Showing papers in "Journal of Physics B in 2011"

Essential entanglement for atomic and molecular physics

Abstract: Entanglement is nowadays considered as a key quantity for the understanding of correlations, transport properties and phase transitions in composite quantum systems, and thus receives interest beyond the engineered applications in the focus of quantum information science. We review recent experimental and theoretical progress in the study of quantum correlations under that wider perspective, with an emphasis on rigorous definitions of the entanglement of identical particles, and on entanglement studies in atoms and molecules.Corrections were made to this article on 28 September 2011. The received date was incorrectly given.

Dynamical decoupling sequence construction as a filter-design problem

Abstract: Over the past decade we have seen an explosion of demonstrations of quantum coherence in atomic, optical and condensed matter systems. These developments have placed a new emphasis on the production of robust and optimal quantum control techniques in the presence of environmental noise. We discuss the use of dynamical decoupling as a form of open-loop quantum control capable of suppressing the effects of dephasing in quantum coherent systems. We introduce the concept of dynamical decoupling pulse-sequence construction as a filter-design problem, making connections with filter design from control theory and electrical engineering in the analysis of pulse-sequence performance for the preservation of the phase degree of freedom in a quantum superposition. A detailed mathematical description of how dephasing and its suppression can be reduced to a linear control problem is provided, and used as motivation and context for studies of the filtration properties of various dynamical decoupling sequences. Our work then takes this practical perspective in addressing both 'standard' sequences derived from nuclear magnetic resonance and novel optimized sequences developed in the context of quantum information. Additionally, we review new techniques for the numerical construction of optimized pulse sequences in this light. We show how the filter-design perspective permits concise comparisons of the relative capabilities of these sequences and reveals the physics underlying their functionality. The use of this new analytical framework allows us to derive new insights into the performance of these sequences and reveals important limiting issues, such as the effect of digital clocking on optimized sequence performance.

Time-resolved photoemission by attosecond streaking. Extraction of time information

Abstract: Attosecond streaking of atomic photoemission holds the promise to provide unprecedented information on the release time of the photoelectron. We show that attosecond streaking phase shifts indeed contain timing (or spectral phase) information associated with the Eisenbud–Wigner–Smith time delay matrix of quantum scattering. However, this is only accessible if the influence of the streaking infrared (IR) field on the emission process is properly accounted for. The IR probe field can strongly modify the observed streaking phase shift. We show that the part of the phase shift ('time shift') due to the interaction between the outgoing electron and the combined Coulomb and IR laser fields can be described classically. By contrast, the strong initial-state dependence of the streaking phase shift is only revealed through the solution of the time-dependent Schrodinger equation in its full dimensionality. We find a time delay between the hydrogenic 2s and 2p initial states in He+ exceeding 20 as for a wide range of IR intensities and XUV energies.

Self-probing of molecules with high harmonic generation

Abstract: This tutorial presents the most important aspects of the molecular self-probing paradigm, which views the process of high harmonic generation as 'a molecule being probed by one of its own electrons'. Since the properties of the electron wavepacket acting as a probe allow a combination of attosecond and Angstrom resolutions in measurements, this idea bears great potential for the observation, and possibly control, of ultrafast quantum dynamics in molecules at the electronic level. Theoretical as well as experimental methods and concepts at the basis of self-probing measurements are introduced. Many of these are discussed as the example of molecular orbital tomography.

Ultracold dipolar gases in optical lattices

Abstract: This tutorial is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules that interact via dipolar forces, and that are cooled below the quantum degeneracy temperature, typically in the nK range. When such a degenerate quantum gas is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur. Then, these systems realize extended Hubbard-type models, and can be brought to a strongly correlated regime. The physical properties of such gases, dominated by the long-range, anisotropic dipole?dipole interactions, are discussed using the mean-field approximations and exact quantum Monte Carlo techniques (the worm algorithm).

Optimal control for generating quantum gates in open dissipative systems

Abstract: Optimal control methods for implementing quantum modules with least amount of relaxative loss are devised to give best approximations to unitary gates under relaxation. The potential gain by optimal control fully exploiting known relaxation parameters against time-optimal control (the alternative for unknown relaxation parameters) is explored and exemplified in numerical and in algebraic terms: for instance, relaxation-based optimal control is the method of choice to govern quantum systems within subspaces of weak relaxation whenever the drift Hamiltonian would otherwise drive the system through fast decaying modes. In a standard model system generalizing ideal decoherence-free subspaces to more realistic scenarios, opengrape-derived controls realize a CNOT with fidelities beyond 95% instead of at most 15% for a standard Trotter expansion. As additional benefit their control fields are orders of magnitude lower in power than bang-bang decouplings.

