Showing papers in "Physical Review A in 2014"

Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects

Abstract: The practical construction of scalable quantum-computer hardware capable of executing nontrivial quantum algorithms will require the juxtaposition of different types of quantum systems. We analyze a modular ion trap quantum-computer architecture with a hierarchy of interactions that can scale to very large numbers of qubits. Local entangling quantum gates between qubit memories within a single register are accomplished using natural interactions between the qubits, and entanglement between separate registers is completed via a probabilistic photonic interface between qubits in different registers, even over large distances. We show that this architecture can be made fault tolerant, and demonstrate its viability for fault-tolerant execution of modest size quantum circuits.

Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes

Abstract: We propose a detailed stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs in whispering-gallery-mode resonators when they are pumped in either the anomalous- or normal-dispersion regime. We analyze the spatial bifurcation structure of the stationary states depending on two parameters that are experimentally tunable; namely, the pump power and the cavity detuning. Our study demonstrates that, in both the anomalous- and normal-dispersion cases, nontrivial equilibria play an important role in this bifurcation map because their associated eigenvalues undergo critical bifurcations that are actually foreshadowing the existence of localized and extended spatial dissipative structures. The corresponding bifurcation maps are evidence of a considerable richness from a dynamical standpoint. The case of anomalous dispersion is indeed the most interesting from the theoretical point of view because of the considerable variety of dynamical behavior that can be observed. For this case we study the emergence of super- and subcritical Turing patterns (or primary combs) in the system via modulational instability. We determine the areas where bright isolated cavity solitons emerge, and we show that soliton molecules can emerge as well. Very complex temporal patterns can actually be observed in the system, where solitons (or soliton complexes) coexist with or without mutual interactions. Our investigations also unveil the mechanism leading to the phenomenon of breathing solitons. Two routes to chaos in the system are identified; namely, a route via the destabilization of a primary comb, and another via the destabilization of solitons. For the case of normal dispersion, we unveil the mechanism leading to the emergence of weakly stable Turing patterns. We demonstrate that this weak stability is justified by the distribution of stable and unstable fixed points in the parameter space (flat states). We show that dark cavity solitons can emerge in the system, and also show how these solitons can coexist in the resonator as long as they do not interact with each other. We find evidence of breather solitons in this normal dispersion regime as well. The Kerr frequency combs corresponding to all these spatial dissipative structures are analyzed in detail, along with their stability properties. A discussion is led about the possibility to gain unifying comprehension of the observed spectra from the dynamical complexity of the system.

Symmetries and conserved quantities in Lindblad master equations

Abstract: This work is concerned with determination of the steady-state structure of time-independent Lindblad master equations, especially those possessing more than one steady state. The approach here is to treat Lindblad systems as generalizations of unitary quantum mechanics, extending the intuition of symmetries and conserved quantities to the dissipative case. We combine and apply various results to obtain an exhaustive characterization of the infinite-time behavior of Lindblad evolution, including both the structure of the infinite-time density matrix and its dependence on initial conditions. The effect of the environment in the infinite time limit can therefore be tracked exactly for arbitrary state initialization and without knowledge of dynamics at intermediate time. As a consequence, sufficient criteria for determining the steady state of a Lindblad master equation are obtained. These criteria are knowledge of the initial state, a basis for the steady-state subspace, and all conserved quantities. We give examples of two-qubit dissipation and single-mode $d$-photon absorption where all quantities are determined analytically. Applications of these techniques to quantum information, computation, and feedback control are discussed.

Concise security bounds for practical decoy-state quantum key distribution

Abstract: Due to its ability to tolerate high channel loss, decoy-state quantum key distribution (QKD) has been one of the main focuses within the QKD community. Notably, several experimental groups have demonstrated that it is secure and feasible under real-world conditions. Crucially, however, the security and feasibility claims made by most of these experiments were obtained under the assumption that the eavesdropper is restricted to particular types of attacks or that the finite-key effects are neglected. Unfortunately, such assumptions are not possible to guarantee in practice. In this work, we provide concise and tight finite-key security bounds for practical decoy-state QKD that are valid against general attacks.

