We study the relation between the maximal violation of Svetlichny's inequality and the mixedness of quantum states and obtain the optimal state (i.e., maximally nonlocal mixed states, or MNMS, for each value of linear entropy) to beat the Clauser-Horne-Shimony-Holt and the Svetlichny games. For the two-qubit and three-qubit MNMS, we showed that these states are also the most tolerant state against white noise, and thus serve as valuable quantum resources for such games. In particular, the quantum prediction of the MNMS decreases as the linear entropy increases, and then ceases to be nonlocal when the linear entropy reaches the critical points $2/3$ and $9/14$ for the two- and three-qubit cases, respectively. The MNMS are related to classical errors in experimental preparation of maximally entangled states.

We consider a class of decoding algorithms that are applicable to error correction for both Abelian and non-Abelian anyons. This class includes multiple algorithms that have recently attracted attention, including the Bravyi-Haah RG decoder and variants thereof. They are applied to both the problem of correcting a single burst of errors (with perfect syndrome measurements) and active correction of continuously occurring errors (with noisy syndrome measurements). For Abelian models we provide a threshold proof in both cases for all decoders in this class, showing that they can arbitrarily suppress errors when the noise rate is under a finite threshold. For non-Abelian models such a proof is found for a single burst of errors. The reasons why the proof cannot be applied to the case of continuously occurring errors are discussed.

We propose an experimental scheme of generating entangled states between two spinor Bose-Einstein condensates (BECs) using Rydberg excitations. Due to the strong interaction between Rydberg atoms, the Rydberg excitation creates an interaction between two closely located BECs. The method is suitable particularly for atom chip and permanent magnetic trap systems, which can create many BECs with an arbitrary two-dimensional geometry. We show two schemes of entangled state generation, based on stimulated Raman adiabatic passage (STIRAP) methods. The first method produces a symmetric state with total $S^x$ spin zero between ground and excited states of the atoms using a single STIRAP pair, while the second produces a NOON state between hyperfine ground states using two STIRAP pairs. We show that despite the additional complexity of the BECs, it is possible to identify the initial and final adiabatic states exactly. We verify our theoretical predictions using numerical simulations on small boson number systems.

A gas of ultracold molecules interacting via the long-range dipolar potential offers a highly controlled environment in which to study strongly correlated phases. However, at particle coalescence the divergent $1/r^3$ dipolar potential and associated pathological wave function hinder computational analysis. For a dipolar gas constrained to two dimensions we overcome these numerical difficulties by proposing a pseudopotential that is explicitly smooth at particle coalescence, resulting in a 2000-times speedup in diffusion Monte Carlo calculations. The pseudopotential delivers the scattering phase shifts of the dipolar interaction with an accuracy of ${10}^{-5}$ and predicts the energy of a dipolar gas to an accuracy of ${10}^{-4}{E}_{\mathrm{F}}$ in a diffusion Monte Carlo calculation.

The photoionization of ${\mathrm{He}}^{+}$ in two-color XUV fields is studied by numerically solving the time-dependent Schrödinger equation. ${\mathrm{He}}^{+}$ may be ionized by directly absorbing one high-energetic photon or by absorbing two photons sequentially by mediating an excited state. The interference of these two pathways results in either enhancement or suppression of photoionization, depending on the propagating direction of the photoelectron and the relative phase of two pulses. The two-pathway interference also induces the split of photoelectron momenta. This study shows that the participation of intermediate states may substantially change photoionization processes.

In this paper, effects of the spatial nonuniformity of an optical near field (ONF) on the molecular photodissociation process are presented. The dissociation dynamics of ${{\mathrm{H}}_2}^{+}$ was theoretically investigated by solving a non-Born-Oppenheimer Schrödinger equation. It was found that in addition to two dissociation mechanisms, which are one-photon and three-photon processes induced by uniform laser light excitation, the nonuniform ONF opens another dissociation path: two-step excitation mediated by vibrationally excited states. The nonuniformity of the ONF causes a transition between vibrational states that is forbidden according to conventional selection rules, leading to the dissociation path. The dependences of photodissociation on the intensity and nonuniformity of the ONF were calculated and the results validated the two-step dissociation mechanism.

