Deriving minimum evolution times is of paramount importance in quantum mechanics. Bounds on the speed of evolution are given by the so called quantum speed limit (QSL). In this work we use quantum optimal control methods to study the QSL for driven m
any level systems which exhibit local two-level interactions in the form of avoided crossings (ACs). Remarkably, we find that optimal evolution times are proportionally smaller than those predicted by the well-known two-level case, even when the ACs are isolated. We show that the physical mechanism for such enhancement is due to non-trivial cooperative effects between the AC and other levels, which are dynamically induced by the shape of the optimized control field.
We study the interaction energy between two surfaces, one of them flat, the other describable as the composition of a small-amplitude corrugation and a slightly curved, smooth surface. The corrugation, represented by a spatially random variable, invo
lves Fourier wavelengths shorter than the (local) curvature radii of the smooth component of the surface. After averaging the interaction energy over the corrugation distribution, we obtain an expression which only depends on the smooth component. We then approximate that functional by means of a derivative expansion, calculating explicitly the leading and next-to-leading order terms in that approximation scheme. We analyze the resulting interplay between shape and roughness corrections for some specific corrugation models in the cases of electrostatic and Casimir interactions.
Quantum mechanics establishes a fundamental bound for the minimum evolution time between two states of a given system. Known as the quantum speed limit (QSL), it is a useful tool in the context of quantum control, where the speed of some control prot
ocol is usually intended to be as large as possible. While QSL expressions for time-independent hamiltonians have been well studied, the time-dependent regime has remained somewhat unexplored, albeit being usually the relevant problem to be compared with when studying systems controlled by external fields. In this paper we explore the relation between optimal times found in quantum control and the QSL bound, in the (relevant) time-dependent regime, by discussing the ubiquitous two-level Landau-Zener type hamiltonian.
We apply a perturbative approach to evaluate the Casimir energy for a massless real scalar field in 3+1 dimensions, subject to Dirichlet boundary conditions on two surfaces. One of the surfaces is assumed to be flat, while the other corresponds to a
small deformation, described by a single function $eta$, of a flat mirror. The perturbative expansion is carried out up to the fourth order in the deformation $eta$, and the results are applied to the calculation of the Casimir energy for corrugated mirrors in front of a plane. We also reconsider the proximity force approximation within the context of this expansion.
Unitary control and decoherence appear to be irreconcilable in quantum mechanics. When a quantum system interacts with an environment, control strategies usually fail due to decoherence. In this letter, we propose a time-optimal unitary control proto
col suitable for quantum open systems. The method is based on succesive diabatic and sudden switch transitions in the avoided crossings of the energy spectra of closed systems. We show that the speed of this control protocol meets the fundamental bounds imposed by the quantum speed limit, thus making this scheme ideal for application where decoherence needs to be avoided. We show that our method can achieve complex control strategies with high accuracy in quantum open systems.
Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications, the quant
um geometric phase was generalized to open systems. The definition takes a kinematical approach, with an initial state that is evolved cyclically but coupled to an environment --- leading to a correction of the geometric phase with respect to the uncoupled case. We obtain this correction by measuring the nonunitary evolution of the reduced density matrix of a spin one-half coupled to an environment. In particular, we consider a bath that can be tuned near a quantum phase transition, and demonstrate how the criticality information imprinted in the decoherence factor translates into the geometric phase. The experiments are done with a NMR quantum simulator, in which the critical environment is modeled using a one-qubit system.
