We develop a coherent control theory for multimode quantum light. It allows us to examine a fundamental problem in quantum optics: what is the optimal pulse form to drive a two-photon-transition? In formulating the question as a coherent control problem, we show that—and quantify how much—the strong frequency quantum correlations of entangled photons enhance the transition compared to shaped classical pulses. In ensembles of collectively driven two-level systems, such enhancement requires nonvanishing interactions.
We investigate how entanglement can enhance two-photon absorption in a three-level system. First, we employ the Schmidt decomposition to determine the entanglement properties of the optimal two-photon state to drive such a transition, and the maximum enhancement which can be achieved in comparison to the optimal classical pulse. We then adapt the optimization problem to realistic experimental constraints, where photon pairs from a down-conversion source are manipulated by local operations such as spatial light modulators. We derive optimal pulse shaping functions to enhance the absorption efficiency, and compare the maximal enhancement achievable by entanglement to the yield of optimally shaped, separable pulses.
We investigate optimal states of photon pairs to excite a target transition in a multilevel quantum system. With the help of coherent control theory for two-photon absorption with quantum light, we infer the maximal population achievable by optimal entangled vs separable states of light. Interference between excitation pathways as well as the presence of nearby states may hamper the selective excitation of a particular target state, but we show that quantum correlations can help to overcome this problem and enhance the achievable "selectivity" between two energy levels, i.e., the relative difference in population transferred into each of them. We find that the added value of optimal entangled states of light increases with broadening linewidths of the target states.
We propose a component-selective scheme for improving two-photon sources in a cavity-coupled two-atom system, where a single cavity mode interacts with two two-level atoms driven by phase-controlled classical fields of the same frequency. By controlling the atomic detunings and driving phase, the system can be tailored toward optimized cavity-field two-photon blockade or strongly correlated fluorescence photon-pair emission. When the two-cavity-photon component is enhanced, the cavity field exhibits optimized two-photon blockade with simultaneous suppression of unwanted one- and three-photon components at a comparable two-photon population. In another parameter regime, strongly correlated fluorescence photon pairs can also be generated from the two atoms by selecting the double-atomic-excitation component in the same two-excitation manifold. This approach provides a route toward high-quality and versatile two-photon sources, with potential applications in few-photon quantum optics and quantum information processing.
Analogous to Coulomb blockade for electrons, photon blockade is a key quantum optical effect in which the presence of one photon prevents the transmission of subsequent ones through a nonlinear medium. Beyond its fundamental interest, photon and multi-photon blockade are actively studied as mechanisms for generating technologically-relevant quantum states of light. Although photon blockade typically requires achieving strong light-matter coupling, increasing the number of atoms fails to enhance antibunching. Here, we analyze the optical transmission properties of a quantum resonator that embeds a two-photon-coupled ensemble of emitters, combining an approximate analytical approach with full quantum numerical simulations. We show that when light and matter are coupled via a two-photon interaction, both single- and multi-photon blockade can benefit from a collective enhancement. We propose different driving schemes in which the second or third-order correlation functions are strongly suppressed with increasing atom number. Differently from established methods, this collective enhancement of non-classical properties occurs with unitary transmission and is ultimately constrained only by decoherence. This demonstrates that collective two-photon couplings are a powerful mechanism for realizing photon blockade even in platforms where individual strong coupling is not achievable.
Wavefront shaping enables control of classical light through scattering media. Extending these techniques to spatially entangled photons promises new quantum applications, but their fundamental limits, especially when both photons scatter, remain unclear. Here, we theoretically and numerically investigate the enhancement of two-photon correlations through thick scattering media. We analyze configurations where a spatial light modulator shapes one or both photons, either before or after the medium, and show that the optimal enhancement differs fundamentally from classical expectations. For a system with
N modes, we show that shaping one photon yields the classical enhancement
η≈(π/4)N, while shaping both photons before the medium reduces it to
η≈(π/4)2N. However, in some symmetric detection schemes, when both photons are measured at the same mode, perfect correlations are restored with
η≈N, resembling digital optical phase conjugation. Conversely, shaping both photons after the medium leads to a complex, NP-hard-like optimization problem, yet achieves superior enhancements, up to
η≈4.6N. These results reveal unique quantum effects in complex media and identify strategies for quantum imaging and communication through scattering environments.