Laser Cooling and Trapping Experiment - Advanced Laboratory | PHYS 3340, Lab Reports of Physics

Download Laser Cooling and Trapping Experiment - Advanced Laboratory | PHYS 3340 and more Lab Reports Physics in PDF only on Docsity! Advanced Laboratory Spring 2001 Laser Cooling LC.1 Spring 2001 Laser cooling and trapping experiment I. INTRODUCTION Laser cooling and trapping of neutral atoms is a rapidly expanding area of physics research which has seen dramatic new developments over the last decade. These include the ability to cool atoms down to unprecedented kinetic temperatures (as low as one microkelvin) and to hold samples of a gas isolated in the middle of a vacuum system for many seconds. This unique new level of control of atomic motion is allowing researchers to probe the behavior of atoms in a whole new regime of matter where DeBroglie wavelengths are much larger than the Bohr radius. Undoubtedly one of the distinct appeals of this research is the leisurely and highly visible motion of the laser cooled and trapped atoms. In this experiment you will operate a laser trap which is equal or superior in performance to what is used in many current research programs. This experiment uses the lasers and saturated absorption spectrometers used in the laser spectroscopy experiment1 and thus you should have done that experiment before doing this one. A small fraction (~10%) of the beams of each of the two lasers goes to their respective saturated absorption spectrometers. This allows for precise detection and control of the laser frequencies, which is essential for cooling and trapping. The remainder of the laser light goes into the trapping cell. Section II of this writeup provides a brief introduction to the relevant physics of the atom trap, section III discusses the laser stabilization, section IV explains the optical layout for sending the laser beams into the cell to create the trap, section V explains the trapping cell construction and section VI discusses the operation of the trap, measurement of the number of trapped atoms, and measurement of the time the atoms remain in the trap. II. THEORY AND OVERVIEW We will present a brief description of the relevant physics of the vapor cell magneto-optical trap. For more information, a relatively nontechnical discussion is given in Ref. 2, while more detailed discussions of the magneto-optical trap and the vapor cell trap can be found in Ref. 3 and Ref. 4, respectively. A. Laser Cooling The primary force used in laser cooling and trapping is the recoil when momentum is transferred from photons scattering off an atom. This radiation-pressure force is analogous to that applied to a bowling ball when it is bombarded by a stream of ping pong balls. The momentum kick that the atom receives from each scattered photon is quite small; a typical velocity change is about 1 cm/s. However, by exciting a strong atomic transition, it is possible to scatter more than 107 photons per second and produce large accelerations (104 • g). The radiation-pressure force is controlled in such a way that it brings the atoms in a sample to a velocity near zero ("cooling"), and holds them at a particular point in space ("trapping"). The cooling is achieved by making the photon scattering rate velocity-dependent using the Doppler effect.5 The basic principle is illustrated in Fig. 1. If an atom is moving in a laser beam, it will see the laser frequency νlaser shifted by an amount (-V/c)νlaser, where V is the velocity of the atom along the direction of the laser beam. If the laser frequency is below the atomic resonance frequency, the atom, as a result of this Doppler shift, will scatter photons at a higher Laser Cooling LC.2 Spring 2001 rate if it is moving toward the laser beam (V negative), than if it is moving away. If laser beams impinge on the atom from all six directions, the only remaining force on the atom is the velocity-dependent part which opposes the motion of the atoms. This provides strong damping of any atomic motion and cools the atomic vapor. This arrangement of laser fields is often known as "optical molasses."6 B. Magneto-optical Trap Although optical molasses will cool atoms, the atoms will still diffuse out of the region if there is no position dependence to the optical force. Position dependence can be introduced in a variety of ways. Here we will only discuss how it is done in the "magneto-optical trap" (MOT), also known as the "Zeeman shift optical trap," or "ZOT." The position-dependent force is created by using appropriately polarized laser beams and by applying an inhomogeneous magnetic field to the trapping region. Through Zeeman