We identify dissipative solitons in a Kerr-nonlinear all-photonic crystal resonator by solving Maxwell's equations directly. The photonic crystal allows for diffraction management, leading to solitons with unique properties. These results are compared to a mean-field model based on Bloch waves, finding excellent agreement even for a high-contrast photonic crystal. By adjusting the quality factor and resonance frequencies of the resonator, optimal Bloch cavity solitons in terms of width and pump energy are identified. In particular, the width is independent of the quality factor, in contrast to the usual homogeneous cavity.

We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analytical predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.

We investigate the use of quantum-jump-based feedback to manipulate the stability of multipartite entangled dark states in an open quantum system. Using the model proposed in Phys. Rev. A 76, 010301(R) (2007) for a pair of atoms, we show a general strategy to produce many-body singlet stationary entangled states for larger number of atoms. In the case of four qubits, we propose a simple local feedback control that, although not optimal, is realistic and stabilizes a highly entangled state. We discuss the limitations and analyze alternative strategies within the framework of direct jump feedback schemes.

Earlier, we proved a duality between two optimizations problems [Phys. Rev. Lett. 104, 120501 (2010)]. The primary one is, given two quantum channels $\mathcal{M}$ and $\mathcal{N}$, to find a quantum channel $\mathcal{R}$ such that $\mathcal{R}\circ \mathcal{N}$ is optimally close to $\mathcal{M}$ as measured by the worst-case entanglement fidelity. The dual problem involves the information obtained by the environment through the so-called complementary channels $\widehat{\mathcal{M}}$ and $\widehat{\mathcal{N}}$, and consists in finding a quantum channel ${\mathcal{R}}^{\prime }$ such that ${\mathcal{R}}^{\prime }\circ \widehat{\mathcal{M}}$ is optimally close to $\widehat{\mathcal{N}}$. It turns out to be easier to find an approximate solution to the dual problem in certain important situations, notably when $\mathcal{M}$ is the identity channel—the problem of quantum error correction—yielding a good near-optimal worst-case entanglement fidelity as well as the corresponding near-optimal correcting channel. Here we provide more detailed proofs of these results. In addition, we generalize the main theorem to the case where there are certain constraints on the implementation of $\mathcal{R}$, namely, on the number of Kraus operators. We also offer a simple algebraic form for the near-optimal correction channel in the case $\mathcal{M}=\mathrm{id}$. For approximate error correction, we show that any $\varepsilon$-correctable channel is, up to appending an ancilla, $\varepsilon$-close to an exactly correctable one. We also demonstrate an application of our theorem to the problem of minimax state discrimination.

We consider the discrimination of lossy bosonic channels and focus on the case when one of the values for the loss parameter is zero, i.e., we address the detection of a possible loss against the alternative hypothesis of an ideal lossless channel. This discrimination is performed by inputting one- or two-mode squeezed thermal states with fixed total energy. By optimizing over this class of states, we find that the optimal inputs are pure, thus corresponding to single- and two-mode squeezed vacuum states. In particular, we show that, for any value of the damping rate smaller than a critical value, there is a threshold on the energy that makes the two-mode squeezed vacuum state more convenient than the corresponding single-mode state, whereas for damping larger than this critical value, two-mode squeezed vacua are always better. We then consider the discrimination in realistic conditions, where it is unlikely to have pure squeezing. Thus, by fixing both input energy and squeezing, we show that two-mode squeezed thermal states are always better than their single-mode counterpart when all the thermal photons are directed into the dissipative channel. Aside from that, this result also holds approximately for unbalanced distribution of the thermal photons. Finally, we also investigate the role of correlations in the improvement of detection. For fixed input squeezing (single mode or two mode), we find that the reduction of the quantum Chernoff bound is a monotone function of the two-mode entanglement as well as the quantum mutual information and the quantum discord. We thus verify that employing squeezing in the form of correlations (quantum or classical) is always a resource for loss detection whenever squeezed thermal states are taken as input.

Various authors have considered schemes for quantum tagging, that is, authenticating the classical location of a classical tagging device by sending and receiving quantum signals from suitably located distant sites, in an environment controlled by an adversary whose quantum information processing and transmitting power is potentially unbounded. All of the schemes proposed elsewhere in the literature assume that the adversary is able to inspect the interior of the tagging device. All of these schemes have been shown to be breakable if the adversary has unbounded predistributed entanglement. We consider here the case in which the tagging device contains a finite key string shared with distant sites but kept secret from the adversary, and show this allows the location of the tagging device to be authenticated securely and indefinitely. Our protocol relies on quantum key distribution between the tagging device and at least one distant site, and demonstrates a new practical application of quantum key distribution. It also illustrates that the attainable security in position-based cryptography can depend crucially on apparently subtle details in the security scenario considered.

