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Velocity gauge formulation of nonlinear optical response in Floquet quantum systems
by S. Sajad Dabiri, Reza Asgari
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Submission summary
| Authors (as registered SciPost users): | S. Sajad Dabiri |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202504_00016v2 (pdf) |
| Date accepted: | June 30, 2025 |
| Date submitted: | June 11, 2025, 11:50 p.m. |
| Submitted by: | Dabiri, S. Sajad |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Using the velocity gauge formalism, we develop a theoretical framework for computing the nonlinear optical responses of time-periodic quantum systems. This approach complements the length gauge formulation and offers distinct advantages in both numerical and analytical treatments, particularly for atomic and solid-state systems with well-defined momentum-space structures. By applying our framework to the Rabi model, we derive numerical solutions in the velocity gauge and compare them with the length gauge, demonstrating full agreement between the two formulations. Our findings reveal rich optical phenomena, including photon-assisted transitions, frequency mixing effects, and emergent Floquet-induced photocurrents that are absent in static systems. We demonstrate that nonlinear responses in Floquet-driven systems exhibit resonances at integer multiples of the driving frequency, providing insights into ultrafast spectroscopy and Floquet engineering of quantum materials. The present formulation establishes a bridge between theoretical models and experimental observations in driven quantum systems, with potential applications in quantum optics, photonics, and next-generation optoelectronic devices.
Author comments upon resubmission
We thank you for sending us the report from the referees. We also thank the referee for his\her positive evaluation of our manuscript. We would like to inform you that we have incorporated all the constructive suggestions and have replied to the comments, which have improved our manuscript.
List of changes
1 The figures are refreshed, showing better results in velocity gauge at low frequencies by using other replacement $\omega \rightarrow \sqrt{\omega(\omega+i\eta)}$ method according to the referee's reply. 2 It is proved that two Rabi Hamiltonians in different gauges yield the same optical conductivity. 3 We have shown how one can obtain sum-rules and, specifically, the linear response in the length gauge is derived from the velocity gauge formula. 4 We have shown how to avoid the derivative of the Bloch wave functions in calculations using sum rules. 5 Some points are added to the text according to the referee's suggestions for more clarity.
Published as SciPost Phys. Core 8, 049 (2025)
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