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We report an experiment that uses the environmental selection, a key concept in the recent theory of quantum Darwinism, as a mechanism to realize the entanglement filter, a useful quantum information device that filters out certain entangled states. In the experiment, the environment of two qubits is controlled to favor an entangled state and kill other competing components in the input state. The initial state has vanishing entanglement, but the state surviving after interaction with the environment is close to a maximally entangled state, with an entanglement fidelity of $(94.7\pm 1.9)%$ measured through the quantum state tomography. We experimentally demonstrate that the generated entanglement is robust under change of the initial state configurations and the environmental parameters.

The practical construction of scalable quantum computer hardware capable of executing non-trivial quantum algorithms will require the juxtaposition of different types of quantum systems. We analyze a modular ion trap quantum computer architecture with a hierarchy of interactions that can scale to very large numbers of qubits. Local entangling quantum gates between qubit memories within a single register are accomplished using natural interactions between the qubits, and entanglement between separate registers is completed via a probabilistic photonic interface between qubits in different registers, even over large distances. We show that this architecture can be made fault-tolerant, and demonstrate its viability for fault-tolerant execution of modest size quantum circuits.

We report an experiment that demonstrates full function of a quantum router using entangled photons, where the paths of a single-photon pulse are controlled in a coherent fashion by polarization of another single photon. Through a projective measurement, we prepare the polarization of the control photon in arbitrary superposition states, leading to coherent routing of the target photon in quantum superposition of different paths. We demonstrate quantum nature of this router through optical measurements based on quantum state tomography and show an average fidelity of $(93.24\pm 0.23)%$ for the quantum routing operation., Comment: "This paper has been withdrawn and it will be replaced by a new experiment that does not require prior entanglement between the control and the data photons."

We report the first state-independent experimental test of quantum contextuality on a single photonic qutrit (three-dimensional system), based on a recent theoretical proposal [Yu and Oh, Phys. Rev. Lett. 108, 030402 (2012)]. Our experiment spotlights quantum contextuality in its most basic form, in a way that is independent of either the state or the tensor product structure of the system.

Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter., Comment: updated to the version published in PRL

We analyze two approaches to quantum state transfer in solid-state spin systems. First, we consider unpolarized spin-chains and extend previous analysis to various experimentally relevant imperfections, including quenched disorder, dynamical decoherence, and uncompensated long range coupling. In finite-length chains, the interplay between disorder-induced localization and decoherence yields a natural optimal channel fidelity, which we calculate. Long-range dipolar couplings induce a finite intrinsic lifetime for the mediating eigenmode; extensive numerical simulations of dipolar chains of lengths up to L=12 show remarkably high fidelity despite these decay processes. We further consider the extension of the protocol to bosonic systems of coupled oscillators. Second, we introduce a quantum mirror based architecture for universal quantum computing which exploits all of the spins in the system as potential qubits. While this dramatically increases the number of qubits available, the composite operations required to manipulate "dark" spin qubits significantly raise the error threshold for robust operation. Finally, as an example, we demonstrate that eigenmode-mediated state transfer can enable robust long-range logic between spatially separated Nitrogen-Vacancy registers in diamond; numerical simulations confirm that high fidelity gates are achievable even in the presence of moderate disorder., Comment: 15 pages, 10 figures

We show that laser assisted hopping of hard core bosons in a square optical lattice can be described by an antiferromagnetic $J_{1}$-$J_{2}$ XY model with tunable ratio of $J_{2}/J_{1}$. We numerically investigate the phase diagram of the $J_{1}$-$J_{2}$ XY model using both the tensor network algorithm for infinite systems and the exact diagonalization for small clusters and find strong evidence that in the intermediate region around $% J_{2}/J_{1}\sim 0.5$, there is a spin liquid phase with vanishing magnetization and valence bond orders, which interconnects the Neel state on the $J_{2}\ll J_{1}$ side and the stripe antiferromagnetic phase on the $% J_{2}\gg J_{1}$ side. This finding opens up the possibility of studying the exotic spin liquid phase in a realistic experimental system using ultracold atoms in an optical lattice., Comment: 5 pages, 5 figures

Quantum error correction in general is experimentally challenging as it requires significant expansion of the size of quantum circuits and accurate performance of quantum gates to fulfill the error threshold requirement. Here we propose a method much simpler for experimental implementation to correct arbitrary detection errors. The method is based on processing of data from repetitive experiments and can correct detection error of any magnitude, as long as the error magnitude is calibrated. The method is illustrated with its application to detection of multipartite entanglement from quantum state engineering., Comment: 5 pages, 2 figures

We show the spin-orbital coupling induced by an artificial light-induced gauge field can fully restore superfluidity suppressed by population imbalance in a two-dimensional (2D) Fermi gas, leading to unconventional superfluid states either with topological Majorana fermion excitations or showing a novel mixture of triplet pairing with spin-up (down) components respectively in the $p_{x}\pm ip_{y}$ pairing channels. We self-consistently calculate the zero temperature phase diagram at the BCS\ side of Feshbach resonance and show that the phase transitions between different superfluid states can be revealed through measurement of the in-situ density profile of the 2D atomic cloud in a weak global trap.

