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Scientific Reports

Landau-Zener-Stückelberg interference in coherent charge oscillations of a one-electron double quantum dot

Takeshi Ota, Kenichi Hitachi, Koji Muraki

Published Mar 29, 2018• 16 citations

Abstract

Landau-Zener (LZ) transition has received renewed interest as an alternative approach to control single-qubit states. An LZ transition occurs when a system passes through an avoided crossing that arises from quantum mechanical coupling of two levels, taking the system to a coherent superposition of the two states. Then, multiple LZ transitions induce interference known as Landau-Zener-Stückelberg (LZS) interference whose amplitude strongly depends on the velocity or adiabaticity of the passage. Here, we study the roles of LZ transitions and LZS interference in coherent charge oscillations of a one-electron semiconductor double quantum dot by time-domain experiments using standard rectangular voltage pulses. By employing density matrix simulations, we show that, in the standard setup using rectangular pulses, even a small distortion of the pulse can give rise to LZ transitions and hence LZS interference, which significantly enhances the measured oscillation amplitude. We further show experimentally that the nature of the coherent charge oscillations changes from Rabi-type to LZS oscillations with increasing pulse distortion. Our results thus demonstrate that it is essential to take into account LZS interference for both precise control of charge qubits and correct interpretation of measurement results.

DOI: 10.1038/s41598-018-23468-2

Related papers

Interplay of charge and spin coherence in Landau-Zener interferometry in double quantum dots

Hugo Ribeiro

Landau-Zener-Stuckelberg-Majorana (LZSM) physics has been exploited to coherently manipulate two-electron spin states in a GaAs double quantum dot (DQD) at a singlet (S)-triplet (T+) anti-crossing. The anti-crossing results from the hyperfine interaction with the nuclear spins of the host material [1,2]. However, the fluctuations of the nuclear spin bath result in spin dephasing within T ∗ 2 ∼ 10− 20 ns. As a consequence, the sweep through the anti-crossing would have to be performed on a timescale comparable to T ∗ 2 to achieve LZSM oscillations with 100% visibility. Moreover, the S-T+ anti-crossing is located near the (1, 1)− (2, 0) interdot charge transition, where (nl, nr) denotes the number of electrons in the left and right quantum dot. As a result the singlet state involved in the dynamics is a superpostion of (1, 1) and (2, 0) singlet states. Here we show that it is possible to increase the oscillation visibility while keeping sweep times less than T ∗ 2 using a tailored pulse with a detuning dependent level velocity. The pulse includes a slow level velocity portion that is chosen to coincide with the passage through the S-T+ anti-crossing and two fast level velocity portions. The latter minimize the time spent in regions where spin and charge degrees of freedom are entangled, which renders the qubit susceptible to charge noise. The slow level velocity portion of the pulse results in a stronger effective coupling between the spins states, which increases the oscillations visibility [3,4]. In particular, we were able to obtain a visibility of ∼ 0.5 for LZSM oscillations. This constitutes an important step towards the implementation of a Hadamard gate.

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Landau-Zener-Stückelberg interferometry of a single electron charge qubit

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We perform Landau-Zener-St\"uckelberg interferometry on a single electron GaAs charge qubit by repeatedly driving the system through an avoided crossing. We observe coherent destruction of tunneling, where periodic driving with specific amplitudes inhibits current flow. We probe the quantum dot occupation using a charge detector, observing oscillations in the qubit population resulting from the microwave driving. At a frequency of 9 GHz we observe excitation processes driven by the absorption of up to 17 photons. Simulations of the qubit occupancy are in good agreement with the experimental data.

