Related papers: Engineering adiabaticity at an avoided crossing wi…
The analysis of traps, i.e., locally but not globally optimal controls, for quantum control systems has attracted a great interest in recent years. The central problem that has been remained open is to demonstrate for a given system either…
This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from the Pontryagin Maximum…
We study the simultaneous control of an ensemble of springs with different frequencies by means of adiabatic, shortcut to adiabaticity and optimal processes. The linearity of the system allows us to derive analytical expressions for the…
We control the current of a single particle quantum ratchet by designing ramping schemes for experimentally accessible control parameters. We harvest on Landau-Zener transitions between Floquet states. Adiabatic and diabatic ramping allow…
A remarkably simple result is derived for the minimal time $T_{\rm min}$ required to drive a general initial state to a final target state by a Landau-Zener type Hamiltonian or, equivalently, by time-dependent laser driving. The associated…
We numerically investigate the performance of atomic transport in optical microtraps via the so called spatial adiabatic passage technique. Our analysis is carried out by means of optimal control methods, which enable us to determine…
We analyze the problem of optimal adiabatic passage through a quantum critical point. We show that to minimize the number of defects the tuning parameter should be changed as a power-law in time. The optimal power is proportional to the…
We derive the theory of open quantum system dynamics intervened by a series of nonselective measurements. We analyze the cases of time independent and time dependent Hamiltonian dynamics in between the measurements and find the approximate…
High control in the preparation and manipulation of states is an experimental and theoretical important task in many quantum protocols. Shortcuts to adiabaticity methods allow to obtain desirable states of a adiabatic dynamics but in short…
The quantum harmonic oscillator with time-dependent frequency is a paradigmatic model of driven quantum dynamics and one of the few nontrivial systems that admits an exact analytical solution. In this review paper, we present a unified…
There is recently a surge of interest to cut down the time it takes to change the state of a quantum system adiabatically. We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes designed to…
When the level separation of a qubit is modulated periodically across an avoided crossing, tunneling to the excited state - and consequently Landau-Zener-St\"uckelberg interference - can occur. The types of modulation studied so far…
Adiabatic processes are important for studying the dynamics of a time-dependent system. Conventionally, the adiabatic processes can only be achieved by varying the system slowly. We speed up both classical and quantum adiabatic processes by…
Stimulated Raman Adiabatic Passage, a very efficient technique for manipulating a quantum system based on the adiabatic theorem, is analyzed in the case where the manipulated physical system is interacting with a spin bath. Exploitation of…
We propose a method to produce fast transitionless dynamics for finite-dimensional quantum systems without requiring additional Hamiltonian components not included in the initial control setup, remaining close to the true adiabatic path at…
We study a two-level transition probability for a finite number of avoided crossings with a small interaction. Landau-Zener formula, which gives the transition probability for one avoided crossing as $e^{-\pi\frac{\varepsilon^{2}}{h}}$,…
Many techniques in quantum control rely on frequency separation as a means for suppressing unwanted couplings. In its simplest form, the mechanism relies on the low bandwidth of control pulses of long duration. Here we perform a…
We compute Landau-Zener probabilities for 3-level systems with a linear sweep of the uncoupled energy levels of the 3$\times$3 Hamiltonian $H(t)$. Two symmetry classes of Hamiltonians are studied: For $H(t) \in$ su(2) (expressible as a…
We study Landau-Zener transitions in a dissipative environment by means of the quasiadiabatic propagator path-integral scheme. It allows to obtain numerically exact results for the full range of the involved parameters. We discover a…
Many complex quantum systems can be described by effectively nonlinear dynamics. While such dynamics have many appealing characteristics, they also make the analysis significantly more involved. This is due to the fact that only a few…