We measure atom number statistics after splitting a gas of ultracold 87 Rb atoms in a purely magnetic double-well potential created on an atom chip. Well below the critical temperature for Bose-Einstein condensation Tc, we observe reduced fluctuations down to −4.9 dB below the atom shot noise level. Fluctuations rise to more than +3.8 dB close to Tc, before reaching the shot noise level for higher temperatures. We use two-mode and classical field simulations to model these results. This allows us to confirm that the super-shot noise fluctuations directly originate from quantum statistics. Since the achievement of Bose-Einstein condensation (BEC) in dilute atomic gases, different experimental techniques have been developed in order to coherently split a BEC into two spatially separate parts [1][2][3][4], with atom interferometry as one of the motivations. Even though BECs are usually in the weakly interacting regime, the interactions between the particles dramatically affect the physics of the splitting. In particular, repulsive interactions limit the phase coherence between the two split parts [5], but also reduce atom number difference fluctuations, giving rise to non-classical squeezed states [6][7][8][9][10].In this Letter, we use a purely static magnetic potential created on an atom chip to realize a nonlinear spatial "beam" splitter for a BEC. We investigate the physics of the splitting and focus on atom number fluctuations and the role of temperature. At low temperatures, where the interaction energy dominates, we directly observe number squeezed states with relative population fluctuations −4.9 dB below shot noise, as first shown in [10] and indirectly observed in [8]. The two separated but weakly linked parts of the BEC constitute a bosonic Josephson junction, usually described by a two mode model (TMM) [11]. Our results are in agreement with the TMM, which also predicts that the observed squeezing is accompanied by high phase coherence.The magnetic trap configuration allows barrier heights up to several µK and straightforward evaporative cooling, so that we can separate clouds with increasing temperature all the way to the non-degenerate regime. In the intermediate temperature regime, where both a significant condensate and thermal fraction are present, we observe large super-binomial fluctuations in the number difference between the two parts. This excess of fluctuations is a direct signature of the Bose statistics, in close analogy to the bunching effect in quantum optics [16].Close to the BEC transition, the condensates show significant depletion and the TMM breaks down. We complement our experiments by a theoretical investigation of this regime using a classical field approach and show that large super-binomial fluctuations are a general feature at thermal equilibrium. Although the experiments are not performed at equilibrium, our observations are still in qualitative agreement with these theoretical results.Our experiment uses a two-layer atom chip to prepare a 87 Rb BEC in the |F = 2, m F = 2 hyp...

The generation of ultrashort pulses from quantum cascade lasers (QCLs) has proved to be challenging. It has been suggested that the ultrafast electron dynamics of these devices is the limiting factor for modelocking and hence pulse formation. Even so, clear modelocking of terahertz (THz) QCLs has been recently demonstrated but the exact mechanism for pulse generation is not fully understood. Here we demonstrate that the dominant factor necessary for active pulse generation is in fact the synchronization between the propagating electronic modulation and the generated THz pulse in the QCL. By using phase resolved detection of the electric field in QCLs embedded in metal-metal waveguides, we demonstrate that active modelocking requires the phase velocity of the microwave round trip modulation to equal the group velocity of the THz pulse. This allows the THz pulse to propagate in phase with the microwave modulation along the gain medium, permitting short pulse generation. Modelocking was performed on QCLs employing phonon depopulation active regions, permitting coherent detection of large gain bandwidths (500 GHz), and the generation of 11 ps pulses centered around 2.6 THz when the above 'phase-matching' condition is satisfied. This work brings an enhanced understanding of QCL modelocking and will permit new concepts to be explored to generate shorter and more intense pulses from mid-infrared, as well as THz, QCLs.

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