We report on the first experimental demonstration of superposition coded modulation (SCM) for polarization-multiplexed coherent-detection optical fiber links. The proposed coded modulation scheme is combined with phase-shifted bit-to-symbol mapping (PSM) in order to achieve geometric and passive shaping of the signal's waveform. The output constellations in SCM-PSM exhibit nonbijective quasi-Gaussian statistical distributions that asymptotically reach the Shannon capacity limit, showing up to 0.7 dB sensitivity improvement for 256-ary SCM-PSM with respect to 256-ary quadrature amplitude modulation (QAM). The characteristic wave formation based on superposition of antipodal symbols and the lack of need for additional encoders for signal shaping, greatly reduces the transmitter and receiver processing complexity in comparison to conventional alternatives. Single-level coding strategy (SL-SCM) is employed in the framework of bit-interleaved coded modulation with iterative decoding (BICM-ID) for forward error correction. The fiber transmission system is characterized in terms of signal-to-noise ratio for back-to-back case and correlated with simulated results for ideal transmission over additive white Gaussian noise channel. Thereafter, successful demodulation and decoding after dispersion-unmanaged transmission over 240-km standard single mode fiber of dual-polarization 6-Gbaud 16-, 32- and 64-ary SCM-PSM is experimentally demonstrated.