Gate count estimates for performing quantum chemistry on small quantum computers

Abstract: Drastic improvements to quantum algorithms for chemistry are required to circumvent the obstacle that the number of coherently executable gates is many orders of magnitude higher than feasible today.

Canonical form of master equations and characterization of non-Markovianity

Abstract: Master equations govern the time evolution of a quantum system interacting with an environment, and may be written in a variety of forms. Time-independent or memoryless master equations, in particular, can be cast in the well-known Lindblad form. Any time-local master equation, Markovian or non-Markovian, may in fact also be written in a Lindblad-like form. A diagonalization procedure results in a unique, and in this sense canonical, representation of the equation, which may be used to fully characterize the non-Markovianity of the time evolution. Recently, several different measures of non-Markovianity have been presented which reflect, to varying degrees, the appearance of negative decoherence rates in the Lindblad-like form of the master equation. We therefore propose using the negative decoherence rates themselves, as they appear in the canonical form of the master equation, to completely characterize non-Markovianity. The advantages of this are especially apparent when more than one decoherence channel is present. We show that a measure proposed by Rivas et al. [Phys. Rev. Lett. 105, 050403 (2010)] is a surprisingly simple function of the canonical decoherence rates, and give an example of a master equation that is non-Markovian for all times $tg0$, but to which nearly all proposed measures are blind. We also give necessary and sufficient conditions for trace distance and volume measures to witness non-Markovianity, in terms of the Bloch damping matrix.

Solution for an interaction quench in the Lieb-Liniger Bose gas

Abstract: We study a quench protocol where the ground state of a free many-particle bosonic theory in one dimension is let unitarily evolve in time under the integrable Lieb-Liniger Hamiltonian of $\ensuremath{\delta}$-interacting repulsive bosons. By using a recently proposed variational method, we here obtain the exact nonthermal steady state of the system in the thermodynamic limit and discuss some of its main physical properties. Besides being a rare case of a thermodynamically exact solution to a truly interacting quench situation, this interestingly represents an example where a standard implementation of the generalized Gibbs ensemble fails.

Laser cooling and slowing of CaF molecules

Abstract: We demonstrate slowing and longitudinal cooling of a supersonic beam of CaF molecules using counter-propagating laser light resonant with a closed rotational and almost closed vibrational transition. A group of molecules are decelerated by about 20 m/s by applying light of a fixed frequency for 1.8 ms. Their velocity spread is reduced, corresponding to a final temperature of about 300 mK. The velocity is further reduced by chirping the frequency of the light to keep it in resonance as the molecules slow down.

Quantum electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

Abstract: In this work, we give a comprehensive derivation of an exact and numerically feasible method to perform ab initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierarchy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac field and the vector potential of the photon field, can be calculated by solving two coupled, nonlinear evolution equations without the need to explicitly determine the (numerically infeasible) many-body wave function of the coupled quantum system. To find reliable approximations to the implicit functionals, we present the appropriate Kohn-Sham construction. In the nonrelativistic limit, this density-functional-type theory of quantum electrodynamics reduces to the densityfunctional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photonfield. By making further approximations, e.g., restricting the allowed modes of the photon field, we derive further density-functional-type theories of coupled matter-photon systems for the corresponding approximate Hamiltonians. In the limit of only two sites and one mode we deduce the appropriate effective theory for the two-site Hubbard model coupled to one photonic mode. This model system is used to illustrate the basic ideas of a density-functional reformulation in great detail and we present the exact Kohn-Sham potentials for our coupled matter-photon model system.