Joint remote state preparation of arbitrary two- and three-qubit states

Abstract: We present a scheme for joint remote preparation of an arbitrary two-qubit pure state in a probabilistic manner from a spatially separated multi-sender to one receiver; the scheme is then extended to the arbitrary three-qubit case. We show that by adding some classical communication and local operations, the success probability of preparation can be increased to four times for two-qubit states and eight times for three-qubit states, and can reach one under certain conditions.

Classical correlation and quantum discord mediated by cavity in two coupled qubits

Abstract: We study the dynamics of classical correlation and quantum discord of two coupled two-level atoms interacting with a cavity initially in vacuum, coherent and thermal equilibrium states, respectively. The interplay between the atom-atom coupling and mean number of photons is considered. We find that, for a cavity in a vacuum state, classical correlation or quantum discord shows a sudden change in behaviour during the evolution, and evolves periodically for zero and very large qubit-qubit couplings. However, for coherent and thermal equilibrium states, the classical correlation and quantum discord present the phenomenon of collapse-revival when the qubit-qubit coupling is much greater than the mean number of photons. The period of collapse-revival becomes long as the qubit-qubit coupling and mean number of photons increase. The relationship between quantum discord and entanglement in the studied system is considered.

Many-body physics with alkaline-earth Rydberg lattices

Abstract: We explore the prospects for confining alkaline-earth Rydberg atoms in an optical lattice via optical dressing of the secondary core–valence electron. Focussing on the particular case of strontium, we identify experimentally accessible magic wavelengths for simultaneous trapping of ground and Rydberg states. A detailed analysis of relevant loss mechanisms shows that the overall lifetime of such a system is limited only by the spontaneous decay of the Rydberg state, and is not significantly affected by photoionization or autoionization. The van der Waals C6 coefficients for the Sr(5sns 1S0) Rydberg series are calculated, and we find that the interactions are attractive. Finally we show that the combination of magic-wavelength lattices and attractive interactions could be exploited to generate many-body Greenberger–Horne–Zeilinger states.

Absolute absorption on the rubidium D1 line including resonant dipole?dipole interactions

Abstract: Here we report on measurements of the absolute absorption spectra of dense rubidium vapour on the D1 line in the weak-probe regime for temperatures up to 170 °C and number densities up to 3 × 1014 cm−3. In such vapours, modifications to the homogeneous linewidth of optical transitions arise due to dipole–dipole interactions between identical atoms, in superpositions of the ground and excited states. Absolute absorption spectra were recorded with a deviation of 0.1% between experiment and a theory incorporating resonant dipole–dipole interactions. The manifestation of dipole–dipole interactions is a self-broadening contribution to the homogeneous linewidth, which grows linearly with number density of atoms. Analysis of the absolute absorption spectra allows us to ascertain the value of the self-broadening coefficient for the rubidium D1 line: β/2π = (0.69 ± 0.04) × 10−7 Hz cm3, in excellent agreement with the theoretical prediction.

Strong impact of light-induced conical intersections on the spectrum of diatomic molecules

Abstract: We show that dressing of diatomic molecules by running laser waves gives rise to conical intersections (CIs). Due to the presence of such CIs, the rovibronic molecular motions are strongly coupled. A pronounced impact of the CI on the spectrum of the Na2 molecule is demonstrated via numerical calculation for weak and moderate laser intensity, and an experiment is suggested on this basis. The position of the light-induced CI and the strength of its non-adiabatic couplings can be chosen by changing the frequency and intensity of the used running laser wave. This offers new possibilities of controlling the photo-induced rovibronic molecular dynamics.

The hyperspherical four-fermion problem

Abstract: The problem of a few interacting fermions in quantum physics has sparked intense interest, particularly in recent years owing to connections with the behaviour of superconductors, fermionic superfluids and finite nuclei. This review addresses recent developments in the theoretical description of four fermions having finite-range interactions, stressing insights that have emerged from a hyperspherical coordinate perspective. The subject is complicated, so we have included many detailed formulae that will hopefully make these methods accessible to others interested in using them. The universality regime, where the dominant length scale in the problem is the two-body scattering length, is particularly stressed, including its implications for the famous BCS–BEC crossover problem. Derivations and relevant formulae are also included for the calculation of challenging few-body processes such as recombination.

