Single site addressability using ultra-cold Rydberg atoms

Experiment: Richard Abel, Christopher Carr, Ulrich Krohn and Charles Adams

Figure 1: Single site adressability experiment outline Outline
The aim of this project is to address atoms stored in a single site of an optical lattice. Since the separation of the individual lattice sites are on the order of μm an approach using optical methods for the addressing are unpractical due to the necessity of very tightly focused beams

In our experiement we hope to exploit the properties of Rydberg atoms to address a single optical lattice site. Rydberg atoms are atoms where at least one electron is excited into a state with a high principal quantum number. Due to the large "distance" between the electron and the atom core a Rydberg atom has a large polarisability which scales with the seventh power of the principal quantum number. This large polarisation makes Rydberg atoms extremely sensitive to electric fields, allowing large Stark shifts to be produced. If a spatially varying electric field is applied the Stark shift will change across the optical lattice, as shown in the digram in figure 1. The engergy of the Rydberg states (ΔV) will be shifted so that only atoms at the target lattice site are on resonace with the Rydberg excitation laser, thus allowing only that lattice site to be addressed. Using this scheme we hope to create a lattice site selective Raman transfer between ground state hyperfine levels similar to that proposed by M. Müller et al. in [1]. If Raman beams are applied to the entire lattice, population is transfered from one ground state hyperfine level to the next via an intermediate state. At the addressed lattice site the Ryderg excitation laser in on resonace producing a dark intermediate state. This will create a suppression of the Raman transfer at the addressed site which can be obsereved using state selective excitation.

Figure 2: Stark map for a Rydberg D-state with n=46
By exploiting the dc-Stark effect of Rydberg atoms it is possible to induce an energy shift of the atomic levels dependent on the applied external electic field. Figure 2 shows a measurement of the energy levels of a Rydberg D-state for a principal quantum number n=46. It can be seen that for moderate electric fields the energy levels are shifted by tens of MHz.

Figure 3: Electric field magnitude and Stark shift calculation for n=70
We aim to exploit this effect using a varying electric field applied over the atomic cloud. In order to create the required electric field gradient we will use four rod shaped elecrodes built into the vacuum chamber. These electrodes can be independently set to different voltages to create the required electric field. Figure 3 shows a calculation fof the electric field in the vacuum chamber and the corresponding Stark shift experienced by the 70S1/2 Rydberg state. Using this state two adjacent lattice sites around E=0 are shifted by Δ=1.9 MHz out of laser resonance and are not excited if the linewidth of the Rydberg excitation laser is on the order of few hundred kHz.

Figure 4: Vacuum chamber with electrode rods visible and CCD image of atoms in the MOT

Figure 5: Revelevent Rubidium 87 energy levels and required transitions
Current progress
A vaccuum chamber has been built for the experiement and a standard 6 beam Rb87; MOT produced as shown in the figure 4. The vacuum chamber features 12 C16 viewports and a 70 mm (NA=0.78) custom made viewport [2] to allow a large collection of light for imaging.
The MOT is directly loaded from the background pressure created by two Rubidium dispensers. The MOT and lattice beams are brought to the chamber using polarisation mainting fibres. The fibre couplers are directly connected to the chamber and assembled with additional optical elements in a cage system to ensure the spatial stability of the lattice sites with respect to the electric field gradient.

The Rydberg excitation and Raman transfer scheme require lasers stabilised to the transitions shown in the energy level diagram in figure 5. All light at 780 nm is derived from a master diode laser (Toptica DL Pro) stabilised using modulation transfer spectroscopy [4]. The repump light and phase stable Raman beams are generated from this laser using an EOM and Faraday filter [5]. The Rydberg excitation laser is provided by a frequency doubled diode laser at 480 nm (Toptica SHG) and stabilised using a cascade EIT technique [6].

Faraday dichroic beam splitter for Raman light using an isotopically pure vapor cell
Light from the stabilised mater laser is passed through an electro-optic modulator (EOM), which adds sidebands at 6.968 GHz onto the light. The carrier frequency is seeded into a slave laser and shifted by an acousto optical modulator (AOM) to be on resonance with the F=2 to F'=3 transition in 87Rb to serve as MOT cooling and resonant probe light. The sidebands on the light have, after passing through an AOM, the correct frequency to serve as repump and Raman light on the F=1 to F'=2 transition. However, since the EOM produces sidebands with only about 2 % efficiency, it is necessary to seed the sideband light into a slave laser. To ensure that the slave laser is seeded by only the sideband light we must separate it from a beam which also contains the carrier light. We have achieved this by developing a Faraday separator technique that is described in [4].

The Faraday effect in a thermal vapour cell produces a frequency dependent rotation in the polarization of light entering the cell. This rotation in polarization can be tuned so that the carrier and sideband frequencies produced by the AOM have orthogonal polarizations and can be separated by a polarising beam splitter cube. The figure oposite shows the input light containing both sideband and carrier frequencies in panel (a). The remaining two panels show the two outputs of the beam splitter, clearly showing the the carrier and sidebands are separated. These beams now have the required optical purity to seed slave lasers.

Figure 6: Fabry-Perot etalon signals (a) with the filter turned off and at the two ouput ports (b) and (c).

Laser stabilisation to excited state transitions using electromagnetically induced transparency:
In order to stabilise a laser to the excited state to Rydbergy state transition an alternative to the familiar laser locking techniques must be used. Typically lasers are locked to a transition from a highly populated ground state or where there is a large Einstein A-coefficient to provide an absorption signal. To lock our Rydberg laser we have developed a scheme based on atomic coherences allowing locking to excited-excited state transitions with no population in either state. Electromagnetically induced transparency in a thermal vapour is used to transfer information about a weak excited-excited state transition to a much stronger probe transition.

A schematic of our locking setup is shown in the diagram in figure 7. A stabilized 780 mn probe beam and 480 nm coupling beam are counter propagated through a vapour cell to provide an EIT reference. To produce an error signal FM spectroscopy is used. The prode beam is modulated to produce sidebands above and below the EIT signal. These sidebands then beat with the probe beam to produce a detector signal at the modulation frequency. Using a phase sensitive detection scheme dispersion and absorption components can be recovered to form an error signal.

Examples of the error signals produced are shown opposite. The coupling beam is tuned to the (a) 26D and (b) 70S Rydberg states and scaned through resonace. A large error signal is produced at modest laser powers and is ideal for locking. This technique has been successfully used in an experiement on EIT in cold Rydberg ensambles described in [5].
Figure 7: EIT locking schematic setup

Figure 8: Error signals with the coupling beam tuned to the (a) 26D and (b) 70S Rydberg state amd scanned through resonance
References & Links
[1] M Müller et al. PRL 102, 170502 (2009)
[2] K Weatherill et al. Rev. Sci. Instrum. 80, 026105 (2009)
[3] D J McCarron et al. Meas. Sci. Technol., 19, 105601 (2008)
[4] R P Abel et al. Opt. Lett., 34, 3071 (2009)
[5] R P Abel et al. Appl. Phys. Lett. 94, 071107 (2009)
[6] K J Weatherill et al.J Phys B-At Mol Opt Phys 41, 201002 (2008)

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Content © Ulrich Krohn and Richard Abel, University of Durham 2009