Shannon K. Mayer
Department of Physics
Pacific Lutheran University
Tacoma, WA 98447
In recent years, the science community has witnessed an increase in research activities among faculty at primarily undergraduate institutions. In particular, there has been increased emphasis on providing meaningful on-campus research opportunities for undergraduate students. In this article I will address some of the unique features of research at an undergraduate institution and describe a tunable diode laser system used for laser cooling and trapping rubidium atoms in my research laboratory at Pacific Lutheran University.
The challenges associated with conducting research at an undergraduate institution are distinct from those encountered at a research university. The principal investigator must select a project that can be accomplished by the students, given their laboratory background, academic preparation, and the time constraints inherent to an undergraduate academic program. In addition, the intense academic-year teaching load and limited resources often encountered at primarily undergraduate institutions add to the challenge; the project must be tractable on a time-available basis and feasible at a reasonable cost. To help address these challenges organizations such as the Council on Undergraduate Research have emerged to encourage research involving students at undergraduate institutions and agencies such as Research Corporation have instituted grant programs specifically designed for these schools.
Faculty at undergraduate institutions who involve students in their work do so because we believe that undergraduate research is a crucial component in the development of physics students. It provides them with the opportunity to gain hands-on experience in a specific area of physics and demonstrates the practical relevance of concepts encountered in their coursework. Moreover, undergraduate research can be a transforming experience for students. By having an opportunity to struggle and successfully find the solution to a challenge encountered in the research laboratory, students learn to think creatively and gain confidence in their abilities as scientists.
Our role as the leaders of undergraduate research groups is fundamentally one of service to our students. Rather than involving students in research simply to gain from their contribution to the project, the goal is to ensure that the research experience is structured primarily for their benefit. I accomplish this in my laboratory in several ways. I seek to provide direction, clarification, and leadership for a project while empowering the student researcher to think and act independently. I incorporate as many practical skills into their work as possible, including training on proper use of machine shop tools, troubleshooting electronic circuits, and computer interfacing. To ensure the students have a firm grasp of the theoretical underpinnings of the research, we hold weekly group meetings to delve into theory and discuss salient papers. Finally, my students have opportunity to present their research results; in so doing they begin to see themselves in connection with the larger scientific community.
Laser cooling and magneto-optic trapping of neutral atoms, first demonstrated experimentally in 1987,1 is a relatively simple but effective tool for producing high-density (1010 atoms/cm3), low-temperature (< 20 mK) atomic samples. Trapped samples have been used for experiments in optical spectroscopy, microwave spectroscopy, and cold-atom collisions, and as a starting point for atom interferometry and Bose-Einstein condensation. Scientists Steven Chu, William Phillips, and Claude Cohen-Tannoudji received the 1997 Nobel Prize in physics for their work in developing the techniques of laser cooling and magneto-optic trapping.
Laser cooling and trapping neutral atoms is an experimental technique that is uniquely suitable for research at an undergraduate institution. The physics is engaging and intellectually accessible to the undergraduate student and the research provides exposure to a variety of experimental skills such as laser fundamentals, optical alignment techniques, electronic circuit design, and operation of a vacuum system. In addition, a trapped atomic sample can be achieved using apparatus that is relatively simple and reasonably inexpensive, and is therefore feasible for an undergraduate research program.
The research project underway in my laboratory involves construction of a vapor-cell magneto-optic trap (MOT)2,3 for rubidium atoms. A MOT relies on radiation pressure from three orthogonal pairs of counterpropagating laser beams to exert a force on the atom. By tuning the laser slightly below resonance, a moving atom will be Doppler shifted closer to resonance with one of the opposing beams and farther from resonance with the other. The imbalance in absorption probability provides a velocity-dependent force to damp the atoms’ velocity. Three-dimensional viscous confinement, designated “optical molasses,”4 provides an effective means for slowing atoms in the low-velocity tail of the Maxwell-Boltzmann distribution. However, no localization of position is inherent in the process. To generate a spatially dependent confining force, a weak, inhomogeneous magnetic field is added that Zeeman shifts the energy of the atomic sub-levels. Using a quadrupole magnetic field, which is zero at the intersection of the six laser beams and linearly increasing in each Cartesian coordinate direction, the Zeeman shift is a linear function of position. By using opposite circular polarizations in the counterpropagating laser beams, one can make the scattering force position dependent, thus trapping the atoms at the origin of the magnetic field.