On the dipole, velocity and acceleration forms in high-order harmonic generation from a single atom or molecule

Abstract: We consider high-order harmonic generation from a single atom or molecule and show that the generated harmonic field is proportional to the dipole velocity. We derive this result by solving Maxwell's wave equation for an infinitely thin gas. Hence, the dipole velocity form is the one that relates directly to the harmonic field, and it should be used as a reference when performing calculations with the dipole or acceleration forms.

Quantum Bose liquids with logarithmic nonlinearity: self-sustainability and emergence of spatial extent

Abstract: The Gross–Pitaevskii (GP) equation is a long-wavelength approach widely used to describe the dilute Bose–Einstein condensates (BEC). However, in many physical situations, such as higher densities, it is unlikely that this approximation suffices; hence, one might need models which would account for long-range correlations and multi-body interactions. We show that the Bose liquid described by the logarithmic wave equation has a number of drastic differences from the GP one. It possesses the self-sustainability property: while the free GP condensate tends to spill all over the available volume, the logarithmic one tends to form a Gaussian-type droplet—even in the absence of an external trapping potential. The quasi-particle modes of the logarithmic BEC are shown to acquire a finite size despite the bare particles being assumed to be point-like, i.e. the spatial extent emerges here as a result of quantum many-body correlations. Finally, we study the elementary excitations and demonstrate that the background density changes the topological structure of their momentum space which, in turn, affects their dispersion relations. Depending on the density, the latter can be of the massive relativistic, massless relativistic, tachyonic and quaternionic type.

Forward angle scattering effects in the measurement of total cross sections for positron scattering

Abstract: Measurements of total scattering by positron impact have typically excluded a significant portion of the forward scattering angles of the differential cross section. This paper demonstrates the effect that this can have on measurements of the total cross section. We show that much of the apparent disagreement between experimental measurements of positron scattering from atoms and molecules may be explained by this excluded angular range. It is shown that this same effect may also lead to an anomalous energy dependence of some cross sections.

Entanglement and squeezing with identical particles: ultracold atom quantum metrology

Abstract: In quantum metrological applications based on ultracold atom systems, entangled initial states are thought necessary to achieve sub-shot-noise accuracies. This conclusion, although strictly true for systems of distinguishable particles, does no longer hold for systems of identical particles. Indeed, while quantum non-locality is necessary, it can be encoded into the interferometric apparatus and not into the initial states. In particular, no preliminary spin-squeezing is necessary to reach quantum performances in metrological applications of ultracold atom physics.

Microwave dressing of Rydberg dark states

Abstract: We study electromagnetically induced transparency (EIT) in the 5s→5p→46s ladder system of a cold 87Rb gas. We show that the resonant microwave coupling between the 46s and 45p states leads to an Autler–Townes splitting of the EIT resonance. This splitting can be employed to vary the group index by ±105 allowing independent control of the propagation of dark state polaritons. We also demonstrate that microwave dressing leads to enhanced interaction effects. In particular, we present evidence for a 1/R3 energy shift between Rydberg states resonantly coupled by the microwave field and the ensuing breakdown of the pairwise interaction approximation.

Conical intersections induced by light: Berry phase and wavepacket dynamics

Abstract: Conical intersections (CIs) play an important role in nonadiabatic molecular processes. Characterizing and localizing them is important for describing and controlling electronic energy flow in molecules. It is known that no CI appears in free diatomic systems. In earlier works (Moiseyev et al 2008 J. Phys. B.: At. Mol. Opt. Phys. 41 221001, Sindelka et al 2011 J. Phys. B.: At. Mol. Opt. Phys. 44 045603) it was pointed out that CIs can be formed both by standing and running laser waves even in diatomics. The energetic and internuclear positions of these CIs depend on the laser frequencies, while the strength of their nonadiabatic couplings can be modified by the field intensities. In this work, we calculate the topological or Berry phase of the light-induced CI in the Na2 molecule. The presence of this phase is a clear fingerprint of the laser-induced CI. In addition, we perform a detailed study of the wavepacket propagation and discuss effects which reflect the significant presence of the laser-induced CI.