Low-distance surface codes under realistic quantum noise

Abstract: Experimental implementation of the surface code will be a significant milestone for quantum computing. We develop a circuit and a decoder targeted for near-term implementation of a distance-3 surface code. We simulate the code under amplitude and phase damping and compare the threshold to a Pauli-twirl approximation. We find that the approximation yields a pessimistic threshold estimate. From numerical Monte Carlo simulations, we identify the gate and measurement speeds required to achieve reliable error correction. For superconductor devices, a qubit encoded in a 17-qubit surface code demonstrates a lower error rate than an unencoded qubit assuming gate times of 5--40 ns and ${T}_{1}$ times of at least 1--2 $\ensuremath{\mu}\mathrm{s}$. If ${T}_{1}\ensuremath{\ge}10$ ns, the difference is significant and can be experimentally measured, allowing near-term implementation and verification of a small surface code. For ion trap devices, gates times of 1 $\ensuremath{\mu}\mathrm{s}$ and ${T}_{1}\ensuremath{\ge}40$ ms admit measurable differences in error rate.

Improved entropic uncertainty relations and information exclusion relations

Abstract: The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes of incompatible measurements on one physical system, and a second reference system. We provide a more stringent formulation of both the uncertainty principle and the information exclusion principle, with direct applications for, e.g., the security analysis of quantum key distribution, entanglement estimation, and quantum communication. We also highlight a fundamental distinction between the complementarity of observables in terms of uncertainty and in terms of information

Tunable double optomechanically induced transparency in an optomechanical system

Abstract: We study the dynamics of a driven optomechanical cavity coupled to a charged nanomechanical resonator via Coulomb interaction, in which the tunable double optomechanically induced transparency (OMIT) can be observed from the output field at the probe frequency by controlling the strength of the Coulomb interaction. We calculate the splitting of the two transparency windows, which varies near linearly with the Coulomb coupling strength in a robust way against the cavity decay. Our double-OMIT is much different from the previously mentioned double-EIT or double-OMIT, and might be applied to measure the Coulomb coupling strength.

PT symmetry in the non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials

Abstract: We study the parity- and time-reversal ($\mathcal{PT}$) symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model with two conjugated imaginary potentials $\ifmmode\pm\else\textpm\fi{}i\ensuremath{\gamma}$ at two end sites. The SSH model is known as one of the simplest two-band topological models which has topologically trivial and nontrivial phases. We find that the non-Hermitian terms can lead to different effects on the properties of the eigenvalues spectrum in topologically trivial and nontrivial phases. In the topologically trivial phase, the system undergos an abrupt transition from the unbroken $\mathcal{PT}$-symmetry region to the spontaneously broken $\mathcal{PT}$-symmetry region at a certain ${\ensuremath{\gamma}}_{c}$, and a second transition occurs at another transition point ${\ensuremath{\gamma}}_{{c}^{{}^{\ensuremath{'}}}}$ when further increasing the strength of the imaginary potential $\ensuremath{\gamma}$. But in the topologically nontrivial phase, the zero-mode edge states become unstable for arbitrary nonzero $\ensuremath{\gamma}$ and the $\mathcal{PT}$ symmetry of the system is spontaneously broken, which is characterized by the emergence of a pair of conjugated imaginary modes.

Two-mode squeezed states in cavity optomechanics via engineering of a single reservoir

Abstract: We study theoretically a three-mode optomechanical system where two mechanical oscillators are independently coupled to a single cavity mode. By optimized two-tone or four-tone driving of the cavity, one can prepare the mechanical oscillators in an entangled two-mode squeezed state, even if they start in a thermal state. The highly pure, symmetric steady state achieved allows the optimal fidelity of standard continuous-variable teleportation protocols to be achieved. In contrast to other reservoir engineering approaches to generating mechanical entanglement, only a single reservoir is required to prepare the highly pure entangled steady state, greatly simplifying experimental implementation. The entanglement may be verified via a bound on the Duan inequality obtained from the cavity output spectrum. A similar technique may be used for the preparation of a highly pure two-mode squeezed state of two cavity modes, coupled to a common mechanical oscillator.

Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code

Abstract: Two implementations of an error-correction algorithm for topological quantum codes are described, and shown to be promising for fighting decoherence and making quantum computing scalable.

Continuous-variable measurement-device-independent quantum key distribution

Abstract: We propose a continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, in which detection is conducted by an untrusted third party. Our protocol can defend all detector side channels, which seriously threaten the security of a practical CV QKD system. Its security analysis against arbitrary collective attacks is derived based on the fact that the entanglement-based scheme of CV-MDI QKD is equivalent to the conventional CV QKD with coherent states and heterodyne detection. We find that the maximal total transmission distance is achieved by setting the untrusted third party close to one of the legitimate users. Furthermore, an alternate detection scheme, a special application of CV-MDI QKD, is proposed to enhance the security of the standard CV QKD system.

Loss-tolerant quantum cryptography with imperfect sources

Abstract: In principle, quantum key distribution (QKD) offers unconditional security based on the laws of physics. Unfortunately, all previous QKD experiments assume perfect state preparation in their security analysis. Therefore, the generated key is not proven to be secure in the presence of unavoidable modulation errors. The key reason that modulation errors are not considered in previous QKD experiments lies in a crucial weakness of the standard Gottesman-Lo-L\"utkenhaus-Preskill (GLLP) model, namely, it is not loss tolerant and Eve may in principle enhance imperfections through losses. Here, we propose a QKD protocol that is loss tolerant to state preparation flaws. Importantly, we show conclusively that the state preparation process in QKD can be much less precise than initially thought. Our method can also be applied to other quantum cryptographic protocols.

Protocol choice and parameter optimization in decoy-state measurement-device-independent quantum key distribution

Abstract: Measurement-device-independent quantum key distribution (MDI-QKD) has been demonstrated in both laboratories and field tests using attenuated lasers combined with the decoy-state technique. Although researchers have studied various decoy-state MDI-QKD protocols with two or three decoy states, a clear comparison between these protocols is still missing. This invokes the question of how many types of decoy states are needed for practical MDI-QKD. Moreover, the system parameters to implement decoy-state MDI-QKD are only partially optimized in all previous works, which casts doubt on the actual performance of former demonstrations. Here, we present analytical and numerical decoy-state methods with one, two, and three decoy states. We provide a clear comparison among these methods and find that two decoy states already enable a near-optimal estimation and more decoy states cannot improve the key rate much in either asymptotic or finite-data settings. Furthermore, we perform a full optimization of system parameters and show that full optimization can significantly improve the key rate in the finite-data setting. By simulating a real experiment, we find that full optimization can increase the key rate by more than one order of magnitude compared to nonoptimization. A local search method to optimize efficiently the system parameters is proposed. This method can be four orders of magnitude faster than a trivial exhaustive search to achieve a similar optimal key rate. We expect that this local search method could be valuable for general fields in physics.

Environmental dynamics, correlations, and the emergence of noncanonical equilibrium states in open quantum systems

Abstract: Quantum systems are invariably open, evolving under surrounding influences rather than in isolation. Standard open quantum system methods eliminate all information on the environmental state to yield a tractable description of the system dynamics. By incorporating a collective coordinate of the environment into the system Hamiltonian, we circumvent this limitation. Our theory provides straightforward access to important environmental properties that would otherwise be obscured, allowing us to quantify the evolving system-environment correlations. As a direct result, we show that the generation of robust system-environment correlations that persist into equilibrium (heralded also by the emergence of non-Gaussian environmental states) renders the canonical system steady state almost always incorrect. The resulting equilibrium states deviate markedly from those predicted by standard perturbative techniques and are instead fully characterized by thermal states of the mapped system-collective coordinate Hamiltonian. We outline how noncanonical system states could be investigated experimentally to study deviations from canonical thermodynamics, with direct relevance to molecular and solid-state nanosystems.

