We explore the efficiency and robustness of population transfer in two-state systems by adiabatic passage (i) when the driving pulse is optimally designed in order to lead to parallel adiabatic passage or (ii) with a linear chirping. We show how one could practically implement the corresponding designs of the pulses in the spectral domain. We analyze the robustness of the two shapings taking into account fluctuations of the phase, amplitude, and the area of the pulse. We show the overall superiority of the parallel adiabatic passage especially when one faces the issue of a pulse area that is not well known. We show that the robustness of parallel adiabatic passage is not improved when it is complemented by a correcting field that cancels out the nonadiabatic losses.

In a recent experiment, a Bose-Einstein condensate of ${}^7$Li has been excited by a harmonic modulation of the atomic $s$-wave scattering length via Feshbach resonance. By combining an analytical perturbative approach with extensive numerical simulations, we analyze the emerging nonlinear dynamics of the system on the mean-field Gross-Pitaevskii level at zero temperature. Resulting excitation spectra are presented and prominent nonlinear features are found: mode coupling, higher harmonics generation, and significant shifts in the frequencies of collective modes. We indicate how nonlinear dynamical properties could be made clearly observable in future experiments and compared to our results.

We consider a two-component Bose-Einstein condensate, which contains atoms with magnetic dipole moments aligned along the $z$ direction (labeled as component 1) and nonmagnetic atoms (labeled as component 2). The problem is studied by means of exact numerical simulations. The effects of dipole-dipole interaction on phase separations are investigated. It is shown that, in the quasi-one-dimensional regime, the atoms in component 2 are squeezed out when the dimensionless dipolar strength parameter is small, whereas the atoms in component 1 are pushed out instead when the parameter is large. This is in contrast to the phenomena in the quasi-two-dimensional regime. These two components are each kicked out by the other in the quasi-one-dimensional regime and this phenomenon is discussed as well.

Precisely measuring the magnetic-field gradient within a vacuum chamber is important for many precision experiments and can be realized by atom interferometry using magnetically sensitive sublevels at different times to make a differential measurement, which had been demonstrated in our previous work. In this paper, we demonstrate a differential method to measure the magnetic-field gradient by means of two simultaneously operated atom interferometers using double atomic fountains. By virtue of this simultaneous differential measurement to reject common-mode noise, the resolution can be improved by one order of magnitude for about a 1000-s integration time.

We demonstrate multiwavelength channel optical logic operations on the Bloch vector of a quantum two-level system in the structured electromagnetic vacuum of a bimodal photonic crystal waveguide. This arises through a bichromatic strong-coupling effect that enables unprecedented control over single quantum-dot (QD) excitation through two beams of ultrashort femtojoule pulses. The second driving pulse (signal) with slightly different frequency and weaker strength than the first (holding) pulse leads to controllable strong modulation of the QD Bloch vector evolution path. This occurs through resonant coupling of the signal pulse with the Mollow sideband transitions created by the holding pulse. The movement of the Mollow sidebands during the passage of the holding pulse leads to an effective chirping in transition frequency seen by the signal. Bloch vector dynamics in the rotating frame of the signal pulse and within the dressed-state basis created by the holding pulse reveals that this chirped coupling between the signal pulse and the Mollow sidebands leads to either augmentation or negation of the final quantum-dot population (after pulse passage) compared to the outcome of the holding pulse alone and depending on the relative frequencies of the pulses. By making use of this extra degree of freedom for ultrafast control of QD excitations, applications in ultrafast all-optical logic and, or, and not gates are proposed in the presence of significant ($0.1$) THz nonradiative dephasing and (about 1%) inhomogeneous broadening.

We describe a mechanism for a controlled generation of a pure Bell state with correlated atoms that involve two or zero excitations. The mechanism inhibits transitions into singly excited collective states of a two-atom system by shifting them from their unperturbed energies. The shift is accomplished by the dipole-dipole interaction between the atoms. The creation of the Bell state is found to be dependent on the relaxation of the atomic excitation. When the relaxation is not present or can be ignored, the state of the system evolves harmonically between a separable to the maximally entangled state. We follow the temporal evolution of the state and find that the concurrence can be different from zero only in the presence of the dipole-dipole interaction. Furthermore, in the limit of a large dipole-dipole interaction, the concurrence reduces to that predicted for an X state of the system. A general inequality is found which shows that the concurrence of an X-state system is a lower bound for the concurrence of the two-atom system. With the relaxation present, the general state of the system is a mixed state that under a strong dipole-dipole interaction reduces the system to an X-state form. We find that mixed states admit of lower level of entanglement, and the entanglement may occur over a finite range of time. A simple analytical expression is obtained for the steady-state concurrence which shows that there is a threshold value for the dipole-dipole interaction relative to the Rabi frequency of the driving field above which the atoms can be entangled over the entire time of the evolution.

In a recent paper [K. Loukopoulos and D. E. Browne, Phys. Rev. A 81, 062336 (2010)], five schemes for secure multiparty computation utilizing the Greenberger-Horne-Zeilinger (GHZ) quantum correlation were presented, which were claimed to be secure in some kinds of security models. However, this study points out that schemes C and D2 could be attacked by corrupted parties replacing photon and exchanging classical information.

