The formations of ${}^{85}{\text{Rb}}_2$ molecules via photoassociation (PA) steered by two-color laser fields are explored theoretically in order to find an efficient and robust PA scheme. The PA processes steered by the PA pulses modulated by two Gaussian pulses and by two chirped pulses are discussed and compared in detail. The two pulses are coherent in the picosecond range and reach their maxima at the same time. The influences of the linear chirp rate, the frequency difference between two pulses, and the phase shift of the modulated envelope with respect to the maximum of the Gaussian envelope on the PA process are investigated. The yield of photoassociated molecules on vibrational levels with a binding energy of $>$1.0 cm${}^{-1}$ with respect to the $5S+5P_{1/2}$ dissociation limit can apparently be enhanced by choosing proper pulse parameters. Especially, the two-color laser field modulated by two chirped pulses can raise the PA efficiency on one side, and weaken the dependence of the PA process on phase shift on the other side.

We experimentally investigate the phenomenon of a quantum ratchet created by exposing a Bose-Einstein condensate to short pulses of a potential which is periodic in both space and time. Such a ratchet is manifested by a directed current of particles, even though there is an absence of a net bias force. We confirm a recent theoretical prediction [M. Sadgrove and S. Wimberger, New J. Phys. 11, 083027 (2009)] that the current direction can be controlled by experimental parameters which leave the underlying symmetries of the system unchanged. We demonstrate that this behavior can be understood using a single variable containing many of the experimental parameters and thus the ratchet current is describable using a single universal scaling law.

We investigate the Zeeman field effects on the bulk superfluid properties and the collective modes in two-dimensional (2D) attractive atomic Fermi gases with Rashba-type spin-orbit coupling. In the presence of a large spin-orbit coupling, the system undergoes a quantum phase transition to a topological superfluid state at a critical Zeeman field. We show that the nonanalyticities of the thermodynamic functions as well as other physical quantities at the quantum phase transition originate from the infrared singularities caused by the gapless fermionic spectrum. The same argument applies also to the BCS-BEC evolution in 2D fermionic superfluids with $p$- or $d$-wave pairing. The superfluid density $n_s$ and the velocity of the Goldstone sound mode $c_s$ behave oppositely in the normal and the topological superfluid phases: they are suppressed by the Zeeman field in the normal superfluid phase, but get enhanced in the topological superfluid phase. The velocity of the Goldstone sound mode also shows nonanalyticity at the quantum phase transition. For large Zeeman field, we find $n_s\to n$ and $c_s\to {\upsilon }_{\mathrm{F}}$, where $n$ is the total fermion density and ${\upsilon }_{\mathrm{F}}$ is the Fermi velocity of noninteracting system. The unusual behavior of the superfluid density and the collective modes can be understood by the fact that the spin-orbit-coupled superfluid state at large Zeeman field can be mapped to the $p_x+i{p}_y$ superfluid state of spinless fermions.

The operation of a surface plasmon amplification by stimulated emission of radiation- (spaser)-based nanolaser is theoretically investigated. We find that the lasing frequency undergoes a shift as the lasing intensity increases, a result that agrees with recent experiments. We show that the mechanism of the intensity-dependent shift involves a spatial deformation of the lasing mode, which is induced by the spatial hole burning in the surrounding gain media. We develop a general analytical scheme to account for the mode deformation. Our numerical calculations demonstrate good correspondence of the lasing frequency shift with the experimental data for the simplest (spherical) geometry of the spaser.

In terms of a tanh-series representation, the stationary dissipative solitons such as arbitrary-amplitude solitons, plain solitons, flattop solitons, and composite solitons in complex Ginzburg-Landau (CGL) systems can be exactly described, as confirmed by extensive simulations. It thus suggests another route to understanding solitons in CGL-like systems that is highly accurate.

We show how to probe multipartite entanglement in $N$ coupled Jaynes-Cummings cells where the degrees of freedom are the electronic energies of each of the $N$ atoms in separate single-mode cavities plus the $N$ single-mode fields themselves. Specifically we propose probing the combined system as though it is a dielectric medium. The spectral properties and transition rates directly reveal multipartite entanglement signatures. It is found that the Hilbert space of the $N$ cell system can be confined to the totally symmetric subspace of two states only that are maximally entangled $W$ states with $2N$ degrees of freedom.

We present the solution to the problem of optimally discriminating among quantum states, i.e., identifying the states with maximum probability of success when a certain fixed rate of inconclusive answers is allowed. By varying the inconclusive rate, the scheme optimally interpolates between unambiguous and minimum error discrimination, the two standard approaches to quantum state discrimination. We introduce a very general method that enables us to obtain the solution in a wide range of cases and give a complete characterization of the minimum discrimination error as a function of the rate of inconclusive answers. A critical value of this rate is identified that coincides with the minimum failure probability in the cases where unambiguous discrimination is possible and provides a natural generalization of it when states cannot be unambiguously discriminated. The method is illustrated on two explicit examples: discrimination of two pure states with arbitrary prior probabilities and discrimination of trine states.

