#### Atomic Clocks and Cold Atom Scattering

Atomic clocks have wide-ranging applications because they can measure small differences in frequencies, or tick-rates, and short time intervals. The Global Positioning System (GPS) is a very prominent example in addition to the synchronization of high-speed communication networks, secure financial transactions, and official U.S. and international time. Scientific applications of atomic clocks include tests of fundamental physics (such as Einstein’s theory of general relativity), geodesy, long baseline interferometry, and metrology. Atomic clocks can address questions such as whether the fundamental constants of the universe (like the ratio of the mass of an electron to the mass of a proton) change in time.

#### Cadmium optical lattice clock and ultracold collisions

We are currently constructing an optical frequency clock based on neutral cadmium atoms trapped in an optical lattice. The attractiveness of cadmium atoms for highly accurate clocks stems from the cadmium clock transition’s insensitivity to frequency shifts from thermal radiation of room-temperature surroundings. This presently limits many atomic clocks. An additional practical aspect is that the lasers needed to make a cadmium clock are expected to be more reliable than for other clock species with small thermal sensitivities. A cadmium lattice clock is also being developed at RIKEN in Japan, by Dr. Atsushi Yamaguchi and Prof. Hidetoshi Katori. Our groups have complementary approaches and are collaborating on the development of cadmium lattice clocks. Cadmium has a variety of isotopes (8 isotopes with different numbers of neutrons in the nucleus) and these interact differently at ultracold temperatures, opening up novel approaches to make better clocks and enabling a variety of fundamental physics experiments.

#### Accuracy Evaluations of Primary Atomic Clocks around the World

Another facet of our research program is advancing the accuracy of the primary atomic clocks around the world that contribute to International Atomic Time (TAI) and Coordinated Universal Time (*UTC*). Microwave cesium clocks are the current keepers of TAI. As of 2011, limiting systematic errors for the best cesium fountain clocks were a first-order Doppler shift due to phase gradients in the microwave cavities, the atom-interferometric microwave-lensing frequency shift, and frequency shifts due to background gas collisions. Our work on these systematic errors, in collaboration with the national labs of France, Germany , and the United Kingdom, has helped these clocks repeatedly improve the accuracy of the best clocks that set the tick-rate of TAI.

The first-order Doppler shifts, also known as the distributed cavity phase shift, arise in fountain clocks because the microwave cavity walls have losses. As a result, power travels to the walls from the feeds that supply the cavity, producing phase gradients in the cavity. These gradients, along with some motion of the cold atoms, yield a Doppler shift. We have published a comprehensive treatment of DCP shifts that shows how to evaluate and minimize them with better microwave cavity designs. Our new cavity design is a component of the latest UK clock.

The microwave lensing frequency shift is an atom-interferometric frequency that has to be considered for clocks with fraction frequency inaccuracies below 5×10^{-16}. The magnetic dipole energy due to the weak microwave field in the clock cavity focuses and defocuses the atomic wave packets, producing deflections of order nanometers of the centimeter-scale wave packets. The microwave lensing frequency corrections that we calculate, fractionally between 4×10^{-17} and 9×10^{-17}, are applied to most of the clocks contributing to TAI.

#### Atomic Clock Ensemble in Space (ACES) and the PHARAO laser-cooled microgravity cesium clock

PHARAO, Projet d’Horloge Atomique par Refroidissement d’Atomes en Orbite, is the laser-cooled caesium clock developed under the CNES for the European Space Agency mission ACES. ACES is scheduled to launch in 2018 and operate for 18 to 36 months on orbit on the International Space Station. ACES also includes a hydrogen maser, and several time-transfer systems. The ACES mission goals include fundamental physics tests of general relativity, searches for the time variation of fundamental constants, precise geodesy, and comparisons between clocks on Earth with a fractional frequency precision of 10^{-17}.

Our group is contributing to the accuracy evaluation of PHARAO, especially on the distributed cavity phase and microwave lensing frequency uncertainties. We have performed large finite-element models (FEM) of the PHARAO cavity. Without the cylindrical symmetry of the cavities used in fountain clocks, our FEM’s are fully 3D and use nearly all of our 1TB of available RAM. With PHARAO Chief Scientist Philippe Laurent and ACES Principal Investigator Christophe Salomon, we have recently evaluated the microwave lensing frequency shift of PHARAO. Its frequency correction is larger than for most fountains, 1.2×10^{-16}, slightly larger than the accuracy goal for PHARAO.

#### Precision measurements of ultracold scattering and Feshbach resonances with an atomic clock

We use lasers to cool atoms to 1 microKelvin, a millionth of a degree above absolute zero. At these low temperatures, the atoms are moving at a centimeter per second, as compared to the speed of sound for room-temperature atoms. These low velocities allow us to observe atoms for a long time, and this enables the high precision of atomic clocks and other measurements. However, at microKelvin temperatures the atoms are moving so slowly that quantum mechanical effects become important. They behave as waves and therefore their effective size for collisions with other atoms is vastly larger than at room-temperature, as the square of the deBroglie wavelength, about a million square Angstroms, whereas a typical size is 30 square Angstroms at room-temperature. These collisions cause a potential large frequency shift in laser-cooled clocks that is the most significant frequency error to minimize and evaluate.

In this experiment, we use an atomic clock to perform a novel scattering experiment to precise probe the atomic scattering. Our interferometric technique directly detects differences in quantum-mechanical scattering phase shifts. Such information is difficult to extract from measurements of scattering cross sections, both because cold atom densities are difficult to measure accurately and because cross sections depend on the squares of scattering lengths. In our atomic clock, a microwave pi/2 pulse creates a coherent superposition of the cesium clock states. This coherent superposition collides with target atoms in another state, acquiring s-wave phase shifts of each scattered clock state. Consequently, the phase of the scattered clock coherence jumps by the difference between the s-wave phase shifts, which we readout as a phase shift of the clock Ramsey fringes. We obtain mrad precision and accuracy, including through a series of Feshbach scattering resonances. This technique unambiguously and precisely tests the interatomic interaction and may set stringent limits on the time variation of fundamental constants.

#### Previous Research

Our research has significantly impacted the field of atomic clocks and cold-atom scattering. Our discovery of a small ultracold collision frequency shift of laser-cooled rubidium clocks led to the first amendment to the definition of atomic time. As a result of the small frequency shift, rubidium fountain clocks built by USNO now form the master clock for GPS, the most widely distributed timescale. We have contributed to space clock design through our Rubidium Atomic Clock Experiment (RACE) project, used juggling atomic fountains to perform scattering experiments, and demonstrated the first juggling fountain clock, which can dramatically improve clock stability.

Our work is made possible through support from the National Science Foundation, the NASA Fundamental Physics Program, and Penn State University

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Previous work was also supported by a NIST Precision Measurement Grant, and an NSF National Young Investigator award, and the Office of Naval Research.