It is known how to construct, in a bipartite quantum system, a unique low-rank entangled mixed state with positive partial transpose (a PPT state) from an unextendible product basis (UPB), defined as an unextendible set of orthogonal product vectors. We point out that a state constructed in this way belongs to a continuous family of entangled PPT states of the same rank, all related by nonsingular unitary or nonunitary product transformations. The characteristic property of a state $\rho$ in such a family is that its kernel $\text{Ker}\hspace{0.5em}\rho$ has a generalized UPB, a basis of product vectors, not necessarily orthogonal, with no product vector in $\mathrm{Im}\hspace{0.5em}\rho$, the orthogonal complement of $\text{Ker}\hspace{0.5em}\rho$. The generalized UPB in $\text{Ker}\hspace{0.5em}\rho$ has the special property that it can be transformed to orthogonal form by a product transformation. In the case of a system of dimension $3\times 3$, we give a complete parametrization of orthogonal UPBs. This is then a parametrization of families of rank 4 entangled (and extremal) PPT states, and we present strong numerical evidence that it is a complete classification of such states. We speculate that the lowest rank entangled and extremal PPT states also in higher dimensions are related to generalized, nonorthogonal UPBs in similar ways.

We have measured the ratio $\gamma$ of the diffusion cross section to the angular momentum reorientation cross section in the colliding Fe-${}^3\mathrm{He}$ and Ni-${}^3\mathrm{He}$ systems. Nickel (Ni) and iron (Fe) atoms are introduced via laser ablation into a cryogenically cooled experimental cell containing cold ($<1$ K) ${}^3\mathrm{He}$ buffer gas. Elastic collisions rapidly cool the translational temperature of the ablated atoms to the ${}^3\mathrm{He}$ temperature. $\gamma$ is extracted by measuring the decays of the atomic Zeeman sublevels. For our experimental conditions, thermal energy is comparable to the Zeeman splitting. As a result, thermal excitations between Zeeman sublevels significantly impact the observed decay. To determine $\gamma$ accurately, we introduce a model of Zeeman-state dynamics that includes thermal excitations. We find ${\gamma }_{\mathrm{Ni}{-}^3\mathrm{He}}=5\times {10}^3$ and ${\gamma }_{\mathrm{Fe}{-}^3\mathrm{He}}⩽3\times {10}^3$ at 0.75 K in a 0.8-T magnetic field. These measurements are interpreted in the context of submerged shell suppression of spin relaxation, as studied previously in transition metals and rare-earth-metal atoms [C. I. Hancox, S. C. Doret, M. T. Hummon, R. V. Krems, and J. M. Doyle, Phys. Rev. Lett. 94, 013201 (2005); C. I. Hancox, S. C. Doret, M. T. Hummon, L. Luo, and J. M. Doyle, Nature (London) 431, 281 (2004); A. Buchachenko, G. Chaasiski, and M. Szczniak, Eur. Phys. J. D 45, 147 (2007)].

We solve the three-dimensional time-dependent Schrödinger equation for a few-cycle circularly polarized femtosecond laser pulse that interacts with an oriented target exemplified by an argon atom, initially in a $3p_x$ or $3p_y$ state. The photoelectron momentum distributions show distinct signatures of the orbital structure of the initial state as well as the carrier-envelope phase of the applied pulse. Our ab initio results are compared with results obtained using the length-gauge strong-field approximation, which allows for a clear interpretation of the results in terms of classical physics. Furthermore, we show that ionization by a circularly polarized pulse completely maps out the angular nodal structure of the initial state, thus providing a potential tool for studying orbital symmetry in individual systems or during chemical reactions.

We present total, energy-sharing, and triple differential cross sections for one-photon, double ionization of lithium and beryllium starting from aligned, excited $P$ states. We employ a recently developed hybrid atomic orbital with numerical grid method based on the finite-element discrete-variable representation and exterior complex scaling. Comparisons with calculated results for the ground-state atoms, as well as analogous results for ground-state and excited helium, serve to highlight important selection rules and show some interesting effects that relate to differences between inter- and intrashell electron correlation.

For a periodically driven quantum system, an effective time-independent Hamiltonian is derived with an eigenenergy spectrum, which in the regime of large driving frequencies approximates the quasienergies of the corresponding Floquet Hamiltonian. The effective Hamiltonian is evaluated for the case of optical lattice models in the tight-binding regime subjected to strong periodic driving. Three scenarios are considered: a periodically shifted one-dimensional (1D) lattice, a two-dimensional (2D) square lattice with inversely phased temporal modulation of the well depths of adjacent lattice sites, and a 2D lattice subjected to an array of microscopic rotors commensurate with its plaquette structure. In the 1D scenario, the rescaling of the tunneling energy, previously considered by Eckardt et al. [Phys. Rev. Lett. 95, 260404 (2005)] is reproduced. The 2D lattice with well-depth modulation turns out as a generalization of the 1D case. In the 2D case with staggered rotation, the expression previously found in the case of weak driving by Lim et al. [Phys. Rev. Lett. 100, 130402 (2008)] is generalized, such that its interpretation in terms of an artificial staggered magnetic field can be extended into the regime of strong driving.

