We present an alternative way to compute and interpret quantum tunneling in a one-dimensional double-well potential. For large transition time we show that the quantum action functional gives an analytical expression for tunneling amplitudes. This has been confirmed by numerical simulations giving relative errors in the order of ${10}^{-5}$. In contrast to the classical potential, the quantum potential has a triple well if the classical wells are deep enough. Its minima are located at the positions of extrema of the ground state wave function. The striking feature is that a single trajectory with a double instanton reproduces the tunneling amplitude. This is in contrast to the standard instanton approach, where infinitely many instantons and anti-instantons have to be taken into account. The quantum action functional is valid in the deep quantum regime in contrast to the semiclassical regime where the standard instanton approach holds. We compare both approaches via numerical simulations. While the standard instanton picture describes only the transition between potential minima of equal depth, the quantum action may give rise to instantons also for asymmetric potential minima. Such a case is illustrated by an example.

We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct bases for these vector spaces for each degree, thereby obtaining a generating set of polynomial invariants. Our approach is based on the description of Clifford operators in terms of linear operations over GF(2). Such a study of polynomial invariants of the local Clifford group is mainly of importance in quantum coding theory, in particular in the classification of binary quantum codes. Some applications in entanglement theory and quantum computing are briefly discussed as well.

Corrections of orders ${\alpha }^5$ and ${\alpha }^6$ are calculated in the hyperfine splitting of the $2S$ state in the muonic hydrogen. The nuclear structure effects are taken into account in the one- and two-loop Feynman amplitudes by means of the proton electromagnetic form factors. The total numerical value of the $2S$ state hyperfine splitting in the muonic hydrogen is $22.8148\mathrm{meV}$. This value can be considered as a reliable estimate in conducting a corresponding experiment with an accuracy ${10}^{-5}$. The value of the Sternheim hyperfine splitting interval $[8\Delta E^{\mathit{HFS}}\left(2S\right)-\Delta E^{\mathit{HFS}}\left(1S\right)]$ is obtained with an accuracy ${10}^{-6}$.

We consider cold collisions of $\mathrm{O}\mathrm{H}$ molecules in the ${}^2\mathrm{\Pi }_{3∕2}$ ground state, under the influence of a magnetic field. We find that modest fields of several thousand gauss can act to suppress inelastic collisions of weak-field-seeking states by two orders of magnitude. We attribute this suppression to two factors: (i) an indirect coupling of the entrance and the exit channel, in contrast to the effect of an applied electric field; and (ii) the relative shift of the entrance and exit scattering thresholds. In view of these results, magnetic trapping of $\mathrm{O}\mathrm{H}$ may prove feasible.

We demonstrate a combination of an isotopically purified atom beam and a magneto-optical trap which enables single-atom detection of all stable isotopes of calcium (40, 42, 43, 44, 46, and 48). These isotopes range in abundance from 96.9% $\left({}^{40}\mathrm{Ca}\right)$ to 0.004% $\left({}^{46}\mathrm{Ca}\right)$. The trap is loaded from an atomic beam which is decelerated in a Zeeman slower and subsequently deflected over an angle of 30° by optical molasses. The isotope selectivity of the Zeeman slower and the deflection stage is investigated experimentally and compared with Monte Carlo simulations.

In newly developed neutron phase tomography, wave properties of neutrons are exploited for the nondestructive testing of the internal structure of matter. We show how limitations due to small available intensities of present neutron sources can be overcome by using an advanced maximum-likelihood reconstruction algorithm. Unlike the standard filtered back-projection, the developed procedure gives reasonable results also when used on very noisy data or data consisting of only a few measured projections. This is demonstrated by means of simulations and also experimentally. The proposed method leads to considerably shorter measuring times and∕or increased precision.

A post-Markovian quantum master equation is derived, which includes bath memory effects via a phenomenologically introduced memory kernel $k\left(t\right)$. The derivation uses as a formal tool a probabilistic single-shot bath-measurement process performed during the coupled system-bath evolution. The resulting analytically solvable master equation interpolates between the exact Nakajima-Zwanzig equation and the Markovian Lindblad equation. A necessary and sufficient condition for complete positivity in terms of properties of $k\left(t\right)$ is presented, in addition to a prescription for the experimental determination of $k\left(t\right)$. The formalism is illustrated with examples.

