arXiv subjects

Jesus Martinez-Linares

Publications and source records attributed to Jesus Martinez-Linares.

6 recordsLinked to original sources

arXiv2013

Phase Space Formulation of Population Dynamics in Ecology

A phase space theory for population dynamics in Ecology is presented. This theory applies for a certain class of dynamical systems, that will be called M-systems, for which a conserved quantity, the M-function, can be defined in phase space. This M-function is the generator of time displacements and contains all the dynamical information of the system. In this sense the M-function plays the role of the hamiltonian function for mechanical systems. In analogy with Hamilton theory we derive equations of motion as derivatives over the resource function in phase space. A M-bracket is defined which allows one to perform a geometrical approach in analogy to Poisson bracket of hamiltonian systems. We show that the equations of motion can be derived from a variational principle over a functional J of the trajectories. This functional plays for M-systems the same role than the action S for hamiltonian systems. Finally, three important systems in population dynamics, namely, Lotka-Volterra, self-feeding and logistic evolution, are shown to be M-systems.

q-bio.PE↗

arXiv2009

Purity Swapping in the Jaynes-Cummings Model: Obtaining Perfect Interference Patterns from Totally Unpolarized Qubits

We show the existence of dynamical purity swapping phenomena in the Jaynes-Cummings model. Moreover we show that purity swapping between a qubit and a generic quantum system is possible, provided they are coupled via non-unitary matrix elements interaction. We particularize to the case of a quantum optical Ramsey interferometer. We show that using purity swapping, a perfect interference pattern can be obtained at the output port of the interferometer even if we start from totally unpolarized sources. This feature is shown to be associated with the phenomena of recreation of the state vector at half of the revival time. In fact, we show that the Gea-Banacloche attractor is robust against degradation of the purity of the qubit input state. We also show that the Tsallis entropy T2 is a useful entanglement monotone allowing one to relate directly entanglement with purity exchange in interacting systems. We conjecture an Araki-Lieb type inequality for T2 that bounds the maximum interchange of purity between interacting systems.

quant-ph↗

arXiv2007

Hierarchy of inequalities for quantitative duality

We derive different relations quantifying duality in a generic two-way interferometer. These relations set different upper bounds to the visibility V of the fringes measured at the output port of the interferometer. A hierarchy of inequalities is presented which exhibits the influence of the availability to the experimenter of different sources of which-way information contributing to the total distinguishability D of the ways. For mixed states and unbalanced interferometers an inequality is derived, V^2+ Xi^2 \leq 1, which can be more stringent than the one associated with the distinguishability (V^2+ D^2 \leq 1).

quant-ph↗

arXiv2003

Duality in asymmetric Quantum optical Ramsey interferometers

A formalism have been recently derived [J. Martinez-Linares and D. Harmin, quantum-ph/0306057] allowing one to separate different sources of which-way information contributing to the total distinguishability D of the ways in a two-way interferometer. Here we apply the formalism to a Quantum Optical Ramsey Interferometer where both sources, the a-priori predictability of the ways P and the quantum "Quality" Q of the which-way detector, stems from the same physical interaction. We show that the formalism is able to separate both sources of which-way information. Moreover, it is shown that Q succeeds in quantifying the amount of quantum which-way information stored in the which-way detector even in cases where D does not.

quant-ph↗

arXiv2003

The Quantum Self-eraser

A scheme for an atomic beam quantum self-eraser is presented. The proposal is based on time reversal invariance on a quantum optical Ramsey fringes experiment, where a realization of complementarity for atomic coherence can be achieved. It consists of two high finesse resonators that are pumped and probed by the same atom. This property relates quantum erasing with time reversal symmetry, allowing for a full quantum erasing of the which-way information stored in the cavity fields. The outlined scheme also prepares and observes a non-local state in the fields of the resonators: a coherent superposition between correlated states of macroscopically separated quantum systems. The proposed scheme emphasizes the role of entanglement swapping in delayed-choice experiments. Finally, we show that the quantum self-eraser violates temporal Bell inequalities and analyze the relation between this violation and the erasability of which-way information.

quant-ph↗

arXiv2003

Quality of a Which-Way Detector

We introduce a measure Q of the "quality" of a quantum which-way detector, which characterizes its intrinsic ability to extract which-way information in an asymmetric two-way interferometer. The "quality" Q allows one to separate the contribution to the distinguishability of the ways arising from the quantum properties of the detector from the contribution stemming from a-priori which-way knowledge available to the experimenter, which can be quantified by a predictability parameter P. We provide an inequality relating these two sources of which-way information to the value of the fringe visibility displayed by the interferometer. We show that this inequality is an expression of duality, allowing one to trace the loss of coherence to the two reservoirs of which-way information represented by Q and P. Finally, we illustrate the formalism with the use of a quantum logic gate: the Symmetric Quanton-Detecton System (SQDS). The SQDS can be regarded as two qubits trying to acquire which way information about each other. The SQDS will provide an illustrating example of the reciprocal effects induced by duality between system and which-way detector.

quant-ph↗