Bragg scattering as a probe of atomic wave functions and quantum phase transitions in optical lattices.

We have observed Bragg scattering of photons from quantum degenerate ^{87}Rb atoms in a three-dimensional optical lattice. Bragg scattered light directly probes the microscopic crystal structure and atomic wave function whose position and momentum width is Heisenberg limited. The spatial coherence of the wave function leads to revivals in the Bragg scattered light due to the atomic Talbot effect. The decay of revivals across the superfluid to Mott insulator transition indicates the loss of superfluid coherence.

Spin gradient demagnetization cooling of ultracold atoms.

We demonstrate a new cooling method in which a time-varying magnetic field gradient is applied to an ultracold spin mixture. This enables preparation of isolated spin distributions at positive and negative effective spin temperatures of ±50   pK. The spin system can also be used to cool other degrees of freedom, and we have used this coupling to cool an apparently equilibrated Mott insulator of rubidium atoms to 350 pK. These are the lowest temperatures ever measured in any system. The entropy of the spin mixture is in the regime where magnetic ordering is expected.

World Year of Physics: a direct test of E=mc2.

One of the most striking predictions of Einstein's special theory of relativity is also perhaps the best known formula in all of science: E=mc(2). If this equation were found to be even slightly incorrect, the impact would be enormous--given the degree to which special relativity is woven into the theoretical fabric of modern physics and into everyday applications such as global positioning systems. Here we test this mass-energy relationship directly by combining very accurate measurements of atomic-mass difference, Delta(m), and of gamma-ray wavelengths to determine E, the nuclear binding energy, for isotopes of silicon and sulphur. Einstein's relationship is separately confirmed in two tests, which yield a combined result of 1-Delta(mc2)/E=(-1.4+/-4.4)x10(-7), indicating that it holds to a level of at least 0.00004%. To our knowledge, this is the most precise direct test of the famous equation yet described.

Cyclotron frequency shifts arising from polarization forces.

The cyclotron frequency of a charged particle in a uniform magnetic field B is related to its mass m and charge q by the relationship omega(c) = qB/m. This simple relationship forms the basis for sensitive mass comparisons using ion cyclotron resonance mass spectroscopy, with applications ranging from the identification of biomolecules and the study of chemical reaction rates to determinations of the fine structure constant of atomic spectra. Here we report the observation of a deviation from the cyclotron frequency relationship for polarizable particles: in high-accuracy measurements of a single CO+ ion, a dipole induced in the orbiting ion shifts the measured cyclotron frequency. We use this cyclotron frequency shift to measure non-destructively the quantum state of the CO+ ion. The effect also provides a means to determine to a few per cent the body-frame dipole moment of CO+, thus establishing a method for measuring dipole moments of molecular ions for which few comparably accurate measurements exist. The general perturbation that we describe here affects the most precise mass comparisons attainable today, with applications including direct tests of Einstein's mass-energy relationship and charge-parity-time reversal symmetry, and possibly the weighing of chemical bonds.

Spin gradient thermometry for ultracold atoms in optical lattices.

We demonstrate spin gradient thermometry, a new general method of measuring the temperature of ultracold atoms in optical lattices. We realize a mixture of spins separated by a magnetic field gradient. Measurement of the width of the transition layer between the two spin domains serves as a new method of thermometry which is observed to work over a broad range of lattice depths and temperatures, including in the Mott insulator regime. We demonstrate the thermometry using ultracold rubidium atoms, and suggest that interesting spin physics can be realized in this system. The lowest measured temperature is 1 nK, indicating that the system has reached the quantum regime, where insulating shells are separated by superfluid layers.

Time to completion of web-based physics problems with tutoring.

We studied students performing a complex learning task, that of solving multipart physics problems with interactive tutoring on the web. We extracted the rate of completion and fraction completed as a function of time on task by retrospectively analyzing the log of student-tutor interactions. There was a spontaneous division of students into three groups, the central (and largest) group (about 65% of the students) being those who solved the problem in real time after multiple interactions with the tutorial program (primarily receiving feedback to submitted wrong answers and requesting hints). This group displayed a sigmoidal fraction-completed curve as a function of logarithmic time. The sigmoidal shape is qualitatively flatter for problems that do not include hints and wrong-answer responses. We argue that the group of students who respond quickly (about 10% of the students) is obtaining the answer from some outside source. The third group (about 25% of the students) represents those who interrupt their solution, presumably to work offline or to obtain outside help.