Pointer states are long-lasting high-fidelity states in open quantum systems. We show how any pure state in a non-Markovian open quantum system can be made to behave as a pointer state by suitably engineering the coupling to the environment via open-loop periodic control. Engineered pointer states are constructed as approximate fixed points of the controlled open-system dynamics, in such a way that they are guaranteed to survive over a long time with a fidelity determined by the relative precision with which the dynamics is engineered. We provide quantitative minimum-fidelity bounds by identifying symmetry and ergodicity conditions that the decoherence-inducing perturbation must obey in the presence of control, and develop explicit pulse sequences for engineering any desired set of orthogonal states as pointer states. These general control protocols are validated through exact numerical simulations as well as semiclassical approximations in realistic single- and two-qubit dissipative systems. We also examine the role of control imperfections, and show that while pointer-state engineering protocols are highly robust in the presence of systematic pulse errors, the latter can also lead to unintended pointer-state generation in dynamical decoupling implementations, explaining the initial-state selectivity observed in recent experiments.

Perfect transfer of a quantum state through a one-dimensional chain is now well understood, allowing one not only to decide whether a fixed Hamiltonian achieves perfect transfer but to design a suitable one. We are particularly interested in being able to design, or understand the limitations imposed upon, Hamiltonians subject to various naturally arising constraints such as a limited coupling topology with low connectivity (specified by a graph) and type of interaction. In this paper, we characterize the necessary and sufficient conditions for transfer through a network and describe some natural consequences such as the impossibility of routing between many different recipients for a large class of Hamiltonians and the limitations on transfer rate. We also consider some of the trade-offs that arise in uniformly coupled networks (both Heisenberg and $XX$ models) between transfer distance and the size of the network as a consequence of the derived conditions.

A few simply stated rules govern the entanglement patterns that can occur in mutually unbiased basis sets (MUBs) and constrain the combinations of such patterns that can coexist in full complements of MUBs. We consider Hilbert spaces of prime power dimensions ($D=p^N$), as realized by systems of $N$ prime-state particles, where full complements of $D+1$ MUBs are known to exist, and we assume only that MUBs are eigenbases of generalized Pauli operators, without using any particular construction. The general rules include the following: (1) In any MUB, a given particle appears either in a pure state or totally entangled and (2) in any full MUB complement, each particle is pure in ($p+1$) bases (not necessarily the same ones) and totally entangled in the remaining ($p^N-p$). It follows that the maximum number of product bases is $p+1$ and, when this number is realized, all remaining ($p^N-p$) bases in the complement are characterized by the total entanglement of every particle. This “standard distribution” is inescapable for two-particle systems (of any $p$), where only product and generalized Bell bases are admissible MUB types. This and the following results generalize previous results for qubits [Phys. Rev. A 65. 032320 (2002); Phys. Rev. A 72, 062310 (2005)] and qutrits [Phys. Rev. A 70, 012302 (2004)], drawing particularly upon [Phys. Rev. A 72, 062310 (2005)]. With three particles there are three MUB types, and these may be combined in ($p+2$) different ways to form full complements. With $N=4$, there are 6 MUB types for $p=2$, but new MUB types become possible with larger $p$, and these are essential to realizing full complements. With this example, we argue that new MUB types that show new entanglement patterns should enter with every step in $N$ and, also, when $N$ is a prime plus 1, at a critical $p$ value, $p=N-1$. Such MUBs should play critical roles in filling complements.

We describe a continuous-variable error correction protocol that can correct the Gaussian noise induced by linear loss on Gaussian states. The protocol can be implemented using linear optics and photon counting. We explore the theoretical bounds of the protocol as well as the expected performance given current knowledge and technology.

We study the localization of a cigar-shaped superfluid Bose-Fermi mixture in a quasiperiodic bichromatic optical lattice (OL) for interspecies attraction and intraspecies repulsion. The mixture is described by the Gross-Pitaevskii equation for the bosons, coupled to a hydrodynamic mean-field equation for fermions at unitarity. We confirm the existence of the symbiotic localized states in the Bose-Fermi mixture and Anderson localization of the Bose component in the interacting Bose-Fermi mixture on a bichromatic OL. The phase diagram in boson and fermion numbers showing the regions of the symbiotic and Anderson localization of the Bose component is presented. Finally, the stability of symbiotic and Anderson localized states is established under small perturbations.

A symmetrical atom interferometer with a thermal calcium atom beam has been developed using a narrow linewidth diode laser stabilized to the resonance of a high-finesse cavity. The linewidth of the diode laser was estimated to be less than 1 Hz relative to the cavity resonance in noise measurement over the range of 100 Hz to 1 MHz, and the phase instability of the interference fringes obtained from the Allan deviation was improved to 2 mrad at an integration time of 300 s. Using this atom interferometer, the ac Stark phase shift between the ${}^1$$S_0$ and ${}^3$$P_1$ states of a Ca atom was measured as a function of a laser power near the resonance of the ${}^1{S}_0{-}^1{P}_1$ transition at a wavelength of 423 nm. The decay rate of the ${}^1$$P_1$ state was determined to be $\gamma =1.91\left(33\right)\times {10}^8$ s${}^{-1}$.

