Population dynamics in a quantum level-band-level system

Mavundla Lwandile Cedrick

Aikaterini Mandilara, Daniil A. Fedotov, V. M. Akulin

Many quantum algorithms can be seen as a transition from a well-defined initial quantum state of a complex quantum system, to an unknown target quantum state, corresponding to a certain eigenvalue either of the Hamiltonian or of a transition operator. Often such a target state corresponds to the minimum energy of a band of states. In this context, approximate quantum calculations imply transition not to the single, minimum energy, state but to a group of states close to the minimum. We consider dynamics and the result of two possible realization of such a process -- transition of population from a single initially populated isolated level to the quantum states at the edge of a band of levels. The first case deals with the time-independent Hamiltonian, while the other with a moving isolated level. We demonstrate that the energy width of the population energy distribution over the band is mainly dictated by the time-energy uncertainty principle, although the specific shape of the distribution depends on the particular setting. We consider the role of the statistics of the coupling matrix elements between the isolated level and the band levels. We have chosen the multiphoton Raman absorption by an ensemble of Rydberg atoms as the model for our analysis, although the results obtained can equally be applied to other quantum computing platforms.

Thomas Müller, Wolfgang Parz, Rudolf Bratschitsch +2 more

Xing Rong, Xie Shuang-Yuan, Xu Jing-Ping +1 more

The spontaneous emission from a V-type three-level atom embedded in an isotropic photonic crystal with dynamic photonic band edge is studied. We consider the situation where the atom interacts with all possible radiation modes, and calculate numerically the evolution of atomic population without using Markov approximation. The calculation method can be used in related researches. In the present paper, we mainly discuss the effects of modulation parameters and the quantum interference on spontaneous emission when the band edge is modulated with step function or triangle function. We hope that the results can contribute to the applications in the dynamic photonic crystal environment in controlling the spontaneous emission via the quantum interference. The results show that in the step-modulated situation, the number of the photon-atom bound dressed states after the modulation has happened depends on atomic transition frequencies and the band edge frequency at that time, and is identical to the one in the unmodulated situation with the same parameters. The long-time evolution of the atomic population is affected by the time when the modulation happens. Depending on the system initial state, after the modulation has happened, the quantum interference can weaken the probability amplitude components corresponding to the photon-atom bound dressed states, and cause the upper-level population to decay quickly from a great value to a value near zero; or on the contrary, it can strengthen the bound dressed states, and make the upper levels retain a high population. In the modulated situation with trigonometric functions, after long enough time, the total upper-level population presents a decaying quasi-periodic oscillation behaviour. And the evolution of the total upper-level population tends to synchronize with the modulation, so the frequency of the quasi-periodic oscillation is approximately equal to the modulation frequency. But, the quantum interference can destroy the synchronization under some conditions. The decay rate of the total upper-level population is affected by the modulation frequency, and also by the initial state of the system and the angle between two dipole moment because of the quantum interference.

M. Kira, S. W. Koch

Xing Rong, Xie Shuang-Yuan, Xu Jing-Ping +1 more

The spontaneous emission of a two-level atom, located in an isotropic photonic crystal with dynamically modulated photonic band edge, has been studied. When the photonic band edge is modulated with step functions or triangle functions, the evolution of atomic population on the upper level has been discussed. When the photonic band edge is modulated with step functions, the dynamics of atomic population depends not only on the detuning value of the atomic transition frequency from the band edge, but also on the time point of stepping. With the different time point of stepping, the dynamics of atomic population after stepping is different. When the photonic band edge is modulated with triangle functions, the atomic population oscillates quasi-periodically while decaying in general. The oscillation frequency, peak and valley values, and the decaying rate of oscillation can be modulated by choosing the frequency and initial phase of triangle functions.