Researching for better instructional methods using AB experiments in MOOCs: results and challenges.

We conducted two AB experiments (treatment vs. control) in a massive open online course. The first experiment evaluates deliberate practice activities (DPAs) for developing problem solving expertise as measured by traditional physics problems. We find that a more interactive drag-and-drop format of DPA generates quicker learning than a multiple choice format but DPAs do not improve performance on solving traditional physics problems more than normal homework practice. The second experiment shows that a different video shooting setting can improve the fluency of the instructor which in turn improves the engagement of the students although it has no significant impact on the learning outcomes. These two cases demonstrate the potential of MOOC AB experiments as an open-ended research tool but also reveal limitations. We discuss the three most important challenges: wide student distribution, "open-book" nature of assessments, and large quantity and variety of data. We suggest possible methods to cope with those.

Itinerant ferromagnetism in a Fermi gas of ultracold atoms.

Can a gas of spin-up and spin-down fermions become ferromagnetic because of repulsive interactions? We addressed this question, for which there is not yet a definitive theoretical answer, in an experiment with an ultracold two-component Fermi gas. The observation of nonmonotonic behavior of lifetime, kinetic energy, and size for increasing repulsive interactions provides strong evidence for a phase transition to a ferromagnetic state. Our observations imply that itinerant ferromagnetism of delocalized fermions is possible without lattice and band structure, and our data validate the most basic model for ferromagnetism introduced by Stoner.

Phase diagram for a Bose-Einstein condensate moving in an optical lattice.

The stability of superfluid currents in a system of ultracold bosons was studied using a moving optical lattice. Superfluid currents in a very weak lattice become unstable when their momentum exceeds 0.5 recoil momentum. Superfluidity vanishes already for zero momentum as the lattice deep reaches the Mott insulator (MI) phase transition. We study the phase diagram for the disappearance of superfluidity as a function of momentum and lattice depth between these two limits. Our phase boundary extrapolates to the critical lattice depth for the superfluid-to-MI transition with 2% precision. When a one-dimensional gas was loaded into a moving optical lattice a sudden broadening of the transition between stable and unstable phases was observed.

Parametric amplification of scattered atom pairs.

We have observed parametric generation and amplification of ultracold atom pairs. A 87Rb Bose-Einstein condensate was loaded into a one-dimensional optical lattice with quasimomentum k0 and spontaneously scattered into two final states with quasimomenta k1 and k2 . Furthermore, when a seed of atoms was first created with quasimomentum k1 we observed parametric amplification of scattered atoms pairs in states k1 and k2 when the phase-matching condition was fulfilled. This process is analogous to optical parametric generation and amplification of photons and could be used to efficiently create entangled pairs of atoms. Furthermore, these results explain the dynamic instability of condensates in moving lattices observed in recent experiments.

Imaging the Mott insulator shells by using atomic clock shifts.

Microwave spectroscopy was used to probe the superfluid-Mott insulator transition of a Bose-Einstein condensate in a three-dimensional optical lattice. By using density-dependent transition frequency shifts, we were able to spectroscopically distinguish sites with different occupation numbers and to directly image sites with occupation numbers from one to five, revealing the shell structure of the Mott insulator phase. We used this spectroscopy to determine the onsite interaction and lifetime for individual shells.

Continuous and pulsed quantum zeno effect.

Continuous and pulsed quantum Zeno effects were observed using a 87Rb Bose-Einstein condensate. Oscillations between two ground hyperfine states of a magnetically trapped condensate, externally driven at a transition rate omega(R), were suppressed by destructively measuring the population in one of the states with resonant light. The suppression of the transition rate in the two-level system was quantified for pulsed measurements with a time interval deltat between pulses and continuous measurements with a scattering rate gamma. We observe that the continuous measurements exhibit the same suppression in the transition rate as the pulsed measurements when gammadeltat=3.60(0.43), in agreement with the predicted value of 4. Increasing the measurement rate suppressed the transition rate down to 0.005 omega(R).

Photon recoil momentum in dispersive media.

A systematic shift of the photon recoil momentum due to the index of refraction of a dilute gas of atoms has been observed. The recoil frequency was determined with a two-pulse light grating interferometer using near-resonant laser light. The results show that the recoil momentum of atoms caused by the absorption of a photon is n variant Planck's k, where n is the index of refraction of the gas and k is the vacuum wave vector of the photon. This