Two-Particle Four-Mode Interferometer for Atoms.

We present a free-space interferometer to observe two-particle interference of a pair of atoms with entangled momenta. The source of atom pairs is a Bose-Einstein condensate subject to a dynamical instability, and the interferometer is realized using Bragg diffraction on optical lattices, in the spirit of our recent Hong-Ou-Mandel experiment. We report on an observation ruling out the possibility of a purely mixed state at the input of the interferometer. We explain how our current setup can be extended to enable a test of a Bell inequality on momentum observables.

Microscopic observation of magnon bound states and their dynamics.

The existence of bound states of elementary spin waves (magnons) in one-dimensional quantum magnets was predicted almost 80 years ago. Identifying signatures of magnon bound states has so far remained the subject of intense theoretical research, and their detection has proved challenging for experiments. Ultracold atoms offer an ideal setting in which to find such bound states by tracking the spin dynamics with single-spin and single-site resolution following a local excitation. Here we use in situ correlation measurements to observe two-magnon bound states directly in a one-dimensional Heisenberg spin chain comprising ultracold bosonic atoms in an optical lattice. We observe the quantum dynamics of free and bound magnon states through time-resolved measurements of two spin impurities. The increased effective mass of the compound magnon state results in slower spin dynamics as compared to single-magnon excitations. We also determine the decay time of bound magnons, which is probably limited by scattering on thermal fluctuations in the system. Our results provide a new way of studying fundamental properties of quantum magnets and, more generally, properties of interacting impurities in quantum many-body systems.

Observation of spatially ordered structures in a two-dimensional Rydberg gas.

The ability to control and tune interactions in ultracold atomic gases has paved the way for the realization of new phases of matter. So far, experiments have achieved a high degree of control over short-range interactions, but the realization of long-range interactions has become a central focus of research because it would open up a new realm of many-body physics. Rydberg atoms are highly suited to this goal because the van der Waals forces between them are many orders of magnitude larger than those between ground-state atoms. Consequently, mere laser excitation of ultracold gases can cause strongly correlated many-body states to emerge directly when atoms are transferred to Rydberg states. A key example is a quantum crystal composed of coherent superpositions of different, spatially ordered configurations of collective excitations. Here we use high-resolution, in situ Rydberg atom imaging to measure directly strong correlations in a laser-excited, two-dimensional atomic Mott insulator. The observations reveal the emergence of spatially ordered excitation patterns with random orientation, but well-defined geometry, in the high-density components of the prepared many-body state. Together with a time-resolved analysis, this supports the description of the system in terms of a correlated quantum state of collective excitations delocalized throughout the gas. Our experiment demonstrates the potential of Rydberg gases to realize exotic phases of matter, thereby laying the basis for quantum simulations of quantum magnets with long-range interactions.

The 'Higgs' amplitude mode at the two-dimensional superfluid/Mott insulator transition.

Spontaneous symmetry breaking plays a key role in our understanding of nature. In relativistic quantum field theory, a broken continuous symmetry leads to the emergence of two types of fundamental excitation: massless Nambu-Goldstone modes and a massive 'Higgs' amplitude mode. An excitation of Higgs type is of crucial importance in the standard model of elementary particle physics, and also appears as a fundamental collective mode in quantum many-body systems. Whether such a mode exists in low-dimensional systems as a resonance-like feature, or whether it becomes overdamped through coupling to Nambu-Goldstone modes, has been a subject of debate. Here we experimentally find and study a Higgs mode in a two-dimensional neutral superfluid close to a quantum phase transition to a Mott insulating phase. We unambiguously identify the mode by observing the expected reduction in frequency of the onset of spectral response when approaching the transition point. In this regime, our system is described by an effective relativistic field theory with a two-component quantum field, which constitutes a minimal model for spontaneous breaking of a continuous symmetry. Additionally, all microscopic parameters of our system are known from first principles and the resolution of our measurement allows us to detect excited states of the many-body system at the level of individual quasiparticles. This allows for an in-depth study of Higgs excitations that also addresses the consequences of the reduced dimensionality and confinement of the system. Our work constitutes a step towards exploring emergent relativistic models with ultracold atomic gases.

Light-cone-like spreading of correlations in a quantum many-body system.

In relativistic quantum field theory, information propagation is bounded by the speed of light. No such limit exists in the non-relativistic case, although in real physical systems, short-range interactions may be expected to restrict the propagation of information to finite velocities. The question of how fast correlations can spread in quantum many-body systems has been long studied. The existence of a maximal velocity, known as the Lieb-Robinson bound, has been shown theoretically to exist in several interacting many-body systems (for example, spins on a lattice)--such systems can be regarded as exhibiting an effective light cone that bounds the propagation speed of correlations. The existence of such a 'speed of light' has profound implications for condensed matter physics and quantum information, but has not been observed experimentally. Here we report the time-resolved detection of propagating correlations in an interacting quantum many-body system. By quenching a one-dimensional quantum gas in an optical lattice, we reveal how quasiparticle pairs transport correlations with a finite velocity across the system, resulting in an effective light cone for the quantum dynamics. Our results open perspectives for understanding the relaxation of closed quantum systems far from equilibrium, and for engineering the efficient quantum channels necessary for fast quantum computations.

