Karen Fonseca | Universidad Nacional de Colombia (National University of Colombia) (original) (raw)

Papers by Karen Fonseca

We set up a semiclassical approximation which helps us clarify by means of several simple example... more We set up a semiclassical approximation which helps us clarify by means of several simple examples the rich variety of time scale in the quantum domain. The underlying structure of quantum and classical mechanics is so completly different that it is naive to expect to reach a classical regime by counting powers of the quantum scale ប. We show although it is possible to define a time scale for nonclassical phenomena, but it is impossible to characterize quantum dynamics through a unique time scale, such as Ehrenfest's time. We use simple systems to critically discuss and illustrate these features of the quantum-classical limit.

The effects of dissipation on a system composed by two quantum-dot qubits interacting with a sing... more The effects of dissipation on a system composed by two quantum-dot qubits interacting with a single mode of light in a microcavity are studied by computing the time evolution of mixedness and entanglement of the qubits and the second order correlation function of the field.

Physica Scripta 86, 065004 , 2012

Journal of Physics A-mathematical and Theoretical, Jan 1, 2009

We investigate the quantum-classical border, the entanglement and decoherence of an analytically ... more We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, comprising a first subsystem (a harmonic oscillator) coupled to a driven and damped second subsystem (another harmonic oscillator). We choose initial states whose dynamics is confined to a couple of two-level systems, and show that the maximum value of entanglement between the two subsystems, as measured by concurrence, depends on the dissipation rate to the coupling-constant ratio and the initial state. While in a related model the entropy of the first subsystem (a two-level system) never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model. the cavity), conserves its purity and suffers a unitary rotation inside the cavity-exactly as if it were controlled by a classical driving field-without entangling with the electromagnetic field. This unexpected behavior was analyzed in [1] employing several short-time approximations, and it was found that in the time needed to rotate the atom, its state remains almost pure.

Consideramos algunos estados particulares de dos sistemas continuos acoplados, para los cuales ti... more Consideramos algunos estados particulares de dos sistemas continuos acoplados, para los cuales tiene sentido el uso de la concurrencia como un cuantificador del enredamiento, y mostramos que existe una conexión accidental entre la distribución de probabilidad de la fase relativa de su función de Husimi y su concurrencia. Mostramos además un sistema cuántico abierto donde se pueden producir tales estados. Por lo tanto, la medición de la función de Husimi permite la cuantificación de la concurrencia para esos estados particulares.

We show that two-atom correlation measurements of the type involved in a recent experimental stud... more We show that two-atom correlation measurements of the type involved in a recent experimental study of the evolution of a mesoscopic superposition state prepared in a definite mode of a high-Q cavity can be used to determine the eigenvalues of the reduced density matrix of the field, provided the assumed dynamical conditions are actually fulfilled to experimental accuracy. These conditions involve ͑i͒ a purely dispersive coupling of the field to the Rydberg atoms used to manipulate and to monitor the cavity field, and ͑ii͒ the effective absence of correlations in the ground state of the system consisting of the cavity coupled to the ''reservoir'' which accounts for the decoherence and damping processes. A microscopic calculation at zero temperature is performed and compared to master equation results.

We consider the spin 1 2 model coupled to a slowly varying magnetic ÿeld in the presence of a wea... more We consider the spin 1 2 model coupled to a slowly varying magnetic ÿeld in the presence of a weak damping represented by a Lindblad-form operators. We show that Berry's geometrical phase remains unaltered by the two dissipation mechanism considered. Dissipation e ects are twofold: a shrinking in the modulus of the Bloch's vector, which characterizes coherence loss and a time-dependent (dissipation related) precession angle. We show that the line broadening of the Fourier transformation of the components of magnetization is only due to the presence of dissipation.

We study and compare the information loss of a large class of Gaussian bipartite systems. It incl... more We study and compare the information loss of a large class of Gaussian bipartite systems. It includes the usual Caldeira-Leggett-type model as well as Anosov models (parametric oscillators, the inverted oscillator environment, etc), which exhibit instability, one of the most important characteristics of chaotic systems. We establish a rigorous connection between the quantum Lyapunov exponents and coherence loss, and show that in the case of unstable environments coherence loss is completely determined by the upper quantum Lyapunov exponent, a behavior which is more universal than that of the Caldeira-Leggetttype model.

Los nanotubos de Nitruro de Boro, BN, son semiconductores con una amplia brecha prohibida en toda... more Los nanotubos de Nitruro de Boro, BN, son semiconductores con una amplia brecha prohibida en todas sus configuraciones. El BN bidimensional y el grafeno poseen redes similares, con la misma estructura hexagonal. Sin embargo, los parámetros de red del nitruro de boro y el carbono son 0.250 nm y 0.245 nm respectivamente, una diferencia de red del orden de 2 %. Estas características sugieren la integración de nanotubos BN y C e impulsa el estudio de los efectos en las propiedades electrónicas al dopar con carbono los nanotubos BN. Nuestros resultados muestran que la brecha prohibida de los nanotubos BN dopados con carbono depende de la geometría de los nanotubos y posee un comportamiento semi-lineal con la concentración de carbono tanto para nanotubos tipo brazo de silla como zigzag.