Analytic results for a quantum quench from free to hard-core one dimensional bosons

Abstract: It is widely believed that the stationary properties after a quantum quench in integrable systems can be described by a generalized Gibbs ensemble (GGE), even if all the analytical evidence is based on free theories in which the pre- and post-quench modes are linearly related. In contrast, we consider the experimentally relevant quench of the one-dimensional Bose gas from zero to infinite interaction, in which the relation between modes is nonlinear, and consequently Wick's theorem does not hold. We provide exact analytical results for the time evolution of the dynamical density-density correlation function at any time after the quench and we prove that its stationary value is described by a GGE in which Wick's theorem is restored.

Fast adiabatic qubit gates using only σ z control

Abstract: A controlled-phase gate was demonstrated in superconducting Xmon transmon qubits with fidelity reaching 99.4%, relying on the adiabatic interaction between the $|11\ensuremath{\rangle}$ and $|02\ensuremath{\rangle}$ states. Here we explain the theoretical concepts behind this protocol, which achieves fast gate times with only ${\ensuremath{\sigma}}_{z}$ control of the Hamiltonian, based on a theory of nonlinear mapping of state errors to a power spectral density and use of optimal window functions. With a solution given in the Fourier basis, optimization is shown to be straightforward for practical cases of an arbitrary state change and finite bandwidth of control signals. We find that errors below ${10}^{\ensuremath{-}4}$ are readily achievable for realistic control wave forms.

Sensitivity limits of a Raman atom interferometer as a gravity gradiometer

Abstract: We evaluate the sensitivity of a dual cloud atom interferometer to the measurement of vertical gravity gradient. We study the influence of most relevant experimental parameters on noise and long term drifts. Results are also applied to the case of doubly differential measurements of the gravitational signal from local source masses. We achieve a short-term sensitivity of $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ g/$\sqrt{\text{Hz}}$ to differential gravity acceleration, limited by the quantum projection noise of the instrument. Active control of the most critical parameters allows us to reach a resolution of $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ g after 8000 s on the measurement of differential gravity acceleration. The long-term stability is compatible with a measurement of the gravitational constant $G$ at the level of ${10}^{\ensuremath{-}4}$ after an integration time of about 100 h.

Optomechanical analog of two-color electromagnetically induced transparency: Photon transmission through an optomechanical device with a two-level system

Abstract: Some optomechanical systems can be transparent to a probe field when a strong driving field is applied. These systems can provide an optomechanical analog of electromagnetically induced transparency (EIT). We study the transmission of a probe field through a hybrid optomechanical system consisting of a cavity and a mechanical resonator with a two-level system (qubit). The qubit might be an intrinsic defect inside the mechanical resonator, a superconducting artificial atom, or another two-level system. The mechanical resonator is coupled to the cavity field via radiation pressure and to the qubit via the Jaynes-Cummings interaction. We find that the dressed two-level system and mechanical phonon can form two sets of three-level systems. Thus, there are two transparency windows in the discussed system. We interpret this effect as an optomechanical analog of two-color EIT (or double EIT). We demonstrate how to switch between one and two EIT windows by changing the transition frequency of the qubit. We show that the absorption and dispersion of the system are mainly affected by the qubit-phonon coupling strength and the transition frequency of the qubit.

Bloch bound states in the radiation continuum in a periodic array of dielectric rods

Abstract: We consider an infinite periodic array of dielectric rods in vacuum with the aim to demonstrate three types of Bloch bound states in the continuum (BSCs): symmetry protected with a zero Bloch vector, embedded in one diffraction channel with nonzero Bloch vector, and embedded in two and three diffraction channels. The first and second types of the BSC exist for a wide range of material parameters of the rods, while the third occurs only at a specific value of the radius of the rods. We show that the second type supports the power flux along the array. In order to find BSCs we put forward an approach based on the expansion over the Hankel functions. We show how the BSC reveals itself in the scattering function when the singular BSC point is approached along a specific path in the parametric space.

