Four-wave mixing enhanced white-light cavity

Abstract

We discuss in-medium propagation dynamics in a white light cavity that leads to an enhancement of the cavity's bandwidth without reducing its maximum intensity buildup. We analyze the spatiotemporal dynamics of our system with a full simulation of the field propagation in a regime that leads to strong absorption of the control fields. We find that an additional coherent field is generated within the medium via four-wave mixing. This self-generated field leads to a backaction of the medium onto the probe field. Counter intuitively, this pronounced in-medium dynamics throughout the propagation leads to an additional enhancement of the cavity bandwidth. PACS numbers: 42.65.Sf, 42.50.Nm, 42.60.Da, 04.80.Nn In an optical cavity, the bandwidth of supported frequencies and the intensity buildup are inversely proportional [1]. Increasing the cavity's finesse, e.g., via the reflectivity of the mirrors, leads to a higher buildup for a smaller range of frequencies and vice versa. The reason is that frequencies away from the cavity resonance correspond to different wavelengths which do not exactly fulfill the resonance condition. Thus, they acquire a phase shift with respect to the resonance frequency and experience loss at the mirrors. In terms of applications, this inverse dependence is a limiting factor for a number of schemes. Perhaps most prominently, gravitational wave detectors (GWD) aim at detecting tiny oscillations that ideally could be amplified by the power buildup in a high-quality cavity with large bandwidth [2]. To overcome this problem, the concept of a so-called white-light cavity (WLC) was developed [3]. Its basic idea is to employ a mechanism inside the cavity that cancels the phase shift for offresonant frequencies, thereby improving the bandwidth of a cavity without the drawback of reducing its maximum buildup. In the case of GWD one could increase sensitivity without restricting detection bandwidth.It may seem that the simplest implementation of a WLC would be to introduce a pair of plain parallel gratings such that their diffraction leads to a frequency dependent path length inside the cavity [4], which, however, is not feasible [5]. A grating causes a phase shift that depends on the position where the wave is diffracted. Since different frequencies are diffracted at different positions at one of the gratings, an additional frequency dependent phase shift occurs and prohibits canceling the frequency dependent phase shift in the cavity.A different implementation of WLC uses a medium with negative dispersion inside the cavity. In such a medium, phase shifts due to wavelength mismatch can be compensated by suitable phase shifts generated via a frequency-dependent index of refraction. Proposed systems include a strongly driven double-Λ system with incoherent pumping [3], a strongly driven two-level atomic resonance, and a Λ-system off-resonantly driven by two strong fields [6]. In the latter case, the negative disper-sion occurs between two gain lines. This has also been used in an experiment to demonst...

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