arXiv subjects

D. A. Wisniacki

Publications and source records attributed to D. A. Wisniacki.

At least 19 recordsLinked to original sources

arXiv2017

Driving-induced amplification of non-Markovianity in open quantum systems evolution

Non-Markovian effects arising in open quantum systems evolution have been a subject of increasing interest over the past decade. One of the most appealing features of non-Markovianity (NM) is that it captures scenarios where loss of information and coherence are reversible, and thus a temporary backflow of information from the environment to the system is possible. In this work we study the interplay between the degree of non-Markovianity and the action of time-dependent control fields in an open two-level quantum system. We find that periodical modulation of a field acting solely on the system can greatly enhance the degree of non-Markovianity with respect to the undriven case. We show that this effect is present only when the coupling between system and environment is weak. Remarkably, the enhancement disappears at strong coupling, which is usually the regime where non-Markovian effects are expected to be more pronounced.

quant-ph↗

arXiv2016

Optimal control of many-body quantum dynamics: chaos and complexity

Achieving full control of the time-evolution of a many-body quantum system is currently a major goal in physics. In this work we investigate the different ways in which the controllability of a quantum system can be influenced by its complexity, or even its chaotic properties. By using optimal control theory, we are able to derive the control fields necessary to drive various physical processes in a spin chain. Then, we study the spectral properties of such fields and how they relate to different aspects of the system complexity. We find that the spectral bandwidth of the fields is, quite generally, independent of the system dimension. Conversely, the spectral complexity of such fields does increase with the number of particles. Nevertheless, we find that the regular o chaotic nature of the system does not affect signficantly its controllability.

quant-ph↗

arXiv2015

Enhancement of quantum speed limit time due to cooperative effects in multilevel systems

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 many 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.

quant-ph↗

arXiv2015

Time-optimal control fields for quantum systems with multiple avoided crossings

We study time-optimal protocols for controlling quantum systems which show several avoided level crossings in their energy spectrum. The structure of the spectrum allows us to generate a robust guess which is time-optimal at each crossing. We correct the field applying optimal control techniques in order to find the minimal evolution or quantum speed limit (QSL) time. We investigate its dependence as a function of the system parameters and show that it gets proportionally smaller to the well-known two-level case as the dimension of the system increases. Working at the QSL, we study the control fields derived from the optimization procedure, and show that they present a very simple shape, which can be described by a few parameters. Based on this result, we propose a simple expression for the control field, and show that the full time-evolution of the control problem can be analytically solved.

quant-ph↗

arXiv2014

Maximum population transfer in a periodically driven two-level system

We study the dynamics of a two-level quantum system under the influence of sinusoidal driving in the intermediate frequency regime. Analyzing the Floquet quasienergy spectrum, we find combinations of the field parameters for which population transfer is optimal and takes place through a series of well defined steps of fixed duration. We also show how the corresponding evolution operator can be approximated at all times by a very simple analytical expression. We propose this model as being specially suitable for treating periodic driving at avoided crossings found in complex multi-level systems, and thus show a relevant application of our results to designing a control protocol in a realistic molecular model

quant-ph↗

arXiv2014

Comment on "Exploring chaos in the Dicke model using ground-state fidelity and the Loschmidt echo"

In [PRE \textbf{90}, 022920 (2014), arXiv:1404.6738] a study of the ground state fidelity of the Dicke model as a function of the coupling parameter is presented. Abrupt jumps of the fidelity in the superradiant phase are observed and are assumed to be related to the transition to chaos. We show that this conclusion results from a misinterpretation of the numerics. In fact, if the parity symmetry is taken into account, the unexpected jumps disappear.

quant-ph↗

arXiv2013

Quantum Speed Limit and optimal evolution time in a two-level system

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 protocol 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.

quant-ph↗

arXiv2013

Sensitivity to perturbations and quantum phase transitions

The local density of states or its Fourier transform, usually called fidelity amplitude, are important measures of quantum irreversibility due to imperfect evolution. In this Rapid Communication we study both quantities in a paradigmatic many body system, the Dicke Hamiltonian, where a single-mode bosonic field interacts with an ensemble of N two-level atoms. This model exhibits a quantum phase transition in the thermodynamic limit, while for finite instances the system undergoes a transition from quasi-integrability to quantum chaotic. We show that the width of the local density of states clearly points out the imprints of the transition from integrability to chaos but no trace remains of the quantum phase transition. The connection with the decay of the fidelity amplitude is also established.

quant-ph↗

arXiv2013

Controlling open quantum systems using fast transitions

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 protocol 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.

quant-ph↗

arXiv2012

Non-Markovian Quantum Dynamics and Classical Chaos

We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular, we remark on the deep relation of the short time non-Markovian behavior with the revivals of the average fidelity amplitude-a fundamental quantity used to measure sensitivity to perturbations and to identify quantum chaos. The long time behavior is established as a finite size effect which vanishes for large enough environments.

