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.

1 aFoss-Feig, Michael1 aGong, Zhe-Xuan1 aGorshkov, Alexey, V.1 aClark, Charles, W. uhttps://arxiv.org/abs/1612.0780501522nas a2200169 4500008004100000245007200041210006900113260001500182300001100197490000800208520100900216100002301225700001901248700002301267700002501290856003701315 2015 eng d00aNearly-linear light cones in long-range interacting quantum systems0 aNearlylinear light cones in longrange interacting quantum system c2015/04/13 a1572010 v1143 a 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. 1 aFoss-Feig, Michael1 aGong, Zhe-Xuan1 aClark, Charles, W.1 aGorshkov, Alexey, V. uhttp://arxiv.org/abs/1410.3466v101241nas a2200181 4500008004100000245007500041210006900116260001500185490000700200520070200207100001300909700001500922700001900937700002000956700002300976700002300999856003701022 2011 eng d00aDetecting paired and counterflow superfluidity via dipole oscillations0 aDetecting paired and counterflow superfluidity via dipole oscill c2011/10/270 v843 a 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. 1 aHu, Anzi1 aMathey, L.1 aTiesinga, Eite1 aDanshita, Ippei1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/1103.3513v301378nas a2200157 4500008004100000245007600041210006900117260001300186490000700199520090300206100001301109700001501122700002301137700002301160856003701183 2010 eng d00aNoise correlations of one-dimensional Bose mixtures in optical lattices0 aNoise correlations of onedimensional Bose mixtures in optical la c2010/6/20 v813 a 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. 1 aHu, Anzi1 aMathey, L.1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/1002.4918v201137nas a2200157 4500008004100000245008200041210006900123260001300192490000700205520065000212100001500862700001900877700002300896700002300919856003700942 2009 eng d00aCollisional cooling of ultra-cold atom ensembles using Feshbach resonances 0 aCollisional cooling of ultracold atom ensembles using Feshbach r c2009/9/80 v803 a 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. 1 aMathey, L.1 aTiesinga, Eite1 aJulienne, Paul, S.1 aClark, Charles, W. uhttp://arxiv.org/abs/0903.2568v101819nas a2200181 4500008004100000245009700041210006900138260001400207490000700221520125900228100001301487700001501500700002001515700001901535700002301554700002301577856003701600 2009 eng d00aCounterflow and paired superfluidity in one-dimensional Bose mixtures in optical lattices 0 aCounterflow and paired superfluidity in onedimensional Bose mixt c2009/8/240 v803 a 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. 1 aHu, Anzi1 aMathey, L.1 aDanshita, Ippei1 aTiesinga, Eite1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/0906.2150v101425nas a2200169 4500008004100000245006800041210006700109260001400176490000700190520091100197100002701108700001801135700001901153700002301172700002301195856003701218 2008 eng d00aTunneling phase gate for neutral atoms in a double-well lattice0 aTunneling phase gate for neutral atoms in a doublewell lattice c2008/5/120 v773 a 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. 1 aStrauch, Frederick, W.1 aEdwards, Mark1 aTiesinga, Eite1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/0712.1856v101812nas a2200169 4500008004100000245010200041210006900143260001300212490000700225520125500232100002601487700002001513700001901533700002301552700002301575856004401598 2006 eng d00aMean-field treatment of the damping of the oscillations of a 1D Bose gas in an optical lattice 0 aMeanfield treatment of the damping of the oscillations of a 1D B c2006/1/90 v733 a 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. 1 aGea-Banacloche, Julio1 aRey, Ana, Maria1 aPupillo, Guido1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/cond-mat/0410677v401217nas a2200169 4500008004100000245006000041210005800101260001500159300001400174490000600188520072400194100001900918700002000937700002300957700002300980856004401003 2006 eng d00aPseudo-fermionization of 1-D bosons in optical lattices0 aPseudofermionization of 1D bosons in optical lattices c2006/08/30 a161 - 1610 v83 a 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. 