We used atomic-layer molecular beam epitaxy to synthesize bilayers of a cuprate metal (La 1.55 Sr 0.45 CuO 4 ) and a cuprate insulator (La 2 CuO 4 ), in which each layer is just one unit cells thick. We have studied the magnetic field and temperature dependence of the complex sheet conductance, σ(ω), of these films. Experiments have been carried out at frequencies between 2-50 MHz using the single-spiral coil technique. We found that: (i) the inductive response starts at ∆T = 3 K lower temperatures than Re σ(T), which in turn is characterized by a peak close to the transition, (ii) this shift is almost constant with magnetic field up to 14 mT; (iii) ∆T increases sharply up to 4 K at larger fields and becomes constant up to 8 T; (iv) the vortex diffusion constant D(T) is not linear with T at low temperatures as in the case of free vortices, but is rather exponential due to pinning of vortex cores, and (v) the dynamic Berezinski-Kosterlitz-Thouless (BKT) transition temperature occurs at the point where Y = (l ω /ξ + ) 2 = 1. Our experimental results can be described well by the extended dynamic theory of the BKT transition and dynamics of bound vortex-antivortex pairs with short separation lengths. Ultrathin films of high-temperature superconductors have been studied intensely, with numerous attempts to observe the Berezinski-Kosterlitz-Thouless (BKT) transition [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. For example, a few unit-cell (UC) thick YBa 2 Cu 3 O 7-x (YBCO) films sandwiched between semiconducting or insulating layers have broader resistive transitions than thicker ones, which have been attributed to the BKT physics [4][5][6]. The same explanation was proposed for the observation of nonlinear current-versus-voltage (I-V) characteristics in YBCO, BiSrCaCuO, and TlBaCaCuO single crystals and thin films (see Ref. 7 and references therein). This has been a matter of substantial debate, though. For example, Repaci et al. [8] found the I-V characteristics to be ohmic even in 1 UC thick YBCO films at temperatures below the critical temperature (T c ), indicating the absence of the BKT transition. Subsequently, however, it was shown that at low currents the addition of current noise can turn nonlinear I-V curves into ohmic behavior [9]. Thus, it is easy to confuse nonlinear I-V tails generated by noise with non-ohmic tails expected from the BKT transition. Moreover, it was recently shown that the size effects may radically alter the I-V curves of superconducting films [10] so that they mimic the dc BKT behavior. Thus, it is important to understand that nonlinear I-V characterizes per se cannot prove the occurrence of the BKT transition; one needs to see a concurrent sharp drop in the superfluid density.Further, it was noted that a precondition [8] for the BKT transition to occur in a superconductor, i.e., that the sample size L s < λ eff , where λ eff = 2λ 2 /d is the effective (Pearl) penetration depth and d is the film thickness, is not satisfied even in 1 UC thick YBCO films [11]. N...