quant-ph↗

arXiv2012

Classical transients and the support of open quantum maps

The basic ingredients in a semiclassical theory are the classical invariant objects serving as a support for the quantization. Recent studies, mainly obtained on quantum maps, have led to the commonly accepted belief that it is the classical repeller -- the set of non escaping orbits in the future and past evolution -- the object that suitably plays this role in open scattering systems. In this paper we present numerical evidence warning that this may not always be the case. For this purpose we study recently introduced families of tribaker maps [L. Ermann, G.G. Carlo, J.M. Pedrosa, and M. Saraceno, Phys. Rev. E {\bf 85}, 066204 (2012)], which share the same asymptotic properties but differ in their short time behavior. We have found that although the eigenvalue distribution of the evolution operator of these maps follows the fractal Weyl law prediction, the theory of short periodic orbits for open maps fails to describe the resonance eigenfunctions of some of them. This is a strong indication that new elements must be included in the semiclassical description of open quantum systems.

quant-ph↗

arXiv2011

The Poincare-Birkhoff theorem in Quantum Mechanics

Quantum manifestations of the dynamics around resonant tori in perturbed Hamiltonian systems, dictated by the Poincaré--Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number of quanta equal to the order of the classical resonance. Moreover, the associated classical phase space structures are mimicked in the quasiprobability density functions and their zeros.

nlin.CD↗

arXiv2010

Discrepancies between decoherence and the Loschmidt echo

The Loschmidt echo and the purity are two quantities that can provide invaluable information about the evolution of a quantum system. While the Loschmidt echo characterizes instability and sensitivity to perturbations, purity measures the loss of coherence produced by an environment coupled to the system. For classically chaotic systems both quantities display a number of -- supposedly universal -- regimes that can lead on to think of them as equivalent quantities. We study the decay of the Loschmidt echo and the purity for systems with finite dimensional Hilbert space and present numerical evidence of some fundamental differences between them.

quant-ph↗

arXiv2009

Semiclassical Description of Wavepacket Revival

We test the ability of semiclassical theory to describe quantitatively the revival of quantum wavepackets --a long time phenomena-- in the one dimensional quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are considered: time-dependent WKB and Van Vleck propagation. We show that both approaches describe with impressive accuracy the autocorrelation function and wavefunction up to times longer than the revival time. Moreover, in the Van Vleck approach, we can show analytically that the range of agreement extends to arbitrary long times.

quant-ph↗

arXiv2009

A dynamical systems approach to Bohmian trajectories

Vortices are known to play a key role in the dynamics of the quantum trajectories defined within the framework of the de Broglie-Bohm formalism of quantum mechanics. It has been rigourously proved that the motion of a vortex in the associated velocity field can induce chaos in these trajectories, and numerical studies have explored the rich variety of behaviors that due to their influence can be observed. In this paper, we go one step further and show how the theory of dynamical systems can be used to construct a general and systematic classification of such dynamical behaviors. This should contribute to establish some firm grounds on which the studies on the intrinsic stochasticity of Bohm's quantum trajectories can be based. An application to the two dimensional isotropic harmonic oscillator is presented as an illustration.

quant-ph↗

arXiv2009

Coherent control of localization, entanglement, and state superpositions in a double quantum dot with two electrons

We have recently proposed a quantum control method based on the knowledge of the energy spectrum as a function of an external control parameter [Phys. Rev. Lett. {\bf 99}, 036806 (2007)]. So far, our method has been applied to connect the ground state to target states that were in all cases energy eigenstates. In this paper we extend that method in order to obtain more general target states, working, for concreteness, with a system of two interacting electrons confined in semiconductor double quantum wells. Namely, we have shown that the same basic method can be employed to obtain localization, entanglement, and general superpositions of eigenstates of the system.

cond-mat.mes-hall↗

arXiv2008

Landau-Zener transitions in a semiconductor quantum dot

We study the transitions between neighboring energy levels in a quasi-one-dimensional semiconductor quantum dot with two interacting electrons in it, when it is subject to a linearly time-dependent electric field. We analyze the applicability of simple two-level Landau-Zener model to describe the evolution of the probability amplitudes in this realistic system. We show that the Landau-Zener model works very well when it is viewed in the adibatic basis, but it is not as robust in the diabatic basis.

cond-mat.str-el↗

arXiv2007

The scar mechanism revisited

Unstable periodic orbits are known to originate scars on some eigenfunctions of classically chaotic systems through recurrences causing that some part of an initial distribution of quantum probability in its vicinity returns periodically close to the initial point. In the energy domain, these recurrences are seen to accumulate quantum density along the orbit by a constructive interference mechanism when the appropriate quantization (on the action of the scarring orbit) is fulfilled. Other quantized phase space circuits, such as those defined by homoclinic tori, are also important in the coherent transport of quantum density in chaotic systems. The relationship of this secondary quantum transport mechanism with the standard mechanism for scarring is here discussed and analyzed.

nlin.CD↗