Motivations for a New Experiment

Intensity Enhancement Cavity

MOT Laser

References[1] S.K. Dutta et al., PRL 85, 5551-5554(2000)[2] K.C. Younge et al., New J. Phys. 12, 023031(2010)

[3] K.C. Younge et al., PRL 104, 173001(2010)[4] S.E. Anderson et al., PRL 107, 263001(2011)

Laser Spectroscopy of Rydberg Atoms in Deep Optical LatticesYun-Jhih Chen and Georg Raithel

University of Michigan, Ann Arbor USA

Various cavity modes captured by an IR camera. Only the Gaussian TEM00 mode is used at this time.

lattice laser

The concentric cavity will be later inserted into a one foot tall ultra-high vacuum chamber. The fab-rication of the chamber and most of its attach-ments has been completed. Presently, we are working on the final integration of all components of the experiment.

We have recently built two amplified 780nm distributed Bragg reflector (DBR) laser systems as our MOT lasers. The lasers are compact and movable, mode-hop-free, and insensitive to mechanical fluctuations.

External Chamber

Designed by Stefan Zigo

Tapered Ampli�er& Cooling Block

to Saturated Spectroscopy

extra entrance to TA

780nm DBR Laser Diode

Cylindrical Lens Galilean Telescope

piezo

λ/4

EOM

1064nmlaser

PDH detectorPID regulator

scope

phasemodulation

PID

beam

pro

�le

The cavity is locked to the laser.

top

bottom

Tripod

The bottom cavity mirror sits on a tripod. The cavity length can be adjusted by changing the position of the tripod. To enhance the stability, we have fabricated three aluminium mounts of different styles to achieve a stable position of the tripod. The method mimics the three-point contact design of a regular mirror mount.

mirror mount

cavity mirror

screw

plane-parallel confocal(L=R)

concentric(L=2R)

concave-convex

hemispherical

Stable cavities. Only the concentric cavity focuses at the center.

Pound-Drever-Hall TechniqueWe use the PDH technique to stabi-lize the cavity length relative to the 1064nm lattice laser (linewidth 100 kHz). The light reflected from the cavity is detected and mixed with the RF that drives the EOM. The mixer output is processed in a PID regulator. The PID output is applied to three piezos, which push one of the cavity mirrors and correct the cavity length. In practice, only one of the piezos is necessary for PDH stabilization. The other two piezos are separately controlled with DC signals to fine-tune the cavity.

The new POL experiment utilizes a concentric cavity to enhance the intensity of the lattice laser and to produce the optical lattice with required lattice depth. The concentric cavity is composed of two spherical mirrors with high reflectivity. The radius of curvature of the mirrors is 2.5cm, and hence the cavity length is 5cm. The calculated finesse of the cavity is about 600, so the laser intensity can be enhanced hundreds of times. The free spectral range and FWHM are about 3000 MHz and 5MHz, respectively.

Cavity Design

top view

MCP

Adiabatic Potentials Rydberg atoms in an optical lattice have three types of motion: the motion of the center of mass, the motion of the Rydberg electron relative to the core, and the quiver motion of the Rydberg electron. The time scales of each motion differ from the others by a factor of order 1000, so the adiabatic potentials can be numerically calculated by applying the Born-Oppenheimer approximation. The quiver motion generates a ponderomotive potential, which is added as a perturba-tion to the Rydberg electon’s Hamiltonian. Diagonalization yields the perturbed Rydberg energy levels, which depend on center-of-mass position (z0 in the figure). Plotting the energy levels vs z0 yields the adiabatic potentials that govern the center-of-mass motion.

relative motion

quiver motion(fastest)

center of mass

(slowest)

e- core

Adiabatic potentials for a Rydberg atom inside a 1D optical lattice with lattice depth 2 GHz [2]. Left:n=30. Right:n=45. mj is �xed to 2.5 in both plots. The wavefunction of each adiabatic potential is a superposition of states with di�erent angular momentum quantum number l.

IntroductionRydberg atoms are atoms in highly excited states. An optical trap for Rydberg atoms, which we refer to as a ponderomotive optical lattice (POL), was proposed in 2000 [1]. Unlike optical lattices for ground-state atoms, the lattice potential seen by a Rydberg atom is the ponderomo-tive potential of a free electron weighted by the Rydberg atom wave-function. Significant differences between a POL and a conventional op-tical lattice arise from the respective types of atom-field coupling and the giant size of Rydberg atoms.

The details of our current POL experiment can be found in refer-ences [3] and [4]. In order to resolve all the adiabatic potentials shown above, a lattice with depth of several GHz is necessary. Our

considerations are:1) We would like the separation between adiabatic po-tentials larger than excitation laser linewidth.2) The lattice must be deep enough to mix S and D states with the higher angular momentum states to make the adiabatic potentials accessible by our two-photon excitation.

In the new setup, the optical lattice will be produced inside an opti-cal resonator, which can easily provide a lattice depth of 10 GHz.

5P3/2

5S1/2

Ryd

480 nm

780 nm