We have studied the effect of plasma energy on the absorption coefficient of metallic photonic crystals doped with an ensemble of three-level quantum dots, which are interacting with each other via dipole-dipole interaction. The quantum dots are also interacting with coupled plasma-photon modes present in the system. A probe laser field is applied in order to study the absorption coefficient. We also consider the effect of quantum interference in our simulations, whereby two absorbed photons interfere with one another. Here the density matrix method has been used to calculate the steady-state and transient behavior of the absorption coefficient for the system. Two different field configurations are considered in our numerical simulations. In the first configuration, a probe field couples the ground state and two closely excited states. Absorption occurs due to transitions from the ground state to the two excited states. It is found that the position of the transparent peak moves when the plasma energy is changed. In other words, changing the plasma energy causes the system to switch between a transparent and an absorbing state. The strong coupling between plasmons and the quantum dots is responsible for this phenomenon. In the second configuration, the probe field couples with only one excited state, while a pump field couples to the other excited state. The transition between excited states is dipole forbidden. We observed that the peak in the absorption profile splits into two and also that the system exhibits gain with inversion due to the change in the plasma frequency, which is caused by quantum interference and coherence. These are interesting results and can be used make nanoscale plasma devices.

We investigate the storage and retrieval of a weak signal pulse in a medium composed of $N\hspace{0.5em}\Lambda$-type three-level atoms in thermal motion. Both atomic internal and translational degrees of freedom are treated quantum mechanically, based on which momentum families that are closed with respect to the action of the interaction Hamiltonian are defined. We introduce momentum-dependent collective atomic density operators by sorting the atoms into groups according to their momenta and establish Heisenberg equations for these atomic operators and the signal field. Because of the thermal-motion-dependent dephasing effect in the establishment of electromagnetically induced transparency of the medium, the efficiency of transfer between the signal pulse and the medium is reduced. The numerical simulations show that the performance of the scheme can be improved by applying the copropagation configuration of the light fields and preparing the atoms initially with a small width of the thermal momentum distribution, which is assumed to be the Gaussian function, or in the state where the Raman-Nath approximation is tenable.

We calculate the probe spectrum for multilevel atoms in a damped, weakly driven cavity supporting two degenerate orthogonally polarized modes. One mode is weakly driven by a linearly polarized external field. The atoms, initially prepared in a $m_F=0$ hyperfine ground state, couple to the driven mode by making a $\Delta m_F=0$ transition and to the orthogonally polarized mode by making $\Delta m_F=\pm 1$ transitions to other hyperfine sublevels. We compare probe spectra, the intensity of the driven mode, the undriven mode, and the atomic excitation probability as a function of the detuning of the driving laser from the cavity resonance for three- and four-level atomic models. In both cases the spectrum of the driven mode is a vacuum Rabi doublet familiar from the driven, damped Jaynes-Cummings model. The undriven mode spectrum is a triplet with the maximum on resonance for the three-level model while the four-level model has a four-peaked spectrum. We discuss the role of strong coupling to the undriven mode in accounting for the qualitative difference between the models.

We theoretically investigate two-photon excitation by correlated photons with energy anticorrelation. A three-level atomic system is used to evaluate selectivity and efficiency of two-photon excitation. It is shown that tailored squeezing of two-photon probability distribution concurrently enhances excitation efficiency and high-contrast selective excitation, without phase manipulation or pulse-shaping techniques. We also discuss candidates to generate such squeezed photons in real material systems.

We show how to distribute with percentage success probabilities almost perfectly entangled qubit memory pairs over repeater channel segments of the order of the optical attenuation distance. In addition to some weak, dispersive light-matter interactions, only Gaussian state transmissions and measurements are needed for this scheme. Our protocol outperforms the existing coherent-state-based schemes for entanglement distribution, even those using error-free non-Gaussian measurements. This is achieved through two innovations: First, optical squeezed states are utilized instead of coherent states. Second, the amplitudes of the bright signal pulses are reamplified at each repeater station. This latter variation is a strategy reminiscent of classical repeaters and would be impossible in single-photon-based schemes.

We study the evolution of entanglement for a pair of coupled nonidentical harmonic oscillators in contact with an environment. For both cases of a common bath and of two separate baths for each of the oscillators, a full master equation is provided without rotating-wave approximation. The entanglement dynamics is analyzed as a function of the diversity between the oscillators’ frequencies and their positive or negative mutual coupling and also the correlation between the occupation numbers. The singular effect of the resonance condition (identical oscillators) and its relationship with the possibility of preserving asymptotic entanglement are discussed. The importance of the bath’s memory properties is investigated by comparing Markovian and non-Markovian evolutions.