We describe an interferometer which is capable of measuring phase at a Heisenberg limit of $1∕3$. The proposed interferometer, which consumes three indistinguishable photons, consists of two beam splitters with two-third reflectivity and two mirrors. It is shown that the oscillation period of the quantum interference is three times shorter than in the classical case and the interference visibility is 100%. A de Broglie wavelength given by ${\lambda }_0∕3$ can then be observed in this scheme, where ${\lambda }_0$ is the wavelength of a single photon. Compared with similar phase measurements [Mitchell et al., Nature (London) 429, 161 (2004); Walter et al., ibid. 429, 158 (2004)] by multiphoton maximally entangled states (MES), a three-photon MES is not generated in our proposal.

The Green function in the quantum defect theory provides an exact account for high-excited and continuum electronic states. We modify it by taking into account the ground and low-excited states using their wave functions calculated ab initio. As an application, we present a simple and efficient semianalytical method for the calculation of atomic electric frequency-dependent scalar dipole polarizability, for both real and imaginary frequencies. The polarizabilities calculated for some atoms (Li, Na, K, Be, Mg, Ca, Si, P, S, O, Al, Ge, C, N, F, He, Ne, Ar, Kr, and Xe) are compared with existing methods of computational quantum chemistry and with experiments; good accuracy of the proposed method is demonstrated.

A kick from a unipolar half-cycle pulse (HCP) can redistribute population and shift the relative phase between states in a radial Rydberg wave packet. We have measured the quantum coherence properties following the kick, and show that selected coherences can be destroyed by applying a HCP at specific times. Quantum mechanical simulations show that this is due to redistribution of the angular momentum in the presence of noise. These results have implications for the storage and retrieval of quantum information in the wave packet.

We predict the existence of an energy barrier for collapse in a system of two tunnel-coupled repulsive and attractive quasi-two-dimensional condensates trapped in a double-well potential. The ground state in such a system can have a lower energy than that of the collapsing state. We find such ground states numerically and analytically determine the domain of their existence; they have a much larger share of atoms confined in the repulsive condensate. The energy barrier for collapse is due to the fact that the energy of the system increases if atoms tunnel from the repulsive condensate to the attractive one.

We present simulations and experimental results for quantum-noise-initiated emission from an optical parametric generator (OPG) fabricated from periodically poled lithium niobate. The model we employ, which includes transverse coupling effects to enable off-axis phase matching, has been successfully used for describing broadband emission spectra in OPG’s and optical parametric amplifiers. The emission spectra and the quantum statistics deduced from macroscopic fluctuations are compared between simulations and experiment.

The dynamics of Bose-Einstein condensates in optical lattices with the long-range dipole-dipole interactions, the short-range on-site interactions, and hopping terms is reduced to the generalized discrete nonlinear Schrödinger equation. We present the different types of solitary excitations which appear in different parameter regions. We anticipate that these excitations will be observable and discuss how the model parameters can be tuned in experiments.

We show that quantum walks interpolate between a coherent “wave walk” and a random walk depending on how strongly the walker’s coin state is measured; i.e., the quantum walk exhibits the quintessentially quantum property of complementarity, which is manifested as a tradeoff between knowledge of which path the walker takes vs the sharpness of the interference pattern. A physical implementation of a quantum walk (the quantum quincunx) should thus have an identifiable walker and the capacity to demonstrate the interpolation between wave walk and random walk depending on the strength of measurement.

We study the effect of inhomogeneities in the magnetic field on the thermal entanglement of a two-spin system. We show that in the ferromagnetic case a very small inhomogeneity is capable of producing large values of thermal entanglement. This shows that the absence of entanglement in the ferromagnetic Heisenberg system is highly unstable against inhomogeneity of magnetic fields, which is inevitably present in any solid state realization of qubits.

We propose two protocols to encode a logical qubit into physical qubits relying on common types of qubit-qubit interactions in as simple forms as possible. We comment on its experimental implementation in several quantum computing architectures, e.g., with trapped atomic ion qubits, atomic qubits inside a high-$Q$ optical cavity, solid-state Josephson junction qubits, and Bose-Einstein condensed atoms.

This paper considers the binding of an electron or a positron to a ground-state hydrogen atom in a uniform magnetic field $B$, concentrating on states with zero orbital angular momentum $J$. It is shown that the affinity of a positron to a hydrogen atom is $2.23b^2{e}^2∕a$, where $a$ is the Bohr radius, $b\equiv B∕B_0$, $B_0=2.3505\times {10}^5\mathrm{T}$, $b⪡1$ is assumed, and the proton is assumed to have infinite mass. With these assumptions it is also shown that no $J=0$ singlet or triplet excited state of ${\mathrm{H}}^{-}$ exists. These results are compared to a previous estimate of the electron affinity of $J=0$ magnetically bound ions [V. G. Bezchastnov, P. Schmelcher, and L. S. Cederbaum, Phys. Rev. A 61, 052152 (2000)].