We present a method to engineer the frequency splitting of polarization eigenmodes in fiber Fabry-Perot (FFP) cavities. Using specific patterns of multiple CO laser pulses, we machine paraboloidal micromirrors with controlled elliptical shape in a large range of radii of curvature. This method is versatile and can be used to produce cavities with maximized or near-zero polarization mode splitting. In addition, we realize dual-wavelength FFP cavities with finesse exceeding 40 000 at 780 nm and at 1559 nm in the telecom range. We provide direct evidence that the birefringent frequency splitting in FFP cavities is governed only by the geometrical shape of the mirrors, and that the astigmatism of the cavity modes needs to be taken into account for specific cavities.

We present an active feedback scheme acting continuously on the state of a quantum gas dispersively coupled to a high-finesse optical cavity. The quantum gas is subject to a transverse pump laser field inducing a self-organization phase transition, where the gas acquires a density modulation and photons are scattered into the resonator. Photons leaking from the cavity allow for a real-time and non-destructive readout of the system. We stabilize the mean intra-cavity photon number through a micro-processor controlled feedback architecture acting on the intensity of the transverse pump field. The feedback scheme can keep the mean intra-cavity photon number n ph constant, in a range between n ph =0.17(4) and n ph =27.6(5), and for up to 4 s. Thus we can engage the stabilization in a regime where the system is very close to criticality as well as deep in the self-organized phase. The presented scheme allows us to approach the self-organization phase transition in a highly controlled manner and is a first step on the path towards the realization of many-body phases driven by tailored feedback mechanisms.

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We describe a method to map the standing-wave pattern inside an open-access Fabry–Perot optical cavity with sub-wavelength resolution by perturbing it with a commercially available tapered fiber. The method is applied to a fiber Fabry–Perot microcavity. We demonstrate its use in determining the relative position of the antinodes at two different wavelengths. In addition, we use the tapered optical fiber as a point-like source, allowing precise positioning of a microscope objective with respect to the cavity mode.