We introduce quantum printing as the imprinting of photon and phonon quantum states onto quantum matter. Focusing on charged fluids and neutral systems, we show how structured light can create topological excitations such as superconducting vortices and magnetic skyrmions. We also discuss induced magnetization in quantum paraelectrics and Dirac materials, and outline future directions including entangled-state printing and light-driven quantum turbulence. This review expands on a shorter version submitted to Nature Physics. 

Using a generalized time-dependent Ginzburg–Landau model, we show that microwave radiation can induce p- and d-wave components in an initially pure s-wave centrosymmetric superconductor. New gradient terms couple the s-wave order parameter to other symmetry-allowed components: quadratic-derivative terms link singlet channels, while spin–orbit coupling allows linear-derivative singlet–triplet coupling. With minimal substitution, these terms couple the order parameters through the vector potential, generating p- and d-wave components. 

We present a new framework for controlling Higgs modes and vortex dynamics in superconductors with structured light. We predict a superconducting analog of the Kapitza–Dirac effect, where Higgs waves scatter from light-induced vortex lattices and form diffraction-like interference patterns. The vortices also allow linear coupling between the Higgs mode and the electromagnetic field, opening a new route to probe nonequilibrium superconductivity and manipulate collective modes through quantum printing. 

We report a light-driven non-equilibrium vortex Berezinskii-Kosterlitz-Thouless (BKT) transition in a superconductor. We use a time-dependent Ginzburg-Landau model to demonstrate vortex-antivortex deconfinement via light induced fields. The transformation occurs independently of thermal fluctuations and is viewed as a quantum phase transition. The resulting phase map mirrors QCD phase diagram, delineating confined, premelted, and fully deconfined vortex phases. The nature of these phases is discussed. Transitions between phases are governed by light induced depairing and phase fluctuations, establishing a new class of light-induced topological transitions. 

We report two light-induced orbital magnetization effects in quantum Hall fluids arising from their transverse response. Circularly polarized light produces a dominant inverse Faraday effect, while linearly polarized light generates an orbital inverse Cotton–Mouton effect that probes the fluid’s chiral orbital response. The induced magnetization is estimated to be about 0.5–10 Bohr magnetons per carrier in graphene and TMDs, and is accompanied by local density changes that enable optical quantum printing of density profiles. 

We show that inverse Faraday magnetization can be induced in Rydberg systems, including both atomic Rydberg states and shallow semiconductor dopants. Their large orbital size gives rise to strong angular momentum and large effective magnetic fields under circularly polarized light. We estimate fields of order microtesla in Rydberg atoms such as Rb and Cs, scaling strongly with principal quantum number, and fields up to about 10^2 T in phosphorus-doped silicon under intense driving. 

Structured light can induce a zero-bias superconducting diode response in films patterned with asymmetric holes. Using time-dependent Ginzburg–Landau simulations, we show that optical driving generates rectified photovoltages and directional supercurrent imbalance. The response is tunable through the optical mode, polarization, and device geometry, offering a route toward light-controlled superconducting transport.