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arXiv:2207.01349 · Advanced Quantum Technologies

Efficient Broadband Frequency Conversion via Shortcuts to Adiabaticity

Koushik Paul, Qian Kong, Xi Chen

Published Oct 11, 2022• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1002/qute.202200076

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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.
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.
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.
Abstract Based on the Lewis-Riesenfeld (LR) invariant based inverse engineering for Shortcuts to adiabaticity (STA), we propose a cascaded frequency conversion technique. The technique maintains the same initial and final states as stimulated Raman adiabatic passage (STIRAP) but does not follow an adiabatic evolution during the intermediate processes. The results of numerical simulations show that the technique transfers the eigenstates from the initial state to the final state by designing an adiabatic evolutionary path, which is free to choose the length of the crystal within the crystal laser-induced damage threshold (LIDT), thus realizing a rapid adiabatic cascaded frequency conversion process with robustness under certain temperature variations and signal-laser wavelength variations.
Abstract The creation of efficient broadband frequency conversion devices while maintaining robustness to manufacturing and setup errors is crucial for accurate multiphoton spectroscopy, broadband imaging and the design of robust optical sources. Traditionally, nonlinear optical conversion processes are either efficient but narrowband or broadband but with low photon conversion yield. Several methods have been introduced in recent years to obtain both with great success, among them we can find adiabatic frequency conversion and Shaka–Pines composite segmented design. Here, we expand the composite design and introduce the detuning modulated composite segmented (DMCS) scheme in nonlinear optics, which offers a broadband, efficient and robust method for frequency conversion. We also present the constant-length DMCS scheme, which offers multiple efficient and robust wavelength regimes for broadband upconversion. We apply these schemes to a system of quasi-phase-matching crystal for the sum frequency generation process, and demonstrate the high robustness and bandwidth of the composite schemes. We show that these schemes are robust to temperature and crystal length variations and can have a superior conversion bandwidth under length and power constraints compared to other conversion schemes, such as periodically poled and adiabatic chirped crystals. We believe that the new family of DMCS schemes will have many uses in applications of frequency conversion, due to their robustness, low energy demand and compact size.
Two frequency-cascaded and spatially simultaneous three-wave-mixing processes, each pumped by a different frequency, are studied in a quasi-phase-matching crystal with chirped poling. Theory, numerical simulation, and experiment all show that efficient two-process adiabatic frequency conversion takes place over a broad range of input wavelengths. Experimentally, up to five process cascades are obtained. Furthermore, it is demonstrated that reversing the chirp sign results in a different conversion for the same input wavelength. This method can be applied to generation of an all-optically tunable frequency comb.
Abstract Nonlinear optical frequency conversion techniques enable the generation of new laser frequencies that are not directly accessible from laser sources. Lasers at different frequencies have distinct applications across various fields, including fiber-optic communication, medical imaging, material processing, display panel manufacturing, and biomolecular detection. We propose a theoretical model for four-process cascaded frequency conversion based on the chainwise stimulated Raman shortcut-to-adiabatic passage (C-STIRSAP) counter-diabatic (CD) driving technique. The model modifies the coupling functions of the chainwise stimulated Raman adiabatic passage (C-STIRAP) scheme by using the shortcuts to adiabaticity (STA) CD-driving method. Numerical simulation results demonstrate that the C-STIRSAP CD-driving technique allows efficient four-process frequency conversion over a wide range of delay and width parameters. Furthermore, it enhances the robustness of the process against variations in temperature and signal wavelength.