shifts of the atomic energy levels, the magnetic field regulates the rate at which an atom in a particular position scatters photons from the various beams and thereby causes the atoms to be pushed to a particular point in space. In addition to holding the atoms in place, this greatly Figure 1. Graph of the atomic scattering rate versus laser frequency. As shown, a laser is tuned to a frequency below the peak of the resonance. Due to the Doppler shift, atoms moving in the direction opposite the laser beam will scatter photons at a higher rate than those moving in the same direction as the beam. This leads to a larger force on the counter propagating atoms. Laser Cooling LC.5 Spring 2001 C. Rb vapor cell trap We will now consider the specific case of Rb (Fig. 4). Essentially all the trapping and cooling is done by one laser which is tuned slightly (1-3 natural linewidths) to the low frequency side of the 5S1/2 F=2 → 5P3/2 F'=3 transition of 87Rb. (For simplicity we will only discuss trapping of this isotope. The other stable isotope, 85Rb, can be trapped equally well using its F=3 → F'=4 transition.) Unfortunately, about one excitation out of 1000 will cause the atom to decay to the F=1 state instead of the F=2 state. This takes the atom out of resonance with the trapping laser. Another laser (called the "hyperfine pumping laser") is used to excite the atom from the 5S F=1 to the 5P F'=1 or 2 state, from which it can decay back to the 5S F=2 state where it will again be excited by the trapping laser. In a vapor cell trap, the MOT is established in a low pressure cell containing a small amount of Rb vapor.4 The Rb atoms in the low energy tail (V < Vmax ≈ 20 m/s) of the Maxwell-Boltzmann distribution are captured in the laser trap. If the trap is turned on at t=0, the number N of atoms in the trap will increase with the same functional form as that of a capacitor charging, /( ) (1 ), 0 tN t N e τ−= − (1) where τ is the time constant for the trap to fill to its steady state value N0 and is also the average time an atom will remain in the trap before it is knocked out by a collision. This time is just the inverse of the loss rate from the trap due to collisions. Under certain conditions, collisions between the trapped atoms can be important, but for conditions that are usually encountered, the loss rate will be dominated by collisions with the room temperature background gas. These "hot" background atoms and molecules (Rb and contaminants) have more than enough energy to knock atoms out of the trap. The time constant τ can be expressed in terms of the cross sections σ, densities n, and velocities of Rb and non-Rio components as 1/ .n V n V Rb Rb Rb non non non τ σ σ= + (2) The steady-state number of trapped atoms is that value for which the capture and loss rates of the trap are equal. The capture rate is simply given by the number of atoms which enter the trap volume (as defined by the overlap of the laser beams) with speeds less than Vmax. It is straightforward to show that this is proportional to the Rb density, (Vmax) 4, and the surface area A Figure 4. 87Rb energy level diagram showing the trapping and hyperfine pumping transitions. The atoms are observed by detecting the 780 nm fluorescence as they decay back to the ground state. Laser Cooling LC.6 Spring 2001 of the trap. When the background vapor is predominantly Rb, the loss and capture rates are both proportional to Rb pressure. In this case N0 is simply 4 0 max(0.1 / )( / ) ,Rb avgN A V Vσ= (3) where Vavg is (2kT/m) 1/2, the average velocity of the Rb atoms in the vapor. If the loss rate due to collisions with non-Rb background gas is significant, Eq. (3) must be multiplied by the factor nRbσRbVavg / (nRbσRbVavg + nnonσnonVnon). The densities are proportional to the respective partial pressures. Finally, if the loss rate is dominated by collisions with non-Rb background gas, the number of atoms in the trap will be proportional to the Rb pressure divided by the non-Rb pressure, but τ will be independent of the Rb pressure. As a final note on the theory of trapping and cooling, we emphasize certain qualitative features that are not initially obvious. This trap is a highly overdamped system; hence damping effects are more important for determining trap performance than is the trapping force. If this is kept in mind it is much easier to gain an intuitive understanding of the trap behavior. Because it is highly overdamped, the critical quantity Vmax is determined almost entirely by the Doppler slowing which provides the damping. Also, the cross sections for collisional loss are only very weakly dependent on the depth