We present the universal features of the hitting probability $Q(x,L)$, the probability that a generic stochastic process starting at $x$ and evolving in a box [0, $L$] hits the upper boundary $L$ before hitting the lower boundary at 0. For a generic self-affine process, we show that $Q(x,L)=Q(z=x/L)$ has a scaling $Q(z)\sim z^{\varphi }$ as $z\to 0$, where $\varphi =\theta /H$, $H$, and $\theta$ being the Hurst and persistence exponent of the process, respectively. This result is verified in several exact calculations, including when the process represents the position of a particle diffusing in a disordered potential. We also provide numerical support for our analytical results.

We simulate the quantum adiabatic algorithm (QAA) for the exact cover problem for sizes up to $N=256$ using quantum Monte Carlo simulations incorporating parallel tempering. At large $N$, we find that some instances have a discontinuous (first-order) quantum phase transition during the evolution of the QAA. This fraction increases with increasing $N$ and may tend to 1 for $N\to \infty$.

Quantum teleportation of an $n$-qubit state performed using as an entangled resource a general bipartite state of $2n$ qubits instead of $n$ Bell states is equivalent to a correlated Pauli channel. This yields a new characterization of such channels in terms of many-body correlation functions of the teleporting media. It provides a relatively simple method for determining whether a correlated quantum channel is able to reliably convey quantum messages by studying the entanglement properties of the teleportation mediating system. Our model is then generalized to the continuous-variable case.

Necessary and sufficient conditions for the equivalence of arbitrary $n$-qubit pure quantum states under local unitary (LU) operations are derived. First, an easily computable standard form for multipartite states is introduced. Two generic states are shown to be LU equivalent iff their standard forms coincide. The LU-equivalence problem for nongeneric states is solved by presenting a systematic method to determine the LU operators (if they exist) which interconvert the two states.

A Brownian particle moving across a porous membrane subject to an oscillating force exhibits stochastic resonance with properties which strongly depend on the geometry of the confining cavities on the two sides of the membrane. Such a manifestation of stochastic resonance requires neither energetic nor entropic barriers, and can thus be regarded as a purely geometric effect. The magnitude of this effect is sensitive to the geometry of both the cavities and the pores, thus leading to distinctive optimal synchronization conditions.

We experimentally demonstrate an optical controlled-NOT (CNOT) gate with arbitrary single inputs based on a 4-photon 6-qubit cluster state entangled both in polarization and spatial modes. We first generate the 6-qubit state, and then, by performing single-qubit measurements, the CNOT gate is applied to arbitrary single input qubits. To characterize the performance of the gate, we estimate its quantum process fidelity and prove its entangling capability. In addition, our results show that the gate cannot be reproduced by local operations and classical communication. Our experiment shows that such hyper-entangled cluster states are promising candidates for efficient optical quantum computation.

The Goos-Hänchen effect is a spatial shift along an interface resulting from an interference effect that occurs for total internal reflection. This phenomenon was suggested by Sir Isaac Newton, but it was not until 1947 that the effect was experimentally observed by Goos and Hänchen. We provide the first direct, absolute, experimental determination of the Goos-Hänchen shift for a particle experiencing a potential well as required by quantum mechanics: namely, wave-particle duality. Here, the particle is a spin-polarized neutron reflecting from a film of magnetized material. We detect the effect through a subtle change in polarization of the neutron. Here, we demonstrate, through experiment and theory, that neutrons do exhibit the Goos-Hänchen effect and postulate that the associated time shift should also be observable.

We report the generation of entanglement between two individual ${}^{87}\mathrm{Rb}$ atoms in hyperfine ground states $|F=1,M=1⟩$ and $|F=2,M=2⟩$ which are held in two optical tweezers separated by $4\mu \mathrm{m}$. Our scheme relies on the Rydberg blockade effect which prevents the simultaneous excitation of the two atoms to a Rydberg state. The entangled state is generated in about 200 ns using pulsed two-photon excitation. We quantify the entanglement by applying global Raman rotations on both atoms. We measure that 61% of the initial pairs of atoms are still present at the end of the entangling sequence. These pairs are in the target entangled state with a fidelity of 0.75.

We present the first demonstration of a CNOT gate between two individually addressed neutral atoms. Our implementation of the CNOT uses Rydberg blockade interactions between neutral atoms held in optical traps separated by $>8\mu \mathrm{m}$. Using two different gate protocols we measure CNOT fidelities of $F=0.73$ and 0.72 based on truth table probabilities. The gate was used to generate Bell states with fidelity $F=0.48\pm 0.06$. After correcting for atom loss we obtain an a posteriori entanglement fidelity of $F=0.58$.

Using angular-position–orbital-angular-momentum entangled photons, we study angular two-photon interference in a scheme in which entangled photons are made to pass through apertures in the form of double angular slits, and using this scheme, we demonstrate an entangled two-qubit state that is based on the angular-position correlations of entangled photons. The entanglement of the two-qubit state is quantified in terms of concurrence. These results provide an additional means for preparing entangled quantum states for use in quantum information protocols.

