Exact, Floquet-based, Single Qubit Control

Mahmoud Youssef Abd‐Rabbou, Reem Altuijri, R. T. Matoog +1 more

Chunqing Deng, Feiruo Shen, Jean-Luc Orgiazzi +2 more

Chunqing Deng, Feiruo Shen, Sahel Ashhab +1 more

We consider the dynamics of a two-level system (qubit) driven by strong and short resonant pulses in the framework of Floquet theory. First we derive analytical expressions for the quasienergies and Floquet states of the driven system. If the pulse amplitude varies very slowly, the system adiabatically follows the instantaneous Floquet states, which acquire dynamical phases that depend on the evolution of the quasienergies over time. The difference between the phases acquired by the two Floquet states corresponds to a qubit state rotation, generalizing the notion of Rabi oscillations to the case of large driving amplitudes. If the pulse amplitude changes very fast, the evolution is nonadiabatic, with transitions taking place between the Floquet states. We quantify and analyze the nonadiabatic transitions during the pulse by employing adiabatic perturbation theory and exact numerical simulations. We find that, for certain combinations of pulse rise and fall times and maximum driving amplitude, a destructive interference effect leads to a remarkably strong suppression of transitions between the Floquet states. This effect provides the basis of a quantum control protocol, which we name Floquet interference efficient suppression of transitions in the adiabatic basis (FIESTA), that can be used to design ultrafast high-fidelity single-qubit quantum gates.

Giulia Pacchioni

Aqsa Rehman, M. Tahir Naseem, Adam Zaman Chaudhry

Controlling heat flow in small quantum systems is a central goal of quantum thermodynamics and nanoscale transport. A key challenge is to achieve strong thermal rectification without suppressing the transmitted heat current, a tradeoff that often arises in static diode configurations. We establish a Floquet-control mechanism in a minimal quantum thermal diode formed by two longitudinally modulated Ising-coupled qubits, each coupled to an independent thermal reservoir. From a microscopic system--bath model, we derive a Floquet--LGKS master equation that resolves the drive-assisted transition channels. The resonant undriven device with left--right symmetric bath couplings serves as the reciprocal benchmark, while static detuning provides a rectifying reference with reduced heat current. Single-side driving breaks this reciprocal structure by creating a Floquet-dressed contact opposite a purely thermal contact. For this configuration, we obtain a compact steady-state current formula and an exact blocking condition for suppressing one bias direction while retaining finite transport in the opposite direction. In the weak sinusoidal-drive regime, rectification begins quadratically in the modulation amplitude. Dual-side driving adds a Floquet pumping contribution to the interaction-mediated current, so complete blocking requires cancellation of both contributions. These results establish contact-selective Floquet dressing as a design principle for controllable heat-flow asymmetry in minimal quantum thermal devices.

Anthony Gandon, Camille Le Calonnec, Ross Shillito +2 more

Time-dependent eigenstates of Hamiltonians offer a large degree of tunability, which can be leveraged to operate single- and two-qubit gates so that they stay dynamically protected from noise. However, the usual analytical techniques for describing these gates are limited for systems subject to drives of different frequencies. Thus the authors generalize the Floquet approach to the understanding of such systems, and provide protocols to robustly control and measure these complex systems.