Coherent light scattering from a two-dimensional Mott insulator.

We experimentally demonstrate coherent light scattering from an atomic Mott insulator in a two-dimensional lattice. The far-field diffraction pattern of small clouds of a few hundred atoms was imaged while simultaneously laser cooling the atoms with the probe beams. We describe the position of the diffraction peaks and the scaling of the peak parameters by a simple analytic model. In contrast to Bragg scattering, scattering from a single plane yields diffraction peaks for any incidence angle. We demonstrate the feasibility of detecting spin correlations via light scattering by artificially creating a one-dimensional antiferromagnetic order as a density wave and observing the appearance of additional diffraction peaks.

Single-spin addressing in an atomic Mott insulator.

Ultracold atoms in optical lattices provide a versatile tool with which to investigate fundamental properties of quantum many-body systems. In particular, the high degree of control of experimental parameters has allowed the study of many interesting phenomena, such as quantum phase transitions and quantum spin dynamics. Here we demonstrate how such control can be implemented at the most fundamental level of a single spin at a specific site of an optical lattice. Using a tightly focused laser beam together with a microwave field, we were able to flip the spin of individual atoms in a Mott insulator with sub-diffraction-limited resolution, well below the lattice spacing. The Mott insulator provided us with a large two-dimensional array of perfectly arranged atoms, in which we created arbitrary spin patterns by sequentially addressing selected lattice sites after freezing out the atom distribution. We directly monitored the tunnelling quantum dynamics of single atoms in the lattice prepared along a single line, and observed that our addressing scheme leaves the atoms in the motional ground state. The results should enable studies of entropy transport and the quantum dynamics of spin impurities, the implementation of novel cooling schemes, and the engineering of quantum many-body phases and various quantum information processing applications.

Single-atom-resolved fluorescence imaging of an atomic Mott insulator.

The reliable detection of single quantum particles has revolutionized the field of quantum optics and quantum information processing. For several years, researchers have aspired to extend such detection possibilities to larger-scale, strongly correlated quantum systems in order to record in situ images of a quantum fluid in which each underlying quantum particle is detected. Here we report fluorescence imaging of strongly interacting bosonic Mott insulators in an optical lattice with single-atom and single-site resolution. From our images, we fully reconstruct the atom distribution on the lattice and identify individual excitations with high fidelity. A comparison of the radial density and variance distributions with theory provides a precise in situ temperature and entropy measurement from single images. We observe Mott-insulating plateaus with near-zero entropy and clearly resolve the high-entropy rings separating them, even though their width is of the order of just a single lattice site. Furthermore, we show how a Mott insulator melts with increasing temperature, owing to a proliferation of local defects. The ability to resolve individual lattice sites directly opens up new avenues for the manipulation, analysis and applications of strongly interacting quantum gases on a lattice. For example, one could introduce local perturbations or access regions of high entropy, a crucial requirement for the implementation of novel cooling schemes.

Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas.

Any state of matter is classified according to its order, and the type of order that a physical system can possess is profoundly affected by its dimensionality. Conventional long-range order, as in a ferromagnet or a crystal, is common in three-dimensional systems at low temperature. However, in two-dimensional systems with a continuous symmetry, true long-range order is destroyed by thermal fluctuations at any finite temperature. Consequently, for the case of identical bosons, a uniform two-dimensional fluid cannot undergo Bose-Einstein condensation, in contrast to the three-dimensional case. However, the two-dimensional system can form a 'quasi-condensate' and become superfluid below a finite critical temperature. The Berezinskii-Kosterlitz-Thouless (BKT) theory associates this phase transition with the emergence of a topological order, resulting from the pairing of vortices with opposite circulation. Above the critical temperature, proliferation of unbound vortices is expected. Here we report the observation of a BKT-type crossover in a trapped quantum degenerate gas of rubidium atoms. Using a matter wave heterodyning technique, we observe both the long-wavelength fluctuations of the quasi-condensate phase and the free vortices. At low temperatures, the gas is quasi-coherent on the length scale set by the system size. As the temperature is increased, the loss of long-range coherence coincides with the onset of proliferation of free vortices. Our results provide direct experimental evidence for the microscopic mechanism underlying the BKT theory, and raise new questions regarding coherence and superfluidity in mesoscopic systems.

Observation of phase defects in quasi-two-dimensional Bose-Einstein condensates.

We have observed phase defects in quasi-2D Bose-Einstein condensates close to the condensation temperature. Either a single or several equally spaced condensates are produced by selectively evaporating the sites of a 1D optical lattice. When several clouds are released from the lattice and allowed to overlap, dislocation lines in the interference patterns reveal nontrivial phase defects.