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We describe an easily implementable method for non-destructive measurements of ultracold atomic clouds based on dark field imaging of spatially resolved Faraday rotation. The signal-to-noise ratio is analyzed theoretically and, in the absence of experimental imperfections, the sensitivity limit is found to be identical to other conventional dispersive imaging techniques. The dependence on laser detuning, atomic density, and temperature is characterized in a detailed comparison with theory. Due to low destructiveness, spatially resolved images of the same cloud can be acquired up to 2000 times. The technique is applied to avoid the effect of shot-to-shot fluctuations in atom number calibration, to demonstrate single-run vector magnetic field imaging and single-run spatial imaging of the system's dynamic behavior. This demonstrates that the method is a useful tool for the characterization of static and dynamically changing properties of ultracold atomic clouds.

We prepare number stabilized ultracold atom clouds through the real-time analysis of non-destructive images and the application of feedback. In our experiments, the atom number N ∼ 10 6 is determined by high precision Faraday imaging with uncertainty ∆N below the shot noise level, i.e., ∆N < √ N . Based on this measurement, feedback is applied to reduce the atom number to a user-defined target, whereupon a second imaging series probes the number stabilized cloud. By this method, we show that the atom number in ultracold clouds can be prepared below the shot noise level.Over the past decade, experiments with ultracold atomic samples have matured from the proof-of-concept level to a development platform for technologies such as quantum sensors and quantum simulators. One rapidly expanding technique is the manipulation of quantum systems using measurements and feedback [1][2][3]. To limit the back-action, usually a 'weak' measurement is employed, such as detecting the phase shift induced by an atomic ensemble on an off-resonant laser beam [4]. Recent experiments have demonstrated feedback control of motion in an optical lattice [5], a quantum memory for light [6], deterministic spin squeezing [7], stabilization of an atomic system against decoherence [8], extending the interrogation time in Ramsey experiments [9] and feedback cooling of a spin ensemble [10].To fully exploit the potential of ultracold clouds in emerging quantum technologies, these atomic samples must be prepared with unprecedented precision. For instance, precise atom number preparation is crucial to improve the precision of atomic clocks, which is presently limited by collisional shifts [11]. It is of particular relevance for techniques that employ interactions to produce non-classical states for improved interferometric sensitivity [12][13][14][15]. In general, if the number fluctuations of an atomic ensemble in a single spatial mode can be suppressed, the many-particle state becomes non-classical, yielding a resource for atom interferometry beyond the standard quantum limit [16].Sub-Poissonian preparation of micro-and mesoscopic atomic samples was recently demonstrated by using single-site addressing in an optical lattice [17], 3-body collisions [18,19], non-destructive measurements of nanofiber-based systems [20], and careful tailoring of the trapping potential for fermionic [21] and bosonic systems [22]. However, despite initial attempts towards the compensation of number fluctuations in ultracold atomic clouds [23], the high precision preparation of large atom numbers remains an unsolved challenge.In this Letter, we stabilize the atom number in ultracold clouds through the real-time analysis of dispersive images and feedback, as shown in Fig. 1(a). After initial evaporative cooling of an atomic cloud, a first set of non-destructive Faraday images, "F1", determines the number of atoms. We characterize this imaging method and show it achieves an atom number uncertainty below the shot noise level. Based on the analysis of the images, feedback is ...

The coherent manipulation of wave packets is an important tool in many areas of physics. We demonstrate the experimental realization of quasifree wave packets of ultra-cold atoms bound by an external harmonic trap. The wave packets are produced by modulating the intensity of an optical lattice containing a Bose-Einstein condensate. The evolution of these wave packets is monitored in situ and their six-photon reflection at a band gap is observed. In direct analogy with pump-probe spectroscopy, a probe pulse allows for the resonant de-excitation of the wave packet into states localized around selected lattice sites at a long, controllable distance of more than 100 lattice sites from the main component. This precise control mechanism for ultra-cold atoms thus enables controlled quantum state preparation and splitting for quantum dynamics, metrology and simulation.