of the trap, and therefore the trap lifetime is usually quite insensitive to everything except background pressure. As a result of these two features, the number of atoms in the trap is very sensitive to laser beam diameter, power, and frequency, all of which affect the Doppler cooling and hence Vmax. However, the number of trapped atoms is insensitive to factors which primarily affect the trapping force but not the damping, such as the magnetic field (stray or applied) and the alignment and polarizations of the laser beams. For example, changing the alignment of the laser beams will dramatically affect the shape of the cloud of trapped atoms since it changes the shape of the trapping potential. However, these very differently shaped clouds will still have similar numbers of atoms until the alignment is changed enough to affect the volume of the laser beam overlap. When this happens, the damping in three dimensions is changed and the number of trapped atoms will change dramatically. Of course, if the trapping potential is changed enough that there is no potential minimum (for example, the zero of the magnetic field is no longer within the region of overlap of the laser beams), there will be no trapped atoms. However, as long as the damping force remains the same, almost any potential minimum will have about the same number of atoms and trap lifetime. D. Overview of the trapping apparatus. Figure 5(a) shows a general schematic of the trapping apparatus. It consists of two diode lasers, two saturated absorption spectrometers, a trapping cell, and a variety of optics. The optical elements are lenses for expanding the laser beams, mirrors and beamsplitters for splitting and steering the beams, and waveplates for controlling their polarizations. To monitor the laser frequency, a small fraction of the output of each laser is split off and sent to a saturated absorption spectrometer. An electronic error signal from the trapping laser's saturated absorption spectrometer is fed back to the laser to actively stabilize its frequency. The trapping cell is a small vacuum chamber with an ion vacuum pump, a Rb source, and windows for transmitting the laser light. In the following sections we will discuss the various components of the apparatus and the operation of the trap. Laser Cooling LC.7 Spring 2001 III. LASER STABILIZATION As mentioned above, two lasers are needed for the trap. A few milliwatts of laser power are plenty for hyperfine pumping (F=1 -> F'=1,2), but the number of trapped atoms is nearly proportional to the amount of power in the trapping laser (F=2 -> F'=3). Setting up and using the trap is much easier with at least 5 mW of trapping laser power, although it can work with less. The trapping laser must have an absolute frequency stability of a few megahertz. This requires you to actively eliminate fluctuations in the laser frequency, Figure 5(a) Overall optical layout for laser trap experiment including both saturated absorption spectrometers. Figure 5 (b) Detail of how laser beams are sent through the trapping cell. To simplify the figure, the A/4 waveplates are not shown. Beam paths (1) and (2) are in the - horizontal plane and beam (3) is angled down and is then reflected up through the bottom of the cell. The retro beams are tilted slightly to avoid feedback to the diode laser. Laser Cooling LC.10 Spring 2001 the bottom of the cell. However, with minimal effort to be close to this condition, the polarization will remain sufficiently well linearly polarized. If you think this might be a problem you can check the ellipticity of the polarization by using a photodiode and a rotatable linear polarizer. An eccentricity of 10 or greater on the polarization ellipse is adequate. After they pass through the cell, the beams are reflected approximately (but not exactly!) back on themselves. The reason for having an optical isolator in the research design is that even a small amount of laser light reflected back into the laser will dramatically shift the laser frequency and cause it to jump out of lock. In the absence of an optical isolator, this will always happen if the laser beams are reflected nearly back on themselves. Feedback can be avoided by insuring that the reflected beams are steered away from the incident beams so that they are spatially offset by many (5-10) beam diameters when they arrive back at the position of the laser. Fortunately, for operation of the trap the return beam need only overlap most of the incident beam in the cell, but its exact direction is unimportant. Thus by making the beams large and placing the retro mirrors close to the trap (within 10 cm