A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or "trajectory" that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.
Spin models are the prime example of simplified manybody Hamiltonians used to model complex, real-world strongly correlated materials 1 . However, despite their simplified character, their dynamics often cannot be simulated exactly on classical computers as soon as the number of particles exceeds a few tens. For this reason, the quantum simulation 2 of spin Hamiltonians using the tools of atomic and molecular physics has become very active over the last years, using ultracold atoms 3 or molecules 4 in optical lattices, or trapped ions 5 . All of these approaches have their own assets, but also limitations. Here, we report on a novel platform for the study of spin systems, using individual atoms trapped in two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100% with exact knowledge of the initial configuration. When excited to Rydberg D-states, the atoms undergo strong interactions whose anisotropic character opens exciting prospects for simulating exotic matter 6 . We illustrate the versatility of our system by studying the dynamics of an Ising-like spin-1/2 system in a transverse field with up to thirty spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. For geometries where the anisotropy is expected to have small effects we find an excellent agreement with ab-initio simulations of the spin-1/2 system, while for strongly anisotropic situations the multilevel structure of the D-states has a measurable influence 7,8 . Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism.Rydberg atoms have recently attracted a lot of interest for quantum information processing 9 and quantum simulation 10 . In this work, we use a system of individual Rydberg atoms to realize highly-tunable artificial quantum Ising magnets. By shining on the atoms lasers that are resonant with the transition between the ground state |g and a chosen Rydberg state |r , we implement the Ising-like Hamiltonianwhich acts on the pseudo-spin states |↓ i and |↑ i corresponding to states |g and |r of atom i, respectively. Here, Ω is the Rabi frequency of the laser coupling, the σ i α (α = x, y, z) are the Pauli matrices acting on atom i, and n i = (1 + σ i z )/2 is the number of Rydberg excitations (0 or 1) on site i. FIG. 1|: Experimental platform. a: An array of microtraps is created by imprinting an appropriate phase on a dipole-trap beam. Siteresolved fluorescence of the atoms, at 780 nm, is imaged on a camera using a dichroic mirror (DM). Rydberg excitation beams at 795 and 475 nm are shone onto the atoms. The inset shows the measured light intensity for an array of Nt = 19 traps. b: Sketch of an experimental sequence. During loading, the camera images are analyzed continuously to extract the number of loaded traps. As soon as a triggering criterion is met, the loading is stopped and an image of the initial configuration is acquired. After Rydberg excitation, a final image is ...
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