Experimental Realization of a Fermionic Spin-Momentum Lattice.

We experimentally realize a spin-momentum lattice with a homogeneously trapped Fermi gas. The lattice is created via cyclically rotated atom-laser couplings between three bare atomic spin states, and are such that they form a triangular lattice in a synthetic spin-momentum space. We demonstrate the lattice and explore its dynamics with spin- and momentum-resolved absorption imaging. This platform will provide new opportunities for synthetic spin systems and the engineering of topological bands. In particular, the use of three spin states in two spatial dimensions would allow the simulation of synthetic magnetic fields of high spatial uniformity, which would lead to ultranarrow Chern bands that support robust fractional quantum Hall states.

Interaction Effects with Varying N in SU(N) Symmetric Fermion Lattice Systems.

The interaction effects in ultracold Fermi gases with SU(N) symmetry are studied nonperturbatively in half filled one-dimensional lattices by employing quantum Monte Carlo simulations. We find that, as N increases, weak and strong interacting systems are driven to a crossover region, but from opposite directions as a convergence of itinerancy and Mottness. In the weak interaction region, particles are nearly itinerant, and interparticle collisions are enhanced by N, resulting in the amplification of interaction effects. In contrast, in the strong coupling region, increasing N softens the Mott-insulating background through the enhanced virtual hopping processes. The crossover region exhibits nearly N-independent physical quantities, including the relative bandwidth, Fermi distribution, and the spin structure factor. The difference between even-N and odd-N systems is most prominent at small N's with strong interactions, since the odd case allows local real hopping with an energy scale much larger than the virtual one. The above effects can be experimentally tested in ultracold atom experiments with alkaline-earth(-like) fermions such as ^{87}Sr (^{173}Yb).

An energy-resolved atomic scanning probe.

We propose a method to probe the local density of states (LDOS) of atomic systems that provides both spatial and energy resolution. The method combines atomic and tunneling techniques to supply a simple, yet quantitative and operational, definition of the LDOS for both interacting and non-interacting systems: It is the rate at which particles can be siphoned from the system of interest by a narrow energy band of non-interacting states contacted locally to the many-body system of interest. Ultracold atoms in optical lattices are a natural platform for implementing this broad concept to visualize the energy and spatial dependence of the atom density in interacting, inhomogeneous lattices. This includes models of strongly correlated condensed matter systems, as well as ones with non-trivial topologies.

Experimental characterization of quantum dynamics through many-body interactions.

We report on the implementation of a quantum process tomography technique known as direct characterization of quantum dynamics applied on coherent and incoherent single-qubit processes in a system of trapped (40)Ca(+) ions. Using quantum correlations with an ancilla qubit, direct characterization of quantum dynamics reduces substantially the number of experimental configurations required for a full quantum process tomography and all diagonal elements of the process matrix can be estimated with a single setting. With this technique, the system's relaxation times T(1) and T(2) were measured with a single experimental configuration. We further show the first, complete characterization of single-qubit processes using a single generalized measurement realized through multibody correlations with three ancilla qubits.

Undoing a quantum measurement.

In general, a quantum measurement yields an undetermined answer and alters the system to be consistent with the measurement result. This process maps multiple initial states into a single state and thus cannot be reversed. This has important implications in quantum information processing, where errors can be interpreted as measurements. Therefore, it seems that it is impossible to correct errors in a quantum information processor, but protocols exist that are capable of eliminating them if they affect only part of the system. In this work we present the deterministic reversal of a fully projective measurement on a single particle, enabled by a quantum error-correction protocol in a trapped ion quantum information processor. We further introduce an in-sequence, single-species recooling procedure to counteract the motional heating of the ion string due to the measurement.

Experimental repetitive quantum error correction.

The computational potential of a quantum processor can only be unleashed if errors during a quantum computation can be controlled and corrected for. Quantum error correction works if imperfections of quantum gate operations and measurements are below a certain threshold and corrections can be applied repeatedly. We implement multiple quantum error correction cycles for phase-flip errors on qubits encoded with trapped ions. Errors are corrected by a quantum-feedback algorithm using high-fidelity gate operations and a reset technique for the auxiliary qubits. Up to three consecutive correction cycles are realized, and the behavior of the algorithm for different noise environments is analyzed.

14-Qubit entanglement: creation and coherence.

