We present theoretical and experimental studies of the decoherence of hyperfine ground-state superpositions due to elastic Rayleigh scattering of light off resonant with higher lying excited states. We demonstrate that under appropriate conditions, elastic Rayleigh scattering can be the dominant source of decoherence, contrary to previous discussions in the literature. We show that the elastic-scattering decoherence rate of a two-level system is given by the square of the difference between the elastic-scattering amplitudes for the two levels, and that for certain detunings of the light, the amplitudes can interfere constructively even when the elastic-scattering rates from the two levels are equal. We confirm this prediction through calculations and measurements of the total decoherence rate for a superposition of the valence electron spin levels in the ground state of ${}^9\mathrm{Be}^{+}$ in a 4.5 T magnetic field.

The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous polynomials to investigate the tensor rank of symmetric states such as the tripartite state $|W_3⟩=\frac{1}{\sqrt{3}}(|100⟩+|010⟩+|001⟩)$ and its $N$-partite generalization $|W_N⟩$. Previous tensor rank estimates are dramatically improved and we show that (i) three copies of $|W_3⟩$ have a rank of either 15 or 16, (ii) two copies of $|W_N⟩$ have a rank of $3N-2$, and (iii) $n$ copies of $|W_N⟩$ have a rank of $O(N)$. A remarkable consequence of these results is that certain multipartite transformations, impossible even probabilistically, can become possible when performed in multiple-copy bunches or when assisted by some catalyzing state. This effect is impossible for bipartite pure states.

We discover a simple factorization law describing how multipartite entanglement of a composite quantum system evolves when one of the subsystems undergoes an arbitrary physical process. This multipartite entanglement decay is determined uniquely by a single factor we call the entanglement resilience factor. Since the entanglement resilience factor is a function of the quantum channel alone, we find that multipartite entanglement evolves in exactly the same way as bipartite (two qudits) entanglement. For the two qubits case, our factorization law reduces to the main result of [T. Konrad, Nature Phys. 4, 99 (2008)]. In addition, for a permutation $P$, we provide an operational definition of $P$ asymmetry of entanglement, and find the conditions when a permuted version of a state can be achieved by local means.

We study the statistics of encounters of Lévy flights by introducing the concept of vicious Lévy flights—distinct groups of walkers performing independent Lévy flights with the process terminating upon the first encounter between walkers of different groups. We show that the probability that the process survives up to time $t$ decays as $t^{-\alpha }$ at late times. We compute $\alpha$ up to the second order in $\epsilon$ expansion, where $\epsilon =\sigma -d$, $\sigma$ is the Lévy exponent, and $d$ is the spatial dimension. For $d=\sigma$, we find the exponent of the logarithmic decay exactly. Theoretical values of the exponents are confirmed by numerical simulations. Our results indicate that walkers with smaller values of $\sigma$ survive longer and are therefore more effective at avoiding each other.

We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.

We show that ultracold Fermi gases in optical superlattices can be used as quantum simulators of relativistic lattice fermions in $3+1$ dimensions. By exploiting laser-assisted tunneling, we find an analogue of the so-called naive Dirac fermions, and thus provide a realization of the fermion doubling problem. Moreover, we show how to implement Wilson fermions, and discuss how their mass can be inverted by tuning the laser intensities. In this regime, our atomic gas corresponds to a phase of matter where Maxwell electrodynamics is replaced by axion electrodynamics: a 3D topological insulator.

Given a single copy of an unknown quantum state, the no-cloning theorem limits the amount of information that can be extracted from it. Given a gapped Hamiltonian, in most situations it is impractical to compute properties of its ground state, even though in principle all the information about the ground state is encoded in the Hamiltonian. We show in this Letter that if you know the Hamiltonian of a system and have a single copy of its ground state, you can use a quantum computer to efficiently compute its local properties. Specifically, in this scenario, we give efficient algorithms that copy small subsystems of the state and estimate the full statistics of any local measurement.

We demonstrate sub-Poissonian number differences in four-wave mixing of Bose-Einstein condensates of metastable helium. The collision between two Bose-Einstein condensates produces a scattering halo populated by pairs of atoms of opposing velocities, which we divide into several symmetric zones. We show that the atom number difference for opposing zones has sub-Poissonian noise fluctuations, whereas that of nonopposing zones is well described by shot noise. The atom pairs produced in a dual number state are well adapted to sub–shot-noise interferometry and studies of Einstein-Podolsky-Rosen–type nonlocality tests.

The unavoidable presence of noise is thought to be one of the major problems to solve in order to pave the way for implementing quantum information technologies in realistic physical platforms. However, here we show a clear example in which noise, in terms of dephasing, may enhance the capability of transmitting not only classical but also quantum information, encoded in quantum systems, through communication networks. In particular, we find analytically and numerically the quantum and classical capacities for a large family of quantum channels and show that these information transmission rates can be strongly enhanced by introducing dephasing noise in the complex network dynamics.

Quantum discord characterizes “nonclassicality” of correlations in quantum mechanics. It has been proposed as the key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. We obtain a necessary and sufficient condition for the existence of nonzero quantum discord for any dimensional bipartite states. This condition is easily experimentally implementable. Based on this, we propose a geometrical way of quantifying quantum discord. For two qubits this results in a closed form of expression for discord. We apply our results to the model of deterministic quantum computation with one qubit, showing that quantum discord is unlikely to be the reason behind its speedup.

