In this Letter we consider a system of $N$ pairwise finite-range interacting atoms and prove rigorously that in the zero-range interaction limit all the eigenstates and eigenenergies of the Hamiltonian converge to those corresponding to $N$ atoms interacting via the Fermi-Huang regularized pseudopotential. Next, we show that the latter eigensystem (if treated exactly) is invariant under a nontrivial transformation of the interaction potential. Finally, we realize that most of the approximate schemes of many-body physics do not exhibit this invariance: We use this property to resolve all inconsistencies of the Hartree-Fock-Bogoliubov variational formalism known thus far.

A 190-day comparison of the optical frequencies defined by an optical cavity and a molecular electronic transition is analyzed for the velocity independence of the speed of light (Kennedy-Thorndike test) and the universality of the gravitational redshift. The modulation of the laboratory velocity and the gravitational potential were provided by Earth’s orbital motion around the Sun. We find a velocity-dependence coefficient of $(1.9\pm 2.1)\times {10}^{-5\mathrm{}}$, 3 times lower compared to the best previous test. Alternatively, the data confirm the gravitational redshift for an electronic transition at the $4\%$ level. Prospects for significant improvements of the tests are discussed.

We demonstrate a simple optical clock based on an optical transition of iodine molecules, providing a frequency stability superior to most rf sources. Combined with a femtosecond-laser-based optical comb to provide the phase coherent clock mechanism linking the optical and microwave spectra, we derive an rf clock signal of comparable stability over an extended period. Measurements suggest the stability ( $5\times {10}^{-14\mathrm{}}$ at 1 s) of the cw laser locked on the iodine transition is transferred to every comb component throughout the optical octave bandwidth (from 532 to 1064 nm) with a precision of $3.5\times {10}^{-15\mathrm{}}$. Characterization of the performance of the optical clock shows (in-)stability below $3\times {10}^{-13\mathrm{}}$ at 1 s (currently limited by the microwave sources), and $4.6\times {10}^{-13\mathrm{}}$ over one year.

We show how entanglement can be used to improve the estimation of an unknown transformation. Using entanglement is always of benefit in improving either the precision or the stability of the measurement. Examples relevant for applications are illustrated, for either qubits or continuous variables.

We derive and investigate an expression for the dynamically modified decay of states coupled to an arbitrary continuum. This expression is universally valid for weak temporal perturbations. The resulting insights can serve as useful recipes for optimized control of decay and decoherence.

We study the Berezinskii-Kosterlitz-Thouless transition in a weakly interacting 2D quantum Bose gas using the concept of universality and numerical simulations of the classical $|\psi {|}^4$ model on a lattice. The critical density and chemical potential are given by relations $n_c=(mT/2\mathrm{}\pi {ħ}^2)\ln (\xi {ħ}^2/mU)$ and ${\mu }_c=(mTU/\pi {ħ}^2)\ln ({\xi }_{\mu }{ħ}^2/mU)$, where $T$ is the temperature, $m$ is the mass, and $U$ is the effective interaction. The dimensionless constant $\xi =380\mathrm{}\pm 3$ is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For ${\xi }_{\mu }$ our result is ${\xi }_{\mu }=13.2\mathrm{}\pm 0.4$. We also report the study of the quasicondensate correlations at the critical point.

We consider the low energy collective mode spectrum of a superfluid Fermi gas in a spherical trap in the collisionless regime. Using a self-consistent random-phase approximation, the effects of superfluidity on modes of dipole and quadrupole symmetries are systematically examined. The spectrum is calculated for varying pairing strength and temperature, and we identify several spectral features such as the emergence of Goldstone modes that can be used to detect the onset of superfluidity. Our analysis is relevant for present experiments aimed at observing a superfluid phase transition in trapped Fermi gases.

We study a spatially extended model of noise-induced magnetization reversal: a classical Ginzburg-Landau model, restricted to a bounded interval and perturbed by weak spatiotemporal noise. By adapting the Coleman-Langer approach to false vacuum decay, we determine the dependence of the activation barrier and Kramers rate prefactor on the interval length. As it increases, a transition between activation regimes occurs, at which the prefactor diverges. Similar transitions between activation regimes should occur in many other bistable, spatially extended classical models.

We have demonstrated a storage ring for ultracold neutral atoms. Atoms with mean velocities of 1 m/s corresponding to kinetic energies of $\sim 100\mathrm{neV}$ are confined to a 2 cm diameter ring by magnetic forces produced by two current-carrying wires. Up to ${10}^6$ atoms are loaded at a time in the ring, and seven revolutions are clearly observed. Additionally, we have demonstrated multiple loading of the ring and deterministic manipulation of the longitudinal velocity distribution of the atoms using applied laser pulses. Applications of this ring include large area atom interferometers and monochromatic atomic beam generation.

