Atomic interferometer measurements of Berry's and Aharonov-Anandan's phases for isolated spins S > 1/2 non-linearly coupled to external fields

The aim of the present paper is to propose experiments for observing the significant features of Berry's phases for S>1, generated by spin-Hamiltonians endowed with two couplings, a magnetic dipole and an electric quadrupole one with external B and E fields, as theoretically studied in our previous work. The fields are assumed orthogonal, this mild restriction leading to geometric and algebraic simplifications. Alkali atoms appear as good candidates for interferometric measurements but there are challenges to be overcome. The only practical way to generate a suitable E-field is to use the ac Stark effect which induces an instability of the dressed atom. Besides atom loss, this might invalidate Berry's phase derivation but this latter problem can be solved by an appropriate detuning. The former puts an upper limit to the cycle duration, which is bounded below by the adiabatic condition. By relying upon our previous analysis of the non-adiabatic corrections, we have been able to reach a compromise for the $^{87}$Rb hf level F=2, m=0 state, which is our candidate for an interferometric measurement of the exotic Berry's phase generated by a rotation of the E-field around the fixed B-field. By a numerical simulation we have shown that the non-adiabatic corrections can be kept below the 0.1% level. As an alternative candidate, we discuss the chromium ground state J=S=3, where the instability problem is easily solved. We make a proposal to extend the measurement of Aharonov-Anandan's phase beyond S=1/2 to the $^{87}$Rb hf level F=m=1, by constructing, with the help of light-shifts, a Hamiltonian able to perform a parallel transport along a closed circuit upon the density matrix space, without any adiabatic constraint. In Appendix A, Berry's phase difference for S=3/2 and 1/2, m=1/2 states is used to perform an entanglement of 3 Qbits.Comment: 23 pages, 6 figures, modifications in the introduction, two paragraphs adde

Counting atoms

partially_open2articolo su invitoopenMassa, Enrico; Mana, GiovanniMassa, Enrico; Mana, Giovann

Exact Foldy-Wouthuysen transformation for spin 0 particle in curved space

Up to now, the only known exact Foldy- Wouthuysen transformation (FWT) in curved space is that concerning Dirac particles coupled to static spacetime metrics. Here we construct the exact FWT related to a real spin-0 particle for the aforementioned spacetimes. This exact transformation exists independently of the value of the coupling between the scalar field and gravity. Moreover, the gravitational Darwin term written for the conformal coupling is one third of the relevant term in the fermionic case.Comment: 10 pages, revtex, improved version to appear in Phys. Rev.

Pseudo-forces in quantum mechanics

Dynamical evolution is described as a parallel section on an infinite dimensional Hilbert bundle over the base manifold of all frames of reference. The parallel section is defined by an operator-valued connection whose components are the generators of the relativity group acting on the base manifold. In the case of Galilean transformations we show that the property that the curvature for the fundamental connection must be zero is just the Heisenberg equations of motion and the canonical commutation relation in geometric language. We then consider linear and circular accelerating frames and show that pseudo-forces must appear naturally in the Hamiltonian.Comment: 6 pages, 1 figure, revtex, new section added, to appear in PR

Does Quantum Mechanics Clash with the Equivalence Principle - and Does it Matter?

With an eye on developing a quantum theory of gravity, many physicists have recently searched for quantum challenges to the equivalence principle of general relativity. However, as historians and philosophers of science are well aware, the principle of equivalence is not so clear. When clarified, we think quantum tests of the equivalence principle won't yield much. The problem is that the clash/not-clash is either already evident or guaranteed not to exist. Nonetheless, this work does help teach us what it means for a theory to be geometric.Comment: 12 page

Spin, gravity, and inertia

The gravitational effects in the relativistic quantum mechanics are investigated. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. As a direct application, we analyze the non-relativistic limit of the theory. The new term describing the specific spin (gravitational moment) interaction effect is recovered in the Hamiltonian. The comparison of the true gravitational coupling with the purely inertial case demonstrates that the spin relativistic effects do not violate the equivalence principle for the Dirac fermions.Comment: Revtex, 12 pages, no figures, accepted in Phys. Rev. Let

Spin-gravity coupling and gravity-induced quantum phases

External gravitational fields induce phase factors in the wave functions of particles. The phases are exact to first order in the background gravitational field, are manifestly covariant and gauge invariant and provide a useful tool for the study of spin-gravity coupling and of the optics of particles in gravitational or inertial fields. We discuss the role that spin-gravity coupling plays in particular problems.Comment: 18 pages, 1 figur

Quantum Theory in Accelerated Frames of Reference

The observational basis of quantum theory in accelerated systems is studied. The extension of Lorentz invariance to accelerated systems via the hypothesis of locality is discussed and the limitations of this hypothesis are pointed out. The nonlocal theory of accelerated observers is briefly described. Moreover, the main observational aspects of Dirac's equation in noninertial frames of reference are presented. The Galilean invariance of nonrelativistic quantum mechanics and the mass superselection rule are examined in the light of the invariance of physical laws under inhomogeneous Lorentz transformations.Comment: 25 pages, no figures, contribution to Springer Lecture Notes in Physics (Proc. SR 2005, Potsdam, Germany, February 13 - 18, 2005

Atom Interferometers

Interference with atomic and molecular matter waves is a rich branch of atomic physics and quantum optics. It started with atom diffraction from crystal surfaces and the separated oscillatory fields technique used in atomic clocks. Atom interferometry is now reaching maturity as a powerful art with many applications in modern science. In this review we first describe the basic tools for coherent atom optics including diffraction by nanostructures and laser light, three-grating interferometers, and double wells on AtomChips. Then we review scientific advances in a broad range of fields that have resulted from the application of atom interferometers. These are grouped in three categories: (1) fundamental quantum science, (2) precision metrology and (3) atomic and molecular physics. Although some experiments with Bose Einstein condensates are included, the focus of the review is on linear matter wave optics, i.e. phenomena where each single atom interferes with itself.Comment: submitted to Reviews of Modern Physic