The (q,t) -Fock space Fq,t(H) , introduced in this paper, is a deformation of the q-Fock space of Bożejko and Speicher. The corresponding creation and annihilation operators now satisfy the commutation relation aq,t(f)aq,t(g)⁎−qaq,t(g)⁎aq,t(f)=⟨f,g⟩HtN, Turn MathJax off a defining relation of the Chakrabarti–Jagannathan deformed quantum oscillator algebra. The moments of the deformed Gaussian element sq,t(h):=aq,t(h)+aq,t(h)⁎ are encoded by the joint statistics of crossings and nestings in pair partitions. The q=0<t specialization yields a natural single-parameter deformation of the full Boltzmann Fock space of free probability, with the corresponding semicircular measure variously encoded via the Rogers–Ramanujan continued fraction, the t-Airy function, the t-Catalan numbers of Carlitz–Riordan, and the first-order statistics of the reduced Wigner process.