PROGRESS TOWARDS CONSTRUCTION OF A FERMIONIC ATOMIC CLOCK FOR NASA S DEEP SPACE NETWORK Megan K. Ivory Advisor: Dr. Seth A. Aubin College of William and Mary Atomic clocks are the most accurate time and frequency measurement devices existing today. Current state of the art fountain clocks have limited accuracy due to atom-atom interactions. We are building an atomic clock using ultracold fermions on a microchip which has the advantage of superior accuracy by essentially eliminating atom-atom interactions. The Ultracold Atomic, Molecular, and Optical Physics Lab at the College of William and Mary is building a dualspecies apparatus for cooling and trapping rubidium and potassium bosons and fermions. Over the past year, we have added significant capability to our apparatus: 1) We have constructed, tested, and installed a magnetic transport system to carry our atoms from an initial MOT vacuum chamber to the second chip vacuum chamber, 2) we have improved the lifetime of our rubidium magnetic trap by an order of magnitude, 3) we have a rubidium dipole trap with lifetimes on the order of 1s, 4) we have assembled the electronics for RF evaporation and the clock pulses, and 5) we have reduced the temperature of our potassium atoms by nearly 2 orders of magnitude. We present this progress towards a 40 K fermion atomic clock with potential application in NASA s Deep Space Network (DSN). I. Introduction Atomic clocks are the most accurate time and frequency measurement devices existing today. They are used in a broad number of applications, including digital communications and satellite navigation systems, as well as in any measurement of standard units which requires an accurate time base. The widespread success of these applications demands continuing developments to produce smaller and more accurate devices. Today s most accurate atomic clock is a cesium fountain clock operated by the National Institute of Standards and Technology which uses ultracold bosonic cesium atoms to reach accuracies of a few parts in 10 15 to 10 16 but requires a height of 2 m to operate 1,2. Recent developments in magnetic microchip traps have produced ultracold bosonic rubidium atomic clocks able to reach accuracies of a few parts in 10 13 with the potential for miniaturization 3. The accuracy of each of these types of clocks is limited by the interactions between the atoms 2. We are building an atomic clock using ultracold fermions on a microchip which has the advantage of superior accuracy by essentially eliminating atom-atom interactions 4. II. Application NASA s DSN tracks space craft using Doppler shifted frequencies from the two-way path between a ground station to a spacecraft and back (see Fig. 1) 5. Not only does the current scheme necessitate the use of one DSN antenna for each spacecraft being tracked, it also requires 7-8 hours for the signal to complete the roundtrip. A reliable frequency source on the spacecraft would allow for oneway DSN navigation in which a signal is sent Ivory 1
from the spacecraft and received by the ground antenna. This allows for shorter link time as well as for tracking of multiple spacecraft by a single antenna, significantly decreasing the time and cost associated with DSN navigation. Fermion atomic clocks provide one possibility for a stable on-board frequency outgoing signal DSN ground station Space craft 7-8 hours! return Doppler shifted signal Fig. 1. NASA s DSN uses Doppler data to track space craft. Each ground station can track only one space craft at a time, which can take 7-8 hours for a signal to be sent and received. An on-board fermion atomic clock cuts this time in half and allows each ground station to track multiple space craft orbiting a planet. source, with their promised accuracy and potentially compact size when produced with atom chip technology 3. Mercury ion clocks have also been proposed as candidates for onboard frequency sources 5. However, the large atomic samples permitted by fermion atomic clocks would have larger signal-to-noise ratios than mercury ion clock counterparts. Additionally, implementing two independent atomic clocks separated by a few centimeters on a single spacecraft allows us to take advantage of the sensitivity of these devices to magnetic fields and create a simple gradient magnetometer. Mapping the magnetic fields of moons and planets (including our own) has been a goal of several NASA missions to date, such as Space Technology 5 and the Mars Global Surveyor Magnetic Field Investigation 6,7. Having a gradient magnetometer on-board the spacecraft navigating via the DSN would allow them to potentially track changes in the magnetic fields of their space environment as well. III. Background Atomic clocks are based on the energy difference between two levels of an atom and the corresponding frequency of a photon which connects those two levels (see Fig. 2a). Since two atoms of the same species have identical energy level structure, we can use the resonant frequency of atoms to develop an extremely reliable and reproducible frequency standard. Atomic clocks