Dimensional enhancement of kinetic energies

Simple thermodynamics considers kinetic energy to be an extensive variable which is proportional to the number, N, of particles. We present a quantum state of N non-interacting particles for which the kinetic energy increases quadratically with N. This enhancement effect is tied to the quantum centrifugal potential whose strength is quadratic in the number of dimensions of configuration space.Comment: 9 pages, accepted by Phys. Rev.

Conformal Mapping and Bound States in Bent Waveguides

Is it possible to trap a quantum particle in an open geometry? In this work we deal with the boundary value problem of the stationary Schroedinger (or Helmholtz) equation within a waveguide with straight segments and a rectangular bending. The problem can be reduced to a one dimensional matrix Schroedinger equation using two descriptions: oblique modes and conformal coordinates. We use a corner-corrected WKB formalism to find the energies of the one dimensional problem. It is shown that the presence of bound states is an effect due to the boundary alone, with no classical counterpart for this geometry. The conformal description proves to be simpler, as the coupling of transversal modes is not essential in this case.Comment: 16 pages, 10 figures. To appear in the Proceedings of the Symposium "Symmetries in Nature, in memoriam Marcos Moshinsky

Overcoming loss of contrast in atom interferometry due to gravity gradients

Long-time atom interferometry is instrumental to various high-precision measurements of fundamental physical properties, including tests of the equivalence principle. Due to rotations and gravity gradients, the classical trajectories characterizing the motion of the wave packets for the two branches of the interferometer do not close in phase space, an effect which increases significantly with the interferometer time. The relative displacement between the interfering wave packets in such open interferometers leads to a fringe pattern in the density profile at each exit port and a loss of contrast in the oscillations of the integrated particle number as a function of the phase shift. Paying particular attention to gravity gradients, we present a simple mitigation strategy involving small changes in the timing of the laser pulses which is very easy to implement. A useful representation-free description of the state evolution in an atom interferometer is introduced and employed to analyze the loss of contrast and mitigation strategy in the general case. (As a by-product, a remarkably compact derivation of the phase-shift in a general light-pulse atom interferometer is provided.) Furthermore, exact results are obtained for (pure and mixed) Gaussian states which allow a simple interpretation in terms of the alignment of Wigner functions in phase-space. Analytical results are also obtained for expanding Bose-Einstein condensates within the time-dependent Thomas-Fermi approximation. Finally, a combined strategy for rotations and nonaligned gravity gradients is considered as well.Comment: 14+7 pages including appendices, 9 figures; v2 minor changes, matches published versio

On the Squeezed Number States and their Phase Space Representations

We compute the photon number distribution, the Q distribution function and the wave functions in the momentum and position representation for a single mode squeezed number state using generating functions which allow to obtain any matrix element in the squeezed number state representation from the matrix elements in the squeezed coherent state representation. For highly squeezed number states we discuss the previously unnoted oscillations which appear in the Q function. We also note that these oscillations can be related to the photon-number distribution oscillations and to the momentum representation of the wave function.Comment: 16 pages, 9 figure