We derive renormalization group equations which allow us to treat order parameter fluctuations near quantum phase transitions in cases where an expansion in powers of the order parameter is not possible. As a prototypical application, we analyze the nematic transition driven by a $d$-wave Pomeranchuk instability in a two-dimensional electron system. We find that order parameter fluctuations suppress the first order character of the nematic transition obtained at low temperatures in mean-field theory, so that a continuous transition leading to quantum criticality can emerge.

We compute analytically, for large $N$, the probability distribution of the number of positive eigenvalues (the index $N_{+}$) of a random $N\times N$ matrix belonging to Gaussian orthogonal ($\beta =1$), unitary ($\beta =2$) or symplectic ($\beta =4$) ensembles. The distribution of the fraction of positive eigenvalues $c=N_{+}/N$ scales, for large $N$, as $\mathcal{P}(c,N)\simeq \exp [-\beta N^2\Phi (c)]$ where the rate function $\Phi (c)$, symmetric around $c=1/2$ and universal (independent of $\beta$), is calculated exactly. The distribution has non-Gaussian tails, but even near its peak at $c=1/2$ it is not strictly Gaussian due to an unusual logarithmic singularity in the rate function.

We show that all multipartite pure states can, under local operations, be transformed into bipartite pairwise entangled states in a “lossless fashion”: An arbitrary distinguished party will keep pairwise entanglement with all other parties after the asymptotic protocol—decorrelating all other parties from each other—in a way that the degree of entanglement of this party with respect to the rest will remain entirely unchanged. The set of possible entanglement distributions of bipartite pairs is also classified. Finally, we point out several applications of this protocol as a useful primitive in quantum information theory.

The quantum dynamics of a one-dimensional bosonic Josephson junction is studied by solving the time-dependent many-boson Schrödinger equation numerically exactly. Already for weak interparticle interactions and on short time scales, the commonly employed mean-field and many-body methods are found to deviate substantially from the exact dynamics. The system exhibits rich many-body dynamics such as enhanced tunneling and a novel equilibration phenomenon of the junction depending on the interaction, which is attributed to a quick loss of coherence.

Judiciously matched experiments, calculations, and theory demonstrate that a higher sensitivity to short-range interactions and, consequently, improved resolution on the atomic scale can be achieved by bimodal noncontact dynamic force microscopy. The combination of sub-Ångström tip oscillation at the second flexural resonance of a commercially available silicon cantilever with the commonly used large amplitude oscillation at the fundamental resonance frequency enables this performance improvement while avoiding potentially damaging jump-to-contact instabilities.

We present a novel method to compute expectation values in the Lieb-Liniger model both at zero and finite temperature. These quantities, relevant in the physics of one-dimensional ultracold Bose gases, are expressed by a series that has a remarkable behavior of convergence. Among other results, we show the computation of the three-body expectation value at finite temperature, a quantity that rules the recombination rate of the Bose gas.

We provide a feasible necessary and sufficient condition for when an unknown quantum operation (quantum device) secretly selected from a set of known quantum operations can be identified perfectly within a finite number of queries, and thus complete the characterization of the perfect distinguishability of quantum operations. We further design an optimal protocol which can achieve the perfect discrimination between two quantum operations by a minimal number of queries. Interestingly, we find that an optimal perfect discrimination between two isometries is always achievable without auxiliary systems or entanglement.

We calculate the one-body temperature Green’s (Matsubara) function of the unitary Fermi gas via quantum Monte Carlo, and extract the spectral weight function $A(p,\omega )$ using the methods of maximum entropy and singular value decomposition. From $A(p,\omega )$ we determine the quasiparticle spectrum, which can be accurately parametrized by three functions of temperature: an effective mass $m^{*}$, a mean-field potential $U$, and a gap $\Delta$. Below the critical temperature $T_c=0.15{\epsilon }_F$ the results for $m^{*}$, $U$, and $\Delta$ can be accurately reproduced using an independent quasiparticle model. We find evidence of a pseudogap in the fermionic excitation spectrum for temperatures up to $T^{*}\approx 0.20{\epsilon }_F>T_c$.

At low temperature, a quasi-one-dimensional ensemble of atoms with an attractive interaction forms a bright soliton. When exposed to a weak and smooth external potential, the shape of the soliton is hardly modified, but its center-of-mass motion is affected. We show that in a spatially correlated disordered potential, the quantum motion of a bright soliton displays Anderson localization. The localization length can be much larger than the soliton size and could be observed experimentally.

We construct a general measure for the degree of non-Markovian behavior in open quantum systems. This measure is based on the trace distance which quantifies the distinguishability of quantum states. It represents a functional of the dynamical map describing the time evolution of physical states, and can be interpreted in terms of the information flow between the open system and its environment. The measure takes on nonzero values whenever there is a flow of information from the environment back to the open system, which is the key feature of non-Markovian dynamics.