use this frequency standard to accurately tune a local oscillator (typically an electronic crystal oscillator) to the resonant frequency of the atom. The atoms used in atomic clocks (as well as all atoms) can be characterized as either bosons or fermions (see Fig. 2b), each of which obeys different quantum statistical laws. Bosons have integer spin and can simultaneously occupy the same quantum state as any number of other bosons. When a) b) Energy e> Energy Bosons E=hf g> Fermions Fig. 2. a) 2-Level Atom: The photon connecting ground state g> and excited state e> will have a frequency f associated with the energy difference E by the relation E=hf where h is Planck s constant. b) Bosons vs. Fermions. Any number of bosons can simultaneously occupy the same energy state. No two identical fermions can occupy the same energy state. Ivory 2
cooled to extremely low temperatures, bosons form a state of matter called Bose-Einstein Condensates (BECs) in which nearly all particles occupy the lowest energy level of the system. Fermions have half-integer spin and follow the Pauli Exclusion Principle: no two identical fermions can simultaneously occupy the same quantum state. At extremely low temperatures, degenerate Fermi gases (DFGs) have the advantage of strongly suppressing atom-atom interactions 4. BECs and DFGs are ideal tools for performing precision measurements due the sensitivity of the atoms. However, measurements made with BECs have limited accuracy due to atom-atom interactions 2. An atomic clock based on a microtrapped DFG promises to provide more accurate time measurements than one based on a BEC. IV. Methods We are building a fermion atomic clock with ultracold 40 K atoms which will operate between the F=9/2 and F=7/2 hyperfine ground states. The Zeeman shift allows us to choose two magnetic hyperfine sub-levels which are both magnetically trappable and experience the same energy shift at a particular magnetic field called the magic magnetic field. While there are several transitions and corresponding magic magnetic fields, we have chosen to initially operate our clock on the F=9/2,m F =7/2> F=7/2,m F =-7/2> 1. Atoms in g> e> 2. π/2 pulse puts atoms in superposition of g> and e> 4 3. The state precesses for some time 2 4. If 0, another π/2 3 pulse only puts some of the atoms into e> 1 5. By examining the ratio of atoms in each state, we g> can tune the oscillator to resonance. Fig. 3. Atomic Clock Function. The atomic states can be visualized as two poles of a sphere. When the atoms are in a superposition of states for some time, they will precess about the equator. A difference between the resonant frequency of the atom and the oscillator will cause some of the atoms to be placed into g> instead of e>. transition at 0.717 G. The expected stability of a fermion atomic clock operating at this frequency is 10-12 to 10-14. In a microgravity environment, a clock operating on the F=9/2,m F =1/2> F=7/2,m F =-1/2> transition at magic magnetic field 0.041 G could produce stabilities on the order of 10-15. The atomic clock will function as follows (see Fig. 3): Approximately 10 4 to 10 5 ultracold 40 K atoms will be magnetically trapped in the F=9/2,m F =7/2> state in a microchip trap. The atoms will be put into a superposition of the clock states using a π/2 pulse generated on the microchip. After precessing for some time T measured by the local quartz oscillator, another π/2 pulse in reverse places the atoms in a combination of the ground and excited states. The atomic population in each state will be measured by spatially separating the two states and imaging them. The number of atoms in each state depends upon the length and accuracy of the precession time T. We can use the ratio of atoms in ground to excited states to servo the quartz oscillator to the atomic transition with electronic feedback. To implement a gradient magnetometer, one can compare the results of two identical atomic clocks and attribute the difference in clock timing to a difference in magnetic fields between the two locations. Ivory 3
V. Current Status and Outlook Since atomic clock experiments with fermions require exquisite atomic and optical control, we are implementing our clock in a series of steps which ease the troubleshooting process. We are currently pursuing demonstration of a proof-of-principle bosonic atomic clock so we can work out experimental kinks before moving to a more difficult fermionic system. As this is an extremely complex experiment, creating a bosonic clock first allows us to optimize our optical dipole trap and test our pulse frequencies and imaging techniques on a previously studied system. The canonical steps to BEC are as follows: 1. The magneto-optical trap (MOT) is the initial cooling and trapping stage. Six counter-propagating lasers are red-detuned from resonance and overlap at the center of a quadrupole magnetic trap created by a pair of anti-helmholtz coils. Our 87 Rb MOT has reached temperatures around 30μK and our 39 K MOT has reached temperatures around 1550μK (potassium is typically more difficult to cool than rubidium). 