arXiv subjects

Carl J. Williams

Publications and source records attributed to Carl J. Williams.

At least 19 recordsLinked to original sources

arXiv2024

Assessing the Benefits and Risks of Quantum Computers

Quantum computing is an emerging technology with potentially far-reaching implications for national prosperity and security. Understanding the timeframes over which economic benefits and national security risks may manifest themselves is vital for ensuring the prudent development of this technology. To inform security experts and policy decision makers on this matter, we review what is currently known on the potential uses and risks of quantum computers, leveraging current research literature. The maturity of currently-available quantum computers is not yet at a level such that they can be used in production for large-scale, industrially-relevant problems, and they are not believed to currently pose security risks. We identify 2 large-scale trends -- new approximate methods (variational algorithms, error mitigation, and circuit knitting) and the commercial exploration of business-relevant quantum applications -- which, together, may enable useful and practical quantum computing in the near future. Crucially, these methods do not appear likely to change the required resources for cryptanalysis on currently-used cryptosystems. From an analysis we perform of the current and known algorithms for cryptanalysis, we find they require circuits of a size exceeding those that can be run by current and near-future quantum computers (and which will require error correction), though we acknowledge improvements in quantum algorithms for these problems are taking place in the literature. In addition, the risk to cybersecurity can be well-managed by the migration to new, quantum-safe cryptographic protocols, which we survey and discuss. Given the above, we conclude there is a credible expectation that quantum computers will be capable of performing computations which are economically-impactful before they will be capable of performing ones which are cryptographically-relevant.

quant-ph↗

arXiv2019

Quantum Physics Meets Music: A "Real-Time" Guitar Recording Using Rydberg-Atoms and Electromagnetically Induced Transparency

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.

physics.atom-ph↗

arXiv2012

Chern numbers hiding in time-of-flight images

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.

cond-mat.quant-gas↗

arXiv2011

Detecting paired and counterflow superfluidity via dipole oscillations

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.

cond-mat.quant-gas↗

arXiv2010

Noise correlations of one-dimensional Bose mixtures in optical lattices

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.

cond-mat.quant-gas↗

arXiv2009

Counterflow and paired superfluidity in one-dimensional Bose mixtures in optical lattices

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 $π/2$ pulse followed by Bragg spectroscopy to detect the counterflow superfluid phase.

cond-mat.quant-gas↗

arXiv2008

Theoretical analysis of perfect quantum state transfer with superconducting qubits

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.

quant-ph↗

arXiv2006

Effects of finite temperature on the Mott insulator state

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.

cond-mat.other↗

arXiv2005

Bragg Spectroscopy of ultracold atoms loaded in an optical lattice

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 $S(q,ω)$ 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.

cond-mat.stat-mech↗

arXiv2005

Mean-field treatment of the damping of the oscillations of a 1D Bose gas in an optical lattice

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.

cond-mat.other↗

arXiv2005

Multichannel quantum-defect theory for slow atomic collisions

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.

physics.atom-ph↗

arXiv2005

Pseudo-fermionization of 1-D bosons in optical lattices

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.

cond-mat.other↗

arXiv2005

Ultracold atoms confined in an optical lattice plus parabolic potential: a closed-form approach

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.

cond-mat.other↗

arXiv2004

Advantages of high-speed technique for quantum key distribution; reply to quant-ph/0407050

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.

quant-ph↗

arXiv2004

Quantum key distribution with 1.25 Gbps clock synchronization

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.

quant-ph↗

arXiv2004

Scalable quantum computation in systems with Bose-Hubbard dynamics

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.

quant-ph↗

arXiv2003

Ultracold Cs$_2$ Feshbach Spectroscopy

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.

cond-mat.soft↗

arXiv2003

Scalable register initialization for quantum computing in an optical lattice

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.

quant-ph↗