Study On Geometric Phase Based On Stimulated Raman Adiabatic Passage

About ten years ago, stimulated Raman adiabatic passage (STIRAP) has becomea coherent technique in terms of implementing complete population transfer betweentwo quantum states. One of the important features of this technique is adiabaticallyfollowing the evolution of the trapped state. So this technique is insensitive toradiative decay from the intermediate excited state and it has high selectivity and highefficiency. An extension of STIRAP is Fractional stimulated Raman adiabatic passage(F-STIRAP), which allows the creation of any preselected coherent superposition ofthe two ground states. Quantum entangled states and quantum superposition states canbe prepared though the two techniques. Besides, since Berry geometric phase wasproposed, geometric phase has been the focus of the research. Because geometricphase has topological and gauge invariant properties, it has important applications insuch diverse areas as mathematics, physics and chemistry, especially aboutpreparation of geometric phase gate with fault tolerant properties. Accumulatinggeometric phases based on STIRAP technique is a feasible scheme for attaininggeometric phase gates, which has been researched widely.Fig.1(a) represents schematic illustration of interacting system between the twoatoms with a three levels Ladder model, the pump pulse with Rabi frequenciesΩ pcouples energy level1and2, the stokes pulse with Rabi frequencies Ω scouples energy level2and r;(b) represents schematic illustration ofinteracting system between the two atoms with a three levels Lambda model, thepump pulse with Rabi frequenciesΩ pcouples energy level1and r, thestokes pulse with Rabi frequenciesΩ scouples energy level2and r; AndV (R)is a vdW potential of the interaction of two atomsOur main work is to study two kinds of atom system, interacting system betweenthe two atoms with a three levels Ladder model (Fig.1(a)) and interacting systembetween the two atoms with a three levels Lambda model (Fig.1(b)). Each atominteracts with pump pulse and Stokes pulse. For the two systems, we study andcompare population transfer though STIRAP technique and F-STIRAP technique, andgeometric phases accumulated based on two techniques (in the evolution of the darkstate). For each system, two atoms become quantum correlated and can not beseparated due to the dipole-dipole interaction related to Rydberg states. In this case,we can write down the two-body interaction Hamiltonian of two atoms, dark state andexpressions of the geometric phase in the evolution of the dark state. And then we uselight pulse mentioned above to solve analytic solution of the geometric phaseaccumulated based on both STIRAP and F-STIRAP, respectively. We find that theresult is consistent completely, when we simulate phases accumulated by numericalmethod and analytical method. Note that when all the parameters is same, phaseaccumulated based on F-STIRAP technique is more larger than that based on STIRAPtechnique for this two systems, about seven times, which is beneficial for attaininggeometric phase gates rapidly. Next, we propose two ways to prepare geometric phasegates, including two time-reversed STIRAP processes and two time-reversedF-STIRAP processes. We have known that the second way has the greater advantageof preparing geometric phase gates rapidly. However, laser pulses can not becontrolled well in F-STIRAP process, which is a barrier for preparing geometricphase gates. Besides, we still propose another way that uses a F-STIRAP process first,and uses a STIRAP process subsequently to prepare geometric phase gates, but laser pulses must be specially treated. Finally, in this paper, we explain the similarities anddifferences of two systems in three aspects which include the system itself, populationtransfer and geometric phases.