A study of the electron structure of endohedrally confined atoms using a model potential

Abstract: A novel model potential for modelling the environment of atoms and molecules inside fullerenes is proposed. The model takes into consideration that the electrons of the guest atom or molecule are affected by an attractive short-range Gaussian shell to simulate the Cn cage. As a test case, the present model is employed to study the electronic structure of an endohedrally confined hydrogen atom by C36 and C60 fullerenes. This study is performed using a new implementation of the p-version of the finite-element method by a self-consistent finite-element methodology. The results are then compared with previous ones obtained by using other short-range model potentials.

Direct measurement of the system?environment coupling as a tool for understanding decoherence and dynamical decoupling

Abstract: Decoherence is a major obstacle to any practical implementation of quantum information processing. One of the leading strategies to reduce decoherence is dynamical decoupling—the use of an external field to average out the effect of the environment. The decoherence rate under any control field can be calculated if the spectrum of the coupling to the environment is known. We present a direct measurement of the bath-coupling spectrum in an ensemble of optically trapped ultra-cold atoms, by applying a spectrally narrow-band control field. The measured spectrum follows a Lorentzian shape at low frequencies but exhibits non-monotonic features at higher frequencies due to the oscillatory motion of the atoms in the trap. These features agree with our analytical models and numerical Monte Carlo simulations of the collisional bath. From the inferred bath-coupling spectrum, we predict the performance of some well-known dynamical decoupling sequences. We then apply these sequences in experiment and compare the results to predictions, finding good agreement in the weak-coupling limit. Thus, our work establishes experimentally the validity of the overlap integral formalism and is an important step towards the implementation of an optimal dynamical decoupling sequence for a given measured bath spectrum.

Adiabatic formation of Rydberg crystals with chirped laser pulses

Abstract: Ultracold atomic gases have been used extensively in recent years to realize textbook examples of condensed matter phenomena. Recently, phase transitions to ordered structures have been predicted for gases of highly excited, 'frozen' Rydberg atoms. Such Rydberg crystals are a model for dilute metallic solids with tunable lattice parameters, and provide access to a wide variety of fundamental phenomena. We investigate theoretically how such structures can be created in four distinct cold atomic systems, by using tailored laser excitation in the presence of strong Rydberg–Rydberg interactions. We study in detail the experimental requirements and limitations for these systems and characterize the basic properties of small crystalline Rydberg structures in one, two and three dimensions.

Quantum interference in interacting three-level Rydberg gases: coherent population trapping and electromagnetically induced transparency

Abstract: In this paper, we consider the effects of strong dipole-dipole interactions on three-level interference phenomena such as coherent population trapping and electromagnetically induced transparency. Experiments are performed on laser cooled rubidium atoms and the results compared to a many-body theory based on either a reduced many-body density matrix expansion or Monte Carlo simulations of many-body rate equations. We show that these approaches permit quantitative predictions of the experimentally observed excitation and transmission spectra. Based on the calculations, we moreover predict a universal scaling of the nonlinear response of cold Rydberg gases.

Joint remote preparation of four-qubit cluster-type states

Abstract: We propose several schemes for the joint remote preparation of four-qubit cluster-type states with real coefficients and complex coefficients by using six Einstein–Podolsky–Rosen (EPR) pairs and two six-qubit entangled states as quantum channels respectively. In these schemes, two senders share the original state which they wish to help the receiver to remotely prepare. It is shown that, only if two senders collaborate with each other, and perform four-qubit projective measurements on their own qubits respectively, the receiver can reconstruct the original state by means of some appropriate unitary operations.

The quantum speed limit of optimal controlled phasegates for trapped neutral atoms

Abstract: We study controlled phasegates for ultracold atoms in an optical potential. A shaped laser pulse drives transitions between the ground and electronically excited states where the atoms are subject to a long-range 1/R 3 interaction. We fully account for this interaction and use optimal control theory to calculate the pulse shapes. This allows us to determine the minimum pulse duration, respectively, gate time T that is required to obtain high fidelity. We accurately analyse the speed limiting factors, and we find the gate time to be limited either by the interaction strength in the excited state or by the ground state vibrational motion in the trap. The latter needs to be resolved by the pulses in order to fully restore the motional state of the atoms at the end of the gate. (Some figures in this article are in colour only in the electronic version)

Shared quantum remote control: quantum operation sharing

Abstract: We consider three-party sharing of unitary operations with the help of the shared entanglement and LOCC. We propose three separate schemes corresponding to decreasing resource requirements and increasing restrictions on the set of possible operations. It can be shown that our protocols are optimal.