We examine the existence and structure of particular sets of mutually unbiased bases (MUBs) in bipartite qudit systems. In contrast to well-known power-of-prime MUB constructions, we restrict ourselves to using maximally entangled stabilizer states as MUB vectors. Consequently, these bipartite entangled stabilizer MUBs (BES MUBs) provide no local information, but are sufficient and minimal for decomposing a wide variety of interesting operators including (mixtures of) Jamiołkowski states, entanglement witnesses, and more. The problem of finding such BES MUBs can be mapped, in a natural way, to that of finding maximum cliques in a family of Cayley graphs. Some relationships with known power-of-prime MUB constructions are discussed, and observables for BES MUBs are given explicitly in terms of Pauli operators.

We propose a Lie-algebraic duality approach to analyze nonequilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of Hubbard-Stratonovich dynamical systems). The first part of the paper utilizes a geometric Hilbert-space-invariant formulation of unitary time evolution, where a quantum Hamiltonian is viewed as a trajectory in an abstract Lie algebra, while the sought-after evolution operator is a trajectory in a dynamic group, generated by the algebra via exponentiation. The evolution operator is uniquely determined by the time-dependent dual generators that satisfy a system of differential equations, dubbed here dual Schrödinger-Bloch equations, which represent a viable alternative to the conventional Schrödinger formulation. These dual Schrödinger-Bloch equations are derived and analyzed on a number of specific examples. It is shown that deterministic dynamics of a closed classical dynamical system occurs as action of a symmetry group on a classical manifold and is driven by the same dual generators as in the corresponding quantum problem. This represents quantum-to-classical correspondence. In the second part of the paper, we further extend the Lie-algebraic approach to a wide class of interacting many-particle lattice models. A generalized Hubbard-Stratonovich transform is proposed and it is used to show that the thermodynamic partition function of a generic many-body quantum lattice model can be expressed in terms of traces of single-particle evolution operators governed by the dynamic Hubbard-Stratonovich fields. The corresponding Hubbard-Stratonovich dynamical systems are generally nonunitary, which yields a number of notable complications, including breakdown of the global exponential representation. Finally, we derive Hubbard-Stratonovich dynamical systems for the Bose-Hubbard model and a quantum spin model and use the Lie-algebraic approach to obtain new nonperturbative dual descriptions of these theories.

The master equation for the state of an open quantum system can be unravelled into stochastic trajectories described by a stochastic master equation. Such stochastic differential equations can be interpreted as an update formula for the system state conditioned on results obtained from monitoring the bath. So far only one parametrization (mathematical representation) for arbitrary diffusive unravellings (quantum trajectories arising from monitorings with Gaussian white noise) of a system described by a master equation with $L$ Lindblad terms has been found [H. M. Wiseman and A. C. Doherty, Phys. Rev. Lett. 94, 070405 (2005)]. This parametrization, which we call the $\mathrm{U}$ representation parameterizes diffusive unravellings by $L^2+2L$ real numbers, arranged in a matrix $\mathsf{U}$ subject to three constraints. In this paper we investigate alternative parametrizations of diffusive measurements. We find, rather surprisingly, the description of diffusive unravellings can be unified by a single equation for a nonsquare complex matrix $\mathsf{M}$ if one is willing to allow for some redundancy by lifting the number of real parameters necessary from $L^2+2L$ to $3L^2+L$. We call this parametrization the $\mathrm{M}$ representation. Both the $\mathrm{M}$ representation and $\mathrm{U}$ representation lack a physical picture of what the measurement should look like. We thus propose another parametrization, the $\mathrm{B}$ representation that details how the measurement is implemented in terms of beam-splitters, phase shifters, and homodyne detectors. Relations between the different representations are derived.

Feedback control engineers have been interested in multiple-input–multiple-output (MIMO) extensions of single-input–single-output (SISO) results of various kinds due to its rich mathematical structure and practical applications. An outstanding problem in quantum feedback control is the extension of the SISO theory of Markovian feedback by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)] to multiple inputs and multiple outputs. Here we generalize the SISO homodyne-mediated feedback theory to allow for multiple inputs, multiple outputs, and arbitrary diffusive quantum measurements. We thus obtain a MIMO framework which resembles the SISO theory and whose additional mathematical structure is highlighted by the extensive use of vector-operator algebra.

We study the quantum communication protocol of remote state preparation (RSP) for pure states of qubits encoded in single photons transmitted through a double slit, the so-called spatial qubits. Two measurement strategies that one can adopt to remotely prepare the states are discussed. The first strategy is the well-known spatial postselection, where a single-pixel detector measures the transverse position of the photon between the focal and the image plane of a lens. The second strategy, proposed by ourselves, is a generalized measurement divided into two steps: the implementation of a two-outcome positive operator-valued measurement (POVM) followed by the spatial postselection at the focal plane of the lens by a two-pixel detector in each output of the POVM. In both cases we analyze the effects of the finite spatial resolution of the detectors over three figures of merit of the protocol, namely, the probability of preparation, the fidelity, and purity of the remotely prepared states. It is shown that our strategy improves these figures compared with spatial postselection, at the expense of increasing the classical communication cost as well as the required experimental resources. In addition, we present a modified version of our strategy for RSP of spatial qudits which is able to prepare arbitrary pure states, unlike spatial postselection alone. We expect that our study may also be extended for RSP of the angular spectrum of a single-photon field as an alternative for quantum teleportation which requires very inefficient nonlinear interactions.

