We present a systematic approach based on Bloch vectors treatment and the Magnus quantum electrodynamical formalism to study qubit manipulation by a train of pulses. These investigations include one of the basic processes involved in quantum computat
ion. The concrete calculations are performed for tunneling quantum dynamics, multiple resonance and off-resonance excitations of qubit driven by Gaussian pulses. In this way, the populations of qubit states due to multiple resonant interactions are investigated for various operational regimes including: single-pulse excitation, two-pulse excitation with phase shift between pulse envelopes being controlling parameter and for excitation with sequential pulses. In the last case, we demonstrate the formation of quasienergetic states and quasienergies of qubit driven by train of identical pulses. In this case the transition probability of qubit exhibits aperiodic oscillations, but also becomes periodically regular for definite values of the quasienergy.
Deflection of atoms in Lambda-type configuration passing through two crossed standing light waves is proposed for probing and visualization of atomic superposition states. For this goal, we use both the large-dispersive and Raman-resonant regimes of
atom-field interaction giving rise to a position-dependent phase shifts of fields and perform double simultaneous spatial measurements on an atom. In this way, it is demonstrated that the deflection spatial patterns of atoms in Lambda-configuration passing through modes of standing waves are essentially modified if the atoms are initially prepared in a coherent superposition of its low levels states as well as when the superposition states are created during the process of deflection. The similar results take place for the joint momentum distribution of atoms. Further, considering both one-photon and two-photon excitation regimes of Lambda-atoms we also illustrate that the two-dimensional patterns of defected atoms qualitatively reflects the efficiency of the Raman processes.
We analyze the dynamics of a superconducting qubit and the phenomenon of multiorder Rabi oscillations in the presence of a time-modulated external field. Such a field is also presented as a bichromatic field consisting of two spectral components, whi
ch are symmetrically detuned from the qubit resonance frequency. This approach leads to obtaining qualitative quantum effects beyond those for the case of monochromatic excitation of qubits. We calculate Floquet states and quasienergies of the composite system superconducting qubit plus time-modulated field for various resonant regimes. We analyze the dependence of quasienergies from the amplitude of an external field, demonstrating the zeros of difference between quasienergies. We show that, as a rule, populations of qubit states exhibit aperiodic oscillations, but we demonstrate the specific important regimes in which dynamics of populations becomes periodically regular.
