It has recently been indicated that the hexagonal manganites exhibit Higgs-and Goldstone-like phonon modes that modulate the amplitude and phase of their primary order parameter. Here, we describe a mechanism by which a silent Goldstone-like phonon mode can be coherently excited, which is based on nonlinear coupling to an infrared-active Higgs-like phonon mode. Using a combination of first-principles calculations and phenomenological modeling, we describe the coupled Higgs-Goldstone dynamics in response to the excitation with a terahertz pulse. Besides theoretically demonstrating coherent control of crystallographic Higgs and Goldstone excitations, we show that the previously inaccessible silent phonon modes can be excited coherently with this mechanism.Order parameters are physical observables that are used to quantify the different states of matter. Their amplitudes and phases can be excited by external stimuli, such as a laser pulse, leading to exotic states of matter that cannot be accessed in equilibrium [1]. Two particular excitations are Higgs and Goldstone modes, which correspond to the modulation of the amplitude and phase of an order parameter that breaks a continuous symmetry. Originally discussed in the context of particle physics [2] and superconductivity [3], Higgs and Goldstone excitations were found in cold atom systems, such as superfluids [4][5][6][7][8] or supersolids [9]. Higgs and Goldstone modes are well-studied in superconductors today [10][11][12][13][14][15][16][17][18][19][20][21], and similar manifestations have recently been reported in charge density wave (CDW) systems [22][23][24], antiferromagnets [25][26][27], and excitonic insulators [28]. It has been debated whether the optical and acoustic vibrational modes of solids can be considered Higgs and Goldstone excitations of the crystal lattice [29]. Several complex transition metal oxide compounds have shown signatures of optical Goldstone-like phonon modes that live in their symmetry-broken potential energy landscape [30][31][32][33][34].Coherent control over Raman-active phonons via impulsive stimulated Raman scattering using visible light pulses is well-established [35,36]. Recently, the excitation of infrared (IR)-active phonons with large amplitudes via IR absorption has become feasible through the development of high intensity terahertz and mid-IR sources. This progress has enabled selective control over the dynamics of the crystal lattice through nonlinear phonon interactions using ionic Raman scattering [37-39] and two-particle absorption mechanisms [40][41][42][43][44][45]. In contrast, phonon modes that do not respond to IR absorption or Raman scattering techniques, so called silent modes, can only be detected through hyper-Raman scattering. As hyper-Raman scattering is a third-order interaction of the electric field component of light with a * djuraschek@seas.harvard.edu † prineha@seas.harvard.edu phonon mode, it is inefficient and no coherent excitation has been achieved yet. Higgs and Goldstone modes, similar to silent p...