Reimann [Phys. Rev. Lett. 101, 190403 (2008)] claimed that generic isolated macroscopic quantum system will equilibrate under experimentally realistic conditions by proving a theorem. We here show that the proof is invalid for most many-body systems and is unable to demonstrate equilibration in realistic experiment.

Dicke states represent a class of multipartite entangled states that can be generated experimentally with many applications in quantum information. We propose a method to experimentally detect genuine multipartite entanglement in the vicinity of arbitrary Dicke states. The detection scheme can be used to experimentally quantity the entanglement depth of many-body systems and is easy to implement as it requires to measure only three collective spin operators. The detection criterion is strong as it heralds multipartite entanglement even in cases where the state fidelity goes down exponentially with the number of qubits., Comment: 4 pages

A quantum simulator is a well controlled quantum system that can simulate the behavior of another quantum system which may require exponentially large classical computing resources to understand otherwise. In the 1980s, Feynman proposed the use of quantum logic gates on a standard controllable quantum system to efficiently simulate the behavior of a model Hamiltonian. Recent experiments using trapped ions and neutral atoms have realized quantum simulation of Ising model in presence of external magnetic fields, and showed almost arbitrary control in generating non-trivial Ising coupling patterns. Here we use laser-cooled trapped 171-Yb+ ions to simulate the emergence of magnetism in a system of interacting spins by implementing a fully-connected non-uniform ferromagnetic Ising model in a transverse magnetic field. To link this quantum simulation to condensed matter physics, we measure scalable correlation functions and order parameters appropriate for the description of larger systems, such as various moments of the magnetization. By increasing the Ising coupling strengths compared with the external field, the crossover from paramagnetism to ferromagnetic order sharpens as the system is scaled up from N = 2 to 9 trapped ion spins. This points toward the onset of a quantum phase transition that should become infinitely sharp as the system approaches the macroscopic scale. We compare the measured ground state order to theory, which may become intractable for non-uniform Ising couplings as the number of spins grows beyond 20- 30 and even NP complete for a fully-connected frustrated Ising model, making this experiment an important benchmark for large-scale quantum simulation., Comment: 7 pages, 4 figures

Sharp quantum phase transitions typically require a large system with many particles. Here we show that for a frustrated fully-connected Ising spin network represented by trapped atomic ions, the competition between different spin orders leads to rich phase transitions whose sharpness scales exponentially with the number of spins. This unusual finite-size scaling behavior opens up the possibility of observing sharp quantum phase transitions in a system of just a few trapped ion spins., Comment: 5 pages, 4 figures

We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can be achieved via certain classes of random, unpolarized (infinite temperature) spin chains. Our method is robust to coupling strength disorder and does not require manipulation or control over individual spins. In principle, it can be used to attain perfect state transfer over arbitrarily long range via purely Hamiltonian evolution and may be particularly applicable in a solid-state quantum information processor. As an example, we demonstrate that it can be used to attain strong coherent coupling between Nitrogen-Vacancy centers separated by micrometer distances at room temperature. Realistic imperfections and decoherence effects are analyzed., Comment: 4 pages, 2 figures. V2: Modified discussion of disorder, added references - final version as published in Phys. Rev. Lett

A Wigner crystal formed with trapped ion can undergo structural phase transition, which is determined only by the mechanical conditions on a classical level. Instead of this classical result, we show that through consideration of quantum and thermal fluctuation, a structural phase transition can be solely driven by change of the system's temperature. We determine a finite-temperature phase diagram for trapped ions using the renormalization group method and the path integral formalism, and propose an experimental scheme to observe the predicted temperature-driven structural phase transition, which is well within the reach of the current ion trap technology., Comment: 4 pages, 5 figures

We perform a quantum simulation of the Ising model with a transverse field using a collection of three trapped atomic ion spins. By adiabatically manipulating the Hamiltonian, we directly probe the ground state for a wide range of fields and form of the Ising couplings, leading to a phase diagram of magnetic order in this microscopic system. The technique is scalable to much larger numbers of trapped ion spins, where phase transitions approaching the thermodynamic limit can be studied in cases where theory becomes intractable., Comment: 5 pages, 4 figures

We show anisotropy of the dipole interaction between magnetic atoms or polar molecules can stabilize new quantum phases in an optical lattice. Using a well controlled numerical method based on the tensor network algorithm, we calculate phase diagram of the resultant effective Hamiltonian in a two-dimensional square lattice - an anisotropic Hubbard model of hard-core bosons with attractive interaction in one direction and repulsive interaction in the other direction. Besides the conventional superfluid and the Mott insulator states, we find the striped and the checkerboard charge density wave states and the supersolid phase that interconnect the superfluid and the striped solid states. The transition to the supersolid phase has a mechanism different from the case of the soft-core Bose Hubbard model., Comment: 5 pages, 5 figures.

