We present a discrete-time, one-dimensional quantum walk based on the entanglement between the momentum of ultracold rubidium atoms (the walk space) and two internal atomic states (the "coin" degree of freedom). Our scheme is highly flexible and can provide a platform for a wide range of applications such as quantum search algorithms, the observation of topological phases, and the realization of walks with higher dimensionality. Along with the investigation of the quantum-to-classical transition, we demonstrate the distinctive features of a quantum walk and contrast them to those of its classical counterpart. Also, by manipulating either the walk or coin operator, we show how the walk dynamics can be steered or even reversed.

Two-dimensional semiconductors, including transition metal dichalcogenides, are of interest in electronics and photonics but remain nonmagnetic in their intrinsic form. Previous efforts to form two-dimensional dilute magnetic semiconductors utilized extrinsic doping techniques or bulk crystal growth, detrimentally affecting uniformity, scalability, or Curie temperature. Here, we demonstrate an in situ substitutional doping of Fe atoms into MoS 2 monolayers in the chemical vapor deposition growth. The iron atoms substitute molybdenum sites in MoS 2 crystals, as confirmed by transmission electron microscopy and Raman signatures. We uncover an Fe-related spectral transition of Fe:MoS 2 monolayers that appears at 2.28 eV above the pristine bandgap and displays pronounced ferromagnetic hysteresis. The microscopic origin is further corroborated by density functional theory calculations of dipoleallowed transitions in Fe:MoS 2. Using spatially integrating magnetization measurements and spatially resolving nitrogen-vacancy center magnetometry, we show that Fe:MoS 2 monolayers remain magnetized even at ambient conditions, manifesting ferromagnetism at room temperature.

We report on a discrete-time quantum walk that uses the momentum of ultra-cold rubidium-87 atoms as the walk space and two internal atomic states as the coin degree of freedom. Each step of the walk consists of a coin toss (a microwave pulse) followed by a unitary shift operator (a resonant ratchet pulse). We carry out a comprehensive experimental study on the effects of various parameters, including the strength of the shift operation, coin parameters, noise, and initialization of the system on the behavior of the walk. The walk dynamics can be well controlled in our experiment; potential applications include atom interferometry and engineering asymmetric walks.

Quantum-resonance ratchets have been realized over the last ten years for the production of directed currents of atoms. These non-dissipative systems are based on the interaction of a Bose-Einstein condensate with an optical standing wave potential to produce a current of atoms in momentum space. In this paper we provide a review of the important features of these ratchets with a particular emphasis on their optimization using more complex initial states. We also examine their stability close to resonance conditions of the kicking. Finally we discuss the way in which these ratchets may pave the way for applications in quantum (random) walks and matter-wave interferometry.

We demonstrate quantum resonance ratchets created with Bose-Einstein condensates exposed to pulses of an off-resonant standing light wave. We show how some of the basic properties of the ratchets are controllable through the creation of different initial states of the system. In particular, our results prove that through an appropriate choice of initial state it is possible to reduce the extent to which the ratchet state changes with respect to time. We develop a simple theory to explain our results and indicate how ratchets might be used as part of a matter wave interferometer or quantum-random walk experiment.