International Journal of

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Considering a temperature dependent two-level quantum system, we have numerically solved the Landau-Zener transition problem. The method includes the incorporation of temperature effect as a thermal noise added Schrödinger equation for the construction of the Hamiltonian. Here, the obtained results which describe the changes in the system including the quantum states and the transition probabilities are investigated and discussed. The results successfully describe the behavior of the transition probabilities by sweeping the temperature.

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In this paper, we have proposed and demonstrated a new method of atomic population transfer. The transition dynamic of a two-level system is studied in a full quantum description of the Jaynes-Cummings model. Solving the time-dependent Schrödinger equation, we have investigated the transition probabilities numerically and analytically by using a sudden boost of the laser frequency. The results show that complete population transfer can be achieved by adjusting the time of the frequency boost.

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An approximate numerical method is proposed and discussed for solving the evolution of the spin density operator when the quantum system has an interaction with an external electromagnetic field. In this method by separating the relaxation and field interaction processes at small steps, instead of solving the conventional Liouville-von Neumann or Bloch differential equations, the time evolution of the density operator is efficiently obtained by a two-stage numerical algorithm. Here we have compared the results of this approach with Bloch equation results for a two-level quantum system. The proposed approach has potential applications in calculation of the time evolution for different atomic system including nuclear or electron spin resonance systems.

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Sub-Doppler dichroic atomic vapor laser lock (DAVLL) is a modulation-free laser stabilization method that combines DAVLL and saturated absorption spectroscopy (SAS). The performance of this highly sensitive stabilization technique strongly depends on the characteristics of the generated error signal. The slope of the error signal determines the lock sensitivity or how fast the frequency compensation could be made in the feedback loop, and the amplitude of the error signal determines the lock stability or how much noise the feedback loop can tolerate before laser unlocking. We have analytically modeled the error signal of the sub-Doppler DAVLL considering all possible transitions between Zeeman sublevels and compared it with the experimental results. Using the analytical and experimental results, it is shown that the values of the required magnetic fields for maximizing the slope and amplitude of the error signal are close to each other. Selecting the mentioned values of the magnetic field for optimization of the sub-Doppler DAVLL error signal is highly useful for sensitive and stable laser locking.