The apparatus for the experiment consists of the vapor-cell MOT, tunable grating-feedback diode lasers, associated optics and electronics, and a CCD camera. The MOT consists of a small stainless steel vacuum chamber with six optical ports and a rubidium reservoir, an ion vacuum pump, and magnetic field coils. The magnetic field for the MOT is provided by a pair of anti-Helmholtz coils, located outside the trapping cell. The coils generate a spherical quadrupole field with a gradient of approximately 10 G/cm. The six trapping laser beams are supplied by a single diode laser, frequency stabilized slightly below the 5S1/2 F = 3 ® 5P3/2 F¢ = 4 hyperfine transition in rubidium (l = 780.24 nm). The six orthogonal beams, with appropriate circular polarization, intersect at the center of the MOT. A second laser, tuned to the 5S1/2 F = 2 ® 5P3/2 F¢ = 3 transition, repumps atoms lost to the F = 2 hyperfine ground state back into the cycling transition. Trap fluorescence is observed using a CCD camera.
A crucial component in laser cooling experiments is the laser system. This experiment uses a diode laser that has been modified by optical feedback from a diffraction grating.5 Diode lasers are particularly suitable for research at undergraduate institutions because they provide a simple, inexpensive alternative to traditional sources such as the titanium-sapphire laser. In addition, they are relatively student-user friendly and their limited output power minimizes laser safety concerns. There are a number of excellent review articles describing the use of diode lasers in atomic physics.6 Several diode laser characteristics pertinent to this project are described below.
The lasers used in this experiment are commercially available AlGaAs double heterostructure semiconductor devices with nominal room temperature emission in the 780-790 nm wavelength range.7 The typical operating output power is 20-50 mW. Double heterostructure devices consist of an undoped active region (AlyGa1-yAs) surrounded by an n-doped and p-doped region (AlxGa1-xAs, x>y). When a current is applied to the device, electrons are injected from the n-type layer into the active region. Simultaneously, a comparable density of holes is injected from the p-type region. The radiative recombination of the electrons and holes produces photons with an energy corresponding to the bandgap of the semiconductor. The laser “cavity” is created by cleaving the semiconductor along natural crystal planes. The difference in index of refraction between the active region (n~3.5) and the surrounding air provides for approximately 30% reflection. These lasers are index guided devices; confinement of the transverse spatial mode is achieved due to the index of refraction of the active region being higher than that of the surrounding cladding.
Since the emission region of the semiconductor laser is small (0.1 mm x 0.3 mm), the output beam is divergent. Typical angles of divergence are 30 degrees for the major axis and 10 degrees for the minor axis. In addition, the beam exhibits astigmatism due to different beam waists for the major and minor axes. Using a small focal length (6-8 mm) collimating lens, a collimated elliptical output beam can be achieved. An anamorphic prism pair can be used to produce a circular output beam. Spatial irregularities can be compensated for through spatial filtering. In the far field, the polarization of the output beam is along the direction of the minor axis.
Spacing of the laser cavity modes is dictated by the free spectral range (FSR) of the cavity (c/2nL). The Sharp lasers have a free spectral range of ~150 GHz, corresponding to a cavity mode spacing of about 0.3 nm at the operating wavelength of 780 nm. A free running diode laser will operate at the cavity mode with the highest gain. Injection current and temperature impact the gain curve, and thereby influence the output wavelength of the laser. The injection current changes the carrier density, modifying both the index of refraction and the bandgap energy of the device. The resulting current tuning of the laser wavelength is approximately 0.01 nm/mA. The temperature affects the cavity length and the gain curve, resulting in variations in wavelength of approximately 0.3 nm/K.
