We investigate the phase diagram of spinless bosons with long range ($\propto 1/r^3$) repulsive interactions, relevant to ultracold polarized atoms or molecules, using density matrix renormalization group. Between the two conventional insulating phases, the Mott and density wave phases, we find a new phase possessing hidden order revealed by nonlocal string correlations analogous to those characterizing the Haldane gapped phase of integer spin chains. We develop a mean field theory that describes the low-energy excitations in all three insulating phases. This is used to calculate the absorption spectrum due to oscillatory lattice modulation. We predict a sharp resonance in the spectrum due to a collective excitation of the new phase that would provide clear evidence for the existence of this phase.

Continuous and pulsed quantum Zeno effects were observed using a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate. Oscillations between two ground hyperfine states of a magnetically trapped condensate, externally driven at a transition rate ${\omega }_R$, were suppressed by destructively measuring the population in one of the states with resonant light. The suppression of the transition rate in the two-level system was quantified for pulsed measurements with a time interval $\delta t$ between pulses and continuous measurements with a scattering rate $\gamma$. We observe that the continuous measurements exhibit the same suppression in the transition rate as the pulsed measurements when $\gamma \delta t=3.60(0.43)$, in agreement with the predicted value of 4. Increasing the measurement rate suppressed the transition rate down to $0.005{\omega }_R$.

We study the density modulation that appears in a Bose-Einstein condensate flowing with supersonic velocity against an obstacle. The experimental density profiles observed at JILA are reproduced by a numerical integration of the Gross-Pitaevskii equation and then interpreted in terms of C̆erenkov emission of Bogoliubov excitations by the defect. The phonon and the single-particle regions of the Bogoliubov spectrum are, respectively, responsible for a conical wave front and a fan-shaped series of precursors.

We demonstrate apertureless near-field microscopy of single molecules at sub-10 nm resolution. With a novel phase filter, near-field images of single organic fluorophores were obtained with $\sim$sixfold improvement in the signal-to-noise ratio. The improvement allowed pairs of molecules separated by $\sim 15\mathrm{nm}$ to be reliably and repeatedly resolved, thus demonstrating the first true Rayleigh resolution test for near-field images of single molecules. The potential of this technique for biological applications was demonstrated with an experiment that measured the helical rise of $A$-form DNA.

We investigate the physics underlying the presence of a quasicondensate in a nearly one dimensional, weakly interacting trapped atomic Bose gas. We show that a Hartree-Fock (mean-field) approach fails to predict the existence of the quasicondensate in the center of the cloud: the quasicondensate is generated by interaction-induced correlations between atoms and not by a saturation of the excited states. Numerical calculations based on Bogoliubov theory give an estimate of the crossover density in agreement with experimental results.

The Born-Markov master equation analysis of the vibrating mirror and photon experiment proposed by Marshall, Simon, Penrose, and Bouwmeester is completed by including the important issues of temperature and friction. We find that at the level of cooling available to date, visibility revivals are purely classical, and no quantum effect can be detected by the setup, no matter how strong the photon-mirror coupling is. Checking proposals of universal nonenvironmental decoherence is ruled out by dominating thermal decoherence; a conjectured coordinate-diffusion contribution to decoherence may become observable on reaching moderately low temperatures.

Parity measurements on qubits can generate the entanglement resource necessary for scalable quantum computation. Here we describe a method for fast optical parity measurements on electron spin qubits within coupled quantum dots. The measurement scheme, which can be realized with existing technology, consists of the optical excitation of excitonic states followed by monitored relaxation. Conditional on the observation of a photon, the system is projected into the odd/even-parity subspaces. Our model incorporates all the primary sources of error, including detector inefficiency, effects of spatial separation and nonresonance of the dots, and also unwanted excitations. Through an analytical treatment we establish that the scheme is robust to such effects. Two applications are presented: a realization of a controlled-NOT gate, and a technique for growing large scale graph states.

We have measured the relative strength ${\epsilon }_{dd}$ of the magnetic dipole-dipole interaction compared with the contact interaction in a dipolar chromium Bose-Einstein condensate. We analyze the asymptotic velocities of expansion of the condensate with different orientations of the atomic magnetic moments. By comparing the experimental results with numerical solutions of the hydrodynamic equations for dipolar condensates, we obtain ${\epsilon }_{dd}=0.159\pm 0.034$. We use this result to determine the $s$-wave scattering length $a=(5.08\pm 1.06\times {10}^{-9})\mathrm{m}=(96\pm 20)a_0$ of ${}^{52}\mathrm{Cr}$. This is fully consistent with our previous measurements on the basis of Feshbach resonances and therefore confirms the validity of the theoretical approach used to describe the dipolar Bose-Einstein condensate.

Any physical transformation that equally distributes quantum information over a large number $M$ of users can be approximated by a classical broadcasting of measurement outcomes. The accuracy of the approximation is at least of the order $O(M^{-1})$. In particular, quantum cloning of pure and mixed states can be approximated via quantum state estimation. As an example, for optimal qubit cloning with 10 output copies, a single user has an error probability $p_{\mathrm{err}}\ge 0.45$ in distinguishing classical from quantum output, a value close to the error probability of the random guess.