for example) it is possible to have the forward and backward going beams almost entirely overlap even when the angle between them is substantially different from 180•. This design eliminates the need for the very expensive ($2500) optical isolator and, as an added benefit, makes the operation of the trap very insensitive to the alignment of the return beams. It is easy to tell if feedback from the return beams is perturbing the laser by watching the signal from the saturated absorption spectrometer on the oscilloscope. If the amplitude of the fluctuations is affected by the alignment of the reflected beam or is reduced when the beam to the trapping cell is blocked, unwanted optical feedback is occurring. B. Polarization The next task is to set the polarizations of the three incident beams. The orientations of the respective circular polarizations are determined by the orientation of the magnetic field gradient coils. The two transverse beams which propagate through the cell perpendicular to the coil axis should have the same circular polarization, while the beam which propagates along the axis should have the opposite circular polarization. Although in principle it is possible to initially determine and set all three polarizations correctly with respect to the field gradient, in practice it is much simpler to set the three polarizations relative to each other and then try both directions of current through the magnetic field coils to determine which sign of magnetic field gradient makes the trap work. To set the relative polarization of the three beams, first identify the same (fast or slow) axis of the three quarter-wave (lambda/4) plates. For the two beams which are to have the same polarization, this axis is set at an angle of 45• clockwise with respect to the linear polarization axis when looking along the laser beam. For the axial beam, the axis is oriented at 45• counterclockwise with respect to the linear polarization. This orientation need only to be set to within about + 10•. The orientation of the l/4 plates through which the beams pass after they have gone through the trapping cell ("retro lambda/4 plates") is arbitrary. No matter what the plates' orientations are, after the beams have passed though them twice, the light's circular polarization will be reversed. Laser Cooling LC.11 Spring 2001 An optional experiment is to see what happens when you replace one or more of the three retro lambda/4 plates with retroreflecting right angle mirrors.' Although this combination of mirrors does not provide an ideal λ/2 retardance, it is fairly close. An added benefit of this approach is that two reflections off a mirror usually result in much less light loss than one reflection and two passes through a λ/4 plate. C. Hyperfine pumping laser optics Minimal optics are needed for the hyperfine pumping laser. You need only send it through the two lens beam expanding telescope in the lab to make a large roughly collimated beam (typically an ellipse with a 2-3 cm major axis) and send it into the cell from a direction which will minimize the scattered light into the detectors that observe the trapped atoms. The trap is insensitive to nearly everything about the hyperfine pumping light, including its polarization. Why should you expect this to be the case based on how the trap works? V. TRAPPING CELL CONSTRUCTION The primary concern in the construction of the trapping cell is that ultrahigh vacuum (UHV) is required. Although trapped atoms can be observed at pressures of 10-5 Pa (~10-7 Torr), trap lifetimes long enough for most experiments of interest require pressures in the 10-6 to 10-7 Pa range. There are three main elements in the trapping cell: (1) a pump to remove unwanted background gas - mostly water, hydrogen, and helium (helium can diffuse through glass), (2) a controllable source of Rb atoms, and (3) windows to transmit the laser light and allow observation of the trapped atoms. A. Vacuum pump The cell is attached to a 20 1/s ion pump. In this pump the atoms are ionized in a high voltage discharge and then embedded in the electrodes, thereby removing them from the system. The 5000 V needed to make the pump operate are provided by a power supply which is attached to the back of the pump by a wire. Although this wire how a grounded outer shield, and therefore in principle quite safe, it is wise to always avoid touching it or the pump near the high voltage connector. The ion pump have the minor drawback that it requires a large magnetic field, which is provided by a permanent magnet. The fringing fields from this magnet can extend into the trap region and will affect the