Efficient Grover search with Rydberg blockade

Abstract: We present efficient methods to implement the quantum computing Grover search algorithm using the Rydberg blockade interaction. We show that simple π-pulse excitation sequences between ground and Rydberg excited states readily produce the key conditional phase shift and inversion-about-the-mean unitary operations for the Grover search. Multi-qubit implementation schemes suitable for different properties of the atomic interactions are identified and the error scaling of the protocols with system size is found to be promising for experimental investigation.

Analytic harmonic approach to the N-body problem

Abstract: We consider an analytic way to make the interacting N-body problem tractable by using harmonic oscillators in place of the relevant two-body interactions. The two-body terms of the N-body Hamiltonian are approximated by considering the energy spectrum and radius of the relevant two-body problem which gives frequency, centre position, and zero point energy of the corresponding harmonic oscillator. Adding external harmonic one-body terms, we proceed to solve the full quantum mechanical N-body problem analytically for arbitrary masses. Energy eigenvalues, eigenmodes, and correlation functions like density matrices can then be computed analytically. As a first application of our formalism, we consider the N-boson problem in two and three dimensions where we fit the two-body interactions to agree with the well-known zero-range model for two particles in a harmonic trap. Subsequently, condensate fractions, spectra, radii, and eigenmodes are discussed as a function of dimension, boson number N, and scattering length obtained in the zero-range model. We find that energies, radii, and condensate fraction increase with scattering length as well as boson number, while radii decrease with increasing boson number. Our formalism is completely general and can also be applied to fermions, Bose–Fermi mixtures, and to more exotic geometries.

Asymptotic dynamics of quantum discord in open quantum systems

Abstract: It is well known that quantum entanglement makes certain tasks in quantum information theory possible. However, there are also quantum tasks that display a quantum advantage without entanglement. Distinguishing classical and quantum correlations in quantum systems is therefore of both practical and fundamental importance. Realistic quantum systems are not closed, and therefore it is important to study the various correlations when the system loses its coherence due to interactions with the environment. In this paper, we study in detail the dynamics of different kinds of correlations, classical correlation, quantum discord and entanglement in open quantum systems, in particular, a two-qubit system evolving under Kossakowski-type quantum dynamical semigroups of completely positive maps. In such an environment, classical and quantum correlations can even persist asymptotically. By analytic and numerical analysis, we find that the quantum discord is larger than the classical correlation for asymptotic states. Furthermore, we show that the quantum discord is more resistant to the action of the environment than quantum entanglement, and it can persist even in the asymptotic long-time regime.

Optimal networks for excitonic energy transport

Abstract: We investigate coherent and incoherent excitation transfer in a random network with dipole–dipole interactions as a model system describing energy transport, e.g., in photosynthetic light-harvesting complexes or gases of cold Rydberg atoms. For this purpose, we introduce and compare two different measures (the maximum output probability and the average transfer time) for the efficiency of transport from the input to the output site. We especially focus on optimal configurations which maximize the transfer efficiency and the impact of dephasing noise on the transport dynamics. For most configurations of the random network, the transfer efficiency increases when adding noise, giving rise to essentially classical transport. These noise-assisted configurations are, however, systematically less efficient than the optimal configurations. The latter reach their highest efficiency for purely coherent dynamics, i.e. in the absence of noise.

Magnetic field effects in the transitions of the HD+ molecular ion and precision spectroscopy

Abstract: We analyse the effects of an external magnetic field on the ro-vibrational, rotational and radiofrequency transitions of the HD+ molecular ion—an important systematic effect in precision spectroscopy of HD+, which is of interest for metrology of the fundamental constants. The effects of an external magnetic field on the ro-vibrational, rotational and radiofrequency (hyperfine) transitions of the HD+ molecular ion are considered, for one-photon and, where relevant, two-photon transitions. The hyperfine structure of the spectrum lines is taken into account. Particular attention has been devoted to those transitions which are most insensitive to the magnetic field and its orientation with respect to the polarization of the radiation field. We identify experimentally accessible two-photon transitions that exhibit no Zeeman shift, one-photon and two-photon transitions that provide symmetrically split doublets, and one-photon transitions that show only a very weak quadratic Zeeman shift. The importance of the spin-stretched states is emphasized. The results can be used to determine the most suitable transitions given the experimental conditions.