Federico M. Pont

Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots

Resonance states of a two-electron quantum dots are studied using a variational expansion with both real basis-set functions and complex scaling methods. The two-electron entanglement (linear entropy) is calculated as a function of the electron repulsion at both sides of the critical value, where the ground (bound) state becomes a resonance (unbound) state. The linear entropy and fidelity and double orthogonality functions are compared as methods for the determination of the real part of the energy of a resonance. The complex linear entropy of a resonance state is introduced using complex scaling formalism.

Controlled energy-selected electron capture and release in double quantum dots

Highly accurate quantum electron dynamics calculations demonstrate that energy can be efficiently transferred between quantum dots. Specifically, in a double quantum dot an incoming electron is captured by one dot and the excess energy is transferred to the neighboring dot and used to remove an electron from this dot. This process is due to long-range electron correlation and shown to be operative at rather large distances between the dots. The efficiency of the process is greatly enhanced by preparing the double quantum dot such that the incoming electron is initially captured by a two-electron resonance state of the system. In contrast to atoms and molecules in nature, double quantum dots can be manipulated to achieve this enhancement. This mechanism leads to a surprisingly narrow distribution of the energy of the electron removed in the process which is explained by resonance theory. We argue that the process could be exploited in practice.

Electron-correlation driven capture and release in double quantum dots.

We recently predicted that the interatomic Coulombic electron capture (ICEC) process, a long-range electron correlation driven capture process, is achievable in gated double quantum dots (DQDs). In ICEC an incoming electron is captured by one quantum dot (QD) and the excess energy is used to remove an electron from the neighboring QD. In this work we present systematic full three-dimensional electron dynamics calculations in quasi-one dimensional model potentials that allow for a detailed understanding of the connection between the DQD geometry and the reaction probability for the ICEC process. We derive an effective one-dimensional approach and show that its results compare very well with those obtained using the full three-dimensional calculations. This approach substantially reduces the computation times. The investigation of the electronic structure for various DQD geometries for which the ICEC process can take place clarify the origin of its remarkably high probability in the presence of two-electron resonances.

Exact finite reduced density matrix and von Neumann entropy for the Calogero model

The information content of continuous quantum variables systems is usually studied using a number of well known approximation methods. The approximations are made to obtain the spectrum, eigenfunctions or the reduced density matrices that are essential to calculate the entropy-like quantities that quantify the information. Even in the sparse cases where the spectrum and eigenfunctions are exactly known the entanglement spectrum, {\em i.e.} the spectrum of the reduced density matrices that characterize the problem, must be obtained in an approximate fashion. In this work, we obtain analytically a finite representation of the reduced density matrices of the fundamental state of the N-particle Calogero model for a discrete set of values of the interaction parameter. As a consequence, the exact entanglement spectrum and von Neumann entropy is worked out.

Ground-state stability diagrams for two identical particles in an external potential

We study the stability of the ground state of a two-identical-particles system in an attractive external potential. We consider a repulsive interaction between the particles. The existence of a bounded ground state as a function of the strength of Hamiltonian parameters is studied for long- and short-range potentials. The possible scenarios of ionization are discussed. Criteria for the existence of a threshold-energy bound state and the energy critical exponent are given. In particular, we show that for the case of an attractive long-range external potential with short-range repulsive inter-particle interaction, a bound system can become unstable increasing the strength of the attractive potential.

The scaling of the density of states in systems with resonance states

Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. We present numerical evidence about the critical behavior of the density of states (DOS) in the region where there are resonances. The critical behavior is signaled by a strong dependence of some features of the DOS on the basis-set size used to calculate it. The resonance energy and lifetime are obtained using the scaling properties of the DOS.

Long- and short-range interaction footprints in entanglement entropies of two-particle Wigner molecules in 2D quantum traps

Abstract The occupancies and entropic entanglement measures for the ground state of two particles in a two-dimensional harmonic anisotropic trap are studied. We implement a method to study the large interaction strength limit for different short- and long-range interaction potentials that allows to obtain the exact entanglement spectrum and several entropies. We show that for long-range interactions, the von Neumann, min-entropy and the family of Renyi entropies remain finite for the anisotropic traps and diverge logarithmically for the isotropic traps. In the short-range interaction case the entanglement measures diverge for any anisotropic parameter due to the divergence of uncertainty in the momentum since for short-range interactions the relative position width vanishes. We also show that when the reduced density matrix has finite support the Renyi entropies present a non-analytical behavior.

Real stabilization of resonance states employing two parameters: basis-set size and coordinate scaling

The resonance states of one- and two-particle Hamiltonians are studied using variational expansions with real basis-set functions. The resonance energies, Er, and widths, ?, are calculated using the density of states and an golden rule-like formula. We present a recipe to select adequately some solutions of the variational problem. The set of approximate energies obtained shows a very regular behaviour with the basis-set size, N. Indeed, these particular variational eigenvalues show a quite simple scaling behaviour and convergence when N ? ?. Following the same prescription to choose particular solutions of the variational problem we obtain a set of approximate widths. Using the scaling function that characterizes the behaviour of the approximate energies as a guide, it is possible to find a very good approximation to the actual value of the resonance width.

Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model

The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heuns confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Renyi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Renyi entropy and entanglement spectrum for the whole parameter space.