We provide the first exact calculation of the height distribution at arbitrary time $t$ of the continuum Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with flat initial conditions. We use the mapping onto a directed polymer with one end fixed, one free, and the Bethe ansatz for the replicated attractive boson model. We obtain the generating function of the moments of the directed polymer partition sum as a Fredholm Pfaffian. Our formula, valid for all times, exhibits convergence of the free energy (i.e., KPZ height) distribution to the Gaussian orthogonal ensemble Tracy-Widom distribution at large time.

We perform high-precision measurements of the condensation temperature of a harmonically trapped atomic Bose gas with widely tunable interactions. For weak interactions we observe a negative shift of the critical temperature in excellent agreement with mean-field theory. However for sufficiently strong interactions we clearly observe an additional positive shift, characteristic of beyond-mean-field critical correlations. We also discuss nonequilibrium effects on the apparent critical temperature for both very weak and very strong interactions.

Symmetry of entangled states under a swap of outcomes (“envariance”) implies their equiprobability and leads to Born’s rule $p_k=|{\psi }_k{|}^2$. Here I show the converse: I demonstrate that the amplitude of a state given by a superposition of sequences of events that share the same total count (e.g., $n$ detections of 0 and $m$ of 1 in a spin-$\frac{1}{2}$ measurement) is proportional to the square root of the fraction—square root of the relative frequency—of all the equiprobable sequences of 0’s and 1’s with that $n$ and $m$.

We report the observation of resolved atomic interaction sidebands (ISB) in the ${}^{87}\mathrm{Sr}$ optical clock transition when atoms at microkelvin temperatures are confined in a two-dimensional optical lattice. The ISB are a manifestation of the strong interactions that occur between atoms confined in a quasi-one-dimensional geometry and disappear when the confinement is relaxed along one dimension. The emergence of ISB is linked to the recently observed suppression of collisional frequency shifts. At the current temperatures, the ISB can be resolved but are broad. At lower temperatures, ISB are predicted to be substantially narrower and useful spectroscopic tools in strongly interacting alkaline-earth gases.

We calculate the energy and wave functions of two particles confined to two spatial dimensions interacting via arbitrary anisotropic potentials with negative or zero net volume. The general rigorous analytic expressions are given in the weak coupling limit where universality or model independence are approached. The monopole part of anisotropic potentials is crucial in the universal limit. We illustrate the universality with a system of two arbitrarily polarized cold dipolar molecules in a bilayer. We discuss the transition to universality as a function of polarization and binding energy and compare analytic and numerical results obtained by the stochastic variational method. The universal limit is essentially reached for experimentally accessible strengths.

We study the transmission of classical information in quantum channels. We present a decoding procedure that is very simple but still achieves the channel capacity. It is used to give an alternative straightforward proof that the classical capacity is given by the regularized Holevo bound. This procedure uses only projective measurements and is based on successive “yes-no” tests only.

Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

One-way quantum computation is a very promising candidate to fulfill the capabilities of quantum information processing. Here we demonstrate an important set of unitary operations for continuous variables using a linear cluster state of four entangled optical modes. These operations are performed in a fully measurement-controlled and completely unconditional fashion. We implement three different levels of squeezing operations and a Fourier transformation, all of which are accessible by selecting the correct quadrature measurement angles of the homodyne detections. Though not sufficient, these linear transformations are necessary for universal quantum computation.

Entanglement in the spatial degrees of freedom of photons is an interesting resource for quantum information. For practical distribution of such entangled photons, it is desirable to use an optical fiber, which in this case has to support multiple transverse modes. Here we report the use of a hollow-core photonic crystal fiber to transport spatially entangled qubits.

Optically trapped ensembles are of crucial importance for frequency measurements and quantum memories but generally suffer from strong dephasing due to inhomogeneous density and light shifts. We demonstrate a drastic increase of the coherence time to 21 s on the magnetic field insensitive clock transition of ${}^{87}\mathrm{Rb}$ by applying the recently discovered spin self-rephasing [C. Deutsch et al., Phys. Rev. Lett. 105, 020401 (2010)]. This result confirms the general nature of this new mechanism and thus shows its applicability in atom clocks and quantum memories. A systematic investigation of all relevant frequency shifts and noise contributions yields a stability of $2.4\times {10}^{-11}{\tau }^{-1/2}$, where $\tau$ is the integration time in seconds. Based on a set of technical improvements, the presented frequency standard is predicted to rival the stability of microwave fountain clocks in a potentially much more compact setup.

We investigate the topological structure of entangled qudits under unitary local operations. Different sectors are identified in the evolution, and their topological aspects are analyzed. The geometric phase is explicitly calculated in terms of the concurrence. As a main result, we predict a fractional phase for cyclic evolutions in the multiply connected space of maximally entangled states. This result is potentially useful for noise robust implementations of quantum gates.

