Browsing by Author "Issoufa, Youssouf Hamidou"

In this study we investigate the effect of dephasing on the performance of the gen- eralized quantum rotation gates implemented by adiabatic passage and static laser pulses proposed in (X.Lacour et al, 2006). The adiabatic passage technique used in the thesis is a stimulated Raman adiabatic passage (STIRAP) which is robust and efficient tool to transfer population between the two lower levels of a three lambda system keeping the population in the excited level negligible. Since the excited level is not populated, the spontaneous emission has no effect on the evolution of the three-level system. However, dephasing caused by collisions or phase fluctuations of the pumped fields influence the evolution and becomes a big challenge when implementing quantum gates. For this reason we study the performance of the quantum gates in the presence of dephasing. Lastly, by applying the quantum jump approach, we show that in an open system the dephasing introduces complex geometrical phases which cannot be recompensated as in the closed system. Numerical solutions for the complex geometrical phases are obtained assuming realistic dephasing rates.

There has been a great interest in manipulating and controlling quantum systems, since Shor proposed an efficient quantum algorithm for factorizing integers into the product of prime numbers by demonstrating that quantum computer can perform interesting computations much faster than any classical computer. Since then different algorithm has been proposed, changing the Hamiltonian of a system in a continuous manner, resulting in a time-dependent Schrödinger equation has no exact solution. However, asymptotic methods provide a systematic approach to developing an approximate solution. The adiabatic theorem is one of these methods. It describes the evolution of a system when its Hamiltonian is a slowly varying function of time. More precisely, if a system starts in one of its eigenstates, it will follow adiabatically the initial eigenstate. The process of Stimulated Raman Adiabatic Passage (STIRAP) is based on this theorem. This process requires large Rabi frequencies, which is undesirable in many experimental applications. To overcome this problem a transition-less (super-adiabatic) STIRAP was proposed. The superadiabatic quantum driving, creating a best adiabatic transfer on the given Hamiltonian by introducing an additional Hamiltonian. Our starting position is the STIRAP, realized via Gaussian laser pulses. Conversely, it is well known that the interaction of a system with its surroundings leads to decoherence (open system). This decoherence has a negative impact on the manipulation of quantum systems. The robust population transfer depends strongly on the type of dissipative effects. These dissipative effects occur due to dephasing, spontaneous emission, and loss of population. The study determines the superadiabatic improvement for stimulated Raman adiabatic pas-sage. The fidelity and robustness of population’s transfers in three levels and four level systems are discussed. The study investigated the robustness of the three-level transition-less quantum driving. In the case when the excited state is barely populated during the evolution, its decay rate has little effect on the adiabatic population transfer. However, the dephasing which is due to collisions or phase fluctuations of the driving fields will produce a significant effect on the evolution. We found that the performance of the population transfer and the fidelity can be far below the quantum computation target even for small dephasing rates. The study also discusses the quantum rotation gates in tripod system. The study shows that Stimulated Raman Adiabatic Passage (STIRAP) requires high Rabi frequencies to have a perfect rotation gate. Moreover, we improve this process by using superadiabatic approach. This approach requires additional Hamiltonian that can be implemented by driving the tripod with additional fields. Furthermore, we show that it is robust to the decay of the excited state, but not to the dephasing caused by collisions or phase fluctuations of the driving fields..