Quantum states inevitably decay with time into a probabilistic mixture of classical states due to their interaction with the environment and measurement instrumentation. We present the first measurement of the decoherence dynamics of complex photon states in a condensed-matter system. By controllably preparing a number of distinct quantum-superposed photon states in a superconducting microwave resonator, we show that the subsequent decay dynamics can be quantitatively described by taking into account only two distinct decay channels: energy relaxation and pure dephasing. Our ability to prepare specific initial quantum states allows us to measure the evolution of specific elements in the quantum density matrix in a very detailed manner that can be compared with theory.

Any residual coupling of a quantum computer to the environment results in computational errors. Encoding quantum information in a so-called decoherence-free subspace provides means to avoid these errors. Despite tremendous progress in employing this technique to extend memory storage times by orders of magnitude, computation within such subspaces has been scarce. Here, we demonstrate the realization of a universal set of quantum gates acting on decoherence-free ion qubits. We combine these gates to realize the first controlled-NOT gate towards a decoherence-free, scalable quantum computer.

Alongside superfluidity, itinerant (Stoner) ferromagnetism remains one of the most well-characterized phases of correlated Fermi systems. A recent experiment has reported the first evidence for novel phase behavior on the repulsive side of the Feshbach resonance in a two-component ultracold Fermi gas. By adapting recent theoretical studies to the atomic trap geometry, we show that an adiabatic ferromagnetic transition would take place at a weaker interaction strength than is observed in experiment. This discrepancy motivates a simple nonequilibrium theory that takes account of the dynamics of magnetic defects and three-body losses. The formalism developed displays good quantitative agreement with experiment.

We study the response of a Bose-Einstein condensate to an unbiased periodic driving potential. By controlling the space and time symmetries of the driving we show how a directed current can be induced, producing a coherent quantum ratchet. Weak driving induces a regular behavior, and space and time symmetries must both be broken to produce a current. For strong driving, the behavior becomes chaotic and the resulting effective irreversibility means that it is unnecessary to explicitly break time symmetry. Spatial asymmetry alone is then sufficient to produce the ratchet effect, even in the absence of interactions, and although the system remains completely coherent.

Natural particle-number entanglement resides between spatial modes in coherent ultracold atomic gases. However, operations on the modes are restricted by a superselection rule that forbids coherent superpositions of different particle numbers. This seemingly prevents mode entanglement being used as a resource for quantum communication. In this Letter, we demonstrate that mode entanglement of a single massive particle can be used for dense coding and quantum teleportation despite the superselection rule. In particular, we provide schemes where the dense coding linear photonic channel capacity is reached without a shared reservoir and where the full quantum channel capacity is achieved if both parties share a coherent particle reservoir.

We introduce a new strongly driven dispersive atom-cavity interaction and develop a new scheme for implementing the nontrivial entangling gates for two logical qubits in decoherence-free subspaces (DFSs). Our scheme combines the robust advantages of DFS and the geometric phase. Moreover, only two neighboring physical qubits, which encode a logical qubit, are required to undergo the collective dephasing in our scheme.

We report on the attainment of Bose-Einstein condensation with ultracold strontium atoms. We use the ${}^{84}\mathrm{Sr}$ isotope, which has a low natural abundance but offers excellent scattering properties for evaporative cooling. Accumulation in a metastable state using a magnetic-trap, narrowline cooling, and straightforward evaporative cooling in an optical trap lead to pure condensates containing $1.5\times {10}^5\mathrm{\text{atoms}}$. This puts ${}^{84}\mathrm{Sr}$ in a prime position for future experiments on quantum-degenerate gases involving atomic two-electron systems.

We report Bose-Einstein condensation of ${}^{84}\mathrm{Sr}$ in an optical dipole trap. Efficient laser cooling on the narrow intercombination line and an ideal $s$-wave scattering length allow the creation of large condensates ($N_0\sim 3\times {10}^5$) even though the natural abundance of this isotope is only 0.6%. Condensation is heralded by the emergence of a low-velocity component in time-of-flight images.

We derive backward and forward fractional Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers [Phys. Rev. Lett. 96, 230601 (2006)] provide the correct fractional framework for the problem. For applications, we calculate the distribution of occupation times in half space and show how the statistics of anomalous functionals is related to weak ergodicity breaking.

We study numerically the outcome of the phase separation instability of a dual-species Bose-Einstein condensate in an optical lattice. When only one excitation mode is unstable a bound pair of bright and dark solitonlike structures periodically appears and disappears, whereas for more than one unstable mode a persistent soliton-antisoliton pair develops. The oscillating soliton represents a regime where the two-species condensate neither remains phase-separated nor is dynamically stable.