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arXiv:1304.0271 · Physical Review A

Realization of geometric Landau-Zener-Stückelberg interferometry

Junhua Zhang, Jing-Ning Zhang, Xiang Zhang, Kihwan Kim

Published Jan 10, 2014• 17 citations
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Abstract

We report an experimental realization of the geometric Landau-Zener-St\"uckelberg (LZS) interferometry proposed by Gasparinetti et al. [Phys. Rev. Lett. 107, 207002 (2011)] in a single-trapped-ion system. Unlike those in a conventional LZS interferometer, the interference fringes of our geometric interferometer originate solely from a geometric phase. We also observe the robustness of the interference contrast against noise or fluctuations in the experimental parameters. Our scheme can be applied to other complex systems subject to relatively large errors in system control.

DOI
10.1103/physreva.89.013608

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High fidelity universal gates for quantum bits form an essential ingredient of quantum information processing. In particular, geometric gates have attracted attention because they have a higher intrinsic resistance to certain errors. However, their realization remains a challenge because of the need for complicated quantum control on a multi-level structure as well as meeting the adiabatic condition within a short decoherence time. Here, we demonstrate non-adiabatic quantum operations for a two-level system by applying a well-controlled geometric Landau-Zener-Stückelberg interferometry. By characterizing the gate quality, we also investigate the operation in the presence of realistic dephasing. Furthermore, the result provides an essential model suitable for understanding an interplay of geometric phase and Landau-Zener-Stückelberg process which are well explored separately.
Geometric quantum manipulation and Landau-Zener interferometry have been separately explored in many quantum systems. In this Letter, we combine these two approaches to study the dynamics of a superconducting phase qubit. We experimentally demonstrate Landau-Zener interferometry based on the pure geometric phases in this solid-state qubit. We observe the interference caused by a pure geometric phase accumulated in the evolution between two consecutive Landau-Zener transitions, while the dynamical phase is canceled out by a spin-echo pulse. The full controllability of the qubit state as a function of the intrinsically robust geometric phase provides a promising approach for quantum state manipulation.
Superconducting circuit quantum electrodynamics (QED) architecture composed of superconducting qubit and resonator is a powerful platform for exploring quantum physics and quantum information processing. By employing techniques developed for superconducting quantum computing, we experimentally investigate phase-sensitive Landau–Zener–Stückelberg (LZS) interference phenomena in a circuit QED. Our experiments cover an extensive range of LZS transition parameters and demonstrate the LZS induced Rabi-like oscillation as well as phase-dependent steady-state population.
We systematically investigate the non-Hermitian generalizations of the Landau-Zener (LZ) transition and the Landau-Zener-St\"uckelberg (LZS) interferometry. The LZ transition probabilities, or band populations, are calculated for a generic non-Hermitian model and their asymptotic behavior is analyzed. We then focus on non-Hermitian systems with a real adiabatic parameter and study the LZS interferometry formed out of two identical avoided level crossings. Four distinctive cases of interferometry are identified and the analytic formulas for the transition probabilities are calculated for each case. The differences and similarities between the non-Hermitian case and its Hermitian counterpart are emphasized. In particular, the geometrical phase originated from the sign change of the mass term at the two level crossings is still present in the non-Hermitian system, indicating its robustness against the non-Hermiticity. We further apply our non-Hermitian LZS theory to describing the Bloch oscillation in one-dimensional parity-time (PT)(\mathcal{PT})(PT) reversal symmetric non-Hermitian Su-Schrieffer-Heeger model and propose an experimental scheme to simulate such dynamics using photonic waveguide arrays. The Landau-Zener transition, as well as the LZS interferometry, can be visualized through the beam intensity profile and the transition probabilities measured by the center of mass of the profile.
Landau–Zener–Stückelberg (LZS) interference has drawn renewed attention to quantum information processing research because it is not only an effective tool for characterizing two-level quantum systems but also a powerful approach to manipulate quantum states. Superconducting quantum circuits, due to their versatile tunability and degrees of control, are ideal platforms for studying LZS interference phenomena. We use a superconducting Xmon qubit to study LZS interference by parametrically modulating the qubit transition frequency nonlinearly. For dc flux biasing of the qubit slightly far away from the optimal flux point, the qubit excited state population shows an interference pattern that is very similar to the standard LZS interference in linear regime, except that all bands shift towards lower frequencies when increasing the rf modulation amplitude. For dc flux biasing close to the optimal flux point, the negative sidebands and the positive sidebands behave differently, resulting in an asymmetric interference pattern. The experimental results are also in good agreement with our analytical and numerical simulations.