Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the achievable benefits in this context are much less clear. Combining recent exact solutions with a controlled expansion in the system size, we analyze quench dynamics in Ising models with power-law (1/r α ) interactions in D dimensions, thereby expanding the understanding of spin squeezing into a broad and experimentally relevant context. In spatially homogeneous systems, we show that for small α the scaling of squeezing with system size is identical to the infinite-range (α = 0) case. This indifference to the interaction range persists up to a critical value α = 2D/3, above which squeezing degrades continuously. Boundaryinduced inhomogeneities present in most experimental systems modify this picture, but it nevertheless remains qualitatively correct for finite-sized systems.

%8 2016/12/22 %G eng %U https://arxiv.org/abs/1612.07805 %0 Journal Article %J Physical Review Letters %D 2015 %T Nearly-linear light cones in long-range interacting quantum systems %A Michael Foss-Feig %A Zhe-Xuan Gong %A Charles W. Clark %A Alexey V. Gorshkov %X In non-relativistic quantum theories with short-range Hamiltonians, a velocity $v$ can be chosen such that the influence of any local perturbation is approximately confined to within a distance $r$ until a time $t \sim r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law ($1/r^{\alpha}$) interactions, when $\alpha$ exceeds the dimension $D$, an analogous bound confines influences to within a distance $r$ only until a time $t\sim(\alpha/v)\log r$, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time. We rule out this possibility; light cones of power-law interacting systems are algebraic for $\alpha>2D$, becoming linear as $\alpha\rightarrow\infty$. Our results impose strong new constraints on the growth of correlations and the production of entangled states in a variety of rapidly emerging, long-range interacting atomic, molecular, and optical systems. %B Physical Review Letters %V 114 %P 157201 %8 2015/04/13 %G eng %U http://arxiv.org/abs/1410.3466v1 %N 15 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.114.157201 %0 Journal Article %J Physical Review A %D 2011 %T Detecting paired and counterflow superfluidity via dipole oscillations %A Anzi Hu %A L. Mathey %A Eite Tiesinga %A Ippei Danshita %A Carl J. Williams %A Charles W. Clark %X We suggest an experimentally feasible procedure to observe paired and counterflow superfluidity in ultra-cold atom systems. We study the time evolution of one-dimensional mixtures of bosonic atoms in an optical lattice following an abrupt displacement of an additional weak confining potential. We find that the dynamic responses of the paired superfluid phase for attractive inter-species interactions and the counterflow superfluid phase for repulsive interactions are qualitatively distinct and reflect the quasi long-range order that characterizes these states. These findings suggest a clear experimental procedure to detect these phases, and give an intuitive insight into their dynamics. %B Physical Review A %V 84 %8 2011/10/27 %G eng %U http://arxiv.org/abs/1103.3513v3 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.84.041609 %0 Journal Article %J Physical Review A %D 2010 %T Noise correlations of one-dimensional Bose mixtures in optical lattices %A Anzi Hu %A L. Mathey %A Carl J. Williams %A Charles W. Clark %X We study the noise correlations of one-dimensional binary Bose mixtures, as a probe of their quantum phases. In previous work, we found a rich structure of many-body phases in such mixtures, such as paired and counterflow superfluidity. Here we investigate the signature of these phases in the noise correlations of the atomic cloud after time-of-flight expansion, using both Luttinger liquid theory and the time-evolving block decimation (TEBD) method. We find that paired and counterflow superfluidity exhibit distinctive features in the noise spectra. We treat both extended and inhomogeneous systems, and our numerical work shows that the essential physics of the extended systems is present in the trapped-atom systems of current experimental interest. For paired and counterflow superfluid phases, we suggest methods for extracting Luttinger parameters from noise correlation spectroscopy. %B Physical Review A %V 81 %8 2010/6/2 %G eng %U http://arxiv.org/abs/1002.4918v2 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.81.063602 %0 Journal Article %J Physical Review A %D 2009 %T Collisional cooling of ultra-cold atom ensembles using Feshbach resonances %A L. Mathey %A Eite Tiesinga %A Paul S. Julienne %A Charles W. Clark %X We propose a new type of cooling mechanism for ultra-cold fermionic atom ensembles, which capitalizes on the energy dependence of inelastic collisions in the presence of a Feshbach resonance. We first discuss the case of a single magnetic resonance, and find that the final temperature and the cooling rate is limited by the width of the resonance. A concrete example, based on a p-wave resonance of $^{40}$K, is given. We