In this paper we provide a recipe for state protection in a network of oscillators under collective damping and diffusion. Our strategy is to manipulate the network topology, i.e., the way the oscillators are coupled together, the strength of their couplings, and their natural frequencies, in order to create a relaxation-diffusion-free channel. This protected channel defines a decoherence-free subspace (DFS) for nonzero-temperature reservoirs. Our development also furnishes an alternative approach to build up DFSs that offers two advantages over the conventional method: it enables the derivation of all the network-protected states at once, and also reveals, through the network normal modes, the mechanism behind the emergence of these protected domains.

Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasiparticle excitations. We develop an efficient means to map between dense and sparse representations of quantum information (qubits) and a simple construction of multiqubit gates, for all anyon models from Chern-Simons-Witten SU(2)${}_k$ theory that support universal quantum computation by braiding ($k⩾3,k\ne 4$). In the process, we show how the constructions of topological quantum memory and gates for $k=2,4$ connect naturally to those for $k⩾3,k\ne 4$, unifying these concepts in a simple framework. Furthermore, we illustrate potential extensions of these ideas to other anyon models outside of Chern-Simons-Witten field theory.

We examine the delayed response of a diatomic gas to a polarizing laser field with the goal of obtaining computationally efficient methods for use with laser pulse propagation simulations. We demonstrate that for broadband pulses, heavy molecules such as ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$, and typical atmospheric temperatures, the initial delayed response requires only classical physics. The linear kinetic Green's function is derived from the Boltzmann equation and shown to be in excellent agreement with full density-matrix calculations. A straightforward perturbation approach for the fully nonlinear, kinetic impulse response is also presented. With the kinetic theory a reduced fluid model of the diatomic gas’ orientation is derived. Transport coefficients are introduced to model the kinetic phase mixing of the delayed response. In addition to computational rapidity, the fluid model provides intuition through the use of familiar macroscopic quantities. Both the kinetic and the fluid descriptions predict a nonlinear steady-state alignment after passage of the laser pulse, which in the fluid model is interpreted as an anisotropic temperature of the diatomic fluid with respect to motion about the polarization axis.

We consider the problem of quantum communication mediated by a passive optical refocusing system. The model captures the basic features of all those situations in which a signal is either refocused by a repeater for long-distance communication, or it is focused on a detector prior to the information decoding process. Introducing a general method for linear passive optical systems, we determine the conditions under which optical refocusing implies information transmission gain. Although the finite aperture of the repeater may cause loss of information, we show that the presence of the refocusing system can substantially enhance the rate of reliable communication with respect to the free-space propagation. We explicitly address the transferring of classical messages over the quantum channel, but the results can be easily extended to include the case of transferring quantum messages as well.

We study the textures of $F=2$ spinor Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) induced by a synthetic non-Abelian gauge field. On the basis of the analysis of the SOC energy and the numerical calculation of the Gross-Pitaevskii equation, we demonstrate that the textures originate from the helical modulation of the order parameter (OP) due to the SOC. In particular, the cyclic OP consists of two-dimensional lattice textures, such as the hexagonal lattice and the $\frac{1}{3}$ vortex lattice, commonly understandable as the two-dimensional network of the helical modulations.

Radio frequency spectra of a trapped unitary ${}^6\mathrm{Li}$ gas are reported and analyzed in terms of a theoretical approach that includes both final-state and trap effects. The different strength of the final-state interaction across the trap is crucial for evidencing two main peaks associated with two distinct phases residing in different trap regions. These are the pairing-gap and pseudo-gap phases below the critical temperature $T_c$, which evolve into the pseudo-gap and no-gap phases above $T_c$. In this way, a long standing puzzle about the interpretation of rf spectra for ${}^6\mathrm{Li}$ in a trap is solved.

We demonstrate that ultracold interacting bosonic atoms in an optical lattice with large on-site population show sub-Poisson on-site and intersite atom-number fluctuations. The experimental observations agree with numerical predictions of the truncated Wigner approximation. The correlations persist in the presence of multimode atom dynamics and even over large spatially extended samples involving several sites.

We study the Rayleigh scattering induced by a diamond nanocrystal in a whispering-gallery-microcavity–waveguide coupling system and find that it plays a significant role in the photon transportation. On the one hand, this study provides insight into future solid-state cavity quantum electrodynamics aimed at understanding strong-coupling physics. On the other hand, benefitting from this Rayleigh scattering, effects such as dipole-induced transparency and strong photon antibunching can occur simultaneously. As a potential application, this system can function as a high-efficiency photon turnstile. In contrast to B. Dayan et al. [Science 319, 1062 (2008)], the photon turnstiles proposed here are almost immune to the nanocrystal’s azimuthal position.