We study one-dimensional trapped Bose gases in the strongly interacting regime. The systems are created in an optical lattice and are subject to a longitudinal periodic potential. Bragg spectroscopy enables us to investigate the excitation spectrum of the one-dimensional gas in different regimes. In the superfluid phase a broad continuum of excitations is observed which calls for an interpretation beyond the Bogoliubov spectrum taking into account the effect of quantum depletion. In the Mott insulating phase a discrete spectrum is measured. The excitation spectra of both phases are compared to the three-dimensional situation and to the crossover regime from one to three dimensions. The coherence length and coherent fraction of the gas in all configurations are measured quantitatively. We observe signatures for increased fluctuations which are characteristic for 1D systems. Furthermore, ceasing collective oscillations near the transition to the Mott insulator phase are found.PACS numbers: 05.30. Jp, 03.75.Kk, 03.75.Lm, 73.43.Nq Quantum gases trapped in the periodic potential of an optical lattice have opened a new experimental window on many-particle quantum physics. The recent observation of the quantum phase transition from a superfluid to a Mott insulating phase in a Bose gas [1] has offered a first glimpse on the physics which is now becoming experimentally accessible. However, the full wealth of possibilities has yet to be explored. Besides controlling the effect of interactions in the trapped gas, it is conceivable to induce disorder, to change the dimensionality of the system, or to trap Fermi gases or Bose-Fermi mixtures. The realization of these systems is expected to provide a deeper understanding of general concepts related to superfluidity and superconductivity.Here we use the optical lattice to realize a strongly interacting Bose gas in one spatial dimension and to study the crossover to three dimensions. Emphasis is put on the measurement of excitation spectra which characterize the transition from the superfluid [2,3] to the Mott insulating state [1,4,5]. Several features observed in the spectra go beyond the description of current theoretical models.Degenerate Bose gases trapped in the lowest band of an optical lattice can be modelled using the Bose-Hubbard Hamiltonian [6,7,8,9], in which the hopping of atoms between neighboring lattice sites is characterized by the tunnelling matrix element J, while the interaction energy for two atoms occupying the same site is given by U . The physics of this model is governed by the ratio between U and J, i.e. between interaction and kinetic energy. This parameter can be controlled by changing the depth of the lattice potential. If the ratio U/J is below a critical value the atoms are superfluid. Above this value the system becomes Mott insulating. We access the one-dimensional regime [6, 10, 11] using an anisotropic optical lattice consisting of three mutually perpendicular standing waves. By choosing large potential depths in two axes we can selectively s...

Nanostructured semiconductors emit light from electronic states known as excitons. For organic materials, Hund's rules state that the lowest-energy exciton is a poorly emitting triplet state. For inorganic semiconductors, similar rules predict an analogue of this triplet state known as the 'dark exciton'. Because dark excitons release photons slowly, hindering emission from inorganic nanostructures, materials that disobey these rules have been sought. However, despite considerable experimental and theoretical efforts, no inorganic semiconductors have been identified in which the lowest exciton is bright. Here we show that the lowest exciton in caesium lead halide perovskites (CsPbX, with X = Cl, Br or I) involves a highly emissive triplet state. We first use an effective-mass model and group theory to demonstrate the possibility of such a state existing, which can occur when the strong spin-orbit coupling in the conduction band of a perovskite is combined with the Rashba effect. We then apply our model to CsPbX nanocrystals, and measure size- and composition-dependent fluorescence at the single-nanocrystal level. The bright triplet character of the lowest exciton explains the anomalous photon-emission rates of these materials, which emit about 20 and 1,000 times faster than any other semiconductor nanocrystal at room and cryogenic temperatures, respectively. The existence of this bright triplet exciton is further confirmed by analysis of the fine structure in low-temperature fluorescence spectra. For semiconductor nanocrystals, which are already used in lighting, lasers and displays, these excitons could lead to materials with brighter emission. More generally, our results provide criteria for identifying other semiconductors that exhibit bright excitons, with potential implications for optoelectronic devices.

