Ponderomotive Optical Lattice Trap for Rydberg Atoms
Georg Raithel lab, University of Michigan
Participating Students: Yun-Jhih Chen, Kaitlin Moore, Andira Ramos
(Illustration credit: Kelly Younge)
The project's main experimental accomplishments are described below.
Establishing the existence of ponderomotive optical lattice:
The ponderomotive optical lattice for Rydberg atoms should have unique state-dependent trapping potentials. To demonstrate that the ponderomotive optical lattice exists and behaves as expected, we have investigated the state-dependence of the ponderomotive level shift for Rydberg atoms in a
one-dimensional optical lattice (periodicity 532 nm, laser wavelength 1064 nm). In the experiment, we drove two-photon microwave
transitions between neighboring Rydberg S states in the lattice. A resultant microwave spectra is shown below
for the case of 50S → 51S. The top spectrum is for the case of no lattice, and the bottom spectrum is for the case with the lattice on. A numerical simulation reproduces our data closely (green solid line).
With the lattice on, the microwave spectra display three features, labeled A, B, and C, which indicate three types of atomic trajectories in the lattice. Atomic trajectories that contribute to feature A are from atoms with little energy that are excited to maxima of the lattice potentials, where they spend the majority of the
experiment. Feature B is due to atoms that are excited with enough energy to roam over several wells during
the experiment. Finally, atoms contributing to feature C are excited partway down the lattice wells due to the
linewidth of the excitation laser. They are excited without enough energy to escape the well and hence oscillate within one well for the duration of the experiment. Signal C is therefore our trapped atom signal, and we estimate here that we have a trapping efficiency of a few percent. The numerical simulation also supports our interpretations of the data.
The bottom line: These experimental microwave spectroscopy results provide the first evidence for the ponderomotive optical
lattice for Rydberg atoms, and we found close agreement between experiment and theory.
The results also highlight the potency of microwave spectroscopy as a method for probing the
lattice's trapping effectiveness. More details concerning our investigation of the state-dependence of the Rydberg-trapping potential in the lattice can be found at Phys. Rev. Lett. 104, 173001 (2010).
Improving the lattice's trapping efficiency:
While our spectroscopic results offered positive support for the existence of the ponderomotive optical lattice, the results
also indicated that the number of trapped atoms was limited to ~5% (in other words, signal C above is our smallest signal).
The limitation is due to the excitation scheme in which the majority of atoms are excited to maxima in the
Rydberg-trapping potential, as depicted below. This excitation scheme arises from the fact that for our
red-detuned lattice, the atoms are anti-trapped in the Rydberg state in the locations where they are trapped in the ground state.
In order to overcome this difficulty, we have implemented a lattice inversion technique. Immediately after Rydberg-atom excitation, the lattice is inverted, resulting in a Rydberg-atom trapping potential that has
minima co-located with the Rydberg atoms. We investigate the effect of a lattice inversion on the Rydberg-atom trapping efficiency of the optical lattice using microwave spectroscopy of the 50S → 51S transition.
The figure above presents experimental microwave spectroscopy results both with and without a lattice inversion. In the top spectrum, which corresponds to a complete lattice inversion, the spectral signal is almost entirely C-component. Since the C-component presents a qualitative measure for the fraction of trapped atoms, the top
spectrum demonstrates that the fully inverted lattice forms a highly efficient Rydberg-atom trap. Simulations indicate that the inverted lattice has a Rydberg-atom trapping efficiency of 90%.
The bottom line: This work provides the first demonstration of a highly effient optical Rydberg trap, paving the way for employment of the trap in applications such as quantum computing or high-precision spectroscopy. Further experimental details can be found at Phys. Rev. Lett. 107, 263001 (2011).
Investigating the angular dependence of the lattice's trapping potentials:
Measuring the lattice-induced lightshift
The potentials experienced by Rydberg atoms in the optical lattice depend on how the Rydberg wavefunctions overlap with the lattice wells. The angular dependence of the potentials therefore arises from the shape of the Rydberg wavefunction and its orientation relative to the lattice axis. A Rydberg state whose wavefunction is elongated in the direction transverse to the lattice axis will experience more deeply modulated lattice potentials than states elongated in the direction of the lattice axis. This is because the first case is able to average over more of the free electron ponderomotive potential. In order to characerize the angular dependence of the Rydberg-trapping potentials in the lattice, we have measured the lattice modulation depth for various angular sublevels of Rydberg nD states.
