We consider a homogeneous 1D Bose gas with contact interactions and a large attractive coupling constant. This system can be realized in tight waveguides by exploiting a confinement induced resonance of the effective 1D scattering amplitude. By using the diffusion Monte Carlo method we show that, for small densities, the gaslike state is well described by a gas of hard rods. The critical density for cluster formation is estimated using the variational Monte Carlo method. The behavior of the correlation functions and of the frequency of the lowest breathing mode for harmonically trapped systems shows that the gas is more strongly correlated than in the Tonks-Girardeau regime.

We report on the observation of coherent, purely collisionally driven spin dynamics of neutral atoms in an optical lattice. For high lattice depths, atom pairs confined to the same lattice site show weakly damped Rabi-type oscillations between two-particle Zeeman states of equal magnetization, induced by spin-changing collisions. Moreover, measurement of the oscillation frequency allows for precise determination of the spin-changing collisional coupling strengths, which are directly related to fundamental scattering lengths describing interatomic collisions at ultracold temperatures.

We measure photoassociation rates in one-dimensional Bose gases, and so determine the local pair correlation function over a wide range of coupling strengths. As bosons become more strongly coupled, we observe a tenfold decrease in their wave function overlap, thus directly observing the fermionization of bosons.

A novel atom-molecule conversion technique has been investigated. Ultracold ${}^{85}\mathrm{Rb}$ atoms sitting in a dc magnetic field near the 155 G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field. There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy. We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the phase space density of the sample. This technique offers high conversion efficiencies without the necessity of crossing or closely approaching the Feshbach resonance and allows precise spectroscopic measurements. Efficiencies of 55% have been observed for pure Bose-Einstein condensates.

We show by general arguments from linear irreversible thermodynamics that for a heat engine, operating between reservoirs at temperatures $T_0$ and $T_1$, $T_0\ge T_1$, the efficiency at maximum power is bounded from above by $1-\sqrt{T_1/T_0}$.

We prove rigorously that for a nonvanishing probability of having electrons in matter, with Coulomb interactions, within a sphere of radius $R$, the latter, necessarily, grows not any slower than $N^{1/3}$ for large $N$, where $N$ denotes the number of electrons. Thus it is not surprising that matter occupies so large a volume.

We have observed phase defects in quasi-2D Bose-Einstein condensates close to the condensation temperature. Either a single or several equally spaced condensates are produced by selectively evaporating the sites of a 1D optical lattice. When several clouds are released from the lattice and allowed to overlap, dislocation lines in the interference patterns reveal nontrivial phase defects.

We discuss the form of the entropy for classical Hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a $N$ particle in the limit $N\to \infty$. The stationary states of the Hamiltonian system are subject to infinite conserved quantities due to the Vlasov dynamics. We show that the stationary states correspond to an extremum of the Boltzmann-Gibbs entropy, and their stability is obtained from the condition that this extremum is a maximum. As a consequence, the entropy is a function of an infinite set of Lagrange multipliers that depend on the initial condition. We also discuss in this context the meaning of ensemble inequivalence and the temperature.

We address the problem of spin dynamics in the presence of a thermal bath, by solving exactly the appropriate quantum master equations with continued-fraction methods. The crossover region between the quantum and classical domains is studied by increasing the spin value $S$, and the asymptote for the classical absorption spectra is eventually recovered. Along with the recognized relevance of the coupling strength, we show the critical role played by the structure of the system-environment interaction in the emergence of classical phenomenology.

We derive a new inequality for entanglement for a mixed four-partite state. Employing this inequality, we present a one-shot lower bound for entanglement cost and prove that entanglement cost is strictly larger than zero for any entangled state. We demonstrate that irreversibility occurs in the process of formation for all nondistillable entangled states. In this way we solve a long standing problem of how “real” is entanglement of bound entangled states. Using the new inequality we also prove the impossibility of local cloning of a known entangled state.

The correspondence principle between the quantum commutator $[\widehat{A},\widehat{B}]$ and the classical Poisson brackets $\iota \hslash \{A,B\}$ is examined in the context of response theory. The classical response function is obtained as the leading term of the $\hslash$ expansion of the phase space representation of the response function in terms of Weyl-Wigner transformations and is shown to increase without bound at long times as a result of ignoring divergent higher-order contributions. Systematical inclusion of higher-order contributions improves the accuracy of the $\hslash$ expansion at finite times. Resummation of all the higher-order terms establishes the classical-quantum correspondence $⟨v+n|\widehat{\alpha }(t)|v⟩\leftrightarrow {\alpha }_n{e}^{\iota n\omega t}{|}_{J_v+n\hslash /2}$. The time interval of the validity of the simple classical limit $[\widehat{A}(t),\widehat{B}(0)]\to \iota \hslash \{A(t),B(0)\}$ is estimated for quasiperiodic dynamics and is shown to be inversely proportional to anharmonicity.