then improve upon this setup by using both a very sharp optical or radio-frequency induced resonance and a very broad magnetic resonance and show that one can improve upon temperatures reached with current technologies. %B Physical Review A %V 80 %8 2009/9/8 %G eng %U http://arxiv.org/abs/0903.2568v1 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.80.030702 %0 Journal Article %J Physical Review A %D 2009 %T Counterflow and paired superfluidity in one-dimensional Bose mixtures in optical lattices %A Anzi Hu %A L. Mathey %A Ippei Danshita %A Eite Tiesinga %A Carl J. Williams %A Charles W. Clark %X We study the quantum phases of mixtures of ultra-cold bosonic atoms held in an optical lattice that confines motion or hopping to one spatial dimension. The phases are found by using Tomonaga-Luttinger liquid theory as well as the numerical method of time evolving block decimation (TEBD). We consider a binary mixture with repulsive intra-species interactions, and either repulsive or attractive inter-species interaction. For a homogeneous system, we find paired- and counterflow-superfluid phases at different filling and hopping energies. We also predict parameter regions in which these types of superfluid order coexist with charge density wave order. We show that the Tomonaga-Luttinger liquid theory and TEBD qualitatively agree on the location of the phase boundary to superfluidity. We then describe how these phases are modified and can be detected when an additional harmonic trap is present. In particular, we show how experimentally measurable quantities, such as time-of-flight images and the structure factor, can be used to distinguish the quantum phases. Finally, we suggest applying a Feshbach ramp to detect the paired superfluid state, and a $\pi/2$ pulse followed by Bragg spectroscopy to detect the counterflow superfluid phase. %B Physical Review A %V 80 %8 2009/8/24 %G eng %U http://arxiv.org/abs/0906.2150v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.80.023619 %0 Journal Article %J Physical Review A %D 2008 %T Tunneling phase gate for neutral atoms in a double-well lattice %A Frederick W. Strauch %A Mark Edwards %A Eite Tiesinga %A Carl J. Williams %A Charles W. Clark %X We propose a new two--qubit phase gate for ultra--cold atoms confined in an experimentally realized tilted double--well optical lattice [Sebby--Strabley et al., Phys. Rev. A {\bf 73} 033605 (2006)]. Such a lattice is capable of confining pairs of atoms in a two--dimensional array of double--well potentials where control can be exercised over the barrier height and the energy difference of the minima of the two wells (known as the ``tilt''). The four lowest single--particle motional states consist of two pairs of motional states in which each pair is localized on one side of the central barrier, allowing for two atoms confined in such a lattice to be spatially separated qubits. We present a time--dependent scheme to manipulate the tilt to induce tunneling oscillations which produce a collisional phase gate. Numerical simulations demonstrate that this gate can be performed with high fidelity. %B Physical Review A %V 77 %8 2008/5/12 %G eng %U http://arxiv.org/abs/0712.1856v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.77.050304 %0 Journal Article %J Physical Review A %D 2006 %T Mean-field treatment of the damping of the oscillations of a 1D Bose gas in an optical lattice %A Julio Gea-Banacloche %A Ana Maria Rey %A Guido Pupillo %A Carl J. Williams %A Charles W. Clark %X We present a theoretical treatment of the surprisingly large damping observed recently in one-dimensional Bose-Einstein atomic condensates in optical lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB) calculations can describe qualitatively the main features of the damping observed over a range of lattice depths. We also derive a formula of the fluctuation-dissipation type for the damping, based on a picture in which the coherent motion of the condensate atoms is disrupted as they try to flow through the random local potential created by the irregular motion of noncondensate atoms. We expect this irregular motion to result from the well-known dynamical instability exhibited by the mean-field theory for these systems. When parameters for the characteristic strength and correlation times of the fluctuations, obtained from the HFB calculations, are substituted in the damping formula, we find very good agreement with the experimentally-observed damping, as long as the lattice is shallow enough for the fraction of atoms in the Mott insulator phase to be negligible. We also include, for completeness, the results of other calculations based on the Gutzwiller ansatz, which appear to work better for the deeper lattices. %B Physical Review A %V 73 %8 2006/1/9 %G eng %U http://arxiv.org/abs/cond-mat/0410677v4 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.73.013605 %0 Journal Article %J New Journal of Physics %D 2006 %T Pseudo-fermionization of 1-D bosons in optical lattices %A Guido Pupillo %A Ana Maria Rey %A Carl J. Williams %A