The realization of large-scale fully controllable quantum systems is an exciting frontier in modern physical science. We use atom-by-atom assembly to implement a novel platform for the deterministic preparation of regular arrays of individually controlled cold atoms. In our approach, a measurement and feedback procedure eliminates the entropy associated with probabilistic trap occupation and results in defect-free arrays of over 50 atoms in less than 400 ms. The technique is based on fast, realtime control of 100 optical tweezers, which we use to arrange atoms in desired geometric patterns and to maintain these configurations by replacing lost atoms with surplus atoms from a reservoir. This bottom-up approach enables controlled engineering of scalable many-body systems for quantum information processing, quantum simulations, and precision measurements.The detection and manipulation of individual quantum particles, such as atoms or photons, is now routinely performed in many quantum physics experiments [1,2]; however, retaining the same control in large-scale systems remains an outstanding challenge. For example, major efforts are currently aimed at scaling up ion-trap and superconducting platforms, where high-fidelity quantum computing operations have been demonstrated in registers consisting of several qubits [3,4]. In contrast, ultracold quantum gases composed of neutral atoms offer inherently large system sizes. However, arbitrary single atom control is highly demanding and its realization is further limited by the slow evaporative cooling process necessary to reach quantum degeneracy. Only in recent years has individual particle detection [5,6] and basic single-spin control [7] been demonstrated in low entropy optical lattice systems.This Report demonstrates a novel approach for rapidly creating scalable quantum matter with inherent single particle control via atom-by-atom assembly of large defect-free arrays of cold neutral atoms [8,9]. We use optical microtraps to directly extract individual atoms from a laser-cooled cloud [10][11][12] and employ recently demonstrated trapping techniques [13][14][15][16][17] and single-atom position control [18][19][20][21][22] to create desired atomic configurations. Central to our approach is the use of single-atom detection and real-time feedback [18,21,22] to eliminate the entropy associated with the probabilistic trap occupation [11] (currently limited to ninety percent even with advanced loading techniques [23][24][25]). Related to the fundamental concept of "Maxwell's demon" [8,9], this method allows us to rapidly create large defect-free atom arrays and to maintain them for long periods of time, providing an excellent platform for large-scale experiments based on techniques ranging from Rydberg-mediated interactions [26][27][28][29][30] to nanophotonic platforms [31,32] and Hubbard model physics [16,17,33].The experimental protocol is illustrated in Fig. 1A. The trap array is produced by an acousto-optic deflector (AOD) and imaged with a 1:1 telescope onto a 0.5 NA...

The early time regime of the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimension, starting from a Brownian initial condition with a drift w, is studied using the exact Fredholm determinant representation. For large drift we recover the exact results for the droplet initial condition, whereas a vanishingly small drift describes the stationary KPZ case, recently studied by weak noise theory (WNT). We show that for short time t, the probability distribution P (H, t) of the height H at a given point takes the large deviation form P (H, t) ∼ exp −Φ(H)/ √ t . We obtain the exact expressions for the rate function Φ(H) for H < Hc2. Our exact expression for Hc2 numerically coincides with the value at which WNT was found to exhibit a spontaneous reflection symmetry breaking. We propose two continuations for H > Hc2, which apparently correspond to the symmetric and asymmetric WNT solutions. The rate function Φ(H) is Gaussian in the center, while it has asymmetric tails, |H| 5/2 on the negative H side and H 3/2 on the positive H side.

We consider the non-equilibrium dynamics of the entanglement entropy of a one-dimensional quantum gas of hard-core particles, initially confined in a box potential at zero temperature. At t = 0 the right edge of the box is suddenly released and the system is let free to expand. During this expansion, the initially correlated region propagates with a non-homogeneous profile, leading to the growth of entanglement entropy. This setting is investigated in the hydrodynamic regime, with tools stemming from semi-classical Wigner function approach and with recent developments of quantum fluctuating hydrodynamics. Within this framework, the entanglement entropy can be associated to a correlation function of chiral twist-fields of the conformal field theory that lives along the Fermi contour and it can be exactly determined. Our predictions for the entanglement evolution are found in agreement with and generalize previous results in literature based on numerical calculations and heuristic arguments.

We consider the Kardar-Parisi-Zhang (KPZ) for the stochastic growth of an interface of height h(x, t) on the positive half line with boundary condition ∂ x h(x, t)| x=0 = A. It is equivalent to a continuum directed polymer (DP) in a random potential in half-space with a wall at x = 0 either repulsive A > 0, or attractive A < 0. We provide an exact solution, using replica Bethe ansatz methods, to two problems which were recently proved to be equivalent [Parekh, arXiv:1901.09449]: the droplet initial condition for arbitrary A −1/2, and the Brownian initial condi-