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arXiv:1101.3194 · Physical Review B

Deterministic chaos can act as a decoherence suppressor

Jing Zhang, Yu-xi Liu, Wei-Min Zhang, Lian-Ao Wu, Re-Bing Wu, Tzyh‐Jong Tarn

Published Dec 7, 2011• 21 citations
arXivHTMLPDF

Abstract

We propose a strategy to suppress non-Markovian decoherence of a qubit by coupling the qubit to a deterministic chaotic setup with the broad power distribution in particular in the high-frequency domain. Although it is widely believed that chaos induces decoherence, we find, surprisingly, that the unitary dynamics induced by the chaotic setup can be helpful for the decoherence suppression. Compared with the existing decoherence control methods such as the usual dynamical decoupling, we do not need to impose high-frequency controls, because the high-frequency components in our method are generated by the chaotic setup, and the design of complex optimized control pulses used in the modified dynamical decoupling approaches is also not necessary. Using superconducting quantum circuits as an example, we demonstrate how to realize our general method. We find that various noises in a wide frequency domain, including low-frequency $1/f$, high-frequency ohmic, subohmic, and superohmic noises, can be efficiently suppressed by coupling the qubit to a Duffing oscillator acting as the chaotic setup. Significantly, the decoherence time of the qubit is prolonged approximately 100 times in magnitude.

DOI
10.1103/physrevb.84.214304

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We propose a strategy to suppress non-Markovian decoherence of a qubit by coupling the qubit to a deterministic chaotic setup with the broad power distribution in particular in the high-frequency domain. Although it is widely believed that chaos induces decoherence, we find, surprisingly, that the unitary dynamics induced by the chaotic setup can be helpful for the decoherence suppression. Compared with the existing decoherence control methods such as the usual dynamical decoupling, we do not need to impose high-frequency controls, because the high-frequency components in our method are generated by the chaotic setup, and the design of complex optimized control pulses used in the modified dynamical decoupling approaches is also not necessary. Using superconducting quantum circuits as an example, we demonstrate how to realize our general method. We find that various noises in a wide frequency domain, including low-frequency 1/f1/f1/f, high-frequency ohmic, subohmic, and superohmic noises, can be efficiently suppressed by coupling the qubit to a Duffing oscillator acting as the chaotic setup. Significantly, the decoherence time of the qubit is prolonged approximately 100 times in magnitude.
To suppress decoherence of solid-state qubits which are coupled to the non-Markovian noises, we propose a strategy to couple the qubit with a chaotic device, of which the broad power distribution in the high-frequency domain can be used to freeze the noises just like the dynamical decoupling control (DDC) method. Compared with the DDC, high-frequency components can be generated by the chaotic device even driven by a low-frequency field and we do not need to optimize the control fields to generate complex control pulses. As an application to superconducting circuits, we find that various noises in a wide frequency domain, including low-frequency 1/f1/f1/f, high-frequency Ohmic, sub-Ohmic, and super-Ohmic noises, can be efficiently suppressed by coupling the qubit to a Duffing oscillator, and the decoherence rate of the qubit is efficiently decreased for about 100 times in magnitude.
To suppress decoherence of solid-state qubits induced by non-Markovian noises, we propose a strategy to couple the qubit with a chaotic device, whose broad power distribution in the high-frequency domain can be used to freeze the noises in the similar way of the dynamical decoupling control (DDC) method. Compared with the DDC, high-frequency components can be generated by the chaotic device even driven by a low-frequency field and thus the control fields do not need any optimization. Thus, our method is easier to be realized in experiments. As an application to superconducting circuits, we find that various noises in a broad band, including low-frequency 1/ƒ, high-frequency Ohmic, sub-Ohmic, and super-Ohmic noises, can be efficiently suppressed by coupling the qubit to a Duffing oscillator, and the decoherence rate of the qubit is efficiently decreased by about 100 times in magnitude. Using experimentally realizable parameters, the decoherence time of the superconducting charge qubit can reach 200 µs by our method, which is 10 ∼ 100 times longer in magnitude than that observed in experiments.
The application of dynamical decoupling pulses to a single qubit interacting with a linear harmonic oscillator bath with 1/f1/f1/f (more generally, strong low-frequency) spectral density is studied, and compared to the Ohmic case. Decoupling pulses that are slower than the fastest bath time scale are shown to drastically reduce the decoherence rate in the 1/f1/f1/f case. Contrary to conclusions drawn from previous studies, this shows that dynamical decoupling pulses do not always have to be ultrafast. Our results explain the recent experiment in which dephasing due to 1/f1/f1/f charge noise affecting a charge qubit in a small superconducting electrode was successfully suppressed using spin-echo-type gate-voltage pulses.
We study the open system dynamics of a circuit quantum electrodynamics (QED) model operating in the ultrastrong coupling regime. If the resonator is pumped periodically in time the underlying classical system is chaotic. Indeed, the periodically driven Jaynes-Cummings model in the Born-Oppenheimer approximation resembles a Duffing oscillator which in the classical limit is a well-known example of a chaotic system. Detection of the field quadrature of the output field acts as an effective position measurement of the oscillator. We address how such detection affects the quantum chaotic evolution in this bipartite system. We differentiate between single measurement realizations and ensembles of repeated measurements. In the former case a measurement/decoherence induced localization effect is encountered, while in the latter this localization is almost completely absent. This is in marked contrast to numerous earlier works discussing the quantum-classical correspondence in measured chaotic systems. This lack of a classical correspondence under relatively strong measurement induced decoherence is attributed to the inherent quantum nature of the qubit subsystem and in particular to the quantum correlations between the qubit and the field which persist despite the decoherence.
We study the open system dynamics of a circuit QED model operating in the ultrastrong coupling regime. If the resonator is pumped periodically in time the underlying classical system is chaotic. Indeed, the periodically driven Jaynes-Cummings model in the Born-Oppenheimer approximation resembles a Duffing oscillator which in the classical limit is a well-known example of a chaotic system. Detection of the field quadrature of the output field acts as an effective position measurement of the oscillator. We address how such detection affects the quantum chaotic evolution in this bipartite system. We differentiate between single measurement realizations and ensembles of repeated measurements. In the former case a measurement/decoherence induced localization effect is encountered, while in the latter this localization is almost completely absent. This is in marked contrast to numerous earlier works discussing the quantum-classical correspondence in measured chaotic systems. This lack of a classical correspondence under relatively strong measurement induced decoherence is attributed to the inherent quantum nature of the qubit subsystem and in particular to the quantum correlations between the qubit and the field which persist despite the decoherence.
We investigate the capability of dynamical decoupling techniques to reduce decoherence from a realistic environment generating 1/f noise. The predominance of low frequency modes in the noise profile allows for decoherence scenarios where relatively slow control rates suffice for a drastic improvement. However, the actual figure of merit is very sensitive to the details of the dynamics, with decoupling performance which may deteriorate for non-Gaussian noise and/or high frequency working points. Our results are promising for robust solid-state qubits and beyond.