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Landau-Zener (LZ) transition has received renewed interest as an alternative approach to control single-qubit states. An LZ transition occurs when a system passes through an avoided crossing that arises from quantum mechanical coupling of two levels, taking the system to a coherent superposition of the two states. Then, multiple LZ transitions induce interference known as Landau-Zener-Stückelberg (LZS) interference whose amplitude strongly depends on the velocity or adiabaticity of the passage. Here, we study the roles of LZ transitions and LZS interference in coherent charge oscillations of a one-electron semiconductor double quantum dot by time-domain experiments using standard rectangular voltage pulses. By employing density matrix simulations, we show that, in the standard setup using rectangular pulses, even a small distortion of the pulse can give rise to LZ transitions and hence LZS interference, which significantly enhances the measured oscillation amplitude. We further show experimentally that the nature of the coherent charge oscillations changes from Rabi-type to LZS oscillations with increasing pulse distortion. Our results thus demonstrate that it is essential to take into account LZS interference for both precise control of charge qubits and correct interpretation of measurement results.

Landau-Zener-Stuckelberg-Majorana (LZSM) physics has been exploited to coherently manipulate two-electron spin states in a GaAs double quantum dot (DQD) at a singlet (S)-triplet (T+) anti-crossing. The anti-crossing results from the hyperfine interaction with the nuclear spins of the host material [1,2]. However, the fluctuations of the nuclear spin bath result in spin dephasing within T ∗ 2 ∼ 10− 20 ns. As a consequence, the sweep through the anti-crossing would have to be performed on a timescale comparable to T ∗ 2 to achieve LZSM oscillations with 100% visibility. Moreover, the S-T+ anti-crossing is located near the (1, 1)− (2, 0) interdot charge transition, where (nl, nr) denotes the number of electrons in the left and right quantum dot. As a result the singlet state involved in the dynamics is a superpostion of (1, 1) and (2, 0) singlet states. Here we show that it is possible to increase the oscillation visibility while keeping sweep times less than T ∗ 2 using a tailored pulse with a detuning dependent level velocity. The pulse includes a slow level velocity portion that is chosen to coincide with the passage through the S-T+ anti-crossing and two fast level velocity portions. The latter minimize the time spent in regions where spin and charge degrees of freedom are entangled, which renders the qubit susceptible to charge noise. The slow level velocity portion of the pulse results in a stronger effective coupling between the spins states, which increases the oscillations visibility [3,4]. In particular, we were able to obtain a visibility of ∼ 0.5 for LZSM oscillations. This constitutes an important step towards the implementation of a Hadamard gate.

We study finite-time Landau-Zener transitions at a singlet-triplet level crossing in a GaAs double quantum dot, both experimentally and theoretically. Sweeps across the anticrossing in the high driving speed limit result in oscillations with a small visibility. Here we demonstrate how to increase the oscillation visibility while keeping sweep times shorter than T(2)(*) using a tailored pulse with a detuning dependent level velocity. Our results show an improvement of a factor of ~2.9 for the oscillation visibility. In particular, we were able to obtain a visibility of ~0.5 for Stückelberg oscillations, which demonstrates the creation of an equally weighted superposition of the qubit states.

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.

A basic requirement for quantum information processing is the ability to universally control the state of a single qubit on timescales much shorter than the coherence time. Although ultrafast optical control of a single spin has been achieved in quantum dots, scaling up such methods remains a challenge. Here we demonstrate complete control of the quantum-dot charge qubit on the picosecond scale [corrected], orders of magnitude faster than the previously measured electrically controlled charge- or spin-based qubits. We observe tunable qubit dynamics in a charge-stability diagram, in a time domain, and in a pulse amplitude space of the driven pulse. The observations are well described by Landau-Zener-Stückelberg interference. These results establish the feasibility of a full set of all-electrical single-qubit operations. Although our experiment is carried out in a solid-state architecture, the technique is independent of the physical encoding of the quantum information and has the potential for wider applications.

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.

We perform Landau-Zener-St\"uckelberg interferometry on a single electron GaAs charge qubit by repeatedly driving the system through an avoided crossing. We observe coherent destruction of tunneling, where periodic driving with specific amplitudes inhibits current flow. We probe the quantum dot occupation using a charge detector, observing oscillations in the qubit population resulting from the microwave driving. At a frequency of 9 GHz we observe excitation processes driven by the absorption of up to 17 photons. Simulations of the qubit occupancy are in good agreement with the experimental data.