Experiments on ultracold attractive Bose-Einstein condensates (BECs) have demonstrated that at low dimensions atomic clouds can form localized objects, propagating for long times without significant changes in their shapes and attributed to bright matter-wave solitons, which are coherent objects. We consider the dynamics of bright soliton trains from the perspective of many-boson physics. The fate of matter-wave soliton trains is actually to quickly lose their coherence and become macroscopically fragmented BECs. The death of the coherent matter-wave soliton trains gives birth to fragmented objects, whose quantum properties and experimental signatures differ substantially from what is currently assumed.

Dynamical decoupling (DD) is a popular technique for protecting qubits from the environment. However, unless special care is taken, experimental errors in the control pulses used in this technique can destroy the quantum information instead of preserving it. Here, we investigate techniques for making DD sequences robust against different types of experimental errors while retaining good decoupling efficiency in a fluctuating environment. We present experimental data from solid-state nuclear spin qubits and introduce a new DD sequence that is suitable for quantum computing and quantum memory.

Attaining the ultimate (Holevo) limit to the classical capacity of a quantum channel requires the receiver to make joint measurements over long code-word blocks. For a pure-state channel, we show that the Holevo limit can be attained by a receiver that uses a multisymbol unitary transformation on the quantum code word followed by separable projective measurements. We show a concatenated coding and joint-detection architecture to approach the Holevo limit. We then construct some of the first concrete examples of codes and structured joint-detection receivers for the lossy bosonic channel, which can achieve fundamentally higher (superadditive) capacity than conventional receivers that detect each modulation symbol individually. We thereby pave the way for research into codes and structured receivers for reliable communication data rates approaching the Holevo limit.

We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface, by modeling it with a discrete time quantum walk. During the evolution, the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants. We find that asymptotically a mobile Ising model anyon becomes so entangled with its environment that its statistical dynamics reduces to a classical random walk with linear dispersion in contrast to particles with Abelian statistics which have quadratic dispersion.

We report on local, in situ measurements of atom number fluctuations in slices of a one-dimensional Bose gas on an atom chip setup. By using current modulation techniques to prevent cloud fragmentation, we are able to probe the crossover from weak to strong interactions. For weak interactions, fluctuations go continuously from super- to sub-Poissonian as the density is increased, which is a signature of the transition between the subregimes where the two-body correlation function is dominated, respectively, by thermal and quantum contributions. At stronger interactions, the super-Poissonian region disappears, and the fluctuations go directly from Poissonian to sub-Poissonian, as expected for a “fermionized” gas.

Entangled inputs can enhance the capacity of quantum channels, this being one of the consequences of the celebrated result showing the nonadditivity of several quantities relevant for quantum information science. In this work, we answer the converse question (whether entangled inputs can ever render noisy quantum channels to have maximum capacity) to the negative: No sophisticated entangled input of any quantum channel can ever enhance the capacity to the maximum possible value, a result that holds true for all channels both for the classical as well as the quantum capacity. This result can hence be seen as a bound as to how “nonadditive quantum information can be.” As a main result, we find first practical and remarkably simple computable single-shot bounds to capacities, related to entanglement measures. As examples, we discuss the qubit amplitude damping and identify the first meaningful bound for its classical capacity.

Sharp quantum phase transitions typically require a large system with many particles. Here we show that, for a frustrated fully connected Ising spin network represented by trapped atomic ions, the competition between different spin orders leads to rich phase transitions whose sharpness scales exponentially with the number of spins. This unusual finite-size scaling behavior opens up the possibility of observing sharp quantum phase transitions in a system of just a few trapped ion spins.

We study the transport dynamics of matter-waves in the presence of disorder and nonlinearity. An atomic Bose-Einstein condensate that is localized in a quasiperiodic lattice in the absence of atom-atom interaction shows instead a slow expansion with a subdiffusive behavior when a controlled repulsive interaction is added. The measured features of the subdiffusion are compared to numerical simulations and a heuristic model. The observations confirm the nature of subdiffusion as interaction-assisted hopping between localized states and highlight a role of the spatial correlation of the disorder.

We describe a simple method for certifying that an experimental device prepares a desired quantum state $\rho$. Our method is applicable to any pure state $\rho$, and it provides an estimate of the fidelity between $\rho$ and the actual (arbitrary) state in the lab, up to a constant additive error. The method requires measuring only a constant number of Pauli expectation values, selected at random according to an importance-weighting rule. Our method is faster than full tomography by a factor of $d$, the dimension of the state space, and extends easily and naturally to quantum channels.