieve quite the contrary: increasing the strength of the control leads to a faster decay of entanglement. The effect of dynamic decoupling schemes on two qualitatively different system-bath interactions are studied in depth. Dynamic decoupling control has the expected effect of slowing down the decay of entanglement in a two-qubit system coupled to a harmonic oscillator bath under a nondemolition interaction. However, nontrivial phenomena are observed when a Josephson charge qubit, strongly coupled to a random telegraph noise bath, is subject to decoupling pulses. The most striking of these reflects the resonance fluorescence scenario, in that an increase in the pulse strength decreases decoherence but also speeds up the sudden death of entanglement. This demonstrates that the behavior of decoherence and entanglement in time can be qualitatively different in the strong-coupling non-Markovian regime.
In this paper, we investigate the non-Markovian heat transfer between a weakly damped harmonic oscillator (system) and a thermal bath. When the system is initially in a thermal state and not correlated with the environment, the mean energy of the system always first increases, then oscillates, and finally reaches equilibrium with the bath, no matter what the initial temperature of the system is. Moreover, the heat transfer between the system and the bath can be controlled by fast bang-bang modulation. This modulation does work on the system, and temporarily inverts the direction of heat flow. In this case, the common sense that heat always transfers from hot to cold does not hold any more. At the long time scale, a new dynamic equilibrium is established between the system and the bath. At this equilibrium, the energy of the system can be either higher or lower than its normal equilibrium value. A comprehensive analysis of the relationship between the dynamic equilibrium and the parameters of the modulation as well as the environment is presented.
Dynamical control of decoherence induced by the environment in a single trapped ion system is investigated.The scheme proposed here is based on the composition of the frequency-shift and parity-kick technique. The former is realized by a homogeneous classical large-detuned optical fields added to the ion system,while the latter is realized by a series of π pulses.With application of this scheme,the decoherence induced by the bath can be efficiently eliminated.Numerical calculation shows that this scheme is superior to the parity-kick scheme.
We study the application of decoupling techniques to the case of a damped vibrational mode of a chain of trapped ions, which can be used as a quantum bus in linear ion trap quantum computers. We show that vibrational heating could be efficiently suppressed using appropriate 'parity kicks'. We also show that vibrational decoherence can be suppressed by this decoupling procedure, even though this is generally more difficult because the rate at which the parity kicks have to applied increases with the effective bath temperature.