Atom chips provide a versatile quantum laboratory for experiments with ultracold atomic gases. They have been used in diverse experiments involving low-dimensional quantum gases, cavity quantum electrodynamics, atom-surface interactions, and chip-based atomic clocks and interferometers. However, a severe limitation of atom chips is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. Such techniques enable chip-based studies of entangled many-body systems and are a key prerequisite for atom chip applications in quantum simulations, quantum information processing and quantum metrology. Here we report the experimental generation of multi-particle entanglement on an atom chip by controlling elastic collisional interactions with a state-dependent potential. We use this technique to generate spin-squeezed states of a two-component Bose-Einstein condensate; such states are a useful resource for quantum metrology. The observed reduction in spin noise of -3.7 +/- 0.4 dB, combined with the spin coherence, implies four-partite entanglement between the condensate atoms; this could be used to improve an interferometric measurement by -2.5 +/- 0.6 dB over the standard quantum limit. Our data show good agreement with a dynamical multi-mode simulation and allow us to reconstruct the Wigner function of the spin-squeezed condensate. The techniques reported here could be directly applied to chip-based atomic clocks, currently under development.

We consider a spin-orbit coupled configuration of spin-1/2 interacting bosons with equal Rashba and Dresselhaus couplings. The phase diagram of the system at T=0 is discussed with special emphasis on the role of the interaction treated in the mean-field approximation. For a critical value of the density and of the Raman coupling we predict the occurrence of a characteristic tricritical point separating the spin mixed, the phase separated, and the zero momentum states of the Bose gas. The corresponding quantum phases are investigated analyzing the momentum distribution, the longitudinal and transverse spin polarization, and the emergence of density fringes. The effect of harmonic trapping as well as the role of the breaking of spin symmetry in the interaction Hamiltonian are also discussed.

Two-dimensional atomic crystals are extensively studied in recent years due to their exciting physics and device applications. However, a molecular counterpart, with scalable processability and competitive device performance, is still challenging. Here, we demonstrate that high-quality few-layer dioctylbenzothienobenzothiophene molecular crystals can be grown on graphene or boron nitride substrate via van der Waals epitaxy, with precisely controlled thickness down to monolayer, large-area single crystal, low process temperature and patterning capability. The crystalline layers are atomically smooth and effectively decoupled from the substrate due to weak van der Waals interactions, affording a pristine interface for high-performance organic transistors. As a result, monolayer dioctylbenzothienobenzothiophene molecular crystal field-effect transistors on boron nitride show record-high carrier mobility up to 10 cm 2 V À 1 s À 1 and aggressively scaled saturation voltage B1 V. Our work unveils an exciting new class of two-dimensional molecular materials for electronic and optoelectronic applications.

Using Bogoliubov theory we calculate the excitation spectrum of a spinor Bose-Einstein condensed gas with equal Rashba and Dresselhaus spin-orbit coupling in the stripe phase. The emergence of a double gapless band structure is pointed out as a key signature of Bose-Einstein condensation and of the spontaneous breaking of translational invariance symmetry. In the long wavelength limit the lower and upper branches exhibit, respectively, a clear spin and density nature. For wave vectors close to the first Brillouin zone, the lower branch acquires an important density character responsible for the divergent behavior of the structure factor and of the static response function, reflecting the occurrence of crystalline order. The sound velocities are calculated as functions of the Raman coupling for excitations propagating orthogonal and parallel to the stripes. Our predictions provide new perspectives for the identification of supersolid phenomena in ultracold atomic gases. . It is characterized by the coexistence of two spontaneously broken symmetries. The breaking of gauge symmetry gives rise to off-diagonal long-range order yielding superfluidity, while the breaking of translational invariance yields diagonal long-range order characterizing the crystalline structure. The First experimental efforts toward the search of supersolidity were carried out in solid helium [5]. The strongly interacting nature of this system makes, however, the effects due to Bose-Einstein condensation (BEC) extremely small and no conclusive proof of supersolidity is still available in such a system [6]. More recently, systematic attempts to predict the occurrence of a supersolid phase have been carried out in atomic gases with dipolar [7][8][9] and soft core, finite range interactions [10][11][12][13][14][15]. However, these configurations have not yet been experimentally realized in the quantum degenerate phase required to observe the new effects.The recent realization of spinor BECs with spin-orbit coupling [17][18][19][20] is opening new perspectives in the field. In systems with equal Rashba and Dresselhaus couplings and for small values of the Raman coupling, theory in fact predicts the occurrence of a stripe phase where translational invariance is spontaneously broken [21][22][23]. Actually these systems are periodic only in one direction and can be considered as superfluid nematic liquid crystals. Experiments are already available in the relevant range of parameters, but no direct evidence of the density modulations is still available, due to the smallness of the contrast and the microscopic distance separating consecutive stripes. A phase transition has been nevertheless detected [20] at values of the Raman coupling below which theory predicts the occurrence of the stripe phase.The purpose of this work is to show that the excitation spectrum of the gas in the stripe phase exhibits typical supersolid features, like the occurrence of two gapless bands and the divergent behavior of the static structure factor for wave vectors approach...

By calculating the density response function we identify the excitation spectrum of a Bose-Einstein condensate with equal Rashba and Dresselhaus spin-orbit coupling. We find that the velocity of sound along the direction of spin-orbit coupling is deeply quenched and vanishes when one approaches the second-order phase transition between the plane wave and the zero momentum quantum phases. We also point out the emergence of a roton minimum in the excitation spectrum for small values of the Raman coupling, providing the onset of the transition to the stripe phase. Our findings point out the occurrence of a strong anisotropy in the dynamic behavior of the gas. A hydrodynamic description accounting for the collective oscillations in both uniform and harmonically trapped gases is also derived.

The problem of spin squeezing with a bimodal condensate in the presence of particle losses is solved analytically by the Monte Carlo wave function method. We find the largest obtainable spin squeezing as a function of the one-body loss rate, the two-body and three-body rate constants, and the s-wave scattering length.

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Abstract.We propose an analytical method to study the entangled spatial and spin dynamics of interacting bimodal Bose-Einstein condensates. We show that at particular times during the evolution spatial and spin dynamics disentangle and the spin squeezing can be predicted by a simple two-mode model. We calculate the maximum spin squeezing achievable in experimentally relevant situations with Sodium or Rubidium bimodal condensates, including the effect of the dynamics and of one, two and three-body losses. PACS. 03.75.Gg Entanglement and decoherence in