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Four snapshots of the time evolution of the quantum state during quantum control by a counter-rotating field.
Source publication
We develop a fully quantum-mechanical theory to describe
non-circular Trojan-like wavepackets. These correspond to nonlinear
resonances in Rydberg hydrogen dressed in a circularly polarized
microwave field. The theory is applied to describe adiabatic
quantum control of Rydberg states via the wavepackets. The
possibility of such quantum control is d...
Context in source publication
Context 1
... are the square modulus of the wavefunction and projections of the quantum state on the adjacent unperturbed (n, m)-states. Note that the quantum state controlled by the field is localized around the stable classical trajectory in the rotating frame, like that in figure 2. Figure 4 shows an example of quantum control via a counter-rotating field of σ − polarization. The initial state was n 0 = 20, m 0 = 15, which was the target state of the previous calculation. ...
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Citations
... These states are perfect test objects for studying the classical limit of atom. Their applications include control of Rydberg electron [1] and squeezing of electromagnetic field in a cavity [2]. Alongside with theoretical description [3], several approaches have been reported to provide formation of such packets by using different combinations of specially arranged external fields456789. ...
We present the results of numerical modelling of population dynamics in a hydrogen atom under the action of laser pulses of various duration, intensity and frequency. The possibility of formation of wave packets, including the states with high values of orbital and magnetic quantum numbers, via multiple transitions between the states of discrete and continuous spectrum under the action of the laser field is studied. The model is based on the expansion of the electron wave function over a large basis of hydrogen eigenstates of discrete and continuous spectrum. Ionization losses are taken into account by using a realistic model of the continuum. Partial localization of electron density in radial and angular variables is demonstrated. Most suitable conditions for wave packet formation are discussed for attainable lasers parameters.
... The development of new approaches to the localized wave packets production and the analysis of their properties are of interest for studying the correspondence principle in the classical limit of atom, for understanding the relation between the orbits of classically chaotic systems and the motion of a quantum wave packet, and for quantum control of the behavior of Rydberg electron [7]. ...
... The first sum in Eq (3) presents the discrete states, the second one includes the continuum states. (6) ), (1,3,5,7,9) are practically not populated. It can be explained by preservation of parity [13]. ...
We present the results of the research of population dynamics in a hydrogen atom driven by a ultra-short laser pulse. The possibil- ity to produce a wave packet of Rydberg states with high values of orbital and magnetic quantum numbers is studied numerically depending on the pulse duration and intensity. To describe the atom-field interaction three models were compared, namely, the one with discrete spec- trum states only, the one with resonance bound states and continuum, and the one with non-resonance discrete spectrum states having high values of orbital and magnetic quantum numbers also taken into account. The wave packet formation is simulated by direct numerical solu- tion of the Schrödinger equation using a large number of basis states both of discrete and continuous spectrum. The continuous spectrum is approximated by a large finite number of states separated by a small wavenumber interval. The role of continuum is shown to be principal in the population dynamics and the wave packed formation. Figs. 9. Ref.: 13 titles.
This festschrift, honoring Joe Eberly, notes the importance of surprises in physics and reviews particularly the contribution he has made to four of these: intense-field stabilization, collapse and revivals of Jaynes-Cummings oscillations, excitation using counterintuitive pulse sequences, and diffractionless laser beams. In each of these topics, as in others, conventional wisdom held views that were dramatically altered, even reversed, as experimental uses of laser light and advances in theoretical techniques presented unexpected results. Original Text
Nonperturbative numerical modeling of the excitation of the hydrogen atom from the ground state into Rydberg states by means of CW or pulsed laser radiation with linear or circular polarization is presented. Temporal population dynamics of Rydberg states is calculated. The results should be considered as preliminary, since the transitions to continuum and the relaxation processes have not been taken into account.
The results of numerical simulation of the Rydberg states laser excitation for the purpose of the forming of localized wave packets, are provided. The action of linear and circularly polarized fields upon an atom is considered for different time dependencies of the pulse envelope. The form and the properties of the obtained packet, constructed from eigen states with low orbital and magnetic quantum numbers have been analyzed. The obtained results are in agreement with the results provided by other authors.
We consider the quantum dynamics of the kicked rotor model in the regime where the last stable resonance islands in the classical phase space disappear. It is found that phase space regions with lower local diffusion rates are able to preserve quantum population. The low-diffusion regions can be moved through phase space in a quasi-adiabatic way by smoothly varying the parameters of the kicking field. With appropriately chosen time-scales for the variation of the field parameters, wave packets initially localized around the low-diffusion areas remain localized around these regions as the regions are moved. The wave packets can then be carried to desired regions of space despite the predominantly chaotic character of the classical phase space. We also comment on the Gong-Brumer scenario of coherent control of quantum chaotic diffusion [Phys. Rev. Lett. 86 1741 (2001)]. While our phase-space inspired control has a clear semiclassical interpretation, it appears that the Gong-Brumer control has a predominantly quantum origin. Furthermore, it is found that our control over wave packet localization disappears in the deeply chaotic regime, while the Gong-Brumer control over the chaotic diffusion persists in this regime but becomes increasingly unstable with increasing chaoticity.
We present the results of the research of population dynamics in a hydrogen atom driven by the ultra-short laser pulses. The possibility to produce a wave packet of Rydberg states with high values of orbital and magnetic quantum numbers is studied numerically depending on duration and shape of a pulse. The wave packet formation is simulated by direct numerical solution of the Schrodinger equation using a large number of basis states both of discrete and continuous spectrum. The continuous spectrum is approximated by a large finite number of states separated by a small wavenumber interval. The conditions of increasing of angular momentum and its projection in system are considered.