Strong majorization entropic uncertainty relations

Abstract: We analyze entropic uncertainty relations in a finite-dimensional Hilbert space and derive several strong bounds for the sum of two entropies obtained in projective measurements with respect to any two orthogonal bases. We improve the recent bounds by Coles and Piani [P. Coles and M. Piani, Phys. Rev. A 89, 022112 (2014)], which are known to be stronger than the well-known result of Maassen and Uffink [H. Maassen and J. B. M. Uffink, Phys. Rev. Lett. 60, 1103 (1988)]. Furthermore, we find a bound based on majorization techniques, which also happens to be stronger than the recent results involving the largest singular values of submatrices of the unitary matrix connecting both bases. The first set of bounds gives better results for unitary matrices close to the Fourier matrix, while the second one provides a significant improvement in the opposite sectors. Some results derived admit generalization to arbitrary mixed states, so that corresponding bounds are increased by the von Neumann entropy of the measured state. The majorization approach is finally extended to the case of several measurements.

Trapping light in open plasmonic nanostructures

Abstract: In open resonators the energy associated with a localized photonic excitation is lost in the form of a radiated wave, in the same manner that a classical charged particle in a curved orbit loses energy in the form of electromagnetic radiation. As a consequence, photonic modes in conventional spatially bounded open resonators have finite decay times. Here, we theoretically show that, surprisingly, in the limit of vanishing material loss, plasmons give the opportunity to have light localization in open spatially bounded systems with infinitely large lifetimes.

Quantum magnetism without lattices in strongly interacting one-dimensional spinor gases

Abstract: We show that strongly interacting multicomponent gases in one dimension realize an effective spin chain, offering an alternative simple scenario for the study of one-dimensional (1D) quantum magnetism in cold gases in the absence of an optical lattice. The spin-chain model allows for an intuitive understanding of recent experiments and for a simple calculation of relevant observables. We analyze the adiabatic preparation of antiferromagnetic and ferromagnetic ground states, and show that many-body spin states may be efficiently probed in tunneling experiments. The spin-chain model is valid for more than two components, opening the possibility of realizing SU(N) quantum magnetism in strongly interacting 1D alkaline-earth-metal or ytterbium Fermi gases. (Less)

Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems

Abstract: Achieving fast population transfer (FPT) in multiparticle systems based on the cavity quantum electronic dynamics is an outstanding challenge. In this paper, motivated by the quantum Zeno dynamics, a shortcut for performing the FPT of ground states in multiparticle systems with the invariant-based inverse engineering is proposed. Numerical simulation demonstrates that a perfect population transfer of ground states in multiparticle systems can be rapidly achieved in one step, and the FPT is robust to both the cavity decay and atomic spontaneous emission. Additionally, this scheme is not only implemented without requiring extra complex conditions, but also insensitive to variations of the parameters.

Designing frequency-dependent relaxation rates and Lamb shifts for a giant artificial atom

Abstract: In traditional quantum optics, where the interaction between atoms and light at optical frequencies is studied, the atoms can be approximated as pointlike when compared to the wavelength of light. So far, this relation has also been true for artificial atoms made out of superconducting circuits or quantum dots, interacting with microwave radiation. However, recent and ongoing experiments using surface acoustic waves show that a single artificial atom can be coupled to a bosonic field at several points wavelengths apart. Here, we theoretically study this type of system. We find that the multiple coupling points give rise to a frequency dependence in the coupling strength between the atom and its environment and also in the Lamb shift of the atom. The frequency dependence is given by the discrete Fourier transform of the coupling-point coordinates and can therefore be designed. We discuss a number of possible applications for this phenomenon, including tunable coupling, single-atom lasing, and other effects that can be achieved by designing the relative coupling strengths of different transitions in a multilevel atom.