Chruściński, Jurkowski, and Kossakowski [Phys. Rev. A 77, 022113 (2008)] studied quantum states with strong positive partial transpose (SPPT) and conjectured that all SPPT states are separable. We construct a two-parameter class of $3\otimes 3$ entangled SPPT states, so the conjecture does not hold true for general SPPT states.

We compute the formation rate of a polar molecule, LiH, into the lowest triplet electronic state, $a\hspace{0.5em}{}^3{\Sigma }^{+}$, via population of the intermediate excited electronic state, $b\hspace{0.5em}{}^3\Pi$, followed by radiative decay. We find large formation rates into the single rovibrational bound state ($v=0,J=0$) of the $a\hspace{0.5em}{}^3{\Sigma }^{+}$, which can be explained by the unusually large overlap of its wave function with those of the two upper-most bound levels of the $b\hspace{0.5em}{}^3\Pi$. With conservative parameters, we estimate that over $10$${}^4$ molecules/s could be produced in the single rovibrational level of the $a\hspace{0.5em}{}^3{\Sigma }^{+}$ state. We also discuss scattering properties of LiH triplet molecules and their relevance to ultracold chemical reactions.

We consider a hypothetical topological quantum computer composed of either Ising or Fibonacci anyons. For each case, we calculate the time and number of qubits (space) necessary to execute the most computationally expensive step of Shor’s algorithm, modular exponentiation. For Ising anyons, we apply Bravyi’s distillation method [S. Bravyi, Phys. Rev. A 73, 042313 (2006)] which combines topological and nontopological operations to allow for universal quantum computation. With reasonable restrictions on the physical parameters we find that factoring a 128-bit number requires approximately ${10}^3$ Fibonacci anyons versus at least $3\times {10}^9$ Ising anyons. Other distillation algorithms could reduce the resources for Ising anyons substantially.

We give a universal recipe for constructing nonlinear entanglement witnesses able to detect nonclassical correlations in arbitrary systems of distinguishable and/or identical particles for an arbitrary number of constituents. The constructed witnesses are expressed in terms of expectation values of observables. As such, they are, at least in principle, measurable in experiments.

We propose a definition for the Pólya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an ensemble in order to minimize the disturbance caused by it. We examine various graphs, including the ring, the line, the higher-dimensional integer lattices, and a number of other graphs, and we calculate their Pólya number. For the timing of the measurements, a Poisson process as well as regular timing are discussed. We find that the speed of decay for the probability at the origin is the key for recurrence.

The creation and destruction of entanglement between a pair of interacting two-level detectors accelerating about diametrically opposite points of a circular path is investigated. It is found that any nonzero acceleration has the effect of suppressing the vacuum entanglement and enhancing the acceleration radiation, thereby reducing the entangling capacity of the detectors. Given that for large accelerations the acceleration radiation is the dominant effect, we investigate the evolution of a two-detector system initially prepared in a Bell state using a perturbative master equation and treating the vacuum fluctuations as an unobserved environment. A general function for the concurrence is obtained for stationary and symmetric world lines in flat space. The entanglement sudden-death time is computed.

We investigate the effectiveness of different dynamical decoupling protocols for storage of a single qubit in the presence of a purely dephasing bosonic bath, with emphasis on comparing quantum coherence preservation under uniform versus nonuniform delay times between pulses. In the limit of instantaneous bit-flip pulses, this is accomplished by establishing a different representation of the controlled qubit evolution, where the decoherence behavior after an arbitrary number of pulses is directly expressed in terms of the uncontrolled decoherence function. In particular, analytical expressions are obtained for approximation of the long- and short-term coherence behavior for both Ohmic and supra-Ohmic environments. By focusing on the realistic case of pure dephasing in an excitonic qubit, we quantitatively assess the impact of physical constraints on achievable pulse separations, and show that little advantage of high-level decoupling schemes based on concatenated or optimal design may be expected if pulses cannot be applied sufficiently fast. In such constrained scenarios, we demonstrate how simple modifications of repeated periodic-echo protocols can offer significantly improved coherence preservation in realistic parameter regimes. We expect similar conclusions to be relevant to other constrained qubit devices exposed to quantum or classical phase noise.

The shot noise of vacuum states is a kind of quantum noise and is totally random. In this paper a nondeterministic random number generation scheme based on measuring the shot noise of vacuum states is presented and experimentally demonstrated. We use a homodyne detector to measure the shot noise of vacuum states. Considering that the frequency bandwidth of our detector is limited, we derive the optimal sampling rate so that sampling points have the least correlation with each other. We also choose a method to extract random numbers from sampling values, and prove that the influence of classical noise can be avoided with this method so that the detector does not have to be shot-noise limited. The random numbers generated with this scheme have passed ent and diehard tests.

By using a reductive perturbation technique applied to a two-level model, this study puts forward a generic two-dimensional sine-Gordon evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in Kerr media beyond the slowly varying envelope approximation. Direct numerical simulations show that, in contrast to the long-wave approximation, no collapse occurs, and that robust ($2+1$)-dimensional ultrashort light bullets may form from adequately chosen few-cycle input spatiotemporal wave forms. In contrast to the case of quadratic nonlinearity, the light bullets oscillate in both space and time and are therefore not steady-state lumps.