Cold Rydberg atoms are known to display dipole-dipole interaction-allowed resonances, also called Förster resonances, which lead to an efficient energy transfer when the proper electric field is used. This electric field also enables resonances, which do not respect the dipole-dipole selection rules under zero field. A few of these quasiforbidden resonances have been observed but they are often overlooked. Here we show that in cold ${}^{133}\mathrm{Cs}$ atoms there is a large number of these resonances that display a significant transfer efficiency due to their strong interactions, even at low electric field. We also develop a graphical method enabling us to find all possible resonances simultaneously. The resulting dramatic increase in the total number of addressable resonant energy transfers at different electric fields could have implications in the search for few-body interactions or macromolecules built from Rydberg atoms.

We calculated the motion of one or two excitons through a small grid of Rydberg atoms. Both one- and two-dimensional grids were studied with the number of sites in a direction between 4 and 10. To mimic the possibility of nonperfect filling, calculations were performed with atoms randomly missing from sites. Results are presented for four qualitatively different situations. (1) The corners and edges, with the randomness of nonperfect filling, strongly affects the exciton motion and can pin the exciton. (2) For the case where a single exciton is simultaneously generated at two sites, the direction in which the exciton moves can be controlled by imprinting a phase difference on the two adjacent sites. (3) For the case where two excitons are generated at adjacent sites, calculations where a pair of excitons move through the grid are compared to the one exciton case to see whether exciton-exciton correlations are measurable. (4) The grid version of an exciton current can be defined by analogy to a continuity equation in one dimension and by using the analogy to a velocity operator in one, two, or three dimensions; for one dimension, the two definitions give similar results which means the direct measurement of the current in one dimension is possible.

We consider two parallel layers of dipolar ultracold Fermi gases at different temperatures and calculate the heat transfer between them. The effective interactions describing screening and correlation effects between the dipoles in a single layer are modeled within the Euler-Lagrange Fermi-hypernetted-chain approximation. The random-phase approximation is used for the interactions across the layers. We investigate the amount of transferred power between the layers as a function of the temperature difference. Energy transfer arises due to the long-range dipole-dipole interactions. A simple thermal model is established to investigate the feasibility of using the contactless sympathetic cooling of the ultracold polar atoms and molecules. Our calculations indicate that dipolar heat transfer is effective for typical polar molecule experiments and may be utilized as a cooling process.

The unstable mean-field dynamics of a Bose gas is shown to break down at time ${\tau }_h=(c_1/\gamma )lnN$, where $\gamma$ is the Lyapunov exponent of the mean-field theory, $N$ is the number of bosons, and $c_1$ is a system-dependent constant. The breakdown time ${\tau }_h$ is essentially the Ehrenfest time that characterizes the breakdown of the correspondence between classical and quantum dynamics. This breakdown can be well described by a quantum fidelity defined for one-particle reduced density matrices. Our results are obtained with the formalism in particle-number phase space and are illustrated with a triple-well model. The logarithmic quantum-classical correspondence time may be verified experimentally with Bose-Einstein condensates.

Enforcing the Pauli principle in many-body systems of fermions to ensure an antisymmetric wave function is typically a numerically expensive task. Numerical methods, such as coupled-cluster, correlated basis function, Monte Carlo, and traditional configuration interaction, scale with powers of $N$ that make the determination of the energy spectrum of these systems a challenge. In a recent paper, we successfully obtained energies for large systems of fermions in the unitary regime in which we applied the Pauli principle “on paper” without obtaining an explicit wave function. This approach, an extension of the symmetry invariant perturbation method to fermions, applies the Pauli principle by imposing restrictions on the quantum numbers used to obtain the energy. As a followup to this study, we perform an explicit test of the validity of this application of the Pauli principle by comparing our energy results against the energies corresponding to explicitly antisymmetrized wave functions for an exactly solvable system of harmonically confined, harmonically interacting fermions. Our results show that our simple method of applying the Pauli principle selects from a spectrum of possible many-body energies only those energies that correspond to explicitly antisymmetrized wave functions. Our results were tested for values of $N$ through $\approx 10 000$ and for weak and strong interactions both repulsive and attractive.

Unidirectional light transport in one-dimensional nanomaterials at the quantum level is a crucial goal to achieve for upcoming computational devices. We here employ a fully quantum mechanical approach based on a master equation to describe unidirectional light transport through a pair of two-level systems coupled to a one-dimensional waveguide. By comparing with published semiclassical results, we find that the nonlinearity of the system is reduced, thereby reducing also the unidirectional light transport efficiency. Albeit not fully efficient, we find that the considered quantum system can work as a light diode with an efficiency of $\approx 60\%$. Our results may be used in quantum computation with classical and quantized light.

Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.

