We report on local, in situ measurements of atom number fluctuations in slices of a onedimensional Bose gas on an atom chip setup. By using current modulation techniques to prevent cloud fragmentation, we are able to probe the crossover from weak to strong interactions. For weak interactions, fluctuations go continuously from super-to sub-Poissonian as the density is increased, which is a signature of the transition between the sub-regimes where the two-body correlation function is dominated respectively by thermal and quantum contributions. At stronger interactions, the super-Poissonian region disappears, and the fluctuations go directly from Poissonian to subPoissonian, as expected for a 'fermionized' gas.PACS numbers: 03.75. Hh, 67.10.Ba Fluctuations witness the interplay between quantum statistics and interactions and therefore their measurement constitutes an important probe of quantum manybody systems. In particular, measurement of atom number fluctuations in ultracold quantum gases has been a key tool in the study of the Mott insulating phase in optical lattices [1], isothermal compressibility of Bose and Fermi gases [2][3][4][5], magnetic susceptibility of a strongly interacting Fermi gas [6], scale invariance of a twodimensional Bose gas [7], generation of atomic entanglement in double-wells [8], and relative number squeezing in pair-production via binary collisions [9,10].While a simple account of quantum statistics can change the atom number distribution, in a small volume of an ideal gas, from a classical-gas Poissonian to superPoissonian (for bosons) or sub-Poissonian (for fermions) distributions, many-body processes can further modify the correlations and fluctuations. For example, threebody losses may lead to sub-Poissonian fluctuations in a Bose gas [11,12]. Even without dissipation, the intrinsic interatomic interactions can also lead to sub-Poissonian fluctuations, such as in a repulsive Bose gas in a periodic lattice potential, where the energetically costly atom number fluctuations are suppressed. This effect has been observed for large ratios of the on-site interaction energy to the inter-site tunnelling energy [13,14], with the extreme limit corresponding to the Mott insulator phase [15,16]. The same physics, accounts for sub-Poissonian fluctuations observed in double-well experiments [8,17]. Sub-Poissonian fluctuations of the total atom number have been also realised via controlled loading of the atoms into very shallow traps [18].In this work, we observe for the first time subPoissonian atom number fluctuations in small slices of a single one-dimensional (1D) Bose gas with repulsive interactions, where each slice approximates a uniform system. Taking advantage of the long scale density varia- Nearly ideal Bose gasQuasi-condensate tion due to a weak longitudinal confinement, we monitor -at a given temperature -the atom number fluctuations in each slice as a function of the local density. For a weakly interacting gas, the measured fluctuations are super-Poissonian at low densities, and t...

We perform measurements of the third moment of atom number fluctuations in small slices of a very elongated weakly interacting degenerate Bose gas. We find a positive skewness of the atom number distribution in the ideal gas regime and a reduced skewness compatible with zero in the quasicondensate regime. For our parameters, the third moment is a thermodynamic quantity whose measurement constitutes a sensitive test of the equation of state, and our results are in agreement with a modified Yang-Yang thermodynamic prediction. Moreover, we show that the measured skewness reveals the presence of true three-body correlations in the system.

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By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasicondensate regime throughout the dimensional crossover from a purely one-dimensional (1D) to an almost three-dimensional (3D) gas. We show that that the entire transition region and the dimensional crossover are described surprisingly well by the modified Yang-Yang model. Furthermore, we find that at low temperatures the linear density at the quasicondensate transition scales according to an interaction-driven scenario of a longitudinally uniform 1D Bose gas, whereas at high temperatures it scales according to the degeneracy-driven critical scenario of transverse condensation of a 3D ideal gas.Low-dimensional (one-or two-dimensional) systems can have physical properties dramatically different from their three-dimensional (3D) counterparts. Experimental realizations of such systems in recent years has been particularly exciting in the field of ultracold atomic gases [1,2]. Here, the reduction of dimensionality is achieved by using highly anisotropic trapping potentials, where lowering the temperature leads to "freezing" out certain motional degrees of freedom to the respective ground state. For situations when the freezing is not perfect, an intriguing fundamental question arises: How does the low-dimensional and 3D physics get reconciled in the dimensional crossover?In this paper we address this question for a weakly interacting Bose gas that is confined transversely by a harmonic trap of frequency ω ⊥ /2π but is homogeneous in the thermodynamic limit with respect to the longitudinal direction. The one-dimensional (1D) regime is obtained when the thermal energy k B T and the chemical potential µ become much smaller than the transverse excitation energyhω ⊥ . In the absence of interatomic interactions, the homogeneous 1D gas is characterized by the absence of Bose-Einstein condensation. In the 3D limit, however, for k B T hω ⊥ , a sharp transverse condensation is expected: The atoms accumulate in the transverse ground state due to the saturation of population in the transversally excited states, yet the resulting 1D gas is still uncondensed with respect to the longitudinal states [3]. By incorporating weak repulsive interactions, in the 1D limit one expects a smooth interaction-driven transition from the ideal-gas regime toward the so-called quasicondensate regime [4] characterized by suppressed density fluctuations while the phase still fluctuates. Quasicondensates can be also created in the 3D limit [5], as observed experimentally [6,7]. In this paper we investigate the nature of the quasicondensate transition throughout the whole 1D-3D dimensional crossover.Our study relies on the measurement of atomic density fluctuations, previously used to identify the two limiting regimes-the ideal gas and the quasicondensate [8]. Owing to a higher measurement precision, we now probe the transition itself, including the crossover from a deeply 1D regime with k B T hω ⊥ ...

