In complementary images of coordinate-space and momentum-space density in a trapped 2D Bose gas, we observe the emergence of presuperfluid behavior. As phase-space density ρ increases toward degenerate values, we observe a gradual divergence of the compressibility κ from the value predicted by a bare-atom model, κ ba . κ/κ ba grows to 1.7 before ρ reaches the value for which we observe the sudden emergence of a spike at p = 0 in momentum space. Momentum-space images are acquired by means of a 2D focusing technique. Our data represent the first observation of non-mean-field physics in the presuperfluid but degenerate 2D Bose gas.PACS numbers: 05.30. Jp, 67.10.Ba, Because of the enhanced role of fluctuations in lowdimensional systems [1], a two-dimensional (2D) Bose gas at nonzero temperature does not have long-range phase coherence. In a homogeneous system there can be at best only a quasicondensate, no true Bose-Einstein condensation (BEC). Under the combined effect of interactions and quantum degeneracy, however, there is nonetheless a phase transition known as Berezinskii-KosterlitzThouless (BKT) associated with the unbinding of vortex pairs [2]. Below the critical temperature T BKT , the system is superfluid.Experiments in 2D atomic gases [3][4][5][6] are usually conducted in the presence of an inhomogeneous trapping potential. In the complete absence of interactions, the confining potential can resurrect a traditional BEC [7], but for realistic experimental parameters, interatomic interactions tend to suppress BEC by smoothing out the spatial profile [3-6, 8, 9] of the mean density to the point where the sample can be understood as a collection of locally uniform spatial regions, each of which is characterized by a particular local density and thus a particular local value of T BKT . Although these local regions may be too small to test in detail the coherence-related predictions of BKT theory, qualitative effects have been observed in experiment [3,6].Our particular interest is in the region just to the warm side of T BKT . In an earlier experiment on bosons trapped in a 2D optical lattice, we observed a proliferation of vortices as we warmed through the discrete-case equivalent of T BKT [10]. But in that experiment a great many mesoscopic condensates were present, one at each lattice site, on both sides of the BKT transition, because they had condensed at a T BEC distinct from and well above T BKT . For the continuous case, in contrast, there is no corresponding second transition temperature above T BKT . But if the cooling gas has by T BKT already become a medium that can support vortices, whether bound or not, then heuristically we see that it must have continuously evolved from a fully fluctuating nondegenerate gas into a sort of presuperfluid with suppressed density fluctuations [11]. Theory [8,[11][12][13][14][15] validates this intuition, and experiments [5] have in turn been consistent with predictions of that theory. Up until now, however, experiments have not been directly sensitive to the proper...

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If quantum information processors are to fulfill their potential, the diverse errors that affect them must be understood and suppressed. But errors typically fluctuate over time, and the most widely used tools for characterizing them assume static error modes and rates. This mismatch can cause unheralded failures, misidentified error modes, and wasted experimental effort. Here, we demonstrate a spectral analysis technique for resolving time dependence in quantum processors. Our method is fast, simple, and statistically sound. It can be applied to time-series data from any quantum processor experiment. We use data from simulations and trapped-ion qubit experiments to show how our method can resolve time dependence when applied to popular characterization protocols, including randomized benchmarking, gate set tomography, and Ramsey spectroscopy. In the experiments, we detect instability and localize its source, implement drift control techniques to compensate for this instability, and then demonstrate that the instability has been suppressed.