Diode lasers exhibit a typical linewidth of about 20-50 MHz. If left unmodified, their usefulness is limited in applications requiring narrowband radiation. Initial measurements of AlGaAs laser linewidths in the early 1980’s revealed a Lorentzian shape linewidth, with a full width at half maximum intensity that varied inversely with laser output power.8 While these features were anticipated based on the modified Schawlow-Townes relation,9 the measured linewidths were about 50 times greater than the predicted values. The linewidth broadening was subsequently attributed to variations of the refractive index of the laser cavity with instantaneous carrier density.10
Several methods have been employed to reduce the laser linewidth; the most widely used method being optical feedback, which consists of directing part of the laser light back into the cavity. Optical feedback reduces the linewidth primarily by increasing the optical cavity length. The extended cavity decouples the resonant laser frequency from strong dependence on the index of refraction of the semiconductor.11 As a result, linewidth broadening due to index of refraction fluctuations is reduced. Optical feedback narrowing of diode laser linewidth has been achieved using a variety of reflecting elements including a mirror,12 Fabry-Perot cavity,13,14 optical fiber cavity,15 and grating.5,16
Optical feedback is also used to influence the laser’s frequency. A diode laser cavity has very low finesse and the gain curve is relatively flat as a function of wavelength.6 As a result, the gain of the system only weakly depends upon wavelength and the lasing wavelength is easily perturbed. By using a wavelength-selective cavity to externally impose the desired wavelength, wavelength selection can be achieved. Tunability of such systems is achieved by appropriate modulation of the external reflecting element.
In this experiment, optical feedback from a diffraction grating5 is used to tune the laser output to the desired wavelength and narrow the linewidth. A schematic of the laser assembly is illustrated in Figure 1. The laser beam is collimated and incident on a holographic diffraction grating mounted in the Littrow configuration.17 In this configuration, the zero order (undiffracted) beam is reflected off the grating and serves as the output beam. The first order diffracted beam provides optical feedback to the laser. A diffraction grating will reflect a given order of the incident beam back along the direction of incidence provided the grating equation 2dcosq = ml is satisfied, where m is the diffraction order, d is the ruling distance, and q is the angle between the propagation direction and the normal to the grating surface. In this configuration the laser cavity is defined primarily by the rear laser facet and the diffraction grating. The resulting grating-controlled wavelength is that which satisfies the grating equation since other wavelengths are not reflected back along the axis of the laser cavity. Tuning of the laser wavelength is accomplished by rotating the grating.
While the output wavelength is determined by the grating orientation, not all wavelengths are accessible at a given injection current and temperature due to the longitudinal cavity mode spacing. To achieve the desired wavelength, the proper combination of temperature and injection current is found. These parameters are then carefully maintained to provide a stable, resonant source. Temperature is controlled and stabilized to a stability of several mK using a Peltier element and a control circuit.18 In addition, the laser assembly is housed in a Plexiglas enclosure to reduce thermal drifts. The injection current is provided by a low-noise current source.14
Fine tuning of the laser wavelength is achieved by applying a voltage to the piezo-electric-transducer (PZT) located in the flexure shown in Figure 1. Application of ±15 V provides ±1 mm of PZT extension, which allows for a tuning range of 5-10 GHz. The linewidth of the laser system is limited by mechanical vibrations and thermal fluctuations of the extended cavity. Correction for small frequency fluctuation is provided by electronic stabilization of the laser injection current. The laser system has a linewidth of approximately 150 kHz.
Figure 1 Diode laser with optical feedback from a diffraction grating.
A grating-feedback diode laser provides tunable, narrow-band laser radiation suitable for a wide range of atomic physics applications, including the laser cooling and trapping experiment herein described. For the atomic physics researcher at an undergraduate institution, the performance characteristics, low-cost, and relative simplicity of grating-feedback diode lasers make them a particularly ideal laser source.
Support for this project has been provided by the Murdock Charitable Trust and Pacific Lutheran University. The author would like to thank Professor David McIntyre of Oregon State University and Pacific Lutheran University undergraduate research partners Alan Davies, Reuben Nelson, and Jonathan Strand for their valuable contributions to this work.
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