Exactly solvable two-level quantum systems and Landau-Zener interferometry

Abstract

I present a simple algorithm based on a type of partial reverse-engineering that generates an unlimited number of exact analytical solutions to the Schrodinger equation for a general time-dependent two-level Hamiltonian. I demonstrate this method by deriving new exact solutions corresponding to fast control pulses that contain arbitrarily many tunable parameters. It is shown that the formalism is naturally suited to generating analytical control protocols that perform precise non-adiabatic rapid passage and Landau-Zener interferometry near the quantum speed limit. A general, exact formula for Landau-Zener interference patterns is derived.

6 pages, 4 figures, v2: PRA version

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• Geometric quantum speed limits: a case for Wigner phase space
• Control of charge migration in molecules by ultrashort laser pulses
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• Geometrical Formalism for Dynamically Corrected Gates in Multiqubit Systems
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• Robustness of error-suppressing entangling gates in cavity-coupled transmon qubits
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• Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid
• Analytically parameterized solutions for robust quantum control using smooth pulses
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• Transporting a single-spin qubit through a double quantum dot
• Pulse sequence designed for robust C-phase gates in SiMOS and Si/SiGe double quantum dots
• Noise-resistant Landau-Zener sweeps from geometrical curves
• Analytical results for a parity-time symmetric two-level system under synchronous combined modulations
• Winding up quantum spin helices: How avoided level crossings exile classical topological protection
• A double-slit proposal for quantum annealing
• Dynamical transitions in a modulated Landau-Zener model with finite driving fields
• Enhancing precision thermometry with nonlinear qubits
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• Floquet Engineering of Lie Algebraic Quantum Systems
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• Symmetry-protected Landau-Zener-Stückelberg-Majorana interference and non-adiabatic topological transport of edge states
• Exact magnetic field control of nitrogen-vacancy center spin for realizing fast quantum logic gates
• Experimental Demonstration of Swift Analytical Universal Control over Nearby Transitions
• Exact quantum dynamics for two-level systems with time-dependent driving
• Time-dependent Hamiltonian estimation for Doppler velocimetry of trapped ions
• Dynamics of observables and exactly solvable quantum problems: Using time-dependent density functional theory to control quantum systems
• Transition Probability for Class of Two Level System Time Dependent Hamiltonians
• Fast magnetic field manipulations and nonadiabatic geometric phases of nitrogen-vacancy center spin in diamond