The solid grey lines show solutions of the Schrödinger equation for several random instances of the interaction disorder (see text), the black line is the average over these instances. Extended Data Fig. 4 Experimental imperfections. a, b, Sweep shape for the average Rabi frequency Ω (a) ...
For Rydberg states, the dipole matrix is calculated by solving the Schrodinger equation for Hatom using the Numerov method. We used the Python library from reference61 to calculate the dipole matrix for each state m. Details are given in Supplementary section III....
The structure is observed for pulse durations as short as 100 fs with indications of residual structure for even shorter pulse excitation. The production mechanism is discussed and the Rydberg states are modeled by analytically solving the Schrödinger equation with a simple jelliumlike potential for...
We have calculated the vibrational states of the first (1)Sigma(u)(+) state by numerically solving the one-dimensional Schrodinger equation using the Numerov method. The Rydberg state situated at the shallow local minimum in the first (1)Sigma(u)(+) potential curve possesses a single ...
In solving the multi-channel equation, I got the analytical expression of the multi-channel wave functions in terms of the solutions of the corresponding homogeneous equations. The homogeneous solutions are described in WKB Wenzel (1926 Z. Phys. 38 518) representation for both open and closed cha...
Quantum computers, which use the best algorithms currently known, offer the possibility of solving certain computational tasks much more effectively than any classical counterpart [1–5]. This has inspired a great deal of searches for building scalable and functional quantum computers over the past tw...
We have calculated the vibrational states of the first 1 Σ u + state by numerically solving the one-dimensional Schrdinger equation using the Numerov method. The Rydberg state situated at the shallow local minimum in the first 1 Σ u + potential curve possesses a single vibrational level, ...
By numerically solving the time-dependent Schrdinger equation, we found that for the superposition state with the optimal Rydberg state, not only is the harmonic efficiency enhanced significantly, but also the width of the continuous spectrum is extended. The ionization probability and the time-...
Analytical solutions can be obtained by solving the Schrodinger equation containing V(r). The parameters in the potential and the wavefunction, which are dependent on the atomic states, can be expressed in terms of a single parameter, the quantum defect. The wavefunctions of the alkali atoms ...
We present numerically accurate calculations of the bound-state spectrum of the highly excited valence electron in the heavy alkali-metal atoms solving the radial Schrodinger eigenvalue problem with a modern spectral collocation method that applies also for a large principal quantum number n >> 1. ...