We studied the RF driven SQUID by a numeric simulation and experimentally. The amplitude and the phase of the RF voltage vs RF driving current and DC flux has been obtained both with the SQUID working in the conventional mode and in a new operating mode based on the 2nd harmonic generation in the system. A spectral analysis has been carried out and we report the characteristics of harmonic and subharmonic generation. For the even harmonic components, and in particular for the second one on which the proposed method is based, the VRFvs IRFstaircase pattern is replaced by a series of peaks. We find that the position of the peaks does not depend on the DC flux level and so they result in a stable marker for RF level measurements. The 2nd harmonic output, as a function of DC flux, shows a triangular behaviour with VRF= 0 at\phi_{DC} = n \phi_{0}/2. The dependence of VRFon φDCis at least as high as in the conventional operating mode. We have experimentally verified the harmonic generation and the half flux quantum periodicity up to the 4th harmonic. The signal amplitude was enough to allow flux-locked-loop operation.We studied the RF driven SQUID by a numeric simulation and experimentally. The amplitude and the phase of the RF voltage vs RF driving current and DC flux has been obtained both with the SQUID working in the conventional mode and in a new operating mode based on the 2nd harmonic generation in the system. A spectral analysis has been carried out and we report the characteristics of harmonic and subharmonic generation. For the even harmonic components, and in particular for the second one on which the proposed method is based, the VRFvs IRFstaircase pattern is replaced by a series of peaks. We find that the position of the peaks does not depend on the DC flux level and so they result in a stable marker for RF level measurements. The 2nd harmonic output, as a function of DC flux, shows a triangular behaviour with VRF= 0 at\phi_{DC} = n \phi_{0}/2. The dependence of VRFon φDCis at least as high as in the conventional operating mode. We have experimentally verified the harmonic generation and the half flux quantum periodicity up to the 4th harmonic. The signal amplitude was enough to allow flux-locked-loop operation.

IEEE Transactions on MagneticsJan 1, 19792 citations

Experimental Study of Josephson Junction 2nd-Harmonic Mixers at 70 GHz

Sadamu Kita, Kazuo Fujisawa

Josephson junction (JJ) harmonic mixers with even-harmonic numbers can operate at zero bias voltage. Among them, low harmonic ones are expected to have a good conversion efficiency. Hence, we have done experiments on the 2nd-harmonic mixer at 70 GHz. It is found that mixing behaviors are classified into three types: zero-bias, finite-bias and intermediate operation. It is also found that the conversion efficiency of the 2nd-harmonic mixer is not so much less than that of the fundamental mixer. We obtained a conversion gain of +1.5 dB with the 2nd-harmonic mixer, and +2.0 dB with the fundamental mixer.Josephson junction (JJ) harmonic mixers with even-harmonic numbers can operate at zero bias voltage. Among them, low harmonic ones are expected to have a good conversion efficiency. Hence, we have done experiments on the 2nd-harmonic mixer at 70 GHz. It is found that mixing behaviors are classified into three types: zero-bias, finite-bias and intermediate operation. It is also found that the conversion efficiency of the 2nd-harmonic mixer is not so much less than that of the fundamental mixer. We obtained a conversion gain of +1.5 dB with the 2nd-harmonic mixer, and +2.0 dB with the fundamental mixer.

Japanese Journal of Applied PhysicsJan 1, 19817 citations

Nonlinear quantum effects in second-harmonic generation

Daniel F. Walls, C. T. Tindle

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoOct 1, 197125 citations

Moderate-terahertz-induced plateau expansion of high-order harmonic generation to soft X-ray region

Doan-An Trieu, Duong D. Hoang-Trong, Cam-Tu Le +5 more

Extending the high-harmonic cutoff with experimentally accessible fields is essential for advancing tabletop coherent extreme ultraviolet (EUV) and soft X-ray sources. Although terahertz (THz) assistance offers a promising route, cutoff extension at weak, laboratory-accessible THz strengths remain poorly understood. In this report, we comprehensively investigate THz-assisted high-order harmonic generation (HHG) using time-dependent Schrödinger equation simulations supported by classical trajectory analysis and Bohmian-based quantum dynamics. By mapping the plateau evolution versus THz strength, we show that even weak THz fields can extend the cutoff, producing a pronounced ``fish-fin'' structure whose prominent rays saturate near $I_p + 8 U_p$ . We trace this extension to long electron excursions spanning several optical cycles before recombination, and provide a fully consistent explanation using both classical analysis and Bohmian trajectories flow. Our findings reveal that this cutoff-extension mechanism is remarkably robust, persisting across different atomic species and remaining insensitive to variations in the driving parameters. These results demonstrate that cutoff control is achievable with laboratory-scale THz fields, offering practical guidelines for engineering coherent high-energy HHG, and providing a robust pathway for tracking ultrafast electron motion in real time.Extending the high-harmonic cutoff with experimentally accessible fields is essential for advancing tabletop coherent extreme ultraviolet (EUV) and soft X-ray sources. Although terahertz (THz) assistance offers a promising route, cutoff extension at weak, laboratory-accessible THz strengths remain poorly understood. In this report, we comprehensively investigate THz-assisted high-order harmonic generation (HHG) using time-dependent Schrödinger equation simulations supported by classical trajectory analysis and Bohmian-based quantum dynamics. By mapping the plateau evolution versus THz strength, we show that even weak THz fields can extend the cutoff, producing a pronounced ``fish-fin'' structure whose prominent rays saturate near $I_p + 8 U_p$. We trace this extension to long electron excursions spanning several optical cycles before recombination, and provide a fully consistent explanation using both classical analysis and Bohmian trajectories flow. Our findings reveal that this cutoff-extension mechanism is remarkably robust, persisting across different atomic species and remaining insensitive to variations in the driving parameters. These results demonstrate that cutoff control is achievable with laboratory-scale THz fields, offering practical guidelines for engineering coherent high-energy HHG, and providing a robust pathway for tracking ultrafast electron motion in real time.

physics.opticsCross-listedarXiv:2601.16747Jan 26, 2026

I_p + 8 U_p

. We trace this extension to long electron excursions spanning several optical cycles before recombination, and provide a fully consistent explanation using both classical analysis and Bohmian trajectories flow. Our findings reveal that this cutoff-extension mechanism is remarkably robust, persisting across different atomic species and remaining insensitive to variations in the driving parameters. These results demonstrate that cutoff control is achievable with laboratory-scale THz fields, offering practical guidelines for engineering coherent high-energy HHG, and providing a robust pathway for tracking ultrafast electron motion in real time.