We report the creation of Greenberger-Horne-Zeilinger states with up to 14 qubits. By investigating the coherence of up to 8 ions over time, we observe a decay proportional to the square of the number of qubits. The observed decay agrees with a theoretical model which assumes a system affected by correlated, Gaussian phase noise. This model holds for the majority of current experimental systems developed towards quantum computation and quantum metrology.

An open-system quantum simulator with trapped ions.

The control of quantum systems is of fundamental scientific interest and promises powerful applications and technologies. Impressive progress has been achieved in isolating quantum systems from the environment and coherently controlling their dynamics, as demonstrated by the creation and manipulation of entanglement in various physical systems. However, for open quantum systems, engineering the dynamics of many particles by a controlled coupling to an environment remains largely unexplored. Here we realize an experimental toolbox for simulating an open quantum system with up to five quantum bits (qubits). Using a quantum computing architecture with trapped ions, we combine multi-qubit gates with optical pumping to implement coherent operations and dissipative processes. We illustrate our ability to engineer the open-system dynamics through the dissipative preparation of entangled states, the simulation of coherent many-body spin interactions, and the quantum non-demolition measurement of multi-qubit observables. By adding controlled dissipation to coherent operations, this work offers novel prospects for open-system quantum simulation and computation.

Remote preparation of single-photon "hybrid" entangled and vector-polarization States.

Quantum teleportation faces increasingly demanding requirements for transmitting large or even entangled systems. However, knowledge of the state to be transmitted eases its reconstruction, resulting in a protocol known as remote state preparation. A number of experimental demonstrations to date have been restricted to single-qubit systems. We report the remote preparation of two-qubit "hybrid" entangled states, including a family of vector-polarization beams. Our single-photon states are encoded in the photon spin and orbital angular momentum. We reconstruct the states by spin-orbit state tomography and transverse polarization tomography. The high fidelities achieved for the vector-polarization states opens the door to optimal coupling of down-converted photons to other physical systems, such as an atom, as required for scalable quantum networks, or plasmons in photonic nanostructures.

Counterfactual quantum computation through quantum interrogation.

The logic underlying the coherent nature of quantum information processing often deviates from intuitive reasoning, leading to surprising effects. Counterfactual computation constitutes a striking example: the potential outcome of a quantum computation can be inferred, even if the computer is not run. Relying on similar arguments to interaction-free measurements (or quantum interrogation), counterfactual computation is accomplished by putting the computer in a superposition of 'running' and 'not running' states, and then interfering the two histories. Conditional on the as-yet-unknown outcome of the computation, it is sometimes possible to counterfactually infer information about the solution. Here we demonstrate counterfactual computation, implementing Grover's search algorithm with an all-optical approach. It was believed that the overall probability of such counterfactual inference is intrinsically limited, so that it could not perform better on average than random guesses. However, using a novel 'chained' version of the quantum Zeno effect, we show how to boost the counterfactual inference probability to unity, thereby beating the random guessing limit. Our methods are general and apply to any physical system, as illustrated by a discussion of trapped-ion systems. Finally, we briefly show that, in certain circumstances, counterfactual computation can eliminate errors induced by decoherence.

Remote state preparation: arbitrary remote control of photon polarization.

We experimentally demonstrate the first remote state preparation of arbitrary single-qubit states, encoded in the polarization of photons generated by spontaneous parametric down-conversion. Utilizing degenerate and nondegenerate wavelength entangled sources, we remotely prepare arbitrary states at two wavelengths. Further, we derive theoretical bounds on the states that may be remotely prepared for given two-qubit resources.

Measurement of geometric phase for mixed states using single photon interferometry.

Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for mixed input states. We report the first experiment to measure mixed-state geometric phases in optics, using a Mach-Zehnder interferometer, and polarization mixed states that are produced in two different ways: decohering pure states with birefringent elements; and producing a nonmaximally entangled state of two photons and tracing over one of them, a form of remote state preparation.

Generation of hyperentangled photon pairs.

We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyperentangled). Using pairs of photons produced in spontaneous parametric down-conversion, we verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode, and time energy. We also produce and characterize maximally hyperentangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a 2 x 2 x 3 x 3 system (36-dimensional Hilbert space), which we believe is the first reported photonic entangled system of this size to be so characterized.