ABSTRACT RADIATION TRAPPING IN OPTICAL MOLASSES By Soo Y. Kim Using three orthogonal pairs of counterpropagating red-detuned lasers and a magnetic field gradient, we have constructed a trap of 85Rb atoms at temperatures reduced to the order of 100 microKelvins and densities of 109 atoms/cm3. When the atoms interact with the light, they are absorbing and spontaneously emitting photons. The emitted photons from atoms can be absorbed by neighboring atoms. This phenomenon, called radiation trapping, limits the density and temperature of the trap and also destroys the atomic coherence. We can non- invasively measure the effects of radiation trapping by measuring the intensity correlation function of the light radiated from the trap. We have found that theoretically, the effects of radiation trapping can be detected in dilute atomic samples with an on-resonance optical depth as low as 0.1, more than an order of magnitude less than seen before. Experimental progress is reported. RADIATION TRAPPING IN OPTICAL MOLASSES A Thesis Submitted to the Faculty of Miami University in partial fulfillment of the requirements for the degree of Master of Science Department of Physics by Soo Y. Kim Miami University Oxford, Ohio 2003 Advisor ____________________________ Samir Bali Reader _____________________________ Perry Rice Reader_____________________________ S. Douglas Marcum Table of Contents 1. Introduction and Motivation 1 2. Laser Cooling and Trapping 3 2.1 Laser Cooling 3 2.2 Magnetic Field Gradient Trapping 5 3. Radiation Trapping 7 3.1 First-order and Second-order Coherence 7 3.2 Optical Bloch Equations with Radiation Trapping for MovingAtoms 9 3.3 Second-order Coherence for Moving Atoms with Radiation Trapping 10 4. The Apparatus 15 4.1 Atomic System 15 4.2 Vacuum Chamber 18 4.3 Frequency Tuned Laser Diode 19 4.3.1 External Cavity Diode Laser 19 4.3.2 Saturated Absorption 25 4.3.3 Locking Mechanisms 29 4.4 The Trapping Setup 31 4.5 Magnetic Coils 35 4.5.1 Magnetic Field Gradient Coils 35 4.5.2 Nulling Coils 37 4.5.3 Switching Circuit 38 5. Characteristics Measurements 40 5.1 Number Measurement 40 5.2 Loading Curve 41 5.3 Density Measurements 43 5.4 Temperature Measurement 45 6. Intensity Correlations 47 7. Conclusion and Future Goals 50 References 51 Appendices 53 Appendix A: Parts and Suppliers 53 Appendix B: Circuits 56 *note that references are in brackets [ ], and parts/supplies are superscript. ii Acknowledgements I would like to thank my advisor, Dr. Samir Bali, for taking me into his lab and giving me the opportunity to experience building a full lab from nothing but an empty optics table. He has truly been an integral part of my graduate career at Miami University. I would also like to thank the people I have closely worked with in lab for the past three years: Matthew Beeler, Ronald Stites, Brian Pollock, Charlie LaPlante, Laura Feeney, and Kristy Kallback-Rose. Without them, the lab would not be where it is today. I would also like to thank our collaborating professors, Dr. Perry Rice and Dr. S. Douglas Marcum for all their help and for being the readers for this thesis. Financial support for this project was provided by the College of Arts and Science, the Office for the Advancement of Scholarship and Teaching (OAST), and Miami University. Also, supports from the Cottrell Foundation (Research Corporation), the Petroleum Research Fund of the American Chemical Society are appreciated. A paper entitled “Sensitive Detection of Radiation Trapping in Cold-Atom Clouds” has been accepted for publication in Physical Review A from work done for this thesis. iii Dedicated to the future Jedis iv 1. Introduction and Motivation Cold atoms have been a hot area of research in recent years. It started in 1933 when R. Frisch at the University of Hamburg showed that light can exert a force on atoms [1]. But it took almost 40 years (1970) for A. Ashkin at Bell Laboratories to show trapping by using a focused laser beam, or optical tweezers, to trap small latex spheres immersed in a medium [2]. He proposed that atoms could be trapped in the same way with resonant light. Five years later, in 1975, the idea of laser cooling was independently presented by two groups: Hänsch and Schawlow at Stanford University [3] and Wineland and Dehmelt at the University of Washington [4]. Both looked at the use of three orthogonal pairs of counterpropagating beams to slow down atoms. The beams are tuned below the resonant frequency of the atoms, so that when the atoms approach the beams, some portion of them are Doppler shifted into resonance and interact with the laser. Any beams that are propagating in the direction of the motion of the atom would be Doppler shifted out of resonance, and not affect the atom. Thus the atoms are slowed down and cooled, given that average speed is related