Making Atoms Jump Through Hoops

Kristian Helmerson

Rodrigo G. Cortiñas

The authors propose a laser tweezer configuration that can trap a Rydberg atom by exploiting the size and geometry of its wave function. The trap, which can naturally trap ground-state atoms too, can be tuned to put the Rydberg state in a highly quantum hula-hoop-like motion.

S. M. Barnett

Edward H. Kerner, Garold Murdachaew

Expanding on earlier work, it is shown how to rewrite the non-relativistic problem of two particles coupled by a spring as one higher-order one-particle (HOOP) problem, which then can be elevated to be Lorentz covariant. The higher-order Lagrangian is then developed into an Ostrogradsky Hamiltonian format, from which canonical commutation rules are invoked and a relativistic wave equation produced. Within the centre-of-momentum frame of reference, the latter is reduced to a radial Schrödinger equation that is solved numerically, with a display of radial eigenfunctions that are compared with non-relativistic ones. The details of this example illustrate conclusively how the HOOP approach to direct-interaction many-particle relativistic dynamics works.

Howard M. Wiseman, Gilman E. S. Toombes

A strongly-driven ($Ω>> γ$) two level atom relaxes towards an equilibrium state rho which is almost completely mixed. One interpretation of this state is that it represents an ensemble average, and that an individual atom is at any time in one of the eigenstates of $ρ$. The theory of Teich and Mahler [Phys. Rev. A 45, 3300 (1992)] makes this interpretation concrete, with an individual atom jumping stochastically between the two eigenstates when a photon is emitted. The dressed atom theory is also supposed to describe the quantum jumps of an individual atom due to photo-emissions. But the two pictures are contradictory because the dressed states of the atom are almost orthogonal to the eigenstates of $ρ$. In this paper we investigate three ways of measuring the field radiated by the atom, which attempt to reproduce the simple quantum jump dynamics of the dressed state or Teich and Mahler models. These are: spectral detection (using optical filters), two-state jumps (using adaptive homodyne detection) and orthogonal jumps (another adaptive homodyne scheme). We find that the three schemes closely mimic the jumps of the dressed state model, with errors of order $(3/4) (γ/Ω)^{2/3}$, $(1/4) (γ/Ω)^{2}$, and $(3/4) (γ/Ω)^{2}$ respectively. The significance of this result to the program of environmentally-induced superselection is discussed.

John Maddox