We study the adiabatic limit in the density matrix approach for a quantum system coupled to a wea... more We study the adiabatic limit in the density matrix approach for a quantum system coupled to a weakly dissipative medium. The energy spectrum of the quantum model is supposed to be non-degenerate. In the absence of dissipation, the geometric phases for periodic Hamiltonians obtained previously by Berry are recovered in the present approach. We determine the necessary condition satisÿed by the coe cients of the linear expansion of the non-unitary part of the Liouvillian in order that the imaginary phases acquired by the elements of the density matrix, due to dissipative e ects, be geometric. The results derived are model independent. We apply them to spin 1 2 model coupled to reservoir at thermodynamic equilibrium.

In Ramsey atomic interferometry, a superposition of atomic states is produced by a mechanism comp... more In Ramsey atomic interferometry, a superposition of atomic states is produced by a mechanism completely equivalent (for experimental purposes) to interaction with a classical field. Since this property holds, in the case of Rydberg atoms, for temperatures close to absolute zero and field intensities of the order of a single photon, the question arises as to why the quantum nature of the field can be neglected. We model the passage of an atom through a Ramsey zone and show that, in order to explain the phenomenon, correlation properties between three subsystems and strong cavity dissipation turn out to be the essential physical ingredients leading to classical behavior. [S0031-9007(99)09302-3] PACS numbers: 39.20. + q, 42.50.Lc Microwave cavities are extensively used in experiments designed to access fundamental issues concerning the interaction of atoms and electromagnetic field modes in the context of cavity quantum electrodynamics [1]. In Ramsey atomic interferometry [2], in particular, they are known to generate quantum superpositions of atomic states as if the field inside them were of a classical nature. Two cavities separated by an intermediate region are filled with fields oscillating with phase coherence so that atomic transition probability amplitudes undergo quantum superpositions observed as interference (Ramsey) fringes. When this situation holds for temperatures close to absolute zero and field intensities of the order of a single photon, one may ask to what extent the quantum nature of the field can be neglected and how can this be theoretically modeled from basic quantum theory.

We show that it is possible to quantify the information content of a nonautonomous free field sta... more We show that it is possible to quantify the information content of a nonautonomous free field state in curved space-time. A covariance matrix is defined and it is shown that, for symmetric Gaussian field states, the matrix is connected to the entropy of the state. This connection is maintained throughout a quadratic nonautonomous (including possible phase transitions) evolution. Although particle-antiparticle correlations are dynamically generated, the evolution is isoentropic. If the current standard cosmological model for the inflationary period is correct, in absence of decoherence such correlations will be preserved, and could potentially lead to observable effects, allowing for a test of the model.

We study the influence of the preparation of an open quantum system on its reduced time evolution... more We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system density matrix and a bath density matrix the time evolution generally is no longer governed by a linear map nor is this map affine. Put differently, the evolution is truly nonlinear and cannot be cast into the form of a linear map plus a term that is independent of the initial density matrix of the open quantum system. As a consequence, the inhomogeneity that emerges in formally exact generalized master equations is in fact a nonlinear term that vanishes for a factorizing initial state. The general results are elucidated with the example of two interacting spins prepared at thermal equilibrium with one spin subjected to an external field. The second spin represents the environment. The field allows the preparation of mixed density matrices of the first spin that can be represented as a convex combination of two limiting pure states, i.e., the preparable reduced density matrices make up a convex set. Moreover, the map from these reduced density matrices onto the corresponding density matrices of the total system is affine only for vanishing coupling between the spins. In general, the set of the accessible total density matrices is nonconvex.

We analytically exploit the two-mode Gaussian states nonunitary dynamics. We show that in the zer... more We analytically exploit the two-mode Gaussian states nonunitary dynamics. We show that in the zero temperature limit, entanglement sudden death (ESD) will always occur for symmetric states (where initial single-mode compression is z 0 ) provided that the two mode squeezing r 0 satisfies 0 o r 0 o 1 2 logðcoshð2z 0 ÞÞ. We also give the analytical expressions for the time of ESD. Finally, we show the relation between the single modes initial impurities and the initial entanglement, where we exhibit that the latter is suppressed by the former. (L.A.M. Souza). Please cite this article as: L.A.M. Souza, et al., Mixedness and entanglement for two-mode Gaussian states, Optics Communications (2012), http://dx.

We propose a simple model for a cavity in a 1D photonic band gap material. It is shown that the e... more We propose a simple model for a cavity in a 1D photonic band gap material. It is shown that the exact dynamics contains three real functions of time, implicitly defined through an integrodifferential equation, all of them experimentally accessible. Several initial conditions are analyzed: (generalized) coherent states at finite temperature and Schro È dinger cat states at zero temperature. We use the simplest energy momentum relation which allows for a band gap and show that the perturbative solution of the integrodifferential equation presents non-Markovian features.

We consider the problem of carrying an initial Bloch vector to a final Bloch vector in a specifie... more We consider the problem of carrying an initial Bloch vector to a final Bloch vector in a specified amount of time under the action of three control fields (a vector control field). We show that this control problem is solvable and therefore it is possible to optimize the control. We choose the physically motivated criteria of minimum energy expended in the control, minimum magnitude of the rate of change of the control and a combination of both. We find exact analytical solutions, determine the fields for a general one-qubit gate, and use the Y gate as an example. We argue that in the case of less than three controls, only the physical intuition does not provide a straight reasonable solution, and solve the problem in the case of a unique control minimizing the energy consumption.

Physica Scripta 86, 065004 , 2012

Journal of Physics A-mathematical and Theoretical, Jan 1, 2009