Two-electron entanglement in elliptically deformed quantum dots

Abstract

Entropic entanglement measures of a two-dimensional system of two Coulombically interacting particles confined in an anisotropic harmonic potential are discussed in dependence on the anisotropy and the interaction strength. The harmonic approximation appears exact in the strong interaction limit, allowing determination of the asymptotic expression for the linear entropy. Entanglement properties are dramatically influenced by the anisotropy of the confining potential in the strong-correlation regime.

The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems

“…Because the interaction |x| −d (d > 0) diverges when x → 0, the ground-state even wavefunction φ (+) of (31) The occupancies and their natural orbitals are determined by the following integral eigenequation ∞ −∞ ρ(x, y)v s (y)dy = λ s v s (x), which can be turned into an algebraic problem by discretizing the variables x and y with equal subintervals of length ∆y (see, for example, [14]). Thus, the eigenvalues of the matrix B = [∆yρ(m i , m j )] K×K , where m i = −c+ △yi, △y = 2c/(K − 1), i, j = 0, ..., K − 1, provide approximations to the K largest occupancies.…”

“…In particular, a few attempts have been made recently towards understanding the entanglement in systems of interacting particles. For example, some light has been shed on entanglement both in quantum dot systems [6][7][8][9][10][11][12][13][14][15] and in systems of harmonically interacting particles in a harmonic trap (the so-called Moshinsky atom) [16][17][18][19][20][21][22][23]. Special attention has also been paid to the study of entanglement in the helium atoms and helium ions [24][25][26][27][28][29][30][31][32].…”

“…For example, when d = 1 the system serves as a prototype for ions in electromagnetic traps and when d = 3, as a model of confined dipolar particles. Here we address mainly the limit as g → ∞ in which the perfect linear Wigner molecule is formed [35][36][37], and the harmonic approximation (HA) is valid [11,14,38,39]. Recently, within the framework of this approximation, we have derived when N = 3 and d = 1 an explicit integral representation for the asymptotic occupancies and their natural orbitals [11].…”

Quantum Entanglement of Two Harmonically Trapped Dipolar Particles

“…The above function is nothing else but a TG wavefunction, which means that the 1D dipolar bosons form a TG gas in the weak interaction regime. We have determined the value of the vN entropy associated with ψ g→0 B by calculating the occupancies numerically through a discretization technique (see, for example, Kościk and Okopińska [29]). The value obtained by us S g→0 B ≈ 0.9851 agrees well with that reported in [32] (0.984).…”

“…Particularly the research activity has expanded towards investigating the entanglement properties in various systems composed of interacting particles. For instance, the recent studies include model systems such as the Moshinsky atom [17][18][19][20][21][22], helium atoms and helium-like atoms [23][24][25][26], quantum dot systems [27][28][29][30], and 1D systems of atoms interacting via a short-range contact interaction [31][32][33]. For details concerning the recent progress in entanglement studies of quantum composite systems, see [34].…”