We study the transfer of energy from an optical potential to atomic and molecular gases and demonstrate that this process is analogous to collisionless Landau damping of electrostatic potentials in plasmas and gravitational potentials observed on astrophysical scales. We show that a signficant fraction of the light attenuation within a cavity can be attributed to this mechanism when the cavity is filled with a gas at high density. The resulting motion of particles created by optical Landau damping can be used to induce transport when a periodic potential produced by two counterpropagating high-intensity pulsed optical fields is used. Bulk drift of the gas also appears feasible even when the mean kinetic energy is much greater that the maximum optical potential.

We show that two evanescently coupled ${\chi }^{\left(2\right)}$ parametric down-converters inside a Fabry-Perot cavity provide a tunable source of quadrature squeezed light, Einstein-Podolsky-Rosen (EPR) correlations and quantum entanglement. Analyzing the operation in the below threshold regime, we show how these properties can be controlled by adjusting the coupling strengths and the cavity detunings. As this can be implemented with integrated optics, it provides a possible route to rugged and stable EPR sources.

We investigate generalized measurements, based on positive-operator-valued measures, and von Neumann measurements for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. In particular, we derive the conditions under which the failure probability of the measurement can reach its absolute lower bound, proportional to the fidelity of the states. The optimum measurement strategy yielding the fidelity bound of the failure probability is explicitly determined for a number of cases. One example involves two density operators of rank $d$ that jointly span a $2d$-dimensional Hilbert space and are related in a special way. We also present an application of the results to the problem of unambiguous quantum state comparison, generalizing the optimum strategy for arbitrary prior probabilities of the states.

We solve the Klein-Gordon equation in the presence of a spatially one-dimensional Woods-Saxon potential. The scattering solutions are obtained in terms of hypergeometric functions and the condition for the existence of transmission resonances is derived. It is shown how the zero-reflection condition depends on the shape of the potential.

When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations can be done with entangling many-qudit Hamiltonians and local unitary control. By entangling we mean that every qudit is coupled to every other qudit, at least indirectly. We demonstrate that the only class of finite-dimensional entangling Hamiltonians that are not universal for simulation is the class of entangling Hamiltonians on qubits whose Pauli operator expansion contains only terms coupling an odd number of systems, as identified by Bremner et al. [Phys. Rev. A 69, 012313 (2004)]. We show that in all other cases entangling many-qudit Hamiltonians are universal for simulation.

The self-consistent derivation of density-functional theory by cluster expansion gives each electron half of the interaction energy. The pair correlation effect maximizing the probability of particle separation recovers a missing energy that increases with the total number of electrons. It provides the first evidence that the virial theorem holds true for atomic and molecular systems. The $3d$ finite element method calculation of water molecule is also presented.

We study the three-body problem for both fermionic and bosonic cold-atom gases in a parabolic transverse trap of length scale $a_{\perp }$. For this quasi-one-dimensional (quasi-1D) problem, there is a two-body bound state (dimer) for any sign of the 3D scattering length $a$ and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths $a_{\mathit{ad}}$ and $b_{\mathit{ad}}$. In the tightly bound “dimer limit” $a_{\perp }∕a\to \infty$, we find $b_{\mathit{ad}}=0$ and $a_{\mathit{ad}}$ is linked to the 3D atom-dimer scattering length. In the weakly bound “BCS limit” $a_{\perp }∕a\to -\infty$, a connection to the Bethe ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is nonuniversal: $a_{\mathit{ad}}$ and $b_{\mathit{ad}}$ depend both on $a_{\perp }∕a$ and on a parameter $R^{*}$ related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.

Two-photon above-threshold ionization (ATI) relative cross sections from the $3{}^{1}P$ state of Mg have been measured using two-color ionization in the focus of a magnetic bottle spectrometer and have been calculated using the Green’s-function method in the Feshbach formalism and an $L^2$-integrable close-coupling approach, with a basis of $L^2$-integrable $B$-spline functions. We report these cross sections in the region of $3d4p$ ${}^{1}F^o$ autoionizing state, with photon energies of $3.3–3.6\mathrm{eV}$. This is one of the few direct comparisons between ab initio theory and experiments in ATI in the vicinity of a Feshbach resonance. A good agreement between theory and experiment is found in the relative total cross sections.

We propose a coherent beam splitter for polarized heteronuclear molecules based on a stimulated Raman adiabatic passage scheme that uses a tripod linkage of electrotranslational molecular states. We show that for strongly polarized molecules the rotational dynamics imposes significantly larger Rabi frequencies than would otherwise be expected, but within this limitation, a full transfer of the molecules to two counterpropagating ground-state wave packets is possible.

A class of optimal quantum repeaters for qubits is suggested. The schemes are minimal, i.e., they involve a single additional probe qubit, and optimal, i.e., they provide the maximum information adding the minimum amount of noise. Information gain and state disturbance are quantified by fidelities which, for our schemes, saturate the ultimate bound imposed by quantum mechanics for randomly distributed signals. Special classes of signals are also investigated, in order to improve the information-disturbance trade-off. Extension to higher-dimensional signals (qudits) is straightforward.

We investigate entanglement dynamics in multipartite systems, establishing a quantitative concept of entanglement flow: both flow through individual particles and flow along general networks of interacting particles. In the former case, the rate at which a particle can transmit entanglement is shown to depend on that particle’s entanglement with the rest of the system. In the latter, we derive a set of entanglement rate equations, relating the rate of entanglement generation between two subsets of particles to the entanglement already present further back along the network. We use the rate equations to derive a lower bound on entanglement generation in qubit chains, and compare this to existing entanglement creation protocols.

