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Zhongguo kexue. Wulixue Lixue Tianwenxue

Superadiabatic evolution and robust energy conversion in sum frequency generation

Yonggang Xu, BaiHong LI, YongFang LI, Pingping Ma, Jie ZHANG, Haifei Zhu, Ruifang Dong, Shougang Zhang

Published Apr 1, 2015• 4 citations
Publisher

Abstract

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.

DOI
10.1360/sspma2014-00479

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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.
Based on the counter-diabatic protocol in quantum physics and the quasi-phase-matching method in nonlinear optics, we present a method of achieving robust energy transfer between the sum frequency and signal fields in an optical crystal system by adding a counter-diabatic field (CDF). Adding the CDF does not loosen the adiabatic condition, but rather separates the single original diabatic step into two so that the system remains adiabatic. The two resulting diabatic steps exhibit nonlinear tunneling, where the second step is the inverse of the first one. Moreover, we predict the fabrication of a nonlinear optical crystal with quasi-periodicity in terms of the CDF. Not only does this work provide a solid theoretical foundation for the design of nonlinear optical devices, but it also elucidates physical processes that can be applied in many areas of modern science, ranging from quantum information processing and coherent manipulation of quantum systems to high-precision measurements.
An analytical method is proposed in this paper to achieve complete energy conversion in sum frequency generation based on the Lewis-Riesenfeld invariants theory. In the proposed scheme, a quasi-adiabatic single control parameter model is established, and the value of single control parameter is selected to make the initial eigenstate perfectly converted to the final eigenstate as needed. Corresponding to the nonlinear frequency conversion process, a nonlinear crystal structure is designed by inverse engineering using the optimal control theory. It is robust against perturbations of the coupling coefficient and phase mismatch, including variations in the pump intensity and crystal polarization period, and achieves almost 100% conversion efficiency at any crystal length. Theoretical simulations show that frequency conversion can be achieved in the wavelength range of 2.6 µm-3.6 µm, and the spectral bandwidth of conversion efficiency exceeds 50% and approaches 400 nm when the crystal length L = 1 mm.
Abstract The method of adiabatic frequency conversion, in analogy with a two‐level atomic system, has been put forward recently and verified experimentally to achieve robust frequency mixing processes such as sum and difference frequency generation. Here a comparative study of efficient frequency mixing using various techniques of shortcuts to adiabaticity such as counter‐diabatic driving and invariant‐based inverse engineering is presented. It is shown here that it is possible to perform sum frequency generation by properly designing the poling structure of a periodically poled crystal and the coupling between the input lights and the crystal. The required crystal length for frequency conversion significantly decreases beyond the adiabatic limit. This approach significantly improves the robustness of the process against the variation in temperature as well as the signal frequency. By introducing a single parameter control technique with constant coupling and combining with the inverse engineering, perturbation theory, and optimal control, it is shown that the phase mismatch can be further optimized with respect to the fluctuations of input wavelength and crystal temperature that results into a novel experimentally realizable mixing scheme.
Based on the dressed state formalism, we obtain the adiabatic criterion of the sum frequency conversion. We show that this constraint restricts the energy conversion between the two dressed fields, which are superpositions of the signal field and the sum frequency field. We also show that the evolution of the populations of the dressed fields, which in turn describes the conversion of light photons from the seed frequency to the sum frequency during propagation through the nonlinear crystal. Take the quasiphased matched (QPM) scheme as an example, we calculate the expected bandwidth of the frequency conversion process, and its dependence on the length of the crystal. We demonstrate that the evolutionary patterns of the sum frequency field's energy are similar to the Fresnel diffraction of a light field. We finally show that the expected bandwidth can be also deduced from the evolution of the adiabaticity of the dressed fileds.
We discuss theoretically and demonstrate experimentally the robustness of the adiabatic sum frequency conversion method. This technique, borrowed from an analogous scheme of robust population transfer in atomic physics and nuclear magnetic resonance, enables the achievement of nearly full frequency conversion in a sum frequency generation process for a bandwidth up to two orders of magnitude wider than in conventional conversion schemes. We show that this scheme is robust to variations in the parameters of both the nonlinear crystal and of the incoming light. These include the crystal temperature, the frequency of the incoming field, the pump intensity, the crystal length and the angle of incidence. Also, we show that this extremely broad bandwidth can be tuned to higher or lower central wavelengths by changing either the pump frequency or the crystal temperature. The detailed study of the properties of this converter is done using the Landau-Zener theory dealing with the adiabatic transitions in two level systems.