We realize an end-to-end no-switching quantum key distribution protocol using continuous-wave coherent light. We encode weak broadband Gaussian modulations onto the amplitude and phase quadratures of light beams. Our no-switching protocol achieves high secret key rate via a post-selection protocol that utilizes both quadrature information simultaneously. We establish a secret key rate of $25\mathrm{Mbits}/\mathrm{s}$ for a lossless channel and $1\mathrm{kbit}/\mathrm{s}$ for 90% channel loss, per 17 MHz of detected bandwidth, assuming individual Gaussian eavesdropping attacks. Since our scheme is truly broadband, it can potentially deliver orders of magnitude higher key rates by extending the encoding bandwidth with higher-end telecommunication technology.

We study the nonequilibrium motion of an elastic string in a two dimensional pinning landscape using Langevin dynamics simulations. The relaxation of a line, initially flat, is characterized by a growing length $L(t)$ separating the equilibrated short length scales from the flat long distance geometry that keeps a memory of the initial condition. We show that, in the long time limit, $L(t)$ has a nonalgebraic growth with a universal distribution function. The distribution function of waiting times is also calculated, and related to the previous distribution. The barrier distribution is narrow enough to justify arguments based on scaling of the typical barrier.

We interpret the recently observed spatial domain formation in spin-1 atomic condensates as a result of dynamical instability. Within the mean field theory, a homogeneous condensate is dynamically unstable (stable) for ferromagnetic (antiferromagnetic) atomic interactions. We find that this dynamical instability naturally leads to spontaneous domain formation as observed in several recent experiments for condensates with rather small numbers of atoms. For trapped condensates, our numerical simulations compare quantitatively to the experimental results, thus largely confirming the physical insight from our analysis of the homogeneous case.

General expressions for quantum electrodynamic corrections to the one-loop self-energy [of order $\alpha (Z\alpha {)}^6$] and for the two-loop Lamb shift [of order ${\alpha }^2(Z\alpha {)}^6$] are derived. The latter includes all diagrams with closed fermion loops. The general results are valid for arbitrary excited non-$S$ hydrogenic states and for the normalized Lamb shift difference of $S$ states, defined as ${\Delta }_n=n^3\Delta E(nS)-\Delta E(1S)$. We present numerical results for one-loop and two-loop corrections for excited $S$, $P$, and $D$ states. In particular, the normalized Lamb shift difference of $S$ states is calculated with an uncertainty of order 0.1 kHz.

The scaling of the conductivity at the superfluid-insulator quantum phase transition in two dimensions is studied by numerical simulations of the Bose-Hubbard model. In contrast to previous studies, we focus on properties of this model in the experimentally relevant thermodynamic limit at finite temperature $T$. We find clear evidence for deviations from ${\omega }_k$ scaling of the conductivity towards ${\omega }_k/T$ scaling at low Matsubara frequencies ${\omega }_k$. By careful analytic continuation using Padé approximants we show that this behavior carries over to the real frequency axis where the conductivity scales with $\omega /T$ at small frequencies and low temperatures. We estimate the universal dc conductivity to be ${\sigma }^{*}=0.45(5)Q^2/h$, distinct from previous estimates in the $T=0$, $\omega /T\gg 1$ limit.

Dynamical decoupling pulse sequences have been used to extend coherence times in quantum systems ever since the discovery of the spin-echo effect. Here we introduce a method of recursively concatenated dynamical decoupling pulses, designed to overcome both decoherence and operational errors. This is important for coherent control of quantum systems such as quantum computers. For bounded-strength, non-Markovian environments, such as for the spin-bath that arises in electron- and nuclear-spin based solid-state quantum computer proposals, we show that it is strictly advantageous to use concatenated pulses, as opposed to standard periodic dynamical decoupling pulse sequences. Namely, the concatenated scheme is both fault tolerant and superpolynomially more efficient, at equal cost. We derive a condition on the pulse noise level below which concatenation is guaranteed to reduce decoherence.

A spin gas is a natural extension of a classical gas. It consists of a large number of particles whose (random) motion is described classically, but, in addition, have internal (quantum mechanical) degrees of freedom that interact during collisions. For specific types of quantum interactions we determine the entanglement that occurs naturally in such systems. We analyze how the evolution of the quantum state is determined by the underlying classical kinematics of the gas. For the Boltzmann gas, we calculate the rate at which entanglement is produced and characterize the entanglement properties of the equilibrium state.

We introduce inequalities for multipartite entanglement, derived from the geometry of spin vectors. The criteria are constructed iteratively from cross and dot products between the spins of individual subsystems, each of which may have arbitrary dimension. For qubit ensembles the maximum violation for our inequalities is larger than that for the Mermin-Klyshko Bell inequalities, and the maximally violating states are different from Greenberger-Horne-Zeilinger states. Our inequalities are violated by certain bound entangled states for which no Bell-type violation has yet been found.

The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a thermal cloud and the dynamical depletion of the condensate. Our numerical results, based on the time-dependent Hartree-Fock-Bogoliubov theory, demonstrate the collapse of the attractively interacting BEC via collisional emission of atom pairs into the thermal cloud, which splits the (quasi-one-dimensional) BEC soliton into two partially coherent solitonic structures of opposite momenta. These incoherent matter waves are analogous to optical random-phase solitons.