In order to investigate the angular sublevels of the nD states individually, we
applied a DC electric field to lift degeneracies. The figure on the left below shows
an optical excitation spectrum of the
50D level in both the lattice and the DC
field. The lattice-induced shifts in transition frequencies for the various angular components yield information on
the Rydberg modulation depth (kRyd)
for the different angular components.
The ground-state modulation depth
(k5S) is a known and fixed value. The
offset (ko) can be measured by inverting the lattice immediately before Rydberg excitation.
An optical excitation spectrum for one of
the angular components of the 50D level
is shown on the right above, for the cases of lattice inverted and lattice not inverted.
This spectrum illustrates how we may
obtain a measurement of kRyd from the
various lattice-induced shifts in transition frequency. From the measurement
of ko in the inverted lattice spectrum and
the known value of k5S, we may obtain
kRyd for this angular component. We then
repeat this procedure for various other
angular components of Rydberg D levels.
As demonstrated in our final measurement results shown below, we find the the Rydberg modulation
depths vary substantially for different angular states, and we also find that the measured values are in close agreement with calculated values.
The bottom line: While the angular dependence of optical lattice potentials for ground-state atoms is well known and widely utilized, our work provides the first experimental investigation of such dependence for Rydberg atoms. An understanding of this dependence is important for the trap to be employed in applications. For example, angular degrees of freedom could be used to tune the Rydberg trapping potentials as desired for specific applications.
Understanding the photoionization process:
Where photoionization happens within the atom
When electromagnetic radiation induces atomic transitions, the size of the atom is usually much smaller than the wavelength of the radiation, allowing the spatial variation of the radiation field's phase to be neglected in the description of transition rates. Somewhat unexpectedly, this approximation, known as the electric dipole approximation, is still valid for the ionization of micrometre-sized atoms in highly excited Rydberg states by laser light with a wavelength of about the same size. In this experiment we employed a standing-wave laser field as a spatially resolving probe within the volume of a Rydberg atom to show that the photoionization process only occurs near the nucleus, within a volume that is small with respect to both the atom and the laser wavelength. This evidence resolves the apparent inconsistency of the electric dipole approximation's validity for photoionization of Rydberg atoms, and it verifies the theory of light-matter interaction in a limiting case. This work was published in Nat. Comm. 4, 2967 (2013).
The bottom line: We have provided direct experimental evidence that the photoionization process occcurs near the nucleus in a Rydberg atom.
Driving Rydberg-Rydberg transitions with POL modulation:
Driving Rydberg-Rydberg transitions with lattice amplitude modulation
The model describing spectroscopy includes a multipole-field interaction, which leads to established spectroscopic selection rules, and the ponderomotive interaction, which is quadratic in the field and often neglected. We have demonstrated spectroscopy using the ponderomotive interaction by using ponderomotive-optical-lattice-trapped Rydberg atoms, pulsating the lattice light at a microwave frequency, and driving a 58S-59S microwave atomic transition that would otherwise be forbidden by established spectroscopic selection rules (Phys. Rev. A 75, 053401 (2007)). The peak showing that transition as a function of modulation frequency is shown in part a of the figure below (part b shows a two-photon reference line).
Driving transitions between Rydberg states
in this manner additionally combines the spectral resolution of microwave spectroscopy with the spatial resolution of optical spectroscopy. Results have been posted at
arXiv 1409.4087 and are under consideration for peer-reviewed publication.
The bottom line: We have driven Rydberg-Rydberg transitions using a fundamentally new form of spectroscopy.
Driving Rydberg-Rydberg transitions with higher harmonics of lattice amplitude modulation
We have recently driven Rydberg-Rydberg transitions with higher harmonics in the lattice amplitude modulation. This intrinsic frequency upconversion enables us to access much higher-frequency transitions than our microwave equipment would otherwise be able to drive. Preliminary analysis of these results indicates that we may use this feature of ponderomotive spectroscopy to access high-frequency transitions with low measurement uncertainty, which will be ideal for performing a new measurement of the Rydberg constant. Results are being submitted for publication, so check back soon!
A cloud of atoms from our magneto-optical trap distorted into the shape of a Michigan 'M'.