ANAMORPHIC PRISM PAIRSATURATED ABSORPTION SPECTROSCOPYABSTRACT

MOTIVATION

Saturated absorption laser spectroscopy of potassium-39 vapor as a preliminary to achieving Bose-Einstein condensation

Julie M. Gillis, Robert W. A. Brooke, Christopher A. Zaccagnini, Theodore A. Corcovilos

Department of Physics, Duquesne University, Pittsburgh, PA 15282

Saturated absorption spectroscopy is an effective and reliable technique that is used frequently in atomic and optical physics in order to precisely measure the hyperfine energy structure of atoms, such as the alkali metals that are used in laser-cooling experiments. We present an effective optical design to measure the D2-line of potassium-39 at 766.700 921 nm (near infrared) that can be used to frequency-lock our laser diode with 6 MHz (~10 ppb) accuracy. Counter-propagating laser beams are passed through an atomic vapor cell of 39K to obtain sub-Doppler resolution peaks of the excited atoms. The design consists of several optical components including the introduction of an anamorphic prism pair to optimize the beam shape and a set of telescoping lenses for magnification and collimation of the beam.

In order to efficiently trap and cool neutral potassium-39 atoms to the micro-Kelvin temperatures required as a precursor to creating Bose-Einstein condensates, a high-frequency stability laser system design was required. The initial temperature of the atoms is approximately 50oC (323 K). A magneto-optical trap (MOT) is responsible for the initial cooling step. In order for the MOT to be effective, the optical frequency of our commercial diode laser (Moglabs 767AR150) must be accurate and stable at 766.700921 nm ± 0.000004 nm. The use of an interferometric wavemeter provides a coarse wavelength measurement of the laser diode to within the Doppler-broadened atomic linewidth resolution of 0.8 GHz. Saturated absorption spectroscopy of the 39K D2-line further improves the resolution of the

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MAGNETO-OPTICAL TRAP

BEAM SHAPE MEASUREMENTS

The magneto-optical trap utilizes a combination of l a s e r b e a m s a n d spatially-varying magnetic fields. Six laser beams (two counter-propagating along each axis) pass through a sample of atoms. The atoms absorb resonant photons from the laser beams and then emit a photon in a randomdirection. Each absorption and emission changes the momentum of the atom by h/λ. We can pick the polarization of the beams to ensure that the atoms are resonant with the lasers opposing their motion.  This permits the atoms to be cooled to the Doppler cooling limit which is proportional to the natural linewidth. For K-39 atoms, we expect the MOT to reach a limit of approximately 300 μK[3]. A quadrupole magnetic field is formed by the addition of a pair of coils arranged in an anti-Helmholtz configuration. The magnetic field shifts the resonance frequency of the atoms by the Zeeman effect. This pushes the atoms towards the center of the field, effectively trapping them in a 3-D space.

In order to obtain the final level of precision f o r t h e f r e q u e n c y m e a s u r e m e n t s necessary for the MOT, we utilize saturated a b s o r p t i o n l a s e r spectroscopy to obtain a D o p p l e r - f r e e spec t rum. A weak probe beam and a strong pump beam are formed by dividing the power of the initial laser beam with a beam splitter. The probe and the pump beams have the same frequency and counter-propagate through the K-39 vapor cell. The pump beam interacts only with atoms of velocity v=ω-ω0/k. These atoms are excited, leaving a

frequency measurement to allow stabilization of the laser diode to within the natural linewidth of the atomic resonance (Γ= 6 MHz)[1]. With this resolution, the laser diode will be sufficiently stable to laser cool atoms in the MOT.  

Schematic diagram of MOT with the six laser beams depicted in red and the magnetic coils in blue. Adopted from [2].

We characterized the shape of the laser beam using the knife-edge method. The total power of the beam was measured by a power meter as a razor blade, a t tached to a ca l ib ra ted translation stage, was moved through the beam path. The power with respect to the

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position is given by the equation:    P0   is   the initial power, x0 is the position of the beam center, and w is the 1/e2 beam radius. We performed a chi-square fitting on the collected data in Excel. Our data show an elliptical beam shape with a horizontal diameter of 1.108 mm ± 0.008 mm and a vertical beam diameter of 2.502 mm ± 0.014 mm. (See graphs to right).

Top right: Schematic diagram of SAS set-up. Adapted from [4].Right: Laboratory set-up o f t h e s a t u r a t e d absorption spectroscopy optical design. Below: Beam shape measurement data plots and best fit lines.

Laboratory set-up of the knife- edge measurement apparatus.

Top: Saturated absorption spectroscopy population density diagram. Adopted from [3].Bottom: Ideal example of expected SAS results, based on transition linewidths provided in [1].

deficit of atoms in the ground state with velocity v. Atoms with velocity near zero with interact with both of the counter propagating beams if and only if the laser frequency is close to resonance (ω ≈ ω0). The “hole” in the lower level population created by the pump beam reduces the absorption of the probe beam for atoms at that specific velocity, and a narrow peak in the transmitted intensity of the probe beam can be seen.

