We describe a novel approach to prepare, detect, and characterize magnetic quantum phases in ultracold spinor atoms loaded in optical superlattices. Our technique makes use of singlet-triplet spin manipulations in an array of isolated double-well potentials in analogy to recently demonstrated control in quantum dots. We also discuss the many-body singlet-triplet spin dynamics arising from coherent coupling between nearest neighbor double wells and derive an effective description for such systems. We use it to study the generation of complex magnetic states by adiabatic and nonequilibrium dynamics.

A Ramsey interrogation scheme was used to measure the phase shift of laser-cooled ${}^{87}\mathrm{Rb}$ clock-transition pseudospins arising as a result of a reversal of a bias-magnetic field, i.e., $\mathbf{B}\to -\mathbf{B}$, during the interrogation. While no phase shift occurred when the reversal was sudden, the Ramsey fringes were shifted by a factor of $\pi$ when the reversal was adiabatic. We thus verified the prediction that the spin states $|F,m=0⟩$ acquire a purely topological and parity-dependent phase factor of $(-1{)}^F$ as a result of $\mathbf{B}\to -\mathbf{B}$.

We develop a mean-field theory of the dynamics of a nonequilibrium Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity. The spectrum of elementary excitations around the stationary state is analytically studied by means of a generalized Gross-Pitaevskii equation. A diffusive behavior of the Goldstone mode is found in the spatially homogeneous case and new features are predicted for the Josephson effect in a two-well geometry.

We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which allows one to explore the interface of quantum optics and condensed matter physics. We propose an experiment where easily detectable atomic spin flips are induced by the cantilever motion. This can be used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as realized in recent experiments, the backaction of the atoms onto the cantilever is significant and the system represents a mechanical analog of cavity quantum electrodynamics. With high but realistic cantilever quality factors, the strong coupling regime can be reached, either with single atoms or collectively with Bose-Einstein condensates. We discuss an implementation on an atom chip.

We study the hydrodynamic expansion of a rotating strongly interacting Fermi gas by releasing a cigar-shaped cloud with a known angular momentum from an optical trap. As the aspect ratio of the expanding cloud approaches unity, the angular velocity increases, indicating quenching of the moment of inertia $I$ to as low as 0.05 of the rigid body value $I_{\mathrm{rig}}$. Remarkably, we observe this behavior in both the superfluid and collisional normal fluid regimes, which obey nearly identical zero-viscosity irrotational hydrodynamics. We attribute irrotational flow in the normal fluid to a decay of the rotational part of the stream velocity during expansion, which occurs when the shear viscosity is negligible. Using conservation of angular momentum, we directly observe a fundamental result of irrotational hydrodynamics, $I/I_{\mathrm{rig}}={\delta }^2$, where $\delta$ is the deformation parameter of the cloud.

We introduce Bell-type inequalities allowing for nonlocality and entanglement tests with two cold heteronuclear molecules. The proposed inequalities are based on correlations between each molecule spatial orientation, an observable which can be experimentally measured with present day technology. Orientation measurements are performed on each subsystem at different times. These times play the role of the polarizer angles in Bell tests realized with photons. We discuss the experimental implementations of the proposed tests, which could also be adapted to other high dimensional quantum angular momenta systems.

We study the interplay between superfluidity and magnetism in a multicomponent gas of ultracold fermions. Ward-Takahashi identities constrain possible mean-field states describing order parameters for both pairing and magnetization. The structure of global phase diagrams arises from competition among these states as functions of anisotropies in chemical potential, density, or interactions. They exhibit first and second order phase transition as well as multicritical points, metastability regions, and phase separation. We comment on experimental signatures in ultracold atoms.

We show that the system of weakly bound molecules of heavy and light fermionic atoms is characterized by a long-range intermolecular repulsion and can undergo a gas-crystal quantum transition if the mass ratio exceeds a critical value. For the critical mass ratio above 100 obtained in our calculations, this crystalline order can be observed as a superlattice in an optical lattice for heavy atoms with a small filling factor. We also find that this novel system is sufficiently stable with respect to molecular relaxation into deep bound states and to the process of trimer formation.

We propose a unifying approach to the separability problem using covariance matrices of locally measurable observables. From a practical point of view, our approach leads to strong entanglement criteria that allow us to detect the entanglement of many bound entangled states in higher dimensions and which are at the same time necessary and sufficient for two qubits. From a fundamental perspective, our approach leads to insights into the relations between several known entanglement criteria—such as the computable cross-norm and local uncertainty criteria—as well as their limitations.

Most known quantum codes are additive, meaning the code can be described as the simultaneous eigenspace of an Abelian subgroup of the Pauli group. While in some scenarios such codes are strictly suboptimal, very little is understood about how to construct nonadditive codes with good performance. Here we present a family of distance 2 nonadditive quantum codes for all odd block lengths $n$, that has a particularly simple form. Our codes detect single qubit errors (or correct single qubit erasures) while encoding a higher dimensional space than is possible with an additive code or, for $n\ge 11$, any previous codes. We exhibit the encoding circuits and automorphism group for our codes as well.