We study thermalization and non-equilibrium dynamics in a dissipative quantum many-body system -- a chain of ions with two points of the chain driven by thermal bath under different temperature. Instead of a simple linear temperature gradient as one expects from the classical heat diffusion process, the temperature distribution in the ion chain shows surprisingly rich patterns, which depend on the ion coupling rate to the bath, the location of the driven ions, and the dissipation rates of the other ions in the chain. Through simulation of the temperature evolution, we show that these unusual temperature distribution patterns in the ion chain can be quantitatively tested in experiments within a realistic time scale., Comment: 5 pages, 5 figures

The coherence of electron spin can be significantly enhanced by locking the Overhauser field from nuclear spins using the nuclear spin preparation. We propose a theoretical model to calculate the long time dynamics of the Overhauser field under intrinsic nuclear spin diffusion in a quantum dot. We obtain a simplified diffusion equation that can be numerically solved and show quantitatively how the Knight shift and the electron-mediated nuclear spin flip-flop affect the nuclear spin diffusion. The results explain several recent experimental observations, where the decay time of Overhauser field is measured under different configurations, including variation of the external magnetic field, the electron spin configuration in a double dot, and the initial nuclear spin polarization rate., Comment: 6 pages, 5 figures

To test effective Hamiltonians for strongly interacting fermions in an optical lattice, we numerically find the energy spectrum for two fermions interacting across a Feshbach resonance in a double well potential. From the spectrum, we determine the range of detunings for which the system can be described by an effective lattice model, and how the model parameters are related to the experimental parameters. We find that for a range of strong interactions the system is well described by an effective $t-J$ model, and the effective superexchange term, $J$, can be smoothly tuned through zero on either side of unitarity. Right at and around unitarity, an effective one-band general Hubbard model is appropriate, with a finite and small on-site energy, due to a lattice-induced anharmonic coupling between atoms at the scattering threshold and a weakly bound Feshbach molecule in an excited center of mass state., Comment: 7 pages, 7 figures; minor typos corrected

We show that the noise threshold for optical quantum computing can be significantly improved by using the EPR-type of photon source. In this implementation, the detector efficiency $\eta_{d}$ is required to be larger than 50%, and the source efficiency $\eta_{s}$ can be an arbitrarily small positive number. This threshold compares favorably with the implementation using the single-photon source, where one requires the combined efficiency $\eta_{d}\eta_{s}>2/3$. We discuss several physical setups for realization of the required EPR photon source, including the photon emitter from a single-atom cavity., Comment: 4 pages, 2 figures

Quantum teleportation is the faithful transfer of quantum states between systems, relying on the prior establishment of entanglement and using only classical communication during the transmission. We report teleportation of quantum information between atomic quantum memories separated by about 1 meter. A quantum bit stored in a single trapped ytterbium ion (Yb+) is teleported to a second Yb+ atom with an average fidelity of 90% over a replete set of states. The teleportation protocol is based on the heralded entanglement of the atoms through interference and detection of photons emitted from each atom and guided through optical fibers. This scheme may be used for scalable quantum computation and quantum communication., Comment: 5 pages, 4 figures

When two atoms interact in the presence of an anharmonic potential, such as an optical lattice, the center of mass motion cannot be separated from the relative motion. In addition to generating a confinement-induced resonance (or shifting the position of an existing Feshbach resonance), the external potential changes the resonance picture qualitatively by introducing new resonances where molecular excited center of mass states cross the scattering threshold. We demonstrate the existence of these resonances, give their quantitative characterization in an optical superlattice, and propose an experimental scheme to detect them through controlled sweeping of the magnetic field., Comment: 6 pages, 5 figures; expanded presentation

We propose to utilize density distributions from a series of time-of-flight images of an expanding cloud to reconstruct single-particle correlation functions of trapped ultra-cold atoms. In particular, we show how this technique can be used to detect off-diagonal correlations of atoms in a quasi-one-dimensional trap, where both real- and momentum- space correlations are extracted at a quantitative level. The feasibility of this method is analyzed with specific examples, taking into account finite temporal and spatial resolutions in experiments., Comment: 7 pages, 4 figures