We analyze the single-particle excitation spectrum of the ultracold fermion atom system close to the unitary limit where there has been found experimental evidence for the Bogoliubov quasiparticles below as well as above the transition temperature $T_c$. We consider the short-range correlations originating from the preformed pairs and try to discuss the experimental data adapting phenomenological self-energy previously used for description of the antinodal spectra of the underdoped cuprate superconductors. We show that this ansatz qualitatively accounts for the momentum-resolved rf spectroscopic data obtained for ${}^{40}$K atoms.

Recently, strong-coupling regimes of superconducting qubits or quantum dots inside a microwave circuit cavity and BEC atoms inside an optical cavity were achieved experimentally. The strong-coupling regimes in these systems were described by the Dicke model. Here, we solve the Dicke model by a $1/N$ expansion. In the normal state, we find a $\sqrt{N}$ behavior of the collective Rabi splitting. In the superradiant phase, we identify an important Berry phase term that has dramatic effects on both the ground state and the excitation spectra of the strongly interacting system. The single photon excitation spectrum has a low-energy quantum phase diffusion mode in imaginary time with a large spectral weight and also a high-energy optical mode with a low spectral weight. The photons are in a number squeezed state that may have wide applications in high sensitive measurements and quantum-information processing. Comparisons with exact diagonalization studies are made. Possible experimental schemes to realize the superradiant phase are briefly discussed.

We study theoretically the dynamics of a hybrid optomechanical system consisting of a macroscopic mechanical membrane magnetically coupled to a spinor Bose-Einstein condensate via a nanomagnet attached at the membrane center. We demonstrate that this coupling permits us to monitor indirectly the center-of-mass position of the membrane via measurements of the spin of the condensed atoms. These measurements normally induce a significant backaction on the membrane motion, which we quantify for the cases of thermal and coherent initial states of the membrane. We discuss the possibility of measuring this quantum backaction via repeated measurements. We also investigate the potential to generate nonclassical states of the membrane, in particular Schrödinger-cat states, via such repeated measurements.

Within the framework of the tight-binding model we demonstrate that Wannier-Stark states can freely accelerate in uniform optical lattices. As opposed to accelerating Airy wave packets in free space, our analysis reveals that in this case the beam main intensity features self-bend along two opposite hyperbolic trajectories. Two-dimensional geometries are also considered and an asymptotic connection between these Wannier-Stark ladders and Airy profiles is presented.

A recent paper by Jones-Smith and Mathur, Phys. Rev. A 82, 042101 (2010) extends $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics from bosonic systems (systems for which ${\mathcal{T}}^2=\mathbf{1}$) to fermionic systems (systems for which ${\mathcal{T}}^2=-\mathbf{1}$). The current paper shows how the formalism developed by Jones-Smith and Mathur can be used to construct $\mathcal{P}\mathcal{T}$-symmetric matrix representations for operator algebras of the form ${\eta }^2=0$, ${\overline{\eta }}^2=0$, $\eta \overline{\eta }+\overline{\eta }\eta =\alpha \mathbf{1}$, where $\overline{\eta }={\eta }^{\mathcal{P}\mathcal{T}}=\mathcal{P}\mathcal{T}\eta {\mathcal{T}}^{-1}{\mathcal{P}}^{-1}$. It is easy to construct matrix representations for the Grassmann algebra ($\alpha =0$). However, one can only construct matrix representations for the fermionic operator algebra ($\alpha \ne 0$) if $\alpha =-1$; a matrix representation does not exist for the conventional value $\alpha =1$.

We investigate entanglement for a composite closed system endowed with a scaling property which allows the dynamics to be kept invariant while the effective Planck constant ${\hslash }_{\mathit{eff}}$ of the system is varied. Entanglement increases as ${\hslash }_{\mathit{eff}}\to 0$. Moreover, for sufficiently low ${\hslash }_{\mathit{eff}}$ the evolution of the quantum correlations, encapsulated, for example, in the quantum discord, can be obtained from the mutual information of the corresponding classical system. We show this behavior is due to the local suppression of path interferences in the interaction that generates the entanglement.

We present a proposal for storing and retrieving a continuous-variable quadripartite polarization-entangled cluster state, using macroscopic atomic ensembles in a magnetic field. The Larmor precession of the atomic spins leads to a symmetry between the atomic canonical operators. In this scheme, each of the four spatially separated pulses passes twice through the respective ensemble in order to map the polarization-entangled cluster state onto the long-lived atomic ensembles. The stored state can then be retrieved by another four read-out pulses, each crossing the respective ensemble twice. By calculating the variances, we analyzed the fidelities of the storage and retrieval, and our scheme is feasible under realistic experimental conditions.

We derive exact time evolution of three two-level atoms coupled to a common environment. The environment is structured and is modeled by a leaky cavity with Lorentzian spectral density. The atoms are initially prepared in a generalized $W$ state and later on experience pairwise dipole-dipole interactions and couplings to the cavity. We study tripartite disentangling and entangling dynamics as well as protecting bipartite entanglement with both atom-atom interactions and atom-cavity couplings taken simultaneously into account.