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Zhongguo kexue. Wulixue Lixue Tianwenxue

Rabi oscillation and Landau-Zener tunneling process of sum

Fukun Lin, Yantao Duan, HaiFei ZHU, Yonggang Xu, Lan An, Qianlan Lin, Yongfang Li

Published Aug 1, 2013• 2 citations
Publisher

Abstract

According to an analogy of the macroscopic phenomena to quantum physics, the physical mechanism that the sum frequency field intensity oscillate with the transmission distance, which is similar Rabi oscillation of the atom transition process in the two-level system, is explained with the interference theory. The energy transfer mechanism of the optics parametric conversion process is revealed from the points of Landau-Zener tunneling (LZT), and the producing process of sum frequency signal is showed detailedly with asymptotic, analytical solution.

DOI
10.1360/132013-7

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According to an analogy of the macroscopic phenomena to quantum physics, the physical mechanism that the sum frequency field intensity oscillate with the transmission distance, which is similar Rabi oscillation of the atom transition process in the two-level system, is explained with the interference theory. The energy transfer mechanism of the optics parametric conversion process is revealed from the points of Landau-Zener tunneling (LZT), and the producing process of sum frequency signal is showed detailedly with asymptotic, analytical solution.
Based on an analogy between the macroscopic phenomena and quantum physics, we study the problem of energy conversion for the sum frequency generation (SFG) process in a linear chirped quasi-phase-matched (QPM) crystal. We show that the process of energy conversion from the signal to the sum frequency field is very similar to the process of Landau-Zener tunneling (LZT) in a two-level system. Therefore, the energy conversion mechanism of SFG process can be explained by the theory of LZT. In addition, we obtain the asymptotic and analytical solution of the sum frequency field by solving the coupled equations with the model of Landau-Zener.
We investigate quantum interference effects in a superconducting Cooper-pair box by taking into account the possibility of tunneling processes involving one and two Cooper pairs. The quantum dynamics is analyzed in a framework of three-level model. We compute Landau–Zener probabilities for a linear sweep of the gate charge and investigate Rabi oscillations in a periodically driven three-level system under in- and off-resonance conditions. It was shown that the Landau–Zener probabilities reveal two different patterns: “step”- and “beats”-like behaviors associated with the quantum interference effects. Control on these two regimes is provided by the change of the ratio between two characteristic time scales of the problem. We demonstrate through the analysis of a periodically driven three-level system, that if a direct transition between certain pairs of levels is allowed and fine-tuned to a resonance, the problem is mapped to the two-level Rabi model. If the transition between a pair of levels is forbidden, the off-resonance Rabi oscillations involving second order in tunneling processes are predicted. This effect can be observed by measuring a population difference slowly varying in time between the states of the Cooper-pair box characterized by the same parity.
We investigate quantum interference effects in a superconducting Cooper-pair box by taking into account the \npossibility of tunneling processes involving one and two Cooper pairs. The quantum dynamics is analyzed in a \nframework of three-level model. We compute Landau–Zener probabilities for a linear sweep of the gate charge \nand investigate Rabi oscillations in a periodically driven three-level system under in- and off-resonance conditions. It was shown that the Landau–Zener probabilities reveal two different patterns: “step”- and “beats”-like \nbehaviors associated with the quantum interference effects. Control on these two regimes is provided by change \nof the ratio between two characteristic time scales of the problem. We demonstrate through the analysis of a periodically driven three-level system, that if a direct transition between certain pairs of levels is allowed and finetuned to a resonance, the problem is mapped to the two-level Rabi model. If the transition between pair of levels \nis forbidden, the off-resonance Rabi oscillations involving second order in tunneling processes are predicted. \nThis effect can be observed by measuring a population difference slowly varying in time between the states of \nthe Cooper-pair box characterized by the same parity
We investigate the many-body Landau-Zener (LZ) process in a two-site Bose-Hubbard model driven by a time-periodic field. We find that the driving field may induce sideband transitions in addition to the main LZ transitions. These photon-induced sideband transitions are a signature of the photon-assisted tunneling in our many-body LZ process. In the Rabi regime, where the system is dominated by the intermode coupling, the system can be looked as an ensemble of identical noninteracting single-particle LZ systems and the photon-induced sideband transitions are similar to the ones in single-particle LZ systems. In the Fock regime, where the system is dominated by the interparticle interaction, we develop an analytical theory for understanding the sideband transitions, which is confirmed by our numerical simulation. Furthermore, we discuss the quantization of the driving field. In the effective model of the quantized driving field, the sideband transitions can be understood as the LZ transitions between states of different ``photon'' numbers.
Based on the QPM technology and the counter diabatic compensation approach in quantum physics, we propose an optimal scheme that the signal field completely converts into the sum frequency field under the condition of the superadiabaticity. With the geometric rotation plane designed, we subtly reveals the physical mechanism of the systems before and after adding a counter diabatic term. The property of the energy conversion which is analogous to the elastic collision is explained for the addition counter diabatic compensation. With the help of Bloch vectors in atoms physics, we can clearly show the physics process of the complete energy conversion and the physical mechanism for the shortcuts of the superadiabaticity from a new perspective. This new scheme can optimize adiabatic process, shorten the coupling region and nonlinear crystal length, reduce the influence of the dispersion effect, and also implement the robust efficient energy conversion under the condition of relatively weak pump intensity. Not only does this scheme provide a good theoretical basis for the design of nonlinear optical devices, but also its physical thoughts can be widely used in many other fields.
Atomic media are important in optics research since they can be conveniently manipulated and controlled due to easy selection of atomic levels, laser fields, and the active adjustment of many system parameters. In this paper, we investigate optical Bloch oscillation, Zener tunneling, and Bloch–Zener oscillation in atomic media both theoretically and numerically. We use two coupling fields to prepare the dynamical optical lattice through interference. To induce a transverse force, we make the frequency difference between the two coupling fields increase linearly along the longitudinal coordinate. These phenomena have potential application for beam splitters and optical interconnects, and are helpful for investigating quantum analogies.