We reveal the existence of a large in-plane heavy-hole $g$ factor in symmetric self-assembled (001) (In,Ga)As/GaAs quantum dots due to the warping of valence-band states. This warping dominates over the well-established mechanism associated with a reduced symmetry of the quantum dots and the corresponding mixing of heavy-hole and light-hole states. The effect of band warping is manifested in a unique angular dependence of the trion photon echo signal on the direction of the external magnetic field with respect to the sample axes. It results in a uniform magnetic-field-induced optical anisotropy for the entire quantum dot ensemble which is a prerequisite for the realization of spin quantum memories and spin-photon entanglement in the ensemble.

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• Magnetic anisotropy
• Optical generation of spin carriers
• Spintronics
• Trions
• Quantum dots
• Semiconductor microcavities
• Density matrix methods
• Four-wave mixing
• Homodyne & heterodyne detection
• Luttinger–Kohn model
• Symmetries in condensed matter