Geometric driving of two-level quantum systems

Abstract

We investigate a class of cyclic evolutions for %the cyclic evolution of driven two-level quantum systems (effective spin-1/2) with a particular focus on the geometric characteristics of the driving and their specific imprints on the quantum dynamics. By introducing the concept of geometric field curvature for any field trajectory in the parameter space we are able to unveil underlying patterns in the overall quantum behavior: the knowledge of the field curvature provides a non-standard and fresh access to the interrelation between field and spin trajectories, and the corresponding quantum phases acquired in non-adiabatic cyclic evolutions. In this context, we single out setups in which the driving field curvature can be employed to demonstrate a pure geometric control of the quantum phases. Furthermore, the driving field curvature can be naturally exploited to introduce the geometrical torque and derive a general expression for the total quantum phase acquired in a cycle. Remarkably, such relation allows to access the mechanisms controlling the changeover of the quantum phase across a topological transition and to disentangle the role of the spin and field topological windings. As for implementations, we discuss a series of physical systems and platforms to demonstrate how the geometric control of the quantum phases can be realized for pendular field drivings. This includes setups based on superconducting islands coupled to a Josephson junction and inversion asymmetric nanochannels with suitably tailored geometric shapes.

13 pages, 5 figures

References in corpus (28)

• Fault-tolerant quantum computation by anyons
• Dynamical Decoupling of Open Quantum Systems
• Noiseless Quantum Codes
• Holonomic Quantum Computation
• Geometric Manipulation of Trapped Ions for Quantum Computation
• Mach-Zehnder Interferometry in a Strongly Driven Superconducting Qubit
• Geometry and non-adiabatic response in quantum and classical systems
• Non-Abelian Berry connections for quantum computation
• Spin interference effects in ring conductors subject to Rashba coupling
• Semiconductor-based Geometrical Quantum Gates
• Holonomic quantum computation with neutral atoms
• Experimental realization of a ballistic spin interferometer based on the Rashba effect using a nanolithographically defined square loop array
• Quantum mechanics of a spin-orbit coupled electron constrained to a space curve
• Edge states and topological insulating phases generated by curving a nanowire with Rashba spin-orbit coupling
• Designing Electron Spin Textures and Spin Interferometers by Shape Deformations
• Geometric phases of mesoscopic spin in Bose-Einstein condensates
• Spin-orbit induced interference in polygon-structures
• Aharonov-Casher effect in Bi${}_2$Se${}_3$ square-ring interferometers
• Signatures of spin-related phases in transport through regular polygons
• Topological transitions in spin interferometers
• Inelastic Electron Tunneling Spectroscopy for Topological Insulators
• Superconductor-insulator transition driven by local dephasing
• A topological quantum pump in serpentine-shaped semiconducting narrow channels
• Geometry-assisted topological transitions in spin interferometry
• From an insulating to a superfluid pair-bond liquid
• Spin resonance under topological driving fields
• Driving Topological Phases by Spatially Inhomogeneous Pairing Centers
• Geometric vector potentials from non-adiabatic spin dynamics

Cited by in corpus (14)

• Doubly geometric quantum control
• Nodes and Spin Windings for Topological Transitions in Light-Matter Interactions: \\ Anisotropic Quantum Rabi Model as a Born Abstract Artist
• Robust topological feature against non-Hermiticity in Jaynes-Cummings Model
• Universal quantum Fisher information and simultaneous occurrence of Landau-class and topological-class transitions in non-Hermitian Jaynes-Cummings models
• Spin Winding and Topological Nature of Transitions in Jaynes-Cummings Model with Stark Non-linear Coupling
• Interface probe for antiferromagnets using geometric curvature
• Nonmonotonic quantum phase gathering in curved spintronic circuits
• Spin dynamics under the influence of elliptically rotating fields: Extracting the field topology from time-averaged quantities
• Spin-texture topology in curved circuits driven by spin-orbit interactions
• Exotic Quantum States in Spin-1 Bose-Einstein Condensate with Spin-Orbit Coupling in Concentric Annular Traps
• Higher order Magnus expansions for driven two-level quantum dynamics
• Parallel spin transport and holonomy in non-Euclidean curved circuits on a spherical two-dimensional electron gas
• A Kaleidoscope of Topological Structures in Dipolar Bose-Einstein Condensates with Weyl-Like Spin-Orbit Coupling in Anharmonic Trap
• Floquet quantum multiparameter estimation with periodic-driving-induced topological phase transition