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We systematically investigate the non-Hermitian generalisations of theLandau-Zener (LZ) transition and the Landau-Zener-St\"{u}ckelberg (LZS)interferometry. The LZ transition probabilities, or band populations, arecalculated for a generic non-Hermitian model and their asymptotic behaviouranalysed. We then focus on non-Hermitian systems with a real adiabaticparameter and study the LZS interferometry formed out of two identical avoidedlevel crossings. Four distinctive cases of interferometry are identified andthe analytic formulae for the transition probabilities are calculated for eachcase. The differences and similarities between the non-Hermitian case and itsHermitian counterpart are emphasised. In particular, the geometrical phaseoriginated from the sign change of the mass term at the two level crossings isstill present in the non-Hermitian system, indicating its robustness againstthe non-Hermiticity. We further apply our non-Hermitian LZS theory todescribing the Bloch oscillation in one-dimensional parity-time$(\mathcal{PT})$ reversal symmetric non-Hermitian Su-Schrieffer-Heeger modeland propose an experimental scheme to simulate such dynamics using photonicwaveguide arrays. The Landau-Zener transition, as well as the LZSinterferometry, can be visualised through the beam intensity profile and thetransition probabilitiess measured by the centre of mass of the profile.

Landau-Zener-St\"{u}ckelberg Interferometry in $\mathcal{PT}$-symmetric Non-Hermitian models