We propose a method for the detection of ground state quantum phases of spinor gases through a series of two quantum nondemolition measurements performed by sending off-resonant, polarized light pulses through the gas. Signatures of various mean-field as well as strongly correlated phases of $F=1$ and $F=2$ spinor gases obtained by detecting quantum fluctuations and mean values of polarization of transmitted light are identified.

We show that a unitary operation (quantum circuit) secretly chosen from a finite set of unitary operations can be determined with certainty by sequentially applying only a finite amount of runs of the unknown circuit. No entanglement or joint quantum operations are required in our scheme. We further show that our scheme is optimal in the sense that the number of the runs is minimal when discriminating only two unitary operations.

A general strategy to maintain the coherence of a quantum bit is proposed. The analytical result is derived rigorously including all memory and backaction effects. It is based on an optimized $\pi$-pulse sequence for dynamic decoupling extending the Carr-Purcell-Meiboom-Gill cycle. The optimized sequence is very efficient, in particular, for strong couplings to the environment.

Evidence is given for Young-type interferences caused by a single electron acting on a given double-center scatterer analogous to an atomic-size double-slit system. The electron is provided by autoionization of a doubly excited He atom following the capture of the electrons of ${\mathrm{H}}_2$ by a ${\mathrm{He}}^{2+}$ incoming ion. The autoionizing projectile is a single-electron source, independent of the interferometer provided by the two ${\mathrm{H}}^{+}$ centers of the fully ionized ${\mathrm{H}}_2$ molecule. This experiment resembles the famous thought experiment imagined by Feynman in 1963, in which the quantum nature of the electron is illustrated from a Young-like double-slit experiment. Well-defined oscillations are visible in the angular distribution of the scattered electrons, showing that each electron interferes with itself.

In this Letter we study discrete symmetries of mean field manifolds of condensates of $F=2$ cold atoms, and various unconventional quantum vortices. Discrete quaternion symmetries result in two species of spin defects that can only appear in integer vortices while cyclic symmetries are found to result in a phase shift of $2\pi /3$ (or $4\pi /3$) and therefore $1/3$– (or $2/3$–) quantum vortices in condensates. We also briefly discuss $1/3$–quantum vortices in condensates of trimers.

Different quantum states of atoms in optical lattices can be nondestructively monitored by off-resonant collective light scattering into a cavity. Angle resolved measurements of photon number and variance give information about atom-number fluctuations and pair correlations without single-site access. Observation at angles of diffraction minima provides information on quantum fluctuations insensitive to classical noise. For transverse probing, no photon is scattered into a cavity from a Mott insulator phase, while the photon number is proportional to the atom number for a superfluid.

We show that the theory of operator quantum error correction can be naturally generalized by allowing constraints not only on states but also on observables. The resulting theory describes the correction of algebras of observables (and may therefore suitably be called “operator algebra quantum error correction”). In particular, the approach provides a framework for the correction of hybrid quantum-classical information and it does not require the state to be entirely in one of the corresponding subspaces or subsystems. We discuss applications to quantum teleportation and to the study of information flows in quantum interactions.

We propose a scheme for encoding logical qubits in a subspace protected against collective rotations around the propagation axis using the polarization and transverse spatial degrees of freedom of single photons. This encoding allows for quantum key distribution without the need of a shared reference frame. We present methods to generate entangled states of two logical qubits using present day down-conversion sources and linear optics, and show that the application of these entangled logical states to quantum information schemes allows for alignment-free tests of Bell’s inequalities, quantum dense coding, and quantum teleportation.

We have experimentally investigated the formation of off-diagonal long-range order in a gas of ultracold atoms. A magnetically trapped atomic cloud prepared in a highly nonequilibrium state thermalizes and thereby crosses the Bose-Einstein condensation phase transition. The evolution of phase coherence between different regions of the sample is constantly monitored and information on the spatial first-order correlation function is obtained. We observe the growth of the spatial coherence and the formation of long-range order in real time and compare it to the growth of the atomic density. Moreover, we study the evolution of the momentum distribution during the nonequilibrium formation of the condensate.

Thermodynamic properties of a Fermi system close to the unitarity limit, where the 2-body scattering length $a$ approaches $\pm \infty$, are studied in the high temperature Boltzmann regime. For dilute systems the virial expansion coefficients in the Boltzmann regime are expected, from general arguments, to be universal. A model independent finite temperature $T$ calculation of the third virial coefficient $b_3(T)$ is presented. At the unitarity limit, $b_3^{\infty }\approx 1.11$ is a universal number. The energy density up to the third virial expansion is derived. These calculations are of interest in dilute neutron matter and could be tested in current atomic experiments on dilute Fermi gases near the Feshbach resonance.

We address the problem of estimating the phase $\varphi$ given $N$ copies of the phase-rotation gate $u_{\varphi }$. We consider, for the first time, the optimization of the general case where the circuit consists of an arbitrary input state, followed by any arrangement of the $N$ phase rotations interspersed with arbitrary quantum operations, and ending with a general measurement. Using the polynomial method, we show that, in all cases where the measure of quality of the estimate $\tilde{\varphi }$ for $\varphi$ depends only on the difference $\tilde{\varphi }-\varphi$, the optimal scheme has a very simple fixed form. This implies that an optimal general phase estimation procedure can be found by just optimizing the amplitudes of the initial state.

