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arXiv:cond-mat/0509735 · Physical Review B

Advanced control with a Cooper-pair box: Stimulated Raman adiabatic passage and Fock-state generation in a nanomechanical resonator

Jens Siewert, Tobias Brandes, G. Falci

Published Jan 13, 2009• 36 citations
arXivHTMLPDF

Abstract

The rapid experimental progress in the field of superconducting nanocircuits gives rise to an increasing quest for advanced quantum-control techniques for these macroscopically coherent systems. Here we demonstrate theoretically that stimulated Raman adiabatic passage should be possible with the quantronium setup of a Cooper-pair box. The scheme appears to be robust against decoherence and should be realizable even with the existing technology. As an application we present a method to generate single-phonon states of a nanomechanical resonator by vacuum-stimulated adiabatic passage with the superconducting nanocircuit coupled to the resonator.

DOI
10.1103/physrevb.79.024504

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The rapid experimental progress in the field of superconducting nanocircuits gives rise to an increasing quest for advanced quantum-control techniques for these macroscopically coherent systems. Here we demonstrate theoretically that stimulated Raman adiabatic passage should be possible with the quantronium setup of a Cooper-pair box. The scheme appears to be robust against decoherence and should be realizable even with the existing technology. As an application we present a method to generate single-phonon states of a nanomechanical resonator by vacuum-stimulated adiabatic passage with the superconducting nanocircuit coupled to the resonator.
We propose a scheme in which the quantum coherence of a nanomechanical resonator can be probed using a superconducting qubit. We consider a mechanical resonator coupled capacitively to a Cooper-pair box and assume that the superconducting qubit is tuned to the degeneracy point so that its coherence time is maximised and the electro-mechanical coupling can be approximated by a dispersive Hamiltonian. When the qubit is prepared in a superposition of states this drives the mechanical resonator progressively into a superposition which in turn leads to apparent decoherence of the qubit. Applying a suitable control pulse to the qubit allows its population to be inverted resulting in a reversal of the resonator dynamics. However, the resonator's interactions with its environment mean that the dynamics is not completely reversible. We show that this irreversibility is largely due to the decoherence of the mechanical resonator and can be inferred from appropriate measurements on the qubit alone. Using estimates for the parameters involved based on a specific realization of the system we show that it should be possible to carry out this scheme with existing device technology.
Recent experiments have demonstrated coherent phenomena in three-level systems based on superconducting nanocircuits. This opens the possibility to detect Stimulated Raman Adiabatic Passage (STIRAP) in artificial atoms. Low-fequency noise (often 1/f) is one of the main sources of decoherence in these systems, and we study its effect on the transfer efficiency. We propose a way to analyze low frequency fluctuations in terms of fictitious correlated fluctuations of external parameters. We discuss a specific implementation, namely the Quantronium setup of a Cooper-pair box, showing that optimizing the trade-off between efficient coupling and protection against noise may allow us to observe coherent population transfer in this nanodevice.
Stimulated Raman adiabatic passage (STIRAP) is a widely-used technique of coherent state-to-state manipulation for many applications in physics, chemistry, and beyond. The adiabatic evolution of the state involved in STIRAP, called adiabatic passage, guarantees its robustness against control errors, but also leads to problems of low efficiency and decoherence. Here we propose and experimentally demonstrate an alternative approach, termed stimulated Raman "user-defined" passage (STIRUP), where a parameterized state is employed for constructing desired evolutions to replace the adiabatic passage in STIRAP. The user-defined passages can be flexibly designed for optimizing different objectives for different tasks, e.g. minimizing leakage error. To experimentally benchmark its performance, we apply STIRUP to the task of coherent state transfer in a superconducting Xmon qutrit. We found that STIRUP completed the transfer more then four times faster than STIRAP with enhanced robustness, and achieved a fidelity of 99.5%, which is the highest among all recent experiments based on STIRAP and its variants. In practice, STIRUP differs from STIRAP only in the design of driving pulses; therefore, most existing applications of STIRAP can be readily implemented with STIRUP.
We propose a potentially practical scheme for quantum state transfer between a Cooper-pair box circuit and an electron spin ensemble of diamond nitrogen-vacancy (NV) centers. Both subsystems are placed into a common circuit QED and can be modeled as effective three-level subsystems under the appropriate external biases. Due to significant suppression of the photon decay, the robust state transfer between the two subsystems can be accomplished by using the technique of stimulated Raman adiabatic passage by individual microwave pulses, where a superconducting coplanar resonator serves as the quantum data bus. Numerical simulations show that the present scheme could offer a viable route towards robust quantum state transfer in hybrid solid-state systems.
Abstract Stimulated Raman adiabatic passage (STIRAP) is a standard technique to combat experimental imperfections and can be used to realize robust quantum state control, which has many applications in physics, chemistry, and beyond. However, STIRAP is susceptible to decoherence since it requires long evolution time. To overcome this problem, stimulated Raman ‘user-defined’ passage (STIRUP) is proposed, which allows users to design the passages unlike the STIRAP but fast and robust against both decoherence and experimental imperfections. Here, we further develop a more general STIRUP method. Comparing with shortcut to adiabaticity and its’ variants, the generalized STIRUP is more simpler and compatible with more complex energy-level structure and many-body systems. Furthermore, the generalized STIRUP has many important applications such as geometric phase measurement, coherent population transfer, and quantum state preparation. Specifically, as examples, we show how to realize the high-fidelity quantum state transfer and entangled state generation in a robust way via STIRUP with the state-of-the-art experimental superconducting circuits.