We demonstrate how Rydberg atoms and the phenomena of electromagnetically induced transparency can be used to aid in the recording of a musical instrument in real time as it is played. Also, by using two different atomic species (cesium and rubidium) in the same vapor cell, we demonstrate the ability to record two guitars simultaneously, where each atomic species detects and allows for the recording of each guitar separately. The approach shows how audio data (the musical composition) can be detected with a quantum system, illustrating how we can control ensembles of atoms to such an extent that we can use them in this "entertaining" example of recording a musical instrument.

%8 04/01/2019 %G eng %U https://arxiv.org/abs/1904.01952 %0 Journal Article %J Physical Review A %D 2011 %T Chern numbers hiding in time-of-flight images %A Erhai Zhao %A Noah Bray-Ali %A Carl J. Williams %A I. B. Spielman %A Indubala I. Satija %X We present a technique for detecting topological invariants -- Chern numbers -- from time-of-flight images of ultra-cold atoms. We show that the Chern numbers of integer quantum Hall states of lattice fermions leave their fingerprints in the atoms' momentum distribution. We analytically demonstrate that the number of local maxima in the momentum distribution is equal to the Chern number in two limiting cases, for large hopping anisotropy and in the continuum limit. In addition, our numerical simulations beyond these two limits show that these local maxima persist for a range of parameters. Thus, an everyday observable in cold atom experiments can serve as a useful tool to characterize and visualize quantum states with non-trivial topology. %B Physical Review A %V 84 %8 2011/12/21 %G eng %U http://arxiv.org/abs/1105.3100v3 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.84.063629 %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 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 B %D 2008 %T Theoretical analysis of perfect quantum state transfer with superconducting qubits %A Frederick W. Strauch %A Carl J. Williams %X Superconducting quantum circuits, fabricated with multiple layers, are proposed to implement perfect quantum state transfer between nodes of a hypercube network. For tunable devices such as the phase qubit, each node can transmit quantum information to any other node at a constant rate independent of the distance between qubits. The physical limits of quantum state transfer in this network are theoretically analyzed, including the effects of disorder, decoherence, and higher-order couplings. %B Physical Review B %V 78 %8 2008/9/24 %G eng %U http://arxiv.org/abs/0708.0577v3 %N 9 %! Phys. Rev. B %R 10.1103/PhysRevB.78.094516 %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 Effects of finite temperature on the Mott insulator state %A Guido Pupillo %A Carl J. Williams %A Nikolay V. Prokof'ev %X We investigate the effects of finite temperature on ultracold Bose atoms confined in an optical lattice plus a parabolic potential in the Mott insulator state. In particular, we analyze the temperature dependence of the density distribution of atomic pairs in the lattice, by means of exact Monte-Carlo simulations. We introduce a simple model that quantitatively accounts for the computed pair density distributions at low enough temperatures. We suggest that the temperature dependence of the atomic pair statistics may be used to estimate the system's temperature at energies of the order of the atoms' interaction energy. %B Physical Review A %V 73 %8 2006/1/20 %G eng %U http://arxiv.org/abs/cond-mat/0407075v3 %N 1 %! Phys. Rev. A %R 10.1103/PhysRevA.73.013408 %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 Physical Review A %D 2005 %T Multichannel quantum-defect theory for slow atomic collisions %A Bo Gao %A Eite Tiesinga %A Carl J. Williams %A Paul S. Julienne %X We present a multichannel quantum-defect theory for slow atomic collisions that takes advantages of the analytic solutions for the long-range potential, and both the energy and the angular-momentum insensitivities of the short-range parameters. The theory provides an accurate and complete account of scattering processes, including shape and Feshbach resonances, in terms of a few parameters such as the singlet and the triplet scattering lengths. As an example, results for $^{23}$Na-$^{23}$Na scattering are presented and compared close-coupling calculations. %B Physical Review A %V 72 %8 2005/10/28 %G eng %U http://arxiv.org/abs/physics/0508060v1 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.72.042719 %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 Optics Express %D 2004 %T Quantum key distribution with 1.25 Gbps clock synchronization %A J. C. Bienfang %A A. J. Gross %A A. Mink %A B. J. Hershman %A A. Nakassis %A X. Tang %A R. Lu %A D. H. Su %A Charles W Clark %A Carl J. Williams %A E. W. Hagley %A Jesse Wen %X We have demonstrated the exchange of sifted quantum cryptographic key over a 730 meter free-space link at rates of up to 1.0 Mbps, two orders of magnitude faster than previously reported results. A classical channel at 1550 nm operates in parallel with a quantum channel at 845 nm. Clock recovery techniques on the classical channel at 1.25 Gbps enable quantum transmission at up to the clock rate. System performance is currently limited by the timing resolution of our silicon avalanche photodiode detectors. With improved detector resolution, our technique will yield another order of magnitude increase in performance, with existing technology. %B Optics Express %V 12 %P 2011 %8 2004/05/17 %G eng %U http://arxiv.org/abs/quant-ph/0405097v1 %N 9 %! Opt. Express %R 10.1364/OPEX.12.002011 %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 %0 Journal Article %J Physical Review A %D 2003 %T A Quantum Computer Architecture using Nonlocal Interactions %A Gavin K. Brennen %A Daegene Song %A Carl J. Williams %X Several authors have described the basic requirements essential to build a scalable quantum computer. Because many physical implementation schemes for quantum computing rely on nearest neighbor interactions, there is a hidden quantum communication overhead to connect distant nodes of the computer. In this paper we propose a physical solution to this problem which, together with the key building blocks, provides a pathway to a scalable quantum architecture using nonlocal interactions. Our solution involves the concept of a quantum bus that acts as a refreshable entanglement resource to connect distant memory nodes providing an architectural concept for quantum computers analogous to the von Neumann architecture for classical computers. %B Physical Review A %V 67 %8 2003/5/27 %G eng %U http://arxiv.org/abs/quant-ph/0301012v2 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.67.050302 %0 Journal Article %D 2003 %T Ultracold Cs$_2$ Feshbach Spectroscopy %A Cheng Chin %A Vladan Vuletic %A Andrew J. Kerman %A Steven Chu %A Eite Tiesinga %A Paul J. Leo %A Carl J. Williams %X We have observed and located more than 60 magnetic field-induced Feshbach resonances in ultracold collisions of ground-state $^{133}$Cs atoms. These resonances are associated with molecular states with up to four units of rotational angular momentum, and are detected through variations in the elastic, inelastic, and radiative collision cross sections. These observations allow us to greatly improve upon the interaction potentials between two cesium atoms and to reproduce the positions of most resonances to accuracies better than 0.5%. Based on the relevant coupling scheme between the electron spin, nuclear spin, and orbital angular momenta of the nuclei, quantum numbers and energy structure of the molecular states beneath the dissociation continuum are revealed. Finally, we predict the relevant collision properties for cesium Bose-Einstein condensation experiments. %8 2003/12/23 %G eng %U http://arxiv.org/abs/cond-mat/0312613v2 %0 Journal Article %J Physical Review A %D 2002 %T `Flat Phase' Loading of a Bose-Einstein Condensate into an Optical Lattice %A Shlomo E. Sklarz %A Inbal Friedler %A David J. Tannor %A Yehuda B. Band %A Carl J. Williams %X It has been proposed that the adiabatic loading of a Bose-Einstein Condensate (BEC) into an optical lattice via the Mott-insulator transition can be used to initialize a quantum computer [D. Jaksch, {\it et al.}, Phys. Rev. Lett. {\bf 81}, 3108 (1998)]. The loading of a BEC into the lattice without causing band excitation is readily achievable; however, unless one switches on an optical lattice very slowly, the optical lattice causes a phase to accumulate across the condensate. We show analytically and numerically that a cancellation of this effect is possible by adjusting the harmonic trap force-constant of the magnetic trap appropriately, thereby facilitating quick loading of an optical lattice for quantum computing purposes. A simple analytical theory is developed for a non-stationary BEC in a harmonic trap. %B Physical Review A %V 66 %8 2002/11/26 %G eng %U http://arxiv.org/abs/physics/0209071v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.66.053620