We report the realization of a novel degenerate Fermi mixture with an $\mathrm{SU}(2)\times \mathrm{SU}(6)$ symmetry in a cold atomic gas. We successfully cool the mixture of the two fermionic isotopes of ytterbium ${}^{171}\mathrm{Yb}$ with the nuclear spin $I=1/2$ and ${}^{173}\mathrm{Yb}$ with $I=5/2$ below the Fermi temperature $T_F$ as $0.46T_F$ for ${}^{171}\mathrm{Yb}$ and $0.54T_F$ for ${}^{173}\mathrm{Yb}$. The same scattering lengths for different spin components make this mixture featured with the novel $\mathrm{SU}(2)\times \mathrm{SU}(6)$ symmetry. The nuclear spin components are separately imaged by exploiting an optical Stern-Gerlach effect. In addition, the mixture is loaded into a 3D optical lattice to implement the $\mathrm{SU}(2)\times \mathrm{SU}(6)$ Hubbard model. This mixture will open the door to the study of novel quantum phases such as a spinor Bardeen-Cooper-Schrieffer-like fermionic superfluid.

A novel metal-coated nanocylinder-cavity architecture fully compatible with III-V GaInAs technology and benefiting from a broad spectral range enhancement of the local density of states is proposed as an integrated source of nonclassical light. Because of a judicious selection of the mode volume, the cavity combines good collection efficiency ($\approx 45\%$), large Purcell factors ($\approx 15$) over a 80 nm spectral range, and a low sensitivity to inevitable spatial mismatches between the single emitter and the cavity mode. This represents a decisive step towards the implementation of reliable solid-state devices for the generation of entangled photon pairs at infrared wavelengths.

Quantum metrology promises improved sensitivity in parameter estimation over classical procedures. However, there is a debate over the question of how the sensitivity scales with the resources and the number of queries that are used in estimation procedures. Here, we reconcile the physical definition of the relevant resources used in parameter estimation with the information-theoretical scaling in terms of the query complexity of a quantum network. This leads to a completely general optimality proof of the Heisenberg limit for quantum metrology. We give an example of how our proof resolves paradoxes that suggest sensitivities beyond the Heisenberg limit, and we show that the Heisenberg limit is an information-theoretic interpretation of the Margolus-Levitin bound, rather than Heisenberg’s uncertainty relation.

We show that the dynamical melting of a Mott insulator in a three-dimensional lattice leads to condensation at nonzero momenta, a phenomenon that can be used to generate strongly interacting atom lasers in optical lattices. For infinite on-site repulsion, the case considered here, the momenta at which bosons condense are determined analytically and found to have a simple dependence on the hopping amplitudes. The occupation of the condensates is shown to scale linearly with the total number of atoms in the initial Mott insulator. Our results are obtained by using a Gutzwiller-type mean-field approach, gauged against exact-diagonalization solutions of small systems.

Decoherence due to contact with a hot environment typically restricts quantum phenomena to the low temperature limit, $k_{B}T/\hslash \omega \ll 1$ ($\hslash \omega$ is the typical energy of the system). Here we report the existence of a nonequilibrium state for two coupled, parametrically driven, dissipative harmonic oscillators which, contrary to generalized intuition, has stationary entanglement at high temperatures. This clarifies the role of temperature and could lighten the burden on quantum experiments requiring delicate precooling setups.

We present an algorithm that prepares thermal Gibbs states of one dimensional quantum systems on a quantum computer without any memory overhead, and in a time significantly shorter than other known alternatives. Specifically, the time complexity is dominated by the quantity $N^{\Vert h\Vert /T}$, where $N$ is the size of the system, $\Vert h\Vert$ is a bound on the operator norm of the local terms of the Hamiltonian (coupling energy), and $T$ is the temperature. Given other results on the complexity of thermalization, this overall scaling is likely optimal. For higher dimensions, our algorithm lowers the known scaling of the time complexity with the dimension of the system by one.

We demonstrate the coherent transport of 2D arrays of small ensembles of neutral atoms in a shift register architecture based on 2D arrays of microlenses. We show the scalability of the transport process by presenting the repeated hand over of atoms from site to site. We prove the conservation of coherence during transport, reloading, and a full shift register cycle. This shows that the fundamental shift sequence can be cascaded and thus scaled to complex and versatile 2D architectures for atom-based quantum information processing, quantum simulation, and the investigation of quantum degenerate gases.

Suppose an experimentalist wishes to verify that his apparatus produces entangled quantum states. A finite amount of data cannot conclusively demonstrate entanglement, so drawing conclusions from real-world data requires statistical reasoning. We propose a reliable method to quantify the weight of evidence for (or against) entanglement, based on a likelihood ratio test. Our method is universal in that it can be applied to any sort of measurements. We demonstrate the method by applying it to two simulated experiments on two qubits. The first measures a single entanglement witness, while the second performs a tomographically complete measurement.

We derive a fractional Fokker-Planck equation for subdiffusion in a general space- and time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights. The governing equation is derived from a generalized master equation and is shown to be equivalent to a subordinated stochastic Langevin equation.

We derive two classes of multimode Bell inequalities under local realistic assumptions, which are violated only by the entangled states negative under partial transposition in accordance with the Peres conjecture. Remarkably, the failure of local realism can be manifested by exploiting wave and particle correlations of readily accessible continuous-variable states, with very large violation of inequalities insensitive to detector efficiency, which makes a strong case for a loophole-free test.