The existence of quantum correlation (as revealed by quantum discord), other than entanglement and its role in quantum-information processing (QIP), is a current subject for discussion. In particular, it has been suggested that this nonclassical correlation may provide computational speedup for some quantum algorithms. In this regard, bulk nuclear magnetic resonance (NMR) has been successfully used as a test bench for many QIP implementations, although it has also been continuously criticized for not presenting entanglement in most of the systems used so far. In this paper, we report a theoretical and experimental study on the dynamics of quantum and classical correlations in an NMR quadrupolar system. We present a method for computing the correlations from experimental NMR deviation-density matrices and show that, given the action of the nuclear-spin environment, the relaxation produces a monotonic time decay in the correlations. Although the experimental realizations were performed in a specific quadrupolar system, the main results presented here can be applied to whichever system uses a deviation-density matrix formalism.

We introduce two entanglement conditions that take the form of inequalities involving expectation values of operators. These conditions are sufficient conditions for entanglement; that is, if they are satisfied the state is entangled, but if they are not, one can say nothing about the entanglement of the state. These conditions are quite flexible, because the operators in them are not specified, and they are particularly useful in detecting multipartite entanglement. We explore the range of utility of these conditions by considering a number of examples of entangled states, and seeing under what conditions entanglement in them can be detected by the inequalities presented here.

We propose how to realize a three-step controlled-phase gate of one qubit simultaneously controlling $n$ qubits in a cavity or coupled to a resonator. The $n$ two-qubit controlled-phase gates, forming this multiqubit phase gate, can be performed simultaneously. The operation time of this phase gate is independent of the number $n$ of qubits. This phase gate controlling at once $n$ qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous cnot gate simultaneously acting on $n$ qubits. We present two alternative approaches to implement this gate. One approach is based on tuning the qubit frequency while in the other method the resonator frequency is tuned. Using superconducting qubits coupled to a resonator as an example, we show how to implement the proposed gate with one superconducting qubit simultaneously controlling $n$ qubits selected from $N$ qubits coupled to a resonator ($1<n<N$). We also give a discussion on realizing the proposed gate with atoms, by using one cavity initially in an arbitrary state.

We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are marked by adding elements to them that impart a specific phase shift to the particle as it enters or leaves the edge. If the complete graph has $N$ vertices and the subgraph has $K$ vertices, the particle becomes localized on the subgraph in $O(N/K)$ steps. This leads to a quantum search that is quadratically faster than a corresponding classical search. We show how to implement the quantum walk using a quantum circuit and a quantum oracle, which allows us to specify the resources needed for a quantitative comparison of the efficiency of classical and quantum searches—the number of oracle calls.

A single-channel joint readout is used to analyze highly entangled two-qubit states in a circuit quantum electrodynamics architecture. The measurement model for the readout is fully characterized, demonstrating a large sensitivity to two-qubit correlations. We quantify the high degree of entanglement by measuring a violation of the Clauser-Horne-Shimony-Holt inequality with a value of $2.61\pm 0.04$, without optimizing the preparation of the two-qubit state. In its present form, this joint readout can resolve improvements to the fidelity of two-qubit operations and be extended to three or four qubits.

A combined gravitomagnetic trap was used to measure how the anharmonicity of a trapping potential affects the dynamics of a cold atomic cloud. A displacement of the effective potential minimum as a function of the ensemble temperature was observed. The effect is a direct consequence of the thermal nature of the atomic sample. The results of both a theory approach to the dynamical evolution of the atomic cloud and a numerical simulation are in very good agreement with the experimental observations. The effect can be exploited to devise a novel measurement technique for the temperature of a trapped atomic cloud, as well as to separate thermal and condensed phases in Bose-Einstein condensation experiments.

We extend the technique originally proposed by [Honda et al., Phys. Rev. A 59, R934 (1999)] to measure the temperature of ytterbium and alkaline-earth-metal atoms confined in a magneto-optical trap (MOT). The method is based on the analysis of excitation spectra obtained by probing the ${}^1{\text{S}}_0\to {}^3{\text{P}}_1$ intercombination line. Thanks to a careful analysis and modeling of the effects caused by the MOT light on the probe transition we overcome the resolution and precision limits encountered in previous works. Ground-state light shift and Rabi broadening are measured and successfully compared with calculated values. This knowledge allows us to properly extract the Doppler contribution to the linewidth, thus obtaining a reliable measurement of the cloud temperature. We finally show how spectroscopy on free-falling atoms provides an alternative method to determine the sample temperature which resembles the standard time-of-flight technique.

High-order harmonic emission by an atom subject to the superposition of a strong infrared (IR) and a weak ultraviolet (UV) laser pulse is studied for the case when the UV photon energy remains below the ionization threshold. A simple analytical treatment is developed on the basis of the Lewenstein approach modified to account for the contribution of excited bound states of the atom. It is found that an order-of-magnitude enhancement of the high-harmonic emission rate can be expected, particularly in IR fields of moderate intensity. The results are discussed in view of recent experimental data and numerical simulations of the problem.

An analytical insight into the symmetry-breaking mechanisms underlying the transition from Josephson to self-trapping regimes in Bose-Einstein condensates is presented. We obtain expressions for the ground-state properties of the system of a gas of attractive bosons modeled by a two-site Bose-Hubbard Hamiltonian with an external bias. Simple formulas are found relating the appearance of fragmentation in the condensate with the large quantum fluctuations of the population imbalance occurring in the transition from the Josephson to the self-trapped regime.