trap to some extent. Although the trap will usually work without it, we put a layer of 0.75 mm (0.03 in) magnetically permeable steel sheet around the pump to shield the trap from this field. For this same reason it is advisable to avoid having magnetic bases very near the trap. Laser Cooling LC.12 Spring 2001 B. Rb sources We will now discuss how to produce the correct pressure of Rb vapor in the cell. The vapor pressure of a room temperature sample of Rb is about 5 x 10-5 Pa. This is much higher than the 10-6 to 10-7 Pa (~10-8 to 10-9 Torr) of Rb vapor pressure that is optimum for trapping. At higher pressures the trap will still work, but the atoms remain in the trap a very short time, and it is often difficult to see them because of the bright fluorescence from the untrapped background atoms. Also, the absorption of the trapping beams when passing through the cell will be significant. Thus you should maintain the Rb at well below its room temperature vapor pressure. Because it is necessary to continuously pump on the system to avoid the buildup of hydrogen and helium vapor, it is necessary to have a constant source of Rb to maintain the correct pressure. Through chemical reactions and physisorption, the walls of the cell usually remove far more Rb than the ion pump does and the rate of pumping by the walls depends on how well they are coated with Rb. In this experiment the Rb vapor is produced by a commercial "getter." This technique was developed specifically for this lab and has not been used before in trapping cells. The getter is several milligrams of a Rb compound which is contained in a small (1.0 x 0.2 x 0.2 cm) stainless steel oven. Two of these ovens are spot-welded onto two pins of a vacuum feedthrough as shown in Fig. 6. When current (3-5 A) is sent through the oven, Rb vapor is produced. The higher the current, the higher the Rb pressure in the chamber. With this system it is unnecessary to coat the Figure 6. Drawing of trapping cell. The tubes on the cross have been elongated in the drawing for ease of display. The Rb getter is inside a stainless steel vacuum tube; we show a cut-away view in this drawing. Laser Cooling LC.15 Spring 2001 the time which atoms remain in the trap. If you have time after completing these, you can consider other experiments. Both of these measurements are made by observing the fluorescence from the trapped atoms with a photodiode. The number of atoms is determined by measuring the amount of light coming from the trapped atoms and dividing by the amount of light scattered per atom, which is calculated from the excited state lifetime. The time the atoms remain in the trap is found by observing the trap filling time and using Eq. (1). To make a reliable measurement of the number of trapped atoms, it is crucial to accurately separate the fluorescence of the trapped atoms from the scattered light and the fluorescence of the background vapor. To do this one must compare the signal difference between having the trap off and on. Therefore, the trap must be disabled in a way that has a negligibly small effect on the background light. We have found that turning off or, even better, reversing the magnetic field is usually the best way to do this. The magnetic field may alter the background fluorescence, but this change is generally smaller than the signal of a typical cloud of trapped atoms. Check how big an effect this is. Once you have determined the photocurrent due to just the trapped atoms, the total amount of light emitted can be found using the photodiode calibration of 0.3 ma/mW and calculating the detection solid angle. rate R at which an individual atom scatters photons is given by 8 2 8 ( / ) , 1 ( / ) 4( / ) I I R I I πΓ = + + ∆ Γ (4) where I is the sum of the intensities of the six trapping beams, I" is the 6 MHz natural linewidth of the transition, ∆ is the detuning of the laser frequency from resonance, and I, is the 4.1 mW/cm2 saturation intensity. The simplest way to find ∆ is to ramp over the saturated absorption spectrum and, when looking at the locking error signal, find the position of the lock point (zero crossing point) relative to the peak of the line. The frequency scale for the ramp can be determined using the known spacing between two hyperfine peaks. A typical number for R is 6 x 106 photons/(s . atom). One can optimize the number of atoms in the trap by adjusting the position of the magnetic field coils, the size of the gradient, the frequencies of both trapping and hyperfine pumping lasers, the beam alignments, and the polarization of the beams. More than 107 trapped atoms have been obtained when the Rb pressure