The discrete quantum properties of matter are manifest in a variety of phenomena. Any particle that is trapped in a sufficiently deep and wide potential well is settled in quantum bound states. For example, the existence of quantum states of electrons in an electromagnetic field is responsible for the structure of atoms, and quantum states of nucleons in a strong nuclear field give rise to the structure of atomic nuclei. In an analogous way, the gravitational field should lead to the formation of quantum states. But the gravitational force is extremely weak compared to the electromagnetic and nuclear force, so the observation of quantum states of matter in a gravitational field is extremely challenging. Because of their charge neutrality and long lifetime, neutrons are promising candidates with which to observe such an effect. Here we report experimental evidence for gravitational quantum bound states of neutrons. The particles are allowed to fall towards a horizontal mirror which, together with the Earth's gravitational field, provides the necessary confining potential well. Under such conditions, the falling neutrons do not move continuously along the vertical direction, but rather jump from one height to another, as predicted by quantum theory.

We report on the realization of a trapped one-dimensional Bose gas and its characterization by means of measuring its lowest lying collective excitations. The quantum degenerate Bose gas is prepared in a 2D optical lattice, and we find the ratio of the frequencies of the lowest compressional (breathing) mode and the dipole mode to be (omega(B)/omega(D))(2) approximately 3.1, in accordance with the Lieb-Liniger and mean-field theory. For a thermal gas we measure (omega(B)/omega(D))(2) approximately 4. By heating the quantum degenerate gas, we have studied the transition between the two regimes. For the lowest number of particles attainable in the experiment the kinetic energy of the system is similar to the interaction energy, and we enter the strongly interacting regime.

An ensemble of emitters can behave very differently from its individual constituents when they interact coherently via a common light field. After excitation of such an ensemble, collective coupling can give rise to a many-body quantum phenomenon that results in short, intense bursts of light-so-called superfluorescence 1. Because this phenomenon requires a fine balance of interactions between the emitters and their decoupling from the environment, together with close identity of the individual emitters, superfluorescence has thus far been observed only in a limited number of systems, such as certain atomic and molecular gases and a few solid-state systems 2-7. The generation of superfluorescent light in colloidal nanocrystals (which are bright photonic sources practically suited for optoelectronics 8,9) has been precluded by inhomogeneous emission broadening, low oscillator strength, and fast exciton dephasing. Here we show that caesium lead halide (CsPbX 3 , X = Cl, Br) perovskite nanocrystals 10-13 that are self-organized into highly ordered three-dimensional superlattices exhibit key signatures of superfluorescence. These are dynamically red-shifted emission with more than 20-fold accelerated radiative decay, extension of the first-order coherence time by more than a factor of four, photon bunching, and delayed emission pulses with Burnham-Chiao ringing behaviour 14 at high excitation density. These mesoscopically extended coherent states could be used to boost the performance of opto-electronic devices 15 and enable entangled multi-photon quantum light sources 16,17. Spontaneous emission of photons-such as happens in the process of fluorescence that is commonly used in displays and lighting-occurs because of coupling between excited two-level systems (TLS) and the vacuum modes of the electromagnetic field, effectively stimulated by its zero-point fluctuations. In 1954, Dicke predicted 18 that an ensemble of N identical TLS confined in a volume smaller than about λ 3 (where λ is the corresponding emission wavelength of the TLS) can exhibit coherent and cooperative spontaneous emission. This so-called superradiant emission results from the coherent coupling between individual TLS through the common vacuum modes, effectively leading to a single giant emitting dipole from all participating TLS. Superradiant emission has been observed in distinctly different physical systems, such as molecular aggregates and crystals 19 , nitrogen vacancy centres in diamond 20 and epitaxially grown quantum dots 21 (QDs). In the case when the excited TLS are initially fully uncorrelated, the coherence can be established only through spontaneously triggered correlations due to quantum fluctuations rather than by coherent excitation. When this occurs, a so-called superfluorescence (SF) pulse is emitted 1 (Fig. 1, illustrated for the present study). Both superradiant emission and coherent SF bursts are characterized by an accelerated radiative decay time τ SF ∝ τ SE /N, where the exponential decay time τ SE of spontaneous emission fr...