2. During a brief (~5ms) molasses stage, the atoms are further cooled by the same lasers at further detuning while the magnetic trap is turned off. With this stage, our 87 Rb atoms have reached temperatures as low as 4μK. Until recently, this stage was thought to be ineffective in potassium 8. We have shown that a modified molasses stage introduced to our 39 K atoms reduces the temperature to 240μK (see Fig. 4) one of our most significant accomplishments this past year because it makes it possible to magnetically trap potassium without introducing additional cooling steps. 3. After the molasses stage, we turn off our lasers and quickly turn on our magnetic trap. A short (~1ms) pulse of circularly polarized light before the magnetic trap can optically Atom cloud size (cm) 0.25 0.2 0.15 Temperature improvements in 39 K 1550μK June 2011 February 2012 0.1 4ms 0.05 1ms TOF 0 1 TOF 2 3 4 5 6 7 Time of flight (ms) 8 87 Rb 240 μk Fig. 4. 39 K temperature measurements using time of flight (TOF). We determine the temperature of our atoms by measuring the velocity. We allow the atom cloud to expand for a known amount of time and measure the change in cloud size. Our temperatures have improved significantly since June 2011. 39 K MOT Fig. 5. Apparatus. Image of MOT vacuum cell (circled in yellow) and science vacuum cell (circled in red) where the atom chip is positioned. False-color images of the 87 Rb and 39 K MOTs are pictured as insets. *Note: this image does not contain the magnetic transport system, which as since then been installed, but obstructs the view of the science cell. pump our atoms into the desired trappable magnetic hyperfine sublevel. The main advantage of the magnetic trap is the long trap Ivory 4
lifetime, allowing us to hold or translate our atoms with magnetic fields during this time. Prior to receiving this fellowship, our magnetic trap lifetimes were on the order of 1s. Our current magnetic trap lifetime is 13s, over an order of magnitude improvement. 4. Our apparatus was designed with two vacuum cells in an L orientation (see Fig. 5) for better vacuum pressure in the second science cell containing the atom chip. With the atoms in a magnetic trap, a magnetic transport system, which was constructed, tested, and installed over the past year, transports the atoms from the MOT cell to the science cell. Recent progress shows we are able to move the atoms 30cm from the MOT cell to the corner and back to the MOT cell (for imaging) in less than 10s, indicating we should be able to successfully transport them to the atom chip. 5. Once at the chip, we transfer the atoms to the magnetic trap produced by the chip for further cooling to BEC. This final cooling step is evaporative cooling, where we apply an RF field which evaporates the hottest atoms to an untrapped state. Since we are still in the process of transporting the atoms to the chip, we have also been dipole trapping directly from the MOT and molasses in the MOT cell to begin testing our electronics and pulse system. We have achieved 87 Rb dipole traps with temperatures around 50μK and lifetimes up to 1s. A summary of the accomplishments since receipt of the award can be found in the table below. Table of accomplishments since receipt of award Accomplishments: Pre-award status: Current status: Transport system designed constructed, tested, installed Chip bias coils --- installation in progress 87 Rb magnetic trap 1.2 s lifetime 13.0 s lifetime 87 Rb dipole trap --- 1 s lifetime RF evaporation --- electronics completed 39 K cooling 1550 microk 240 microk Clock electronics --- assembled 87 Rb dipole trap 87 Rb 1D optical lattice Once in the dipole trap, we can begin implementing a proof-of-principle bosonic clock. We will first optimize the timing and pulsing system for a bosonic 39 K clock, before moving to the more difficult fermionic clock. It is important to note that all of these steps are also important tools for obtaining DFG. Once we have a better understanding of our bosonic system, we can implement and characterize a proof-of-principle fermionic 40 K clock. Ivory 5
VI. References 1 S. R. Jefferts, et al. Accuracy evaluation of NIST F1, Metrologia 39, 321-336 (2002). 2 S. R. Jefferts, et al. NIST Cesium Fountains Current Status and Future Prospects, Acta Physica Polonica 112, 759-767 (2007). 3 P. Treutlein, et al. Coherence in Microchip Traps, Phys. Rev. Lett. 92, 203005 (2004). 4 B. DeMarco and D. Jin, Exploring a quantum degenerate gas of fermionic atoms, Phys. Rev. A 58, R4267 (1998) 5 J. D. Prestage, et al. A One-Liter Mercury Ion Clock for Space and Ground Applications, IPN Progress Report 42-155, 1-5 (15 Nov 2003). 6 J. A. Slavin, et al. Space Technology 5 multi-point measurements of near-earth magnetic fields: Initial results, Geophys. Res. Lett., 35, L02107 (2008). 7 M. H. Acuña, et al. Global Distribution of Crustal Magnetism Discovered by the Mars Global Surveyor MAG/ER Experiment, Science 284, 790-793, (1999). 8 G. Modugno, et al. Sub-Doppler laser cooling of potassium atoms, Phys. Rev. A 84, 043432 (2011) Ivory 6