We discuss a novel method of efficiently producing multi-photon states using repeated spontaneous parametric downconversion. Specifically, by attempting downconversion several times, we can pseudo-deterministically add photons to a mode, producing various several-photon states. We discuss both expected performance and experimental limitations. [4]), reliably and deterministically creating even simple quantum optical states remains a challenge. For example, on-demand singlephoton production is still elusive, despite significant recent progress [5]. More complicated states can often be created probabilistically using single photons, linear optics, and feed-forward, but these schemes typically scale exponentially poorly with the number of photons in the state [6] or are prohibitively complicated [3]. In this letter, we propose a novel method using repeated spontaneous parametric downconversion to closely approximate applying the creation operator, allowing efficient pseudodeterministic preparation of a variety of states, with critical implications for applications including quantum computing and quantum metrology.Spontaneous parametric downconversion (a nonlinear optical process in which one high energy photon in a laser beam splits into a pair of lower energy photons, called the signal and idler) has for many years been the workhorse for producing high quality simple photon states, such as heralded single photons [7] and entangled photons. More recently, four-wave mixing (FWM) has been used to produce these states as well [8,9]. Downconversion has also been used to add a photon to a classical light field, with nonclassical results [10]. However, one of the drawbacks of these approaches is that they are nondeterministic, i.e., the number of pairs of photons that are produced is described by a random (thermal) distribution. One way to overcome this problem and produce single photons deterministically is to monitor the signal mode of several downconversion sources [11], or a single source pulsed at several times [12,13]; this allows one to herald the output of the idler mode without directly measuring it, and then select the source/pulse that produced the desired output. We propose modifying this technique to drive downconversion (or FWM) weakly in a cavity until we produce exactly one pair, thereby deterministically adding a photon to the idler mode. Repeating this process, we can "build up" a desired number state. Furthermore, by manipulating the polarization of the photon that is being added (or equivalently, manipulating the polarization of the pho-PBS DC PC1