to temperature. Then ten years later, in 1985, S. Chu et al at AT&T Bell Laboratories, created an optical molasses with laser beams [5]. In 1987, again at AT&T Bell Laboratories, Raab et al developed the magneto-optical trap (MOT) using a magnetic field gradient to cool and trap atoms [6]. Finally in 1997, S. Chu, C. Cohen-Tannoudji, and W. Phillips received the Nobel Prize for the atom trap. Also in 2001, E. Cornell, W. Ketterle, and W. Phillips were awarded the Nobel Prize for creating Bose-Einstein condensates (BEC). Cold atoms have been used to create atomic clocks [7], further BEC research [8,9,10] and many other applications. We use the MOT to observe the effects of radiation trapping. Atoms trapped in a MOT are continuously interacting with laser light and absorbing and emitting photons. In a dense atom trap, the likelihood that an atom could absorb the emitted photons from another atom increases. The absorption of the photon pushes the two atoms apart, increasing the temperature and decreasing the density of the trap. This also decreases the coherence of the trap due to the random phase and polarization of the spontaneously emitted photon [11,12]. This feature, called radiation trapping, was first seen in cold atom clouds by Walker et al 1 [13,14] in 1990. They found that for traps of 1010~1011 atoms/cm3 and an optical depth of 3, radiation trapping became evident. In 1996, Bali et al [15] studied the intensity correlations of scattered light from laser-cooled atoms and encountered preliminary effects of radiation trapping, but further study was not done on the effects. In 2001, Matsko, Novikova, Scully, and Welch [16] noticed that in their electromagnetically induced transparency (EIT) experiments, radiation trapping effects are present. To explain them, they developed a simple theory for radiation trapping. However, this applies specifically to EIT experiments, which involve three-level atoms, usually hot. They neglect Doppler broadening and direct interactions with the laser. We present a theory using intensity correlations to express the effects of radiation trapping, including Doppler broadening and direct interactions, for an optical molasses. We find that radiation trapping is prevalent in traps with a density of 109 and an optical depth of 0.1, which is more than one order of magnitude less than seen before [13,14] and can be measured with a non-invasive technique. 2 2. Laser Cooling and Trapping To trap atoms, first they must be slowed down to very low velocities. This can be achieved by having resonant counterpropagating laser beams bombard an atom in three orthogonal directions. Since for a monatomic ideal gas, temperature is related to kinetic energy, 3 1 k T = mv 2 , (2.1) 2 B 2 the reduction of velocity leads to a reduction of temperature and therefore slow atoms are said to be cold. The situation of the cooled atoms and six cooling laser beams is called an optical molasses. However, the lasers do not exert a position-dependent force upon the atoms. A magnetic field gradient is necessary to provide the position-dependent force to create an atom trap. 2.1 Laser Cooling At room temperature, gas atoms are moving with average speeds around half a kilometer per second. The kinetic energies of the atoms can be described by a Maxwell-Boltzmann distribution. The atoms in the low velocity tail of the distribution can be slowed down to speeds of centimeters per second using photons. The atom can be imagined as a big bowling ball and the little photons of light as ping pong balls. Conservation of momentum shows that one ping pong ball may be insufficient to significantly affect the bowling ball, but with enough ping pong balls, the bowling ball can be slowed down. Thus, a gas atom can be slowed down to low velocities with a massive quantity of photons, which a laser can supply. For example, a 1mW beam of a 780 nm laser provides 3.9×1015 photons/sec. Although the bowling ball and ping pong ball model provides a nice picture, it does not accurately depict what actually occurs. When a photon encounters an atom, the energy from the photon excites an electron in a ground state of the atom to an excited state. Therefore, only photons with the correct energy, or matching frequency ωo, will be absorbed by the atom. However, since the atom is moving at a velocity v, the atom perceives the frequency of the photon ω to have been Doppler C G G shifted by k ⋅ v , where k is the wave propagation vector of the light. Since the momentum 3 G of a photon is >k , this multiplied with the average photon absorption rate of an atom gives the average force [17] on the atom, G G I I > γ o Fcool = k G G , (2.1.1) 2 2 1 + I I o + [2(δ + k ⋅ v) γ ] where γ is the decay rate of the atom, I is the intensity of the laser light, and δ is the laser detuning, δ = ωo −ω .