Parametric resonances: from the Mathieu equation to QASER

Chen, Goong; Tian, Jing; Bin‐Mohsin, Bandar; Nessler, Reed; Svidzinsky, Anatoly A.; Scully, Marlan O.

doi:10.1088/0031-8949/91/7/073004

Cited by 8 publications

(7 citation statements)

References 20 publications

(22 reference statements)

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“…Also, coupled parametric oscillators has been shown to exhibit a variety of combination (i.e. frequency-mixing) resonances [18,19,87], closely connected to the interbranch processes discussed here.…”

Section: Frequency Mixing Of Vacuum Radiationmentioning

confidence: 71%

Vacuum radiation and frequency-mixing in linear light-matter systems

et al. 2019

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Recent progress in photonics has led to a renewed interest in time-varying media that change on timescales comparable to the optical wave oscillation time. However, these studies typically overlook the role of material dispersion that will necessarily imply a delayed temporal response or, stated alternatively, a memory effect. We investigate the influence of the medium memory on a specific effect, i.e. the excitation of quantum vacuum radiation due to the temporal modulation. We construct a framework which reduces the problem to single-particle quantum mechanics, which we then use to study the quantum vacuum radiation. We find that the delayed temporal response changes the vacuum emission properties drastically: frequencies mix, something typically associated with nonlinear processes, despite the system being completely linear. Indeed, this effect is related to the parametric resonances of the light-matter system, and to the parametric driving of the system by frequencies present locally in the drive but not in its spectrum.

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Section: Frequency Mixing Of Vacuum Radiationmentioning

confidence: 71%

Vacuum radiation and frequency-mixing in linear light-matter systems

et al. 2019

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“…The full Floquet analysis is given in Ref. [6]. When considering the evolution of the system for a short time or for small coupling constant δ, only the base component (n = 0) is important, resulting in (see Appendix A for more detail)α Eqs.…”

Section: Basic Model Of Qaser For Two Coupled Oscillatorsmentioning

confidence: 99%

“…The essence of QASER is coupling atomic superradiance and a combination parametric resonance to get exponential generation of X-rays. Surprisingly the QASER shares many aspects of two-coupled oscillators asymmetrically and parametrically driven by a lowfrequency field [4,6]. The asymmetry in the parametric coupling is especially interesting as in physics typically we deal with Hermitian couplings.…”

Section: Introductionmentioning

confidence: 99%

Hidden PT symmetry and quantization of a coupled-oscillator model of quantum amplification by superradiant emission of radiation

et al. 2017

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Using Maxwell-Bloch equations it has been shown how the superradiance can lead to amplification and gain at a frequency much larger than the pumping frequency. This remarkable effect has been examined in terms of a simpler model involving two coupled oscillators with one of them parametrically driven. We show that this coupled oscillator model has a hidden parity-time (PT) symmetry for QASER, we thus bring PT symmetry to the realm of parametrically coupled resonators. Moreover, we find that the QASER gain arises from the broken PT symmetry phase. We then quantize the simplified version of the QASER using quantum Langevin equations. The quantum description enables us to understand how the system starts from quantum fluctuations.

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“…On the one hand, the properties of these fundamental frequencies, as mentioned above, have been extensively studied in the case of particles motion in the different backgrounds [33][34][35][36][37][38][39][40][41][42][43] among many others. On the other hand, still there are open questions in this area.…”

Section: Introductionmentioning

confidence: 99%

Quasi-periodic oscillatory motion of particles orbiting a distorted deformed compact object

Faraji,

Trova

2021

Preprint

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This work explores the dynamic properties of test particles surrounding a distorted, deformed compact object. The astrophysical motivation was to choose such background, which could constitute a more reasonable model of a real situation that arises in the vicinity of compact objects with the possibility of having parameters as the extra physical degrees of freedom. This can facilitate associating observational data with astrophysical systems. This work's main goal is to study the dynamic regime of motion and quasi-periodic oscillation in this background, depending on different parameters of the system. Also, we exercise the resonant phenomena of the radial and vertical oscillations at their observed quasi-periodic oscillations frequency ratio of 3 : 2.

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Parametric resonances: from the Mathieu equation to QASER

Cited by 8 publications

References 20 publications

Vacuum radiation and frequency-mixing in linear light-matter systems

Vacuum radiation and frequency-mixing in linear light-matter systems

Hidden PT symmetry and quantization of a coupled-oscillator model of quantum amplification by superradiant emission of radiation

Quasi-periodic oscillatory motion of particles orbiting a distorted deformed compact object

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