It is hard to stabilize the p-wave superfluid state of cold atomic gas in free space due to inelastic collisional losses. We consider the p-wave Feshbach resonance in an optical lattice, and show that it is possible to have a stable p-wave superfluid state where the multi-atom collisional loss is suppressed through the quantum Zeno effect. We derive the effective Hamiltonian for this system, and calculate its phase diagram in a one-dimensional optical lattice. The results show rich phase transitions between the p-wave superfluid state and different types of insulator states induced either by interaction or by dissipation., Comment: 5 pages, 5 figures

We demonstrate tunable spin-spin couplings between trapped atomic ions, mediated by laser forces on multiple transverse collective modes of motion. A $\sigma_x \sigma_x$-type Ising interaction is realized between quantum bits stored in the ground hyperfine clock states of Yb ions. We demonstrate entangling gates and tailor the spin-spin couplings with two and three trapped ions. The use of closely-spaced transverse modes provides a new class of interactions relevant to quantum computing and simulation with large collections of ions in a single crystal.

We demonstrate a probabilistic entangling quantum gate between two distant trapped ytterbium ions. The gate is implemented between the hyperfine "clock" state atomic qubits and mediated by the interference of two emitted photons carrying frequency encoded qubits. Heralded by the coincidence detection of these two photons, the gate has an average fidelity of 90+-2%. This entangling gate together with single qubit operations is sufficient to generate large entangled cluster states for scalable quantum computing.

We propose a large-scale quantum computer architecture by stabilizing a single large linear ion chain in a very simple trap geometry. By confining ions in an anharmonic linear trap with nearly uniform spacing between ions, we show that high-fidelity quantum gates can be realized in large linear ion crystals under the Doppler temperature based on coupling to a near-continuum of transverse motional modes with simple shaped laser pulses., Comment: 5 pages, 4 figures

We study through controlled numerical simulation the ground state properties of spin-polarized strongly interacting fermi gas in an anisotropic optical lattice, which is described by an effective one-dimensional general Hubbard model with particle correlated hopping rate. We show that the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type of state, while enhanced by a negative correlated hopping rate, can be completely suppressed by positive particle correlated hopping, yielding to an unusual magnetic phase even for particles with on-site attractive interaction We also find several different phase separation patterns for these atoms in an inhomogeneous harmonic trap, depending on the correlated hopping rate.

Fermions in an optical lattice near a wide Feshbach resonance are expected to be described by an effective Hamiltonian of the general Hubbard model with particle-assisted tunneling rates resulting from the strong atomic interaction [Phys. Rev. Lett. 95, 243202 (2005)]. Here, we propose a scheme to unambiguously test the predictions of this effective Hamiltonian through manipulation of ultracold atoms in an inhomogeneous optical superlattice. The structure of the low-energy Hilbert space as well as the particle assisted tunneling rates can be inferred from measurements of the time-of-flight images., Comment: 4 pages, 4 figures

We study the superfluid transition in a quasi-two-dimensional Fermi gas with a magnetic field tuning through a Feshbach resonance. Using an effective two-dimensional Hamiltonian with renormalized interaction between atoms and dressed molecules, we investigate the Berezinskii-Kosterlitz-Thouless transition temperature by studying the phase fluctuation effect. We also take into account the trapping potential in the radial plane, and discuss the number and superfluid density distributions. These results can be compared to experimental outcomes for gases prepared in one-dimensional optical lattices., Comment: 6 pages, 4 figures

We study the crossover of a quasi-two-dimensional Fermi gas trapped in the radial plane from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime by crossing a wide Feshbach resonance. We consider two effective two-dimensional Hamiltonians within the mean-field level, and calculate the zero-temperature cloud size and number density distribution. For a model 1 Hamiltonian with renormalized atom-atom interaction, we observe a constant cloud size for arbitrary detunings. For a model 2 Hamiltonian with renormalized interactions between atoms and dressed molecules, the cloud size deceases from the BCS to BEC side, which is consistent with the picture of BCS-BEC crossover. This qualitative discrepancy between the two models indicates that the inclusion of dressed molecules is essential for a mean-field description of quasi-two-dimensional Fermi systems, especially on the BEC side of the Feshbach resonance., Comment: 5 pages, 3 figures

We discuss several possible experimental signatures of the Bose-Einstein condensation (BEC) transition for an ultracold Bose gas in an inhomogeneous optical lattice. Based on the commonly used time-of-flight imaging technique, we show that the momentum-space density profile in the first Brillouin zone, supplemented by the visibility of interference patterns, provides valuable information about the system. In particular, by crossing the BEC transition temperature, the appearance of a clear bimodal structure sets a qualitative and universal signature of this phase transition. Furthermore, the momentum distribution can also be applied to extract the condensate fraction, which may serve as a promising thermometer in such a system., Comment: 12 pages, 13 figures; Revised version with new figures; Phys. Rev. A 77, 043626 (2008)