Quantum carpets: a tool to observe decoherence

Abstract

Quantum carpets-the spatio-temporal de Broglie density profiles-woven by an atom or an electron in the near-field region of a diffraction grating bring to light, in real time, the decoherence of each individual component of the interference term of the Wigner function characteristic of superposition states. The proposed experiments are feasible with present-day technology.

Entanglement and analytical continuation: an intimate relation told by the Riemann zeta function

“…(19) for σ = 1/2 and n 0 = 10 giving rise via (32) to the Wigner matrix W | . As expected, the diagonal matrix element W | 1 2 ,τ 10 associated with the excited atomic state, given by (35) and depicted in the upper row, rotates clockwise around the origin, whereas W | 1 2 ,−τ n 0 , connected with the ground state and shown below, rotates counter-clockwise. As in the case of W |σ,τ shown in figures 1 and 2, the Wigner functions W |σ,τ n 0 and W |σ,−τ n 0 get blurred due to the different velocities of the individual photon number states.…”

“…Since the Wigner matrix is Hermitian, we find W |σ,−τ n 0 σ,τ | = W * |σ,τ n 0 σ,−τ | . In contrast to the diagonal elements W |σ,τ n 0 given by (35), both sums in (36) have timedependent phase factors. However, they simply act as complex scaling factors.…”

“…However, they simply act as complex scaling factors. Indeed, we add in the double sum the real parts of the unrotated Moyal functions {W |n−1 m−1| } whereas in W |σ,τ n 0 defined by (35) we sum over {e −iτ ln n m W |n−1 m−1| }, which corresponds to adding rotated Moyal functions. Therefore, the off-diagonal elements do not rotate in phase space and the symmetry in k is preserved for all times, that is…”

“…Furthermore, the initial off-diagonal elements are equal to the diagonal ones (35), W |σ,0 n 0 σ,0| = W |σ,0 n 0 , depicted in figure 3.…”

How to Observe Coherent Electron Dynamics Directly

“…In terms of the electronic state of the core, at 13 ps the population of the 2 P ∘ 1=2 core (channels 4-5) reaches a maximum of 75%, while the 2 P ∘ 3=2 core (channels 1-3) has a maximum population of 85% after 28 ps. Figure 3 shows the radial probability density as a function of time in a multichannel version of a quantum carpet [35]. The radial density has a distinct nodal structure, with the inner nodes in the 2 P ∘ 3=2 channels spaced by 15 au and the outer nodes spaced by 85 au.…”