Practical security of the continuous-variable quantum key distribution (CVQKD) system with finite sampling bandwidth of analog-to-digital converter (ADC) at the receiver's side is investigated. We find that the finite sampling bandwidth effects may decrease the lower bound of secret key rate without awareness of the legitimate communicators. This leaves security loopholes for Eve to attack the system. In addition, this effect may restrains the linear relationship of secret key bit rate with repetition rate of the system; subsequently, there is a saturation value for the secret key bit rate with the repetition rate. To resist such kind of effects, we propose a dual sampling detection approach in which two ADCs are employed so that the finite sampling bandwidth effects are removed.

Quantum memory is an essential building block for quantum communication and scalable linear quantum computation. Storing two-color entangled photons with one photon being at the telecommunication (telecom) wavelength while the other photon is compatible with quantum memory has great advantages toward the realization of the fiber-based long-distance quantum communication with the aid of quantum repeaters. Here, we report an experimental realization of storing a photon entangled with a telecom photon in polarization as an atomic spin wave in a cold atomic ensemble, thus establishing the entanglement between the telecom-band photon and the atomic-ensemble memory in a polarization degree of freedom. The reconstructed density matrix and the violation of the Clauser-Horne-Shimony-Holt inequality clearly show the preservation of quantum entanglement during storage. Our result is very promising for establishing a long-distance quantum network based on cold atomic ensembles.

A special feature of the ground state in a topologically ordered phase is the existence of large-scale correlations depending only on the topology of the regions. These correlations can be detected by the topological entanglement entropy or by a measure called irreducible correlation. We show that these two measures coincide for states obeying an area law and having zero correlation length. Moreover, we provide an operational meaning for these measures by proving its equivalence to the optimal rate of a particular class of secret sharing protocols. This establishes an information-theoretical approach to multipartite correlations in topologically ordered systems.

Strong-field ionization (SFI) has been shown to prepare wave packets with few-femtosecond periods. Here, we explore whether this technique can be extended to the attosecond time scale. We introduce an intuitive model, which is based on the Fourier transform of the subcycle SFI rate, for predicting the bandwidth of ionic states that can be coherently prepared by SFI. The coherent bandwidth decreases considerably with increasing central wavelength of the ionizing pulse but it is much less sensitive to its intensity. Many-body calculations based on time-dependent configuration-interaction singles support these results. The influence of channel interactions and laser-induced dynamics within the ion is discussed. Our results further predict that multicycle femtosecond pulses can coherently prepare subfemtosecond wave packets with higher selectivity and versatility compared to single-cycle pulses with an additional sensitivity to the mutual parity of the prepared states.

The interaction of an intense laser pulse with atoms and molecules depends extremely nonlinearly on the laser intensity. Yet experimentally there still exists no simple reliable methods for determining the peak laser intensity within the focused volume. Here we present a simple method, based on an improved Perelomov-Popov-Terent'ev model, that would allow the calibration of laser intensities from the measured ionization signals of atoms or molecules. The model is first examined by comparing ionization probabilities (or signals) of atoms and several simple diatomic molecules with those from solving the time-dependent Schrödinger equation. We then show the possibility of using this method to calibrate laser intensities for atoms, diatomic molecules as well as large polyatomic molecules, for laser intensities from the multiphoton ionization to tunneling ionization regimes.

We describe a method for initializing an ensemble of qubits in a pure ground state by applying collective cavity cooling techniques in the presence of local dephasing noise on each qubit. To solve the dynamics of the ensemble system we introduce a method for dissipative perturbation theory that applies average Hamiltonian theory in an imaginary-time dissipative interaction frame to find an average effective dissipator for the system dynamics. We use SU(4) algebra generators to analytically solve the first-order perturbation for an arbitrary number of qubits in the ensemble. We find that to first order the effective dissipator describes local $T_1$ thermal relaxation to the ground state of each qubit in the ensemble at a rate equal to the collective cavity cooling dissipation rate. The proposed technique should permit the parallel initialization of high purity states in large ensemble quantum systems based on solid-state spins.

We present a model of a spin-squeezed rotation sensor utilizing the Sagnac effect in a spin-1 Bose-Einstein condensate in a ring trap. The two input states for the interferometer are seeded using Raman pulses with Laguerre-Gauss beams and are amplified by the bosonic enhancement of spin-exchange collisions, resulting in spin-squeezing and potential quantum enhancement of the interferometry. The ring geometry has an advantage over separated beam path atomic rotation sensors due to the uniform condensate density. We model the interferometer both analytically and numerically for realistic experimental parameters and find that significant quantum enhancement is possible, but this enhancement is partially degraded when working in a regime with strong atomic interactions.