is large enough to dominate the lifetime. The filling of the trap can also be observed using the same photodiode signal. This is best done by suddenly fuming on the current to the field coils to produce a trap. The fluorescence signal from the photodiode will then follow the dependence given by Eq. 1, as shown in Fig. 7. This can be most easily observed by sending the photodiode signal into a storage scope. The value of the 1/e trap lifetime τ (the characteristic time an atom remains trapped) can then be determined from this curve. Eq. 1 tells us that it is the same as the time for the trap to fill to 1/e of its final value. Lifetimes between a fraction of a second and a few seconds are reasonable. Laser Cooling LC.16 Spring 2001 By changing the current through the getter, you should vary the Rb pressure and see how it affects the number and lifetime of the trapped atoms. This can be compared with the predictions of Eqs. (1) and (2) and can be used to determine the collision cross sections if you also measure the Rb density in the cell. There are many other experiments which can be done with the trapped atoms. The choices are only limited by your imagination and/or available equipment. You might look at how the number of atoms and the lifetime depends on the various parameters such as magnetic field, laser intensity, etc. You could also think about how to measure the spring constant and damping constant for the trap. You can also turn off the magnetic field and watch the atoms spread out. In this situation, known as optical molasses and discussed in references 6 and 7, the laser light provides damping of the velocity but no trapping. In these conditions the atoms reach the lowest possible temperatures, but it is necessary to use additional field coils to cancel the magnetic fields from the earth and the ion pump. If you do, you will be able to watch the atoms spread out slowly (in a fraction of a second or longer) if the laser is detuned well to the red of the resonance line. We conclude with both a challenge and a warning about all such possible experiments: you are likely to observe phenomena which have not yet been studied or are just being studied in research labs around the world. Often you will not find explanations (or will find incorrect explanations) in the current research literature, your instructor will not be able to provide much help, and the subject is too new for you to find textbooks which provide answers. On the other Figure 7. Typical curve of number of trapped atoms versus time after the trap is turned on at 0 sec., as shown on oscilloscope. Laser Cooling LC.17 Spring 2001 hand, this means that if you do observe new phenomena and can explain them you will be able to publish your results in a scientific journal. REFERENCES 1. K. B. MacAdam, A. Steinbach, and C. Wieman, "A narrow-band tunable diode laser system with grating feedback and a saturated absorption spectrometer for Cs and Rb," Am. J. Phys., 60, 1098-1111 (1992) and the Senior Lab manual. 2. S. L. Gilbert and C. E. Wieman, "Laser Cooling and Trapping for the Masses," Optics and Photonics News, 4, 8-14 (1993). 3. The initial demonstration and discussion is E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. Pritchard, "Trapping of neutral sodium atoms with radiation pressure," Phys. Rev. Lett. 59, 2631-2634 (1987). More detailed analysis of the trap is given in A. M. Steane, M. Chowdhury, and C. J. Foot, "Radiation force in the magneto-optical trap," J. Opt. Soc. Am B 9, 2142 (1992), while a discussion of many of the novel aspects of the behavior of atoms in the trap is given in D. Sesko, T. Walker and C. Wieman, "Behavior of neutral atoms in a spontaneous force trap," J. Opt. Soc. Am. B 8, 946-958 (1991). 4. C. Monroe, W. Swann, H. Robinson, and C. Wieman, "Very cold atoms in a vapor cell," Phys. Rev. Lett. 65, 1990, 1571-1574; K. Lindquist, M. Stephens, and C. Wieman, "Experimental and theoretical study of the vapor-cell Zeeman optical trap," Phys. Rev. A 46, 4082-4090 (1992). 5. T. W. Hansch and A. L. Schawlow, "Cooling of gases by laser radiation," Opt. Commun. 13, 68-69 (1975). 6. S. Chu, L. Hollberg, J. Bjorkholm, A. Cable, and A. Ashkin, "Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure," Phys. Rev. Lett. 55, 48-51 (1985). 7. J. Dalibard and C. Cohen-Tannoudii, "Laser cooling below the Doppler limit by polarization gradients: simple theoretical models," J. Opt. Soc. Am. B 6, 2023-2045 (1989); P. Ungar, D. Weiss, E. Riis, S. Chu, "Optical molasses and multilevel atoms: theory," J. Opt. Soc. Am. B 6, 2058-2072 (1989). 8. L. Orozco, SUNY at Stony Brook, private communication.