If time-evolution equations are formulated in terms of thermodynamic building blocks, two possibilities arise to judge the consistency of models: By the properties of the building blocks (strong or structural consistency), or solely by the implied evolution equations (weak or dynamic consistency). We propose a straightforward procedure to check for strong consistency by means of the eigenvalues and eigenmodes of the linearized equations, which is related to establishing a fluctuation-dissipation theorem. By applying the general ideas to hydrodynamics, we clarify the role of the controversial diffusion terms in hydrodynamic equations.

A Knill-Laflamme-Milburn (KLM) type quantum computation with bosonic neutral atoms or bosonic ions is suggested. Crucially, as opposite to other quantum computation schemes involving atoms (ions), no controlled interactions between atoms (ions) involving their internal levels are required. Versus photonic KLM computation, this scheme has the advantage that single-atom (ion) sources are more natural than single-photon sources, and single-atom (ion) detectors are far more efficient than single-photon ones.

The Stern-Gerlach effect is well known as spin-dependent splitting of a beam of atoms with magnetic moments by a magnetic-field gradient. Here, we show that an induced gauge potential may lead to a similar effect for chiral molecules. In the presence of three inhomogeneous light fields, the center of mass of a three-level chiral molecule is subject to an optically induced gauge potential, and the internal dynamics of the molecule can be described as an adiabatic evolution in the reduced pseudospin subspace of the two lowest energy levels. We demonstrate numerically that such an induced gauge potential can lead to observable pseudospin-dependent and chirality-dependent generalized Stern-Gerlach effects for mixed left- and right-handed chiral molecules under realistic conditions.

A strong laser field and the Coulomb field of a nucleus can produce $e^{+}{e}^{-}$ pairs. It is shown for the first time that there is a large probability that electrons and positrons created in this process collide after one or several oscillations of the laser field. These collisions can take place at high energy, resulting in several phenomena. The quasielastic collision $e^{+}{e}^{-}\to e^{+}{e}^{-}$ allows acceleration of leptons in the laser field to higher energies. The inelastic collisions allow production of high-energy photons $e^{+}{e}^{-}\to 2\gamma$ and muons $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$. The yield of high-energy photons and muons produced via this mechanism exceeds exponentially their production through conventional direct creation in laser and Coulomb fields. A relation of the phenomena considered with the antenna mechanism of multiphoton absorption in atoms is discussed.

A non-Hermitian operator with a real spectrum and a complete set of eigenvectors may serve as the Hamiltonian operator for a unitary quantum system provided that one makes an appropriate choice for the defining the inner product of physical Hilbert state. We study the consequences of such a choice for the representation of states in terms of projection operators and the geometry of the state space. This allows for a careful treatment of the quantum Brachistochrone problem and shows that it is indeed impossible to achieve faster unitary evolutions using $\mathcal{P}\mathcal{T}$-symmetric or other non-Hermitian Hamiltonians than those given by Hermitian Hamiltonians.

We theoretically consider a spin polarized, optically trapped condensate of ${}^{87}\mathrm{Rb}$ atoms in $F=1$. We observe a transfer of atoms to other Zeeman states due to the dipolar interaction which couples the spin and the orbital degrees of freedom. Therefore the transferred atoms acquire an orbital angular momentum. This is a realization of the Einstein–de Haas effect in systems of cold gases. We find resonances which make this phenomenon observable even in very weak dipolar systems, when the Zeeman energy difference on transfer is fully converted to rotational kinetic energy.

We discuss dynamics of a slow quantum phase transition in a spin-1 Bose-Einstein condensate. We analytically determine the scaling properties of the system magnetization and verify them with numerical simulations in a one dimensional model.

We apply a notion of static renormalization to the preparation of entangled states for quantum computing, exploiting ideas from percolation theory. Such a strategy yields a novel way to cope with the randomness of nondeterministic quantum gates. This is most relevant in the context of optical architectures, where probabilistic gates are common, and cold atoms in optical lattices, where hole defects occur. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of conditional dynamics; we furthermore show that except for a single layer of gates during the preparation, all subsequent operations can be shifted to the final adapted single-qubit measurements. Remarkably, cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available.

A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows us to address fundamental questions such as the degree of hyperbolicity, which can be quantified in terms of the transversality of these intrinsic vectors. For spatially extended systems, the covariant Lyapunov vectors have localization properties and spatial Fourier spectra qualitatively different from those composing the orthonormalized basis obtained in the standard procedure used to calculate the Lyapunov exponents.

We present the experimental realization of optimal symmetric and asymmetric phase-covariant $1\to 2$ cloning of qubit states using fiber optics. The state of each qubit is encoded into a single photon which can propagate through two optical fibers. The operation of our device is based on one- and two-photon interference. We have demonstrated the creation of two copies for a wide range of qubit states from the equator of the Bloch sphere. The measured fidelities of both copies are close to the theoretical values and they surpass the theoretical maximum obtainable with the universal cloner.