We study a rotating atomic Fermi gas near a narrow $s$-wave Feshbach resonance in a uniaxial trap with frequencies ${\Omega }_{\perp }$, ${\Omega }_z$. We predict the upper-critical angular velocity, ${\omega }_{c2}(\delta ,T)$, as a function of temperature $T$ and detuning $\delta$ across the BEC-BCS crossover. The suppression of superfluidity at ${\omega }_{c2}$ is distinct in the BCS and BEC regimes, with the former controlled by depairing and the latter by the dilution of bosonic molecules. At low $T$ and ${\Omega }_z\ll {\Omega }_{\perp }$, in the BCS and crossover regimes of $0\lesssim \delta \lesssim {\delta }_c$, ${\omega }_{c2}$ is implicitly given by $\hslash \sqrt{{\omega }_{c2}^2+{\Omega }_{\perp }^2}\approx 2\Delta \sqrt{\hslash {\Omega }_{\perp }/{ϵ}_F}$, vanishing as ${\omega }_{c2}\sim {\Omega }_{\perp }(1-\delta /{\delta }_c{)}^{1/2}$ near ${\delta }_c\approx 2{ϵ}_F+\frac{\gamma }{2}{ϵ}_F\ln ({ϵ}_F/\hslash {\Omega }_{\perp })$ (with $\Delta$ the BCS gap and $\gamma$ the resonance width), and extending the bulk result $\hslash {\omega }_{c2}\approx 2{\Delta }^2/{ϵ}_F$ to a trap. In the BEC regime of $\delta <0$ we find ${\omega }_{c2}\to {\Omega }_{\perp }^{-}$, where molecular superfluidity is destroyed only by large quantum fluctuations associated with comparable boson and vortex densities.

Unconditionally secure nonrelativistic bit commitment is known to be impossible in both the classical and the quantum world. However, when committing to a string of $n$ bits at once, how far can we stretch the quantum limits? In this Letter, we introduce a framework of quantum schemes where Alice commits a string of $n$ bits to Bob, in such a way that she can only cheat on $a$ bits and Bob can learn at most $b$ bits of information before the reveal phase. Our results are twofold: we show by an explicit construction that in the traditional approach, where the reveal and guess probabilities form the security criteria, no good schemes can exist: $a+b$ is at least $n$. If, however, we use a more liberal criterion of security, the accessible information, we construct schemes where $a=4{log}_{2}n+O(1)$ and $b=4$, which is impossible classically. Our findings significantly extend known no-go results for quantum bit commitment.

We study entanglement distillability of bipartite mixed spin states under Wigner rotations induced by Lorentz transformations. We define weak and strong criteria for relativistic isoentangled and isodistillable states to characterize relative and invariant behavior of entanglement and distillability. We exemplify these criteria in the context of Werner states, where fully analytical methods can be achieved and all relevant cases presented.

We use the system-plus-reservoir approach to study the dynamics of a system composed of two independent Brownian particles. We present an extension of the well-known model of a bath of oscillators which is capable of inducing an effective coupling between the two particles depending on the choice made for the spectral function of the bath oscillators. The coupling is nonlinear in the variables of interest, and an exponential dependence on these variables is imposed in order to guarantee the translational invariance of the model if the two particles are not subject to any external potential. The effective equations of motion for the particles are obtained by the Laplace transform method, and, besides recovering all the local dynamical properties for each particle, we end up with an effective interaction potential between them. We explicitly analyze one of its possible forms.

The destruction of quantum coherence can pump energy into a system. For our examples this is paradoxical because the destroyed correlations are ordinarily considered negligible. Mathematically the explanation is straightforward and physically one can identify the degrees of freedom supplying this energy. Nevertheless, the energy input can be calculated without specific reference to those degrees of freedom.

A simple model of quantum ratchet transport that can generate unbounded linear acceleration of the quantum ratchet current is proposed, with the underlying classical dynamics fully chaotic. The results demonstrate that generic quantum ratchet transport can occur with any type of classical phase space structure. The quantum ratchet transport with full classical chaos is also shown to be very robust to noise due to the large linear acceleration afforded by the quantum dynamics. One possible experiment allowing observation of these predictions is suggested.

We report the first demonstration of a matter-wave interference gyroscope that meets both the short-term noise and long-term stability requirements for high accuracy navigation. This performance level resulted from implementation of a novel technique to precisely reverse the input axis of the gyroscope.

We present simulation results of the vortex dynamics in a trapped Bose-Einstein condensate in the presence of a rotating optical lattice. Changing the potential amplitude and the relative rotation frequency between the condensate and the optical lattice, we find a rich variety of dynamical phases of vortices. The onset of these different phases is described by the force balance of a driving force, a pinning force, and vortex-vortex interactions. In particular, when the optical lattice rotates faster than the condensate, an incommensurate effect leads to a vortex-liquid phase supported by the competition between the driving force and the dissipation.

We propose an experimental scheme to observe spin Hall effects with cold atoms in a light-induced gauge potential. Under an appropriate configuration, the cold atoms moving in a spatially varying laser field experience an effective spin-dependent gauge potential. Through numerical simulation, we demonstrate that such a gauge field leads to observable spin Hall currents under realistic conditions. We also discuss the quantum spin Hall state in an optical lattice.

We report the observation of vortex pinning in rotating gaseous Bose-Einstein condensates. Vortices are pinned to columnar pinning sites created by a corotating optical lattice superimposed on the rotating Bose-Einstein condensates. We study the effects of two types of optical lattice: triangular and square. In both geometries we see an orientation locking between the vortex and the optical lattices. At sufficient intensity the square optical lattice induces a structural crossover in the vortex lattice.

The fully complex domain semiclassical theory based upon the complexified stable-unstable manifold theory, which we have developed in our recent studies, is successfully applied to explain anomalous tunneling phenomena numerically observed in a periodically modulated round-off-step potential. Numerical experiments show that tunneling through the oscillating step potential is characterized by a spatially nondecaying tunneling tail and an anomalously slow relaxation. The key is the existence of a critical trajectory exhibiting singular behavior, and the analysis of neighboring trajectories around it reproduces the essence of such anomalous phenomena.