arXiv subjects

A. B. Tchapda

Publications and source records attributed to A. B. Tchapda.

3 recordsLinked to original sources

arXiv2017

Landau-Zener transitions in a qubit periodically driven in both longitudinal and transverse directions

We theoretically investigate the dynamics of a spin-qubit periodically driven in both longitudinal and transverse directions by two classical fields respectively a radio-frequency (RF) and a microwave (MW) field operating at phase difference $ϕ$. The qubit is simultaneously locally subject to a linearly polarized magnetic field which changes its sign at a degeneracy point in the longitudinal direction and remains constant in the transverse direction. We superimpose the RF and MW signals respectively to the longitudinal and transverse components of the magnetic field. The proposed model may be used to optimize the control of a qubit in quantum devices. The various fields applied are relevant to {\it nearly-decouple} the spin-qubit from its environment, minimize decoherence effects and improve on the coherence time. The study is carried out in the Schrödinger and Bloch pictures. We consider the limits of weak and strong longitudinal drives set up by comparing the characteristic time of non-adiabatic transitions with the coherence time of the longitudinal drive. Expressions for populations are compared with numerics and remarkable agreements are observed as both solutions are barely discernible.

quant-ph↗

arXiv2017

SU(3) Landau-Zener interferometry with a transverse periodic drive

Quantum triangles can work as interferometers. Depending on their geometric size and interactions between paths, "beats" {\it and/or} "steps" patterns are observed. We show that when inter-level distances between level positions in quantum triangles periodically change with time, formation of beats {\it and/or} steps no longer depends only on the geometric size of the triangles but also on the characteristic frequency of the transverse signal. For large-size triangles, we observe the coexistence of beats {\it and} steps when the frequency of the signal matches that of non-adiabatic oscillations and for large frequencies, a maximum of four steps instead of two as in the case with constant interactions is observed. Small-size triangles also revealed counter-intuitive interesting dynamics for large frequencies of the field: unexpected two-step patterns are observed. When the frequency is large and tuned such that it matches the uniaxial anisotropy, three-step patterns are observed. We have equally observed that when the transverse signal possesses a static part, steps maximize to six. These effects are semi-classically explained in terms of Fresnel integrals and quantum mechanically in terms of quantized fields with a photon-induced tunneling process. Our expressions for populations are in excellent agreement with the gross temporal profiles of exact numerical solutions. We compare the semi-classical and quantum dynamics in the triangle and establish the conditions for their equivalence.

quant-ph↗

arXiv2016

Demkov-Kunike Models with Decay

Exact analytical solutions to the dissipative time-dependent Schrödinger equation are obtained for a decaying two-state system with decay rates $Γ_{1}$ and $Γ_{2}$ for levels with extremal spin projections. The system is coherently driven with a pulse whose detuning is made up of two parts: a time-dependent part (chirp) of hyperbolic-tangent shape and a static part with real and imaginary terms. This gives us a wide range of possibilities to arbitrarily select the interaction terms. We considered two versions which led to decaying Demkov-Kunike (DK) models; the version in which the Rabi frequency (interaction) is a time-dependent hyperbolic-secant function (called decaying DK1 model) and the case when it is constant in time and never turns off (decaying DK2 model). Our analytical solutions account for all possible initial moments instead of only $t_{0}=0$ or $t_{0}=-\infty$ as for non-decaying models and may be useful for experiments on level crossings. Two complementary limits of the pulse detuning are considered and explored: the limit of fast (i) and slow rise (ii). In the case (i), the coupling between level positions in the first DK model collapses while the second DK model reduces to a Rabi model (constant Hamiltonian), in the case (ii), both DK models reduce to the LZ model. In both cases (i) and (ii), analytical approximated solutions which conveniently approach the exact solutions are derived.

cond-mat.str-el↗