Dirac sea and Rydberg atoms in weak optical fields: why antimatter matters

It turns out it is important to include positron Dirac sea into the relativistic (meaning starting from the Dirac equation) description of how Rydberg electrons respond to weak optical fields.

Yes, positrons were invented to avoid the collapse of electrons into the continuum of states below the rest-mass gap and that brilliant speculation led to the entire idea of experimentally-observed antimatter. And, yes, Rydberg electrons are non-relativistic (in fact, nearly classical) so why would they know about antimatter? Is not it surprising?  What we find is that in certain gauges one would fail to recover even the leading order of  the AC Stark effect without including antimatter.  Here is the link to the full paper, which has other goodies as well.

Dynamic polarizability of Rydberg atoms: applicability of the near-free-electron approximation, gauge invariance, and the Dirac sea, T. Topcu and A. Derevianko, Phys. Rev. A 88, 042510 (2013), http://arxiv.org/abs/1308.0573

Abstract: Ponderomotive energy shifts experienced by Rydberg atoms in optical fields are known to be well approximated by the classical quiver energy of a free electron. We examine such energy shifts quantum mechanically and elucidate how they relate to the ponderomotive shift of a free electron in off-resonant fields. We derive and evaluate corrections to the ponderomotive free-electron polarizability in the length and velocity (transverse or Coulomb) gauges, which agree exactly as mandated by the gauge invariance. We also show how the free electron value emerges from the Dirac equation through summation over the Dirac sea states. We find that the free-electron ac Stark shift comes as an expectation value of a term proportional to the square of the vector potential in the velocity gauge. On the other hand, the same dominant contribution can be obtained to first order via a series expansion of the exact energy shift from the second-order perturbation theory in the length gauge. Finally, we numerically examine the validity of the free-electron approximation. The correction to the free-electron value becomes smaller with increasing principal quantum number, and it is well below a percent for 60s states of Rb and Sr away from the resonances.

Related posts:

  1. Magic Rydberg
  2. Tug-of-war model and tuned-out Rydberg
  3. Tutorial on translating particle physics effective Lagrangians to conventional atomic physics and quantum chemistry operators
  4. Fundamental physics at the precision frontier: questions to ponder

Magic Rydberg

 

Rydberg electron in circular orbit can be attracted to laser intensity maxima. Thereby a laser beam can serve as a tractor beam for cold Rydberg atoms.

Rydberg atoms in circular states can be attracted to laser intensity maxima. Thereby a laser beam can serve as a tractor beam for cold Rydberg atoms.

Here is our recent paper  on the possibility of decoherence-free design of quantum gates mediated by Rydberg-excited neutral atoms. This quantum computing architecture utilizes atoms  trapped in optical fields, e.g., in optical lattices. In order to reduce motional dephasing we determine trapping conditions where AC Stark shifts of both ground and Rydberg levels are the same (so-called magic trapping).

 

 

 

Intensity landscape and the possibility of magic trapping of alkali Rydberg atoms in infrared optical lattices, T. Topcu and A. Derevianko, arxiv.org:1305.6570

Motivated by compelling advances in manipulating cold Rydberg  atoms in optical traps, we consider the effect of large extent of Rydberg electron wave function on trapping potentials. We find that when the Rydberg orbit lies outside inflection points in laser intensity landscape, the atom can stably reside in laser intensity maxima. Effectively, the free-electron  polarizability of Rydberg electron is modulated by intensity landscape and can accept both positive and negative values. We apply these insights to determining magic wavelengths for Rydberg-ground-state transitions for alkali atoms trapped in infrared optical lattices. We find magic wavelengths to be around 10 um, with exact values that depend on Rydberg state quantum numbers.

This result is somewhat unusual and more details can be found in this talk (link to pdf)  given at the Dresden workshop on ultracold Rydberg physics.

UPDATE: published: Phys. Rev. A 88, 043407 (2013)

Related posts:

  1. Tug-of-war model and tuned-out Rydberg
  2. Dirac sea and Rydberg atoms in weak optical fields: why antimatter matters
  3. Research themes

Tutorial on translating particle physics effective Lagrangians to conventional atomic physics and quantum chemistry operators

Occasionally we have to carry out calculations with some effective Lagrangians
supplied by our particle physics friends (possibly related to new physics
beyond the standard model). For example, we could be given a Lagrangian density


where is some scalar field, is the Dirac field (electrons) and is a coupling constant. The Dirac equation that is conventionally used in atomic physics reads

(I suppress interactions of electrons with each other and with the nucleus). Given what is that extra operator that I would have to add to my Dirac Hamiltonian? I consistently derive in this tutorial (pdf).

For the impatient, the result is \begin{equation}
V^{\prime}\psi=-\gamma_{0}\left( \frac{\partial\mathcal{L}^{\prime}}
{\partial\bar{\psi}}-\partial_{\mu}\left( \frac{\partial\mathcal{L}^{\prime}
}{\partial\left( \partial_{\mu}\bar{\psi}\right) }\right) \right) .
\end{equation} Applications to axions and "Higgs portal" interactions are also covered in the tutorial (pdf).

Related posts:

  1. History of atomic physics at the University of Nevada, Reno
  2. Dirac sea and Rydberg atoms in weak optical fields: why antimatter matters
  3. Fundamental physics at the precision frontier: questions to ponder
  4. When would an unanticipated “new physics” event be apparent to an unsuspecting experimentalist?

Collaborative tools of the trade

I think you would agree that with recent introduction of cloud services collaboration has become easier.  Ftp/sftp/scp have become nearly obsolete. Here is a couple of tools that we find useful:

  1. Dropbox. This is a cloud file service. The first 2 Gb (which is a lot) are free. An essential tool for sharing projects between group members. Indispensible for  synchronizing files across various platforms, PCs, Macs, smartphones, ipads, etc. Five out of five stars.
  2. Mendeley. Bibliography manager. Free. Multiplatform. We share citations and papers (pdf's) between group members; anyone can add and modify references. Mendeley has a convenient option for exporting bibliography into latex .bib file (library.bib). At the moment flaky but still useful. Three out of five stars.

Related posts:

  1. Nature bibliography style bst-file with no URLs

Setting working directory in mathematica

One of mathematica annoyances when working with external files (various import/export functions), is that it defaults to the user's Documents directory. I usually keep the data/graphics files  in the same directory as the mmka notebook and its painful to specify the full path every time.

Here is a command that sets the working directory to the notebook directory.

SetDirectory[
DirectoryName[
ToFileName["FileName" /. NotebookInformation[SelectedNotebook[]]]]]

UPDATE: Easier (thanks Pedro!):
SetDirectory@NotebookDirectory[]

 

Related posts:

  1. How to dropbox on quicksilver using command line
  2. Collaborative tools of the trade
  3. Nature bibliography style bst-file with no URLs