We present a novel framework demonstrating zero-shot sim-to-real transfer of visual control policies learned in a Neural Radiance Field (NeRF) environment for quadrotors to fly through racing gates. Robust transfer from simulation to real flight poses a major challenge, as standard simulators often lack sufficient visual fidelity. To address this, we construct a photorealistic simulation environment of quadrotor racing tracks, called FalconGym, which provides effectively unlimited synthetic images for training. Within FalconGym, we develop a pipelined approach for crossing gates that combines (i) a Neural Pose Estimator (NPE) coupled with a Kalman filter to reliably infer quadrotor poses from single-frame RGB images and IMU data, and (ii) a self-attention-based multi-modal controller that adaptively integrates visual features and pose estimation. This multi-modal design compensates for perception noise and intermittent gate visibility. We train this controller purely in FalconGym with imitation learning and deploy the resulting policy to real hardware with no additional fine-tuning. Simulation experiments on three distinct tracks (circle, U-turn and figure-8) demonstrate that our controller outperforms a vision-only state-of-the-art baseline in both success rate and gate-crossing accuracy. In 30 live hardware flights spanning three tracks and 120 gates, our controller achieves a 95.8% success rate and an average error of just 10 cm when flying through 38 cm-radius gates.