We study the geometry dependence of the Casimir energy for deformed metal plates by a path integral quantization of the electromagnetic field. For the first time, we give a complete analytical result for the deformation induced change in Casimir energy $\delta E$ in an experimentally testable, nontrivial geometry, consisting of a flat and a corrugated plate. Our results show an interesting crossover for $\delta E$ as a function of the ratio of the mean plate distance $H$, to the corrugation length $\lambda$: For $\lambda \ll H$ we find a slower decay $\sim H^{-4\mathrm{}}$, compared to the $H^{-5\mathrm{}}$ behavior predicted by the commonly used pairwise summation of van der Waals forces, which is valid only for $\lambda \gg H$.

We study the pattern of three-state topological phases that appears in systems with real Hamiltonians and wave functions. We give a simple geometric construction for representing these phases. We then apply our results to understand previous work on three-state phases. We show that the “mirror symmetry” of wave functions noticed in microwave experiments can be simply understood in our framework.

Ergodic theory has been approached from the side of the time averages with correlation functions from many-body models. The condition for ergodic behavior is formulated in terms of infinite products of certain numbers associated with time evolution. Physical properties that make a model ergodic are identified.

Noise-induced dynamics of a prototypical bistable system with delayed feedback is studied theoretically and numerically. For small noise and magnitude of the feedback, the problem is reduced to the analysis of the two-state model with transition rates depending on the earlier state of the system. Analytical solutions for the autocorrelation function and the power spectrum have been found. The power spectrum has a peak at the frequency corresponding to the inverse delay time, whose amplitude has a maximum at a certain noise level, thus demonstrating coherence resonance. The linear response to the external periodic force also has maxima at the frequencies corresponding to the inverse delay time and its harmonics.

The two-time retarded and advanced Green's function technique is formulated in nonextensive classical statistical mechanics within the optimal Lagrange multiplier framework. The main spectral properties are presented and a spectral decomposition for the spectral density is obtained. Finally, the nonextensive version of the spectral density method is given and its effectiveness is tested by exploring the equilibrium properties of a classical ferromagnetic spin chain.

Loss processes that remove particles from an atom trap leave holes behind in the single particle distribution if the trapped gas is a degenerate fermion system. The appearance of holes increases the temperature and we show that the heating (i) is significant if the initial temperature is well below the Fermi temperature $T_F$, and (ii) increases the temperature to $T\ge T_F/4\mathrm{}$ after half of the system’s lifetime, regardless of the initial temperature. The hole heating has important consequences for the prospect of observing Cooper pairing in atom traps.

A combination of analytical and numerical approaches obtains the complete dispersion curve for surface excitations in a condensate held in a plane linear potential. This improvement on previous approximate results yields an accurate formula for the local Landau critical velocity for vortex formation at the surface of a sufficiently large condensate, which agrees very well with recent experiments.

An open quantum system in steady state ${\hat{\rho }}_{\mathrm{ss}}$ can be represented by a weighted ensemble of pure states ${\hat{\rho }}_{\mathrm{ss}}=\Sigma k^{}{\wp }_k|{\psi }_k〉〈{\psi }_k|$ in infinitely many ways. A physically realizable (PR) ensemble is one for which some continuous measurement of the environment will collapse the system into a pure state $|\psi \left(t\right)〉$, stochastically evolving such that the proportion of time for which $|\psi \left(t\right)〉=|{\psi }_k〉$ equals ${\wp }_k$. Some, but not all, ensembles are PR. This constitutes the preferred ensemble fact. We present the necessary and sufficient conditions for a given ensemble to be PR, and illustrate the method by showing that the coherent state ensemble is not PR for an atom laser.

We study finite-size scaling of the roughness of signals in systems displaying Gaussian $1/f$ power spectra. It is found that one of the extreme value distributions, the Fisher-Tippett-Gumbel (FTG) distribution, emerges as the scaling function when boundary conditions are periodic. We provide a realistic example of periodic $1/f$ noise, and demonstrate by simulations that the FTG distribution is a good approximation for the case of nonperiodic boundary conditions as well. Experiments on voltage fluctuations in GaAs films are analyzed and excellent agreement is found with the theory.

A scheme is proposed for generating maximally entangled Greenberger-Horne-Zeilinger (GHZ) atomic states for testing quantum nonlocality. In the scheme, three atoms are simultaneously sent through a nonresonant cavity in a vacuum state. They are initially in the same state, and thus there is no energy exchange in the process. The cavity-assisted collision results in a phase-shift which depends upon the collective atomic excitations. In principle, the scheme can be generalized to generate $N$-atom GHZ states. The scheme is insensitive to cavity decay and requires only one cavity, providing new prospects for testing fundamental aspects of quantum mechanics and for quantum information processing.

Considering a moving vortex line in a dilute atomic Bose-Einstein condensate within time-dependent Hartree-Fock-Bogoliubov-Popov theory, we derive a criterion for the quasiparticle excitations to follow the vortex core rigidly. The assumption of adiabaticity, which is crucial for the validity of the stationary self-consistent theories in describing such time-dependent phenomena, is shown to imply a stringent criterion for the velocity of the vortex line. Furthermore, this condition is shown to be violated in the recent vortex precession experiments.