No abstract

We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation of the domain of self-adjointness in terms of boundary conditions that relate sectors with different numbers of bosons. We treat both models in which the Hamiltonian may be defined as a form perturbation of the free operator, such as Fröhlich's polaron, and renormalisable models, such as the massive Nelson model.

We consider a way of defining quantum Hamiltonians involving particle creation and annihilation based on an interior-boundary condition (IBC) on the wave function, where the wave function is the particle-position representation of a vector in Fock space, and the IBC relates (essentially) the values of the wave function at any two configurations that differ only by the creation of a particle. Here we prove, for a model of particle creation at one or more point sources using the Laplace operator as the free Hamiltonian, that a Hamiltonian can indeed be rigorously defined in this way without the need for any ultraviolet regularization, and that it is self-adjoint. We prove further that introducing an ultraviolet cutoff (thus smearing out particles over a positive radius) and applying a certain known renormalization procedure (taking the limit of removing the cut-off while subtracting a constant that tends to infinity) yields, up to addition of a finite constant, the Hamiltonian defined by the IBC. MSC: 81T10, 81Q10, 47F05. Key words: Ultraviolet divergence problem; renormalization in quantum field theory; self-adjoint Hamiltonian; self-adjoint extensions of the Laplace operator; particle-position representation; ultraviolet cut-off.

Optical trapping and ions combine unique advantages of independently striving fields of research. Light fields can form versatile potential landscapes, such as optical lattices, for neutral and charged atoms, while avoiding detrimental implications of established radiofrequency traps. Ions interact via long-range Coulomb forces and permit control and detection of their motional and electronic states on the quantum level. Here we show optical trapping of 138 Ba þ ions in the absence of radio-frequency fields via a far-detuned dipole trap, suppressing photon scattering by three orders of magnitude and the related recoil heating by four orders of magnitude. To enhance the prospects for optical as well as hybrid traps, we demonstrate a method for stray electric field compensation to a level below 9 mV m À 1 . Our results will be relevant, for example, for ion-atom ensembles, to enable 4-5 orders of magnitude lower common temperatures, accessing the regime of ultracold interaction and chemistry, where quantum effects are predicted to dominate.