We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multisystem interactions. For a Hamiltonian with $k$-system parameter-sensitive terms, the quantum limit scales as $1/N^k$, where $N$ is the number of systems. These quantum limits remain valid when the Hamiltonian is augmented by any parameter-independent interaction among the systems and when adaptive measurements via parameter-independent coupling to ancillas are allowed.

We calculate perturbatively the effect of a dipolar interaction upon the Bose-Einstein condensation temperature. This dipolar shift depends on the angle between the symmetry axes of the trap and the aligned atomic dipole moments, and is extremal for parallel or orthogonal orientations, respectively. The difference of both critical temperatures exhibits most clearly the dipole-dipole interaction and can be enhanced by increasing both the number of atoms and the anisotropy of the trap. Applying our results to chromium atoms, which have a large magnetic dipole moment, shows that this dipolar shift of the critical temperature could be measured in the ongoing Stuttgart experiment.

Can quantum-information theory shed light on black-hole evaporation? By entangling the in-fallen matter with an external system we show that the black-hole information paradox becomes more severe, even for cosmologically sized black holes. We rule out the possibility that the information about the in-fallen matter might hide in correlations between the Hawking radiation and the internal states of the black hole. As a consequence, either unitarity or Hawking’s semiclassical predictions must break down. Any resolution of the black-hole information crisis must elucidate one of these possibilities.

Cold atoms in periodic potentials are versatile quantum systems for implementing simple models prevalent in condensed matter theory. Here we realize the 2D Bose-Hubbard model by loading a Bose-Einstein condensate into an optical lattice, and study the resulting Mott insulator. The measured momentum distributions agree quantitatively with theory (no adjustable parameters). In these systems, the Mott insulator forms in a spatially discrete shell structure which we probe by focusing on correlations in atom shot noise. These correlations show a marked dependence on the lattice depth, consistent with the changing size of the insulating shell expected from simple arguments.

Atomic Bose-Einstein condensates are singular forms of matter with the coherence between constituent atoms as a defining characteristic. Although this viewpoint is increasingly validated through experimental findings, the mechanisms behind the observed losses are still understood with classical recombinant collision arguments between particles within the condensate itself. By incorporating a general interparticle interaction into the Hamiltonian, a coherent decay rate can be obtained, thus providing a direct link between the observed losses and the microscopic two-body parameters. Appearing in the lifetime, the interaction strength, $\lambda$, is expressed as $\lambda =8\pi a/(1-\delta )$, where the small parameter $\delta$ is obtained from a fit to experimental loss data. Most importantly, the lowest order rate exhibits a novel density dependence (${\rho }^{3/2}$) that can be identified in low temperature tests.

Particle systems admit a variety of tensor product structures (TPSs) depending on the algebra of observables chosen for analysis. Global symmetry transformations and dynamical transformations may be resolved into local unitary operators with respect to certain TPSs and not with respect to others. Symmetry-invariant and dynamical-invariant TPSs are defined and various notions of entanglement are considered for scattering states.

Conservation laws constrain the stationary state statistics of driven dissipative systems because the average flux of a conserved quantity between driving and dissipation scales should be constant. This requirement leads to a universal scaling law for flux-measuring correlation functions, which generalizes the $\frac{4}{5}$th law of Navier-Stokes turbulence. We demonstrate the utility of this simple idea by deriving new exact scaling relations for models of aggregating particle systems in the fluctuation-dominated regime and for energy and wave action cascades in models of strong wave turbulence.

We show, through a refinement of the work theorem, that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by $⟨W_{\mathrm{diss}}⟩=⟨W⟩-\Delta F=kTD(\rho \parallel \tilde{\rho })=kT⟨\ln (\rho /\tilde{\rho })⟩$, where $\rho$ and $\tilde{\rho }$ are the phase-space density of the system measured at the same intermediate but otherwise arbitrary point in time, for the forward and backward process. $D(\rho \parallel \tilde{\rho })$ is the relative entropy of $\rho$ versus $\tilde{\rho }$. This result also implies general inequalities, which are significantly more accurate than the second law and include, as a special case, the celebrated Landauer principle on the dissipation involved in irreversible computations.

We propose to study the origin of algebraic decay of two-point correlation functions observed in glasses, proteins, and quantum dots by their nonlinear response to sequences of ultrafast laser pulses. Power-law spectral singularities and temporal relaxation in two-dimensional correlation spectroscopy signals are predicted for a continuous time random walk model of stochastic spectral jumps in a two-level system with a power-law distribution of waiting times $\psi (t)\sim t^{-\alpha -1}$. Spectroscopic signatures of stationary ensembles for $1<\alpha <2$ and aging effects in nonstationary ensembles with $0<\alpha <1$ are identified.