We calculate the shift, due to interatomic interactions, of an optical transition in an atomic Fermi gas trapped in an optical lattice, as in recent experiments of Campbell et al. [Science 324, 360 (2009)]. Using a pseudospin formalism to describe the density matrix of atoms, we derive a Bloch equation which incorporates both spatial inhomogeneity of the probe laser field and interatomic interactions. Expressions are given for the frequency shift as a function of pulse duration, detuning of the probe laser, and the spatial dependence of the electric field of the probe beam. In the low temperature semiclassical regime, we find that the magnitude of the shift is proportional to the temperature.

We study many-body contributions to the effective interaction between fermions in a three-component Fermi mixture. We find that effective interactions induced by the third component can lead to a phase diagram different from that predicted if interactions with the third component are neglected. As a result, in a confining potential a superfluid shell structure can arise even for equal populations of the components. We also find a critical temperature for the BCS transition in a ${}^6\mathrm{Li}$ mixture which can deviate strongly from the one in a weakly interacting two-component system.

Recent experiments have measured collisional frequency shifts in polarized fermionic alkaline-earth atoms using ${}^{1}S_0\mathrm{\text{−}}{}^{3}P_0$ Rabi spectroscopy. Here, we provide a first-principles nonequilibrium theoretical description of the interaction frequency shifts starting from the microscopic many-body Hamiltonian. Our formalism describes the dependence of the frequency shift on excitation inhomogeneity, interactions, temperature, and many-body dynamics, provides a fundamental understanding of the effects of the measurement process, and explains the observed density shift data.

We propose a novel way to communicate signals in the form of waves across a $d$-dimensional lattice. The mechanism is based on quantum search algorithms and makes it possible to both search for marked positions in a regular grid and to communicate between two (or more) points on the lattice. Remarkably, neither the sender nor the receiver needs to know the position of each other despite the fact that the signal is only exchanged between the contributing parties. This is an example of using wave interference as a resource by controlling localization phenomena effectively. Possible experimental realizations will be discussed.

On general grounds, a nonequilibrium temperature can be consistently defined from generalized fluctuation-dissipation relations only if it is independent of the observable considered. We argue that the dependence on the choice of observable generically occurs when the phase-space probability distribution is nonuniform on constant energy shells. We relate quantitatively this observable dependence to a fundamental characteristics of nonequilibrium systems, namely, the Shannon entropy difference with respect to the equilibrium state with the same energy. This relation is illustrated on a mean-field model in contact with two heat baths at different temperatures.

We suggest pump-probe spectroscopy to study pair correlations that determine the many-body dynamics in weakly interacting, dilute ultracold gases. A suitably chosen, short laser pulse depletes the pair density locally, creating a “hole” in the electronic ground state. The dynamics of this nonstationary pair density is monitored by a time-delayed probe pulse. The resulting transient signal allows us to spectrally decompose the hole and to map out the pair correlation function.

The computer simulations of fluctuational dynamics of an annular system governed by the sine-Gordon model with a white noise source are performed. It is demonstrated that the mean escape time (MET) of a phase string for an annular structure can be much larger than for a linear one and has a strongly pronounced maximum as a function of system’s length. The location of the MET maximum roughly equals the size of the kink-antikink pair, which leads to evidence of a spatial crossover between two dynamical regimes: when the phase string escapes over the potential barrier as a whole and when the creation of kink-antikink pairs is the main mechanism of the escape process. For large lengths and in the limit of small noise intensity $\gamma$, for both MET and inverse concentration of kinks, we observe the same dependence versus the kink energy $E_k$: $\sim \exp (2E_k/\gamma )$ for the annular structure and $\sim \exp (E_k/\gamma )$ for the linear one.

We present experimental results approximating the Jones polynomial using 4 qubits in a liquid state nuclear magnetic resonance quantum information processor. This is the first experimental implementation of a complete problem for the deterministic quantum computation with one quantum bit model of quantum computation, which uses a single qubit accompanied by a register of completely random states. The Jones polynomial is a knot invariant that is important not only to knot theory, but also to statistical mechanics and quantum field theory. The implemented algorithm is a modification of the algorithm developed by Shor and Jordan suitable for implementation in NMR. These experimental results show that for the restricted case of knots whose braid representations have four strands and exactly three crossings, identifying distinct knots is possible 91% of the time.

We put forward a reconstruction scheme prompted by the relation between a von Neumann measurement and the corresponding informationally complete measurement induced in a relevant reconstruction subspace. This method is especially suited for the full tomography of complex quantum systems, where the intricacies of the detection part of the experiment can be greatly reduced provided some prior information is available. In broader terms this shows the importance of prior information in quantum theory. The proposed technique is illustrated with an experimental tomography of photonic vortices of moderate dimension.

Nonlinear compression of periodic signals is a key feature of the active amplifier in inner ear organs of all vertebrates. Different exponents ${\alpha }_0\in [-0.88,-0.5]$ of the sensitivity vs forcing amplitude $|\chi |\sim f^{{\alpha }_0}$ have been observed. Here we calculate analytically the local exponent for a generic oscillator, the normal form of a Hopf bifurcation driven by noise and a periodic signal. For weak noise and sufficient distance from the bifurcation on the unstable side, the exponent may be close to $-1$ for moderate forcing amplitudes beyond linear response. Such strong compression is also found in a model of hair bundle motility.