1 aPupillo, Guido1 aRey, Ana, Maria1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/cond-mat/0505325v201431nas a2200169 4500008004100000245007100041210006900112260001400181490000700195520091200202100002001114700001801134700001901152700002301171700002301194856004401217 2005 eng d00aBragg Spectroscopy of ultracold atoms loaded in an optical lattice0 aBragg Spectroscopy of ultracold atoms loaded in an optical latti c2005/8/120 v723 a 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. 1 aRey, Ana, Maria1 aBlakie, Blair1 aPupillo, Guido1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/cond-mat/0406552v201428nas a2200181 4500008004100000245008400041210006900125260001500194300001600209490000700225520086200232100002301094700001901117700002001136700002301156700002301179856004401202 2005 eng d00aScalable register initialization for quantum computing in an optical lattice 0 aScalable register initialization for quantum computing in an opt c2005/06/14 a1687 - 16940 v383 a 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. 1 aBrennen, Gavin, K.1 aPupillo, Guido1 aRey, Ana, Maria1 aClark, Charles, W.1 aWilliams, Carl, J. uhttp://arxiv.org/abs/quant-ph/0312069v101494nas a2200157 4500008004100000245010300041210006900144260001400213490000700227520097300234100002001207700001901227700002301246700002301269856004401292 2005 eng d00aUltracold atoms confined in an optical lattice plus parabolic potential: a closed-form approach 0 aUltracold atoms confined in an optical lattice plus parabolic po c2005/9/220 v723 a 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. 1 aRey, Ana, Maria1 aPupillo, Guido1 aClark, Charles, W.1 aWilliams, Carl, J. uhttp://arxiv.org/abs/cond-mat/0503477v200922nas a2200157 4500008004100000245009800041210006900139260001500208520039600223100002100619700002300640700002300663700001900686700001500705856004400720 2004 eng d00aAdvantages of high-speed technique for quantum key distribution; reply to quant-ph/0407050 0 aAdvantages of highspeed technique for quantum key distribution r c2004/07/183 a 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. 1 aBienfang, J., C.1 aClark, Charles, W.1 aWilliams, Carl, J.1 aHagley, E., W.1 aWen, Jesse uhttp://arxiv.org/abs/quant-ph/0407139v101193nas a2200145 4500008004100000245012200041210006900163260001400232490000700246520068300253100002200936700002300958700002300981856004301004 2004 eng d00aRelativistic many-body calculations of electric-dipole matrix elements, lifetimes and polarizabilities in rubidium 0 aRelativistic manybody calculations of electricdipole matrix elem c2004/2/270 v693 a 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. 1 aSafronova, M., S.1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/physics/0307057v101546nas a2200181 4500008004100000245007100041210006900112260001500181300001600196490000700212520099700219100001901216700002001235700001901255700002301274700002301297856004401320 2004 eng d00aScalable quantum computation in systems with Bose-Hubbard dynamics0 aScalable quantum computation in systems with BoseHubbard dynamic c2004/02/15 a2395 - 24040 v513 a 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. 1 aPupillo, Guido1 aRey, Ana, Maria1 aBrennen, Gavin1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/quant-ph/0403052v201370nas a2200193 4500008004100000245007200041210006900113260001500182300001400197490000700211520079400218100002001012700001901032700001701051700001801068700002301086700002301109856004401132 2003 eng d00aBogoliubov approach to superfluidity of atoms in an optical lattice0 aBogoliubov approach to superfluidity of atoms in an optical latt c2003/03/14 a825 - 8410 v363 a 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. 1 aRey, Ana, Maria1 aBurnett, Keith1 aRoth, Robert1 aEdwards, Mark1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/cond-mat/0210550v201061nas a2200145 4500008004100000245004500041210004500086260001400131490000700145520065100152100002200803700002300825700002300848856004400871 2003 eng d00aOptimizing the fast Rydberg quantum gate0 aOptimizing the fast Rydberg quantum gate c2003/4/170 v673 a 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. 1 aSafronova, M., S.1 aWilliams, Carl, J.1 aClark, Charles, W. uhttp://arxiv.org/abs/quant-ph/0212081v1