The optical design of o u r s a t u r a t e d a b s o r p t i o n spectroscopy utilizes a series of mirrors, beam splitters, and l e n s e s . A b e a m sampler t ransmits most of the power a long the beam’s initial path for use in the laser coo l ing apparatus. A small fraction (~5%) of the total power is used for t he spec t roscopy measurements. A 4× telescope (lenses of focal lengths, f1= 50

OPTICAL DESIGN

mm and f2=200 mm), increases the beam radius to ~10mm to maximize the number of atoms in the vapor cell that interact with the laser. The beam is split into three paths. A small portion of the light (~10%) is transmitted through the potassium vapor cell as the probe beam. An identical beam follows a parallel path through the cell as the reference beam. The majority of the power from the initial beam enters the vapor cell along the same path as the probe beam, but in the opposite direction, becoming the pump beam. The probe and reference beams end at a differential photodetector, which measures the difference in light intensity between the two beams. The wavelength of the laser may be scanned by varying the laser diode  

Because the output of t h e l a s e r h a s a n elliptical cross section (see data in bottom center column), an anamorphic prism pair is used to change the shape of the beam. Circular beams are

[1] Tobias G. Tiecke. Properties of Potassium. van der Waals-Zeeman institute, University of Amsterdam, 2010.[2] Vescent Photonics. Denver, 2014. www.vescent.com/applications/cold-atom-science/[3] Christopher J. Foot. Atomic Physics (Oxford University Press, Oxford, 2005.)[4] M. Pichler and D. C. Hall. Simple laser frequency locking based on Doppler-free magnetically induced dichroism. Optics Communications, 285, 2012.[5] C.J Hawthorn, K.P. Weber, and R.E Scholten. Review of Scientific Instruments. 72.12. December 2001.

•  Bayer School of Natural and Environmental Sciences

•  Duquesne University Department of Physics

ACKNOWLEDGEMENTS

REFERENCES

•  Duquesne Faculty Development Fund

•  Duquesne University Undergraduate Research Program

CONCLUSIONS AND FUTURE WORKWe are currently waiting for the parts of the interferometric wavemeter to be machined. Once we have those components, the wavemeter will be assembled and we will be able to measure the wavelength of the commercial diode laser within the Doppler-broadened atomic linewidth. Within this parameter, we will be able to efficiently use the saturated absorption spectroscopy set-up to lock the laser to a frequency within the natural linewidth of the D2-line of the K-39 atoms. When these measurements are completed, the next step in our lab will be to design and build the components for the magneto-optical trap, including the vacuum system in which the atoms will eventually be contained. Our long-term goal is to model the interfaces of different materials with ultracold atoms in two-dimensions and eventually, in three-dimensional lattices.

SolidWorks design of interferometric wavemetwer.

Extended Cavi ty Diode Laser:Later on, we will be u s i n g s i m i l a r techniques with a diode laser with a w a v e l e n g t h o f approximately 400 nm to reach the final leve ls o f coo l ing ( n a n o - K e l v i n temperatures). This  

preferable in laser optics because it reduces aberrations, particularly astigmatism. The anamorphic prism pair magnifies the beam along the horizontal direction only, leaving the vertical direction unchanged. For our laser beam, we had to increase the horizontal dimensions of the beam in order to make it spherical. The prisms we used were made from N-SF11 glass which has an index of refraction of 1.7667 for our wavelength of 766.7 nm. In order to achieve the necessary 2.5x magnification, we had to determine the correct orientation angles for the prisms. Using mathematics software (Maple) we created a program that calculates the angles based on the wavelength of the laser, magnification desired, and the index of refraction at the given wavelength

laser system will need to be accurate within a linewidth of 100 kHz. In order to obtain this level of precision, an extended cavity diode laser was designed to obtain optimal mechanical and thermal stability, with a low-noise current driver circuit to power the laser. Using techniques to eliminate the thermal expansion of the materials and the placement of a Peltier device beneath the copper block in which the laser diode will be clamped, maximum thermal stability is achieved. The ECDL system is enclosed in an aluminum box in which a Fabry-Perot cavity is created between a diffraction grating (pitch = 1200 lines/mm) and the diode. The design is adapted from the Littrow configuration[5].

current and the p o s i t i o n o f a diffraction grating, resul t ing in an a b s o r p t i o n spectrum of the potassium vapor with the Doppler b r o a d e n e d b a c k g r o u n d removed.

Top view of SolidWorks design of extended cavity diode laser (ECDL) system with beam transmission.

Diagram of anamorphic prism pair alignment with laser beam expansion along the horizontal axis.

288.6  MHz   171.3  MHz  

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