Charles W. Clark %X We present a model that generalizes the Bose-Fermi mapping for strongly correlated 1D bosons in an optical lattice, to cases in which the average number of atoms per site is larger than one. This model gives an accurate account of equilibrium properties of such systems, in parameter regimes relevant to current experiments. The application of this model to non-equilibrium phenomena is explored by a study of the dynamics of an atom cloud subject to a sudden displacement of the confining potential. Good agreement is found with results of recent experiments. The simplicity and intuitive appeal of this model make it attractive as a general tool for understanding bosonic systems in the strongly correlated regime. %B New Journal of Physics %V 8 %P 161 - 161 %8 2006/08/30 %G eng %U http://arxiv.org/abs/cond-mat/0505325v2 %N 8 %! New J. Phys. %R 10.1088/1367-2630/8/8/161 %0 Journal Article %J Physical Review A %D 2005 %T Bragg Spectroscopy of ultracold atoms loaded in an optical lattice %A Ana Maria Rey %A P. Blair Blakie %A Guido Pupillo %A Carl J. Williams %A Charles W. Clark %X We study Bragg spectroscopy of ultra-cold atoms in one-dimensional optical lattices as a method for probing the excitation spectrum in the Mott insulator phase, in particular the one particle-hole excitation band. Within the framework of perturbation theory we obtain an analytical expression for the dynamic structure factor $S(q,\omega)$ and use it to calculate the imparted energy which has shown to be a relevant observable in recent experiments. We test the accuracy of our approximations by comparing them with numerically exact solutions of the Bose-Hubbard model in restricted cases and establish the limits of validity of our linear response analysis. Finally we show that when the system is deep in the Mott insulator regime, its response to the Bragg perturbation is temperature dependent. We suggest that this dependence might be used as a tool to probe temperatures of order of the Mott gap. %B Physical Review A %V 72 %8 2005/8/12 %G eng %U http://arxiv.org/abs/cond-mat/0406552v2 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.72.023407 %0 Journal Article %J Journal of Physics B: Atomic, Molecular and Optical Physics %D 2005 %T Scalable register initialization for quantum computing in an optical lattice %A Gavin K. Brennen %A Guido Pupillo %A Ana Maria Rey %A Charles W. Clark %A Carl J. Williams %X The Mott insulator state created by loading an atomic Bose-Einstein condensate (BEC) into an optical lattice may be used as a means to prepare a register of atomic qubits in a quantum computer. Such architecture requires a lattice commensurately filled with atoms, which corresponds to the insulator state only in the limit of zero inter-well tunneling. We show that a lattice with spatial inhomogeneity created by a quadratic magnetic trapping potential can be used to isolate a subspace in the center which is impervious to hole-hoping. Components of the wavefunction with more than one atom in any well can be projected out by selective measurement on a molecular photo-associative transition. Maintaining the molecular coupling induces a quantum Zeno effect that can sustain a commensurately filled register for the duration of a quantum computation. %B Journal of Physics B: Atomic, Molecular and Optical Physics %V 38 %P 1687 - 1694 %8 2005/06/14 %G eng %U http://arxiv.org/abs/quant-ph/0312069v1 %N 11 %! J. Phys. B: At. Mol. Opt. Phys. %R 10.1088/0953-4075/38/11/010 %0 Journal Article %J Physical Review A %D 2005 %T Ultracold atoms confined in an optical lattice plus parabolic potential: a closed-form approach %A Ana Maria Rey %A Guido Pupillo %A Charles W. Clark %A Carl J. Williams %X We discuss interacting and non-interacting one dimensional atomic systems trapped in an optical lattice plus a parabolic potential. We show that, in the tight-binding approximation, the non-interacting problem is exactly solvable in terms of Mathieu functions. We use the analytic solutions to study the collective oscillations of ideal bosonic and fermionic ensembles induced by small displacements of the parabolic potential. We treat the interacting boson problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From analysis of the dependence upon lattice depth of the low-energy excitation spectrum of the interacting system, we consider the problems of "fermionization" of a Bose gas, and the superfluid-Mott insulator transition. The spectrum of the noninteracting system turns out to provide a useful guide to understanding the collective oscillations of the interacting system, throughout a large and experimentally relevant parameter regime. %B Physical Review A %V 72 %8 2005/9/22 %G eng %U http://arxiv.org/abs/cond-mat/0503477v2 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.72.033616 %0 Journal Article %D 2004 %T Advantages of high-speed technique for quantum key distribution; reply to quant-ph/0407050 %A J. C. Bienfang %A Charles W. Clark %A Carl J. Williams %A E. W. Hagley %A Jesse Wen %X We respond to a comment on