We develop a practical Hartree-Fock theory for trapped Bose and Fermi gases that interact with dipole-dipole interactions. This theory is applicable at zero and finite temperature. Our approach is based on the introduction of local momentum distortion fields that characterize the exchange effects in terms of a local effective potential. We validate our theory against existing theories, finding excellent agreement with full Hartree-Fock calculations.

Recently, Vértesi and Bene [Phys. Rev. A 82, 062115 (2010)] derived a two-qubit Bell inequality $I_{\mathrm{CH}3}$, which they show to be maximally violated only when more general positive operator-valued measures (POVMs) are used instead of the usual von Neumann measurements. Here we consider a general parametrization for the three-element POVM involved in the Bell test and obtain a higher quantum bound for the $I_{\mathrm{CH}3}$ inequality. With a higher quantum bound for $I_{\mathrm{CH}3}$, we investigate whether there is an experimental setup that can be used for observing that POVMs give higher violations in Bell tests based on this inequality. We analyze the maximum errors supported by the inequality to identify a source of entangled photons that can be used for the test. Then we study whether POVMs are also relevant in the more realistic case where partially entangled states are used in the experiment. Finally, we investigate the required efficiencies of the $I_{\mathrm{CH}3}$ inequality, and the type of measurements involved, for closing the detection loophole. We obtain the result that POVMs allow for the lowest threshold detection efficiency, and that it is comparable to the minimal required detection efficiency (in the case of two qubits) of the Clauser-Horne-Bell inequality.

Ever since the inception of gravitational-wave detectors, limits imposed by quantum mechanics to the detection of time-varying signals have been a subject of intense research and debate. Drawing insights from quantum information theory, quantum detection theory, and quantum measurement theory, here we prove lower error bounds for waveform detection via a quantum system, settling the long-standing problem. In the case of optomechanical force detection, we derive analytic expressions for the bounds in some cases of interest and discuss how the limits can be approached using quantum control techniques.

We investigate the backflow effect in elementary quantum mechanics—the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. We compute the current and flux for states consisting of superpositions of Gaussian wave packets. These are experimentally realizable but the amount of backflow is small. Inspired by the numerical results of Penz et al. [Penz, Grübl, Kreidl, and Wagner, J. Phys. A 39, 423 (2006)], we find two nontrivial wave functions whose current at any time may be computed analytically and which have periods of significant backflow, in one case with a backward flux equal to about 70$\%$ of the maximum possible backflow, a dimensionless number $c_{bm}\approx 0.04$, discovered by Bracken and Melloy [Bracken and Melloy, J. Phys. A 27, 2197 (1994)]. This number has the unusual property of being independent of $\hslash$ (and also of all other parameters of the model), despite corresponding to an obviously quantum-mechanical effect, and we shed some light on this surprising property by considering the classical limit of backflow. We discuss some specific measurement models in which backflow may be identified in certain measurable probabilities.

The noise in optical source preparation needs to be characterized for the security of practical continuous-variable quantum key distribution (CVQKD). Two feasible schemes, based on either an active optical switch or a passive beamsplitter, are proposed to monitor the variance of the source noise. We derive the security bounds for both schemes against collective attacks in the asymptotical limit and find that the passive scheme performs better. The finite-size effect is also discussed briefly for both schemes.

Apart from their foundational significance, entropic uncertainty relations play a central role in proving the security of quantum cryptographic protocols. Of particular interest are therefore relations in terms of the smooth min-entropy for Bennett-Brassard 1984 (BB84) and six-state encodings. The smooth min-entropy $H_{\min }^{\epsilon }(X/B)$ quantifies the negative logarithm of the probability for an attacker $B$ to guess $X$, except with a small failure probability $\epsilon$. Previously, strong uncertainty relations were obtained which are valid in the limit of large block lengths. Here, we prove an alternative uncertainty relation in terms of the smooth min-entropy that is only marginally less strong but has the crucial property that it can be applied to rather small block lengths. This paves the way for a practical implementation of many cryptographic protocols. As part of our proof we show tight uncertainty relations for a family of Rényi entropies that may be of independent interest.

From both theoretical and experimental points of view symmetric states constitute an important class of multipartite states. Still, entanglement properties of these states, in particular those with positive partial transposition (PPT), lack a systematic study. Aiming at filling in this gap, we have recently affirmatively answered the open question of existence of four-qubit entangled symmetric states with PPT and thoroughly characterized entanglement properties of such states [J. Tura et al., Phys. Rev. A 85, 060302(R) (2012)]. With the present contribution we continue on characterizing PPT entangled symmetric states. On the one hand, we present all the results of our previous work in a detailed way. On the other hand, we generalize them to systems consisting of an arbitrary number of qubits. In particular, we provide criteria for separability of such states formulated in terms of their ranks. Interestingly, for most of the cases, the symmetric states are either separable or typically separable. Then, edge states in these systems are studied, showing in particular that to characterize generic PPT entangled states with four and five qubits, it is enough to study only those that assume few (respectively, two and three) specific configurations of ranks. Finally, we numerically search for extremal PPT entangled states in such systems consisting of up to 23 qubits. One can clearly notice regularity behind the ranks of such extremal states, and, in particular, for systems composed of odd numbers of qubits we find a single configuration of ranks for which there are extremal states.

Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure from ideal bosonic behavior is quantified by the normalization ratio of $N$-composite-boson states. We derive the two-fermion states that extremize the normalization ratio for a fixed single-fermion purity $P$, and establish general tight bounds for this indicator. For very small purities, $P<1/N^2$, the upper and lower bounds converge, which allows us to quantify accurately the departure from perfectly bosonic behavior, for any state of many composite bosons.

Codeword-stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and nonadditive quantum codes. Standard codeword-stabilized quantum codes encode quantum information into subspaces. The more general notion of encoding quantum information into a subsystem is known as an operator (or subsystem) quantum error-correcting code. Most operator codes studied to date are based in the usual stabilizer formalism. We introduce operator quantum codes based on the codeword-stabilized quantum code framework. Based on the necessary and sufficient conditions for operator quantum error correction, we derive an error-correction condition for operator codeword-stabilized quantum codes. Based on this condition, the word operators of a operator codeword-stabilized quantum code are constructed from a set of classical binary errors induced by generators of the gauge group. We use this scheme to construct examples of both additive and nonadditive codes that encode quantum information into a subsystem.

One of the classical results concerning quantum channels is the characterization of entanglement-breaking channels [M. Horodecki, P. W. Shor, and M. B. Ruskai, Rev. Math. Phys. 15, 629 (2003)]. We address the question whether there exists a similar characterization on the level of quantum correlations which may go beyond entanglement. The answer is fully affirmative in the case of breaking quantum correlations down to the, so-called, QC (quantum-classical) type, while it is no longer true in the CC (classical-classical) case. The corresponding channels turn out to be measurement maps. Our study also reveals an unexpected link between quantum state and local correlation broadcasting and finite Markov chains. We present a possibility of broadcasting via non von Neumann measurements, which relies on the Perron-Frobenius theorem. Surprisingly, this is not the typical generalized controlled-not (c-not) gate scenario appearing naturally in this context.

The Simon-Zhislin-Hunziker theorem implies that $Z_c$, the critical charge below which the three electron atom is not bound, is at most 2. The vanishing electron affinity of He implies that $Z_c$ is not less than 2. Hence, $Z_c=2$. To elucidate the approach to the critical charge, we calculated nonrelativistic binding energies for the third electron in the ground state, $1s^{2}2s{}^{2}S$, and in the first and second excited states, $1s^{2}2p{}^{2}P$ and $1s^{2}3s{}^{2}S$, for nuclear charges approaching $Z_c$. At this limit the quantum defects for both ${}^{2}S$ states are found to approach unity. This implies that the orbital specifying the outer ($ns,n=2,3$) electron becomes a very diffuse $(n-1)s$-type orbital, except within the relatively tiny space occupied by the inner two-electron shell. For the ${}^{2}P$ state the quantum defect approaches zero both as $Z\to \infty$ and as $Z\to 2$. An expression for the $s$-$p$ splitting at $Z\to 2$ is suggested, that improves upon earlier results based on energies computed (or measured) at integer values of $Z$. Rigorous large $Z$ asymptotic expressions for the quantum defects in the $1s^{2}ns{}^{2}S$ states are presented, exhibiting the expected mild dependence on the principal quantum number.

Using an ab initio model to account the polarization effects of molecules in the presence of slow positrons, we have obtained low-energy positron cross sections for ${\text{H}}_2$ and ${\text{N}}_2$ molecules. The polarization model proposed here is calculated with the expected values of the positron-electron interaction operator in the polarized target wave function for each fixed distance of the positron. Together with the electrostatic potential, this polarization describes the interaction potential in a static-polarization approximation. Within this interaction level, we have obtained differential and integral cross sections that are in good agreement with recent measurements of the Trento group and other theoretical approaches.

We present a method to control photodissociation by manipulating the bond-softening mechanism occurring in strong shaped laser fields, namely by varying the chirp sign and magnitude of an ultrashort laser pulse. Manipulation of bond softening is experimentally demonstrated for strong-field (${10}^{12}–{10}^{13}$ W/cm${}^2$) photodissociation of H${}_2^{+}$, exhibiting a substantial increase of dissociation by positively chirped pulses with respect to both negatively chirped and transform-limited pulses. The measured kinetic energy release and angular distributions are used to quantify the degree of dissociation control. The control mechanism is attributed to the interplay of dynamic alignment and chirped light induced potential curves.