We report on Fourier spectroscopy experiments performed with near-surface nitrogen-vacancy centers in a diamond chip. By detecting the free precession of nuclear spins rather than applying a multipulse quantum sensing protocol, we are able to unambiguously identify the NMR species devoid of harmonics. We further show that by engineering different Hamiltonians during free precession, the hyperfine coupling parameters as well as the nuclear Larmor frequency can be selectively measured with high precision (here 5 digits). The protocols can be combined to demonstrate two-dimensional Fourier spectroscopy. The technique will be useful for mapping nuclear coordinates in molecules en route to imaging their atomic structure.Nitrogen-vacancy (NV) centers in diamond have opened exciting perspectives for the ultrasensitive detection of nuclear magnetic resonance (NMR), with possible applications to molecular structure imaging and chemical nanoanalytics [1][2][3]. NMR signals are detected by placing an analyte on a diamond chip engineered with a surface layer of NV centers, and measuring the weak magnetic dipole fields of nuclei via optically detected magnetic resonance [4,5]. Examples of the rapid recent progress in NV-NMR include the detection of small numbers of nuclei within voxels of a few (nm) 3 [6,7], the detection of multiple nuclear isotopes [8,9] and naturally occurring adsorption layers [6], the observation of surface diffusion and molecular motion [10,11], scanning imaging with < 20 nm spatial resolution [9,12], and the spatial mapping of up to 8 internal 13 C nuclei [13]. One of the far goals of NV-NMR is the detection and three-dimensional localization of individual nuclei in single molecules deterministically placed on the diamond chip [1,13,14].Sensitive detection of nuclear magnetic signals is possible with multipulse sequences that consist of a series of π pulses (see Fig. 1a). These sequences act like a narrow-band lock-in amplifier [15] whose demodulation frequency f = 1/(2τ ) is set by the delay time τ between the pulses [14,16,17]. By varying τ a frequency spectrum of the magnetic field can be recorded. Multipulse spectroscopy of NMR signals has been reported for many nuclear isotopes, including 1 H, 13 C, 14 N, 15 N, 19 F, and possibly 29 Si and 31 P [3, 6-9, 12, 18]. These experiments have, however, also revealed some important shortcomings of the method, including a modest spectral resolution [2,19] and ambiguities in peak assignments due to signal harmonics [18]. The fundamental reason for both effects is the indirect way nuclear spin signals are detected via their influence on the electronic spin.A more natural way for measuring NMR signals is to observe the free nuclear precession in the absence of microwave or radio-frequency pulses, reminiscent of the "free induction decay" in conventional NMR Fourier spectroscopy. The free nuclear precession can be detected by performing two consecutive nuclear spin measurements and incrementing the duration t 1 between the measurements. Mamin et al. [2] have ...

We report the first direct observation of collective quantum fluctuations in a continuous field. Shot-to-shot atom number fluctuations in small subvolumes of a weakly interacting, ultracold atomic 1D cloud are studied using in situ absorption imaging and statistical analysis of the density profiles. In the cloud centers, well in the quantum quasicondensate regime, the ratio of chemical potential to thermal energy is μ/k(B)T≃4, and, owing to high resolution, up to 20% of the microscopically observed fluctuations are quantum phonons. Within a nonlocal analysis at variable observation length, we observe a clear deviation from a classical field prediction, which reveals the emergence of dominant quantum fluctuations at short length scales, as the thermodynamic limit breaks down.

We present a method to demonstrate Anderson localization in an optically induced randomized potential. By usage of computer controlled spatial light modulators, we are able to implement fully randomized nondiffracting beams of variable structural size in order to control the modulation length (photonic grain size) as well as the depth (disorder strength) of a random potential induced in a photorefractive crystal. In particular, we quantitatively analyze the localization length of light depending on these two parameters and find that they are crucial influencing factors on the propagation behavior leading to variably strong localization. Thus, we corroborate that transverse light localization in a random refractive index landscape strongly depends on the character of the potential, allowing for a flexible regulation of the localization strength by adapting the optical induction configuration.

In 2016, a massive harmful algal bloom (HAB) of Alexandrium catenella around Chiloé island caused one of the major socio-ecological crisis in Chilean history. This red tide occurred in two distinct pulses, the second, most anomalous, bursting with extreme toxicity on the Pacific coast, weeks after the highly controversial dumping off Chiloé of 4,700 t of rotting salmons, killed by a previous HAB of Pseudochattonella verruculosa. We study the transport of this pollution, analyzing the physical oceanographic conditions during and after the dumping. We find that a cyclonic gyre was present between the dumping site and the coast, visible in satellite altimetry and sea surface temperature data. Using Lagrangian simulations, we confirm that near-surface currents could have brought part of the pollution to the coast, and fueled the bloom. This scenario explains also the anomalous later finding of ammonium near Chiloé. Finally we discuss the mismanagement of risk throughout the events. Highlights► Some rotting salmon biomass could have fueled the extraordinary 2016 red tide. ► A cylconic gyre was present between the pollution location and Chiloé's coast. ► Part of the salmon pollution off Chiloé could have reached coastal surface waters. ► Transported salmon biomass can explain the coastal ammonium patch found later.