Quantum probes are atomic-sized devices mapping information of their environment to quantum mechanical states. By improving measurements and at the same time minimizing perturbation of the environment, they form a central asset for quantum technologies. We realize spin-based quantum probes by immersing individual Cs atoms into an ultracold Rb bath. Controlling inelastic spin-exchange processes between probe and bath allows mapping motional and thermal information onto quantum-spin states. We show that the steady-state spin-population is well suited for absolute thermometry, reducing temperature measurements to detection of quantum spin distributions. Moreover, we find that the information gain per inelastic collision can be maximized by accessing the nonequilibrium spin dynamic. The sensitivity of nonequilibrium quantum probing effectively beats the steady-state Cramér Rao limit of quantum probing by almost an order of magnitude, while reducing the perturbation of the bath to only three quanta of angular momentum. Our work paves the way for local probing of quantum systems at the Heisenberg limit, and moreover for optimizing measurement strategies via control of nonequilibrium dynamics.
We report on the single-atom-resolved measurement of the distribution of momentahk in a weaklyinteracting Bose gas after a 330 ms time-of-flight. We investigate it for various temperatures and clearly separate two contributions to the depletion of the condensate by their k-dependence. The first one is the thermal depletion. The second contribution falls off as k −4 , and its magnitude increases with the in-trap condensate density as predicted by the Bogoliubov theory at zero temperature. These observations suggest associating it with the quantum depletion. How this contribution can survive the expansion of the released interacting condensate is an intriguing open question.In quantum systems, intriguing many-body phenomena emerge from the interplay between quantum fluctuations and interactions. Quantum depletion is an emblematic example of such an effect, occurring in one of the simplest many-body systems: a gas of interacting bosons at zero temperature. In the absence of interactions, the ground state corresponds to all particles occupying the same single-particle state. Taking into account inter-particle repulsive interactions at the meanfield level leads to a similar solution where all particles are condensed in the same one-particle state whose shape is determined by the trapping potential and interactions. In a beyond mean-field approach, which can be interpreted as taking into account quantum fluctuations and twobody interactions, the description is dramatically different. The many-body ground state consists of several components: a macroscopically occupied single-particle state, the condensate, and a population of single-particle states different from the condensate, the depletion.This many-body description applies to diverse bosonic systems such as superfluid Helium [1], exciton-polaritons [2] and degenerate Bose gases [3]; it has also found analogies in phenomena such as Hawking radiation from a black-hole [4] and spontaneous parametric down conversion in optics [5]. The fraction of atoms not in the condensate at zero temperature, the quantum depletion, increases with the strength of inter-particle interactions and with the density, rising up to 90% in liquid 4 He [1]. In ultracold gases, where the density is significantly smaller, the quantum depletion usually represents a small fraction (less than 1%) of the total population. At non-zero temperature there is an additional contribution to the population of single-particle states above the condensate, originating from the presence of thermal fluctuations.For weakly interacting systems, Bogoliubov theory describes quantum and thermal contributions to the condensate depletion [6,7]. This approach shows that the elementary, low-energy excitations are collective quasiparticle (phonon) modes, as has been verified in experimental studies with liquid 4 He [8], degenerate quantum gases [9] and exciton-polaritons [2]. At zero temperature, the many-body ground state is defined as a vacuum of these quasi-particle modes. When projected onto a basis of single-particl...
Quantum heat engines are subjected to quantum fluctuations related to their discrete energy spectra. Such fluctuations question the reliable operation of thermal machines in the quantum regime. Here, we realize an endoreversible quantum Otto cycle in the large quasi-spin states of Cesium impurities immersed in an ultracold Rubidium bath. Endoreversible machines are internally reversible and irreversible losses only occur via thermal contact. We employ quantum control to regulate the direction of heat transfer that occurs via inelastic spin-exchange collisions. We further use full-counting statistics of individual atoms to monitor quantized heat exchange between engine and bath at the level of single quanta, and additionally evaluate average and variance of the power output. We optimize the performance as well as the stability of the quantum heat engine, achieving high efficiency, large power output and small power output fluctuations.
We report on spin dynamics of individual, localized neutral impurities immersed in a Bose-Einstein condensate. Single Cesium atoms are transported into a cloud of Rubidium atoms, thermalize with the bath, and the ensuing spin-exchange between localized impurities with quasi-spin Fi = 3 and bath atoms with F b = 1 is resolved. Comparing our data to numerical simulations of spin dynamics we find that, for gas densities in the BEC regime, the dynamics is dominated by the condensed fraction of the cloud. We spatially resolve the density overlap of impurities and gas by the spin-population of impurities. Finally we trace the coherence of impurities prepared in a coherent superposition of internal states when coupled to a gas of different densities. For our choice of states we show that, despite high bath densities and thus fast thermalization rates, the impurity coherence is not affected by the bath, realizing a regime of sympathetic cooling while maintaining internal state coherence. Our work paves the way toward non-destructive probing of quantum many-body systems via localized impurities. arXiv:1802.08702v2 [cond-mat.quant-gas]
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