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arXiv:1909.04291 · Physical Review Research

Geometric driving of two-level quantum systems

Zu-Jian Ying, Paola Gentile, José Pablo Baltanás, Diego Frustaglia, Carmine Ortix, Mario Cuoco

Published May 13, 2020• 24 citations
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Abstract

The authors investigate a class of cyclic evolutions for driven two-level quantum systems to unveil a geometric resource of the driving field. The paper presents a series of physical platforms to prove how the geometric control of the quantum phases can be realized for paradigmatic pendular field drivings. This includes experimentally feasible setups based on superconducting islands coupled to a Josephson junction and inversion asymmetric nanochannels with tailored geometric shapes.

DOI
10.1103/physrevresearch.2.023167

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The authors investigate a class of cyclic evolutions for driven two-level quantum systems to unveil a geometric resource of the driving field. The paper presents a series of physical platforms to prove how the geometric control of the quantum phases can be realized for paradigmatic pendular field drivings. This includes experimentally feasible setups based on superconducting islands coupled to a Josephson junction and inversion asymmetric nanochannels with tailored geometric shapes.
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Abstract When a quantum-mechanical system undergoes an adiabatic cyclic evolution, it acquires a geometrical phase factor1 in addition to the dynamical one; this effect has been demonstrated in a variety of microscopic systems2. Advances in nanotechnology should enable the laws of quantum dynamics to be tested at the macroscopic level3, by providing controllable artificial two-level systems (for example, in quantum dots4 and superconducting devices5, 6). Here we propose an experimental method to detect geometric phases in a superconducting device. The setup is a Josephson junction nanocircuit consisting of a superconducting electron box. We discuss how interferometry based on geometrical phases may be realized, and show how the effect may be applied to the design of gates for quantum computation.
We study the role of driving in a two-level system evolving under the presence of a structured environment in different regimes. We find that adding a periodic modulation to the two-level system can greatly enhance the survival of the geometric phase for many time periods in an intermediate coupling to the environment. In this regime, where there are some non-Markovian features characterizing the dynamics, we note that adding driving to the system leads to a suppression of non-Markovianity altogether, allowing for a smooth dynamical evolution and an enhancement of the robustness condition of the geometric phase. As the model studied herein is the one used to model experimental situations such as hybrid quantum classical systems feasible with current technologies, this knowledge can aid the search for physical setups that best retain quantum properties under dissipative dynamics.
We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time.
Geometric phase for novel analytical solutions (Barnes and Das Sarma) of time-dependent two-level quantum systems is discussed, specically for a general single-axis driving term, which is represented by a function J(t) in the Hamiltonian, and its corresponding evolution operator.It is demonstrated how general results for corresponding phases (total, dynamic and geometric) can be obtained.Using a specic case, it was found that over time in which the driving eld is appreciably dierent from zero, the corresponding geometric phase changes (in the specic example by ∆β ≈ 0.8 radians) thus enabling detection.The results are relevant to qubit control and to quantum computing applications.