Frequency-stabilized cavity ring-down spectroscopy (FS-CRDS) was used to measure magnetic dipole transitions in the $b\hspace{0.5em}{}^1$${\Sigma }_g^{+}$ $\leftarrow$ $X\hspace{0.5em}$${}^3{\Sigma }_g^{-}$($0,0$) band of ${\mathrm{O}}_2$. The ${}^{17}\mathrm{O}$-containing isotopologues show unresolved hyperfine structure due to magnetic hyperfine splitting in the ground state. The sensitivity and stability of FS-CRDS allow for quantitative sub-Doppler measurements of the hyperfine constants, even when the hyperfine splittings are much smaller than the Doppler width. Unlike saturation spectroscopy, this linear absorption technique can be applied to weak transitions and employed to quantitatively measure intensities and line shapes. This method may be an attractive approach for measuring unresolved hyperfine structure in excited electronic states.

We present a method that implements directional, perfect state transfers within a branched spin network by exploiting quantum interferences in the time domain. This method provides a tool for isolating subsystems from a large and complex one. Directionality is achieved by interrupting the spin-spin coupled evolution with periods of free Zeeman evolutions, whose timing is tuned to be commensurate with the relative phases accrued by specific spin pairs. This leads to a resonant transfer between the chosen qubits and to a detuning of all remaining pathways in the network, using only global manipulations. Since the transfer is perfect when the selected pathway is mediated by two or three spins, distant state transfers over complex networks can be achieved by successive recouplings among specific pairs or triads of spins. These effects are illustrated with a quantum simulator involving ${}^{13}\mathrm{C}$ NMR on leucine’s backbone; a six-spin network.

In this article we provide experimental evidence of an interference phenomenon that, to the best of our knowledge, has so far not been observed with either matter or light. In a nanometer-sized version of Feynman’s famous two-slit “thought” experiment with single electrons, we managed to observe that the width of a quasi-monochromatic line oscillates with the detection angle. Furthermore, we find that it occurs in counterphase with the line intensity. We discuss the underlying mechanism that produces this unexpected result.

We investigate the energetics of reactions involving pairs of alkali-metal dimers. Atom exchange reactions to form homonuclear dimers are energetically allowed for some but not all of the heteronuclear dimers. We carry out high-level electronic structure calculations on the potential energy surfaces of all the heteronuclear alkali-metal trimers and show that trimer formation reactions are always energetically forbidden for low-lying singlet states of the dimers. The results have important implications for the stability of quantum gases of alkali-metal dimers.

We consider quantum states under the renormalization-group (RG) transformations introduced by Verstraete et al. [Phys. Rev. Lett. 94, 140601 (2005)] and propose a quantification of entanglement under such RGs (via the geometric measure of entanglement). We examine the resulting entanglement under RG transformations for the ground states of “matrix-product-state” Hamiltonians constructed by Wolf et al. [Phys. Rev. Lett. 97, 110403 (2006)] that possess quantum phase transitions. We find that near critical points, the ground-state entanglement exhibits singular behavior. The singular behavior within finite steps of the RG obeys a scaling hypothesis and reveals the correlation length exponent. However, under the infinite steps of RG transformation, the singular behavior is rendered different and is universal only when there is an underlying conformal-field-theory description of the critical point.

In this article, we give a simple proof of the fact that the optimal collective attacks against continuous-variable quantum key distribution with a Gaussian modulation are Gaussian attacks. Our proof, which makes use of symmetry properties of the protocol in phase space, is particularly relevant for the finite-key analysis of the protocol and therefore for practical applications.

Any bipartite nonlocal unitary operation can be carried out by teleporting a quantum state from one party to the other, performing the unitary gate locally, and teleporting a state back again. This paper investigates unitaries which can be carried out using less prior entanglement and classical communication than are needed for teleportation. Large families of such unitaries are constructed using (projective) representations of finite groups. Among the tools employed are: a diagrammatic approach for representing entangled states, a theorem on the necessary absence of information at certain times and locations, and a representation of bipartite unitaries based on a group Fourier transform.

We present a method of optimizing recently designed protocols for implementing an arbitrary nonlocal unitary gate acting on a bipartite system. These protocols use only local operations and classical communication with the assistance of entanglement, and they are deterministic while also being “one-shot,” in that they use only one copy of an entangled resource state. The optimization minimizes the amount of entanglement needed, and also the amount of classical communication, and it is often the case that less of each of these resources is needed than with an alternative protocol using two-way teleportation.

We calculate quantum-mechanically exact wave functions of resonances in spectra of the hydrogen atom in crossed external fields and prove the existence of long-lived decaying quantum states localized at the Stark saddle point. A spectrum of ground and excited states reproducing the nodal patterns expected from simple quadratic and cubic expansions of the potential in the vicinity of the saddle point can be identified. The results demonstrate the presence of resonances in the vicinity of the saddle predicted by simple approximations.

We study the equilibrium properties of dipolar Fermi gases at finite temperatures. We introduce a variational ansatz for the phase-space distribution function that can describe the deformation in both real and momentum space. The effect of dipole-dipole interactions on thermal equilibrium is discussed, with particular emphasis on the deformation in momentum space. We examine the stability of the system by varying the temperature, trap aspect ratio, and dipole moment. In addition, we discuss how the deformation in both real and momentum space can be observed in the high-temperature regime, which is relevant to the current experiment at JILA (Institute for Laboratory Astrophysics) [K. K. Ni et al., Science 322, 231 (2008)].

An efficient method to generate an isolated short attosecond pulse is investigated theoretically. A broadband extreme ultraviolet supercontinuum harmonics can be generated when a model He${}^{+}$ ion is exposed to the combination of an intense few-cycle laser pulse and a low-frequency field. By properly adding a $27$th harmonics pulse to resonantly excite the He${}^{+}$ ion, the intensity of the high-order harmonic generation (HHG) plateau is enhanced by $3-4$ orders of magnitude. As a result, an isolated $24$-as pulse with a bandwidth of $138$ eV can be obtained directly from the supercontinuum around the cutoff of HHG.