We analyze the power of the quantum adiabatic evolution algorithm (QAA) for solving random computationally hard optimization problems within a theoretical framework based on random matrix theory (RMT). We present two types of driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that nonadiabatic corrections in the QAA are due to the interaction of the ground state with the “cloud” formed by most of the excited states, confirming that in driven RMT models, the Landau-Zener scenario of pairwise level repulsions is not relevant for the description of nonadiabatic corrections. We show that the QAA has a finite probability of success in a certain range of parameters, implying a polynomial complexity of the algorithm. The second model corresponds to the standard QAA with the problem Hamiltonian taken from the RMT Gaussian unitary ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. For this reason, the driven GUE model can also lead to polynomial complexity of the QAA. The main contribution to the failure probability of the QAA comes from the nonadiabatic corrections to the eigenstates, which only depend on the absolute values of the transition amplitudes. Due to the mapping between the two models, these absolute values are the same in both cases. Our results indicate that this “phase irrelevance” is the leading effect that can make both the Markovian- and GUE-type QAAs successful.

In the system with superconducting quantum interference devices (SQUIDs) in cavity, the quantum logic gates operation and entanglement can be achieved by using a quantized cavity field and classical microwave pluses, via Raman transition. In this scheme, no transfer of quantum information between the SQUIDs and cavity is required, the cavity field is only virtually excited and thus the cavity decay is suppressed during the gate operation and entanglement generations. The gate operation and entanglement generations are realized by using only the two lower flux states of the SQUID system and the excited state would not be excited. Therefore, the effect of docoherence based on the levels of the SQUID system is possible to minimize.

The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error correction (ancilla adding, coding and decoding) and the quantum Zeno effect. A demonstration of our method on a simple atomic system—namely, a rubidium isotope—is proposed.

It is a hard and important problem to find the criterion of a set of positive-definite matrices which can be written as reduced density operators of a multipartite global quantum state. This problem is closely related to the study of many-body quantum entanglement, which is one of the focuses of current quantum-information theory. We give several results on the necessary compatibility relations between a set of reduced and global density matrices, including (i) compatibility conditions for the one-party reduced density matrices of any $(N_A\times N_B)$-dimensional bipartite mixed quantum state, (ii) compatibility conditions for the one-party reduced matrices of any $M$-partite quantum states with the dimension $N^{\otimes M}$, and (iii) compatibility conditions for the two-party reduced density matrixes of $(2\times 2\times 2)$-dimensional tripartite mixed quantum state.

We present high-precision trap loss spectroscopy of excited molecules obtained by the photoassociation of ultracold sodium atoms. Near the dissociation limit, hyperfine and rotational (Coriolis-type) interactions cause significant mixing of states of different nominal Hund’s case (c) symmetry resulting in a complex pattern of spectral lines. We construct a theoretical model of the large, slowly rotating molecule starting from a long-range, atomic viewpoint. Interaction potentials are derived from the known long-range resonant dipole and van der Waals forces between atoms, supplemented at short range by the results of electronic-structure calculations. Spin-dependent interactions coupling the various angular momenta—nuclear spin, electron spin, electron orbit, and the mechanical rotation of the molecule as a whole—are derived from known atomic parameters. We avoid imposing approximate symmetries or coupling schemes and consequently include all nonadiabatic mixing of different degrees of freedom. Quantitative agreement between experiment and theory for both line positions and intensities is found. Specifically, we observe and calculate mixing of levels of , , and symmetry bound by below the asymptote.

We have applied a high-resolution-electron–momentum-resolved-ion coincidence technique to the Auger emission from $\mathrm{C}{\mathrm{F}}_4$ following the F $1s\to a_1^{*}$ excitation and found that the Auger electron emitted from the atomic F fragment during the ultrafast dissociation is backscattered by the residual fragment $\mathrm{C}{\mathrm{F}}_3$. We find also that more than half of the excess energy goes into the vibrational excitation of the $\mathrm{C}{\mathrm{F}}_3$ fragment.

We consider the transformation of multipartite states in the single-copy setting under positive-partial-transpose-preserving operations (PPT operations) and obtain both qualitative and quantitative results. First, for some pure-state transformations that are impossible under local operations and classical communication (LOCC), we demonstrate that they become possible with a surprisingly large success probability under PPT operations. Furthermore, we clarify the convertibility of arbitrary multipartite pure states under PPT operations and show that a drastic simplification in the classification of pure-state entanglement occurs when the set of operations is switched from LOCC to PPT operations. Indeed, the infinitely many types of LOCC-incomparable entanglement are reduced to only one type under the action of PPT operations. This is a clear manifestation of the increased power afforded by the use of PPT-bound entanglement. In addition, we further enlarge the set of operations to clarify the effect of another type of bound entanglement, multipartite unlockable bound entanglement, and show that a further simplification occurs. As compared to pure states a more complicated situation emerges in mixed-state settings. While single-copy distillation becomes possible under PPT operations for some mixed states it remains impossible for other mixed states.

We study the equivalence of a realistic quantum key distribution protocol using coherent states and homodyne detection with a formal entanglement purification protocol. Maximally entangled qubit pairs that one can extract in the formal protocol correspond to secret key bits in the realistic protocol. More specifically, we define a qubit encoding scheme that allows the formal protocol to produce more than one entangled qubit pair per entangled oscillator pair or, equivalently for the realistic protocol, more than one secret key bit per coherent state. The entanglement parameters are estimated using quantum tomography. We analyze the properties of the encoding scheme and investigate the resulting secret key rate in the important case of the attenuation channel.

We show how the entanglement of two atoms, trapped in distant separate cavities, can be generated with arbitrarily high probability of success. The scheme proposed employs sudden excitation of the atoms proving that the weakly driven condition is not necessary to obtain the success rate close to unity. The modified scheme works properly even if each cavity contains many atoms interacting with the cavity modes. We also show that our method is robust against spontaneous atomic decay.