our high-speed technique for the implementation of free-space quantum key distribution (QKD). The model used in the comment assigns inappropriately high link losses to the technique in question. We show that the use of reasonable loss parameters in the model invalidates the comment's main conclusion and highlights the benefits of increased transmission rates. %8 2004/07/18 %G eng %U http://arxiv.org/abs/quant-ph/0407139v1 %0 Journal Article %J Physical Review A %D 2004 %T Relativistic many-body calculations of electric-dipole matrix elements, lifetimes and polarizabilities in rubidium %A M. S. Safronova %A Carl J. Williams %A Charles W. Clark %X Electric-dipole matrix elements for ns-n'p, nd-n'p, and 6d-4f transitions in Rb are calculated using a relativistic all-order method. A third-order calculation is also carried out for these matrix elements to evaluate the importance of the high-order many-body perturbation theory contributions. The all-order matrix elements are used to evaluate lifetimes of ns and np levels with n=6, 7, 8 and nd levels with n=4, 5, 6 for comparison with experiment and to provide benchmark values for these lifetimes. The dynamic polarizabilities are calculated for ns states of rubidium. The resulting lifetime and polarizability values are compared with available theory and experiment. %B Physical Review A %V 69 %8 2004/2/27 %G eng %U http://arxiv.org/abs/physics/0307057v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.69.022509 %0 Journal Article %J Journal of Modern Optics %D 2004 %T Scalable quantum computation in systems with Bose-Hubbard dynamics %A Guido Pupillo %A Ana Maria Rey %A Gavin Brennen %A Carl J. Williams %A Charles W. Clark %X Several proposals for quantum computation utilize a lattice type architecture with qubits trapped by a periodic potential. For systems undergoing many body interactions described by the Bose-Hubbard Hamiltonian, the ground state of the system carries number fluctuations that scale with the number of qubits. This process degrades the initialization of the quantum computer register and can introduce errors during error correction. In an earlier manuscript we proposed a solution to this problem tailored to the loading of cold atoms into an optical lattice via the Mott Insulator phase transition. It was shown that by adding an inhomogeneity to the lattice and performing a continuous measurement, the unit filled state suitable for a quantum computer register can be maintained. Here, we give a more rigorous derivation of the register fidelity in homogeneous and inhomogeneous lattices and provide evidence that the protocol is effective in the finite temperature regime. %B Journal of Modern Optics %V 51 %P 2395 - 2404 %8 2004/02/15 %G eng %U http://arxiv.org/abs/quant-ph/0403052v2 %N 16-18 %! Journal of Modern Optics %R 10.1080/09500340408231798 %0 Journal Article %J Journal of Physics B: Atomic, Molecular and Optical Physics %D 2003 %T Bogoliubov approach to superfluidity of atoms in an optical lattice %A Ana Maria Rey %A Keith Burnett %A Robert Roth %A Mark Edwards %A Carl J. Williams %A Charles W. Clark %X We use the Bogoliubov theory of atoms in an optical lattice to study the approach to the Mott-insulator transition. We derive an explicit expression for the superfluid density based on the rigidity of the system under phase variations. This enables us to explore the connection between the quantum depletion of the condensate and the quasi-momentum distribution on the one hand and the superfluid fraction on the other. The approach to the insulator phase may be characterized through the filling of the band by quantum depletion, which should be directly observable via the matter wave interference patterns. We complement these findings by self-consistent Hartree-Fock-Bogoliubov-Popov calculations for one-dimensional lattices including the effects of a parabolic trapping potential. %B Journal of Physics B: Atomic, Molecular and Optical Physics %V 36 %P 825 - 841 %8 2003/03/14 %G eng %U http://arxiv.org/abs/cond-mat/0210550v2 %N 5 %! J. Phys. B: At. Mol. Opt. Phys. %R 10.1088/0953-4075/36/5/304 %0 Journal Article %J Physical Review A %D 2003 %T Optimizing the fast Rydberg quantum gate %A M. S. Safronova %A Carl J. Williams %A Charles W. Clark %X The fast phase gate scheme, in which the qubits are atoms confined in sites of an optical lattice, and gate operations are mediated by excitation of Rydberg states, was proposed by Jaksch et al. Phys. Rev. Lett. 85, 2208 (2000). A potential source of decoherence in this system derives from motional heating, which occurs if the ground and Rydberg states of the atom move in different optical lattice potentials. We propose to minimize this effect by choosing the lattice photon frequency \omega so that the ground and Rydberg states have the same frequency-dependent polarizability \alpha(omega). The results are presented for the case of Rb. %B Physical Review A %V 67 %8 2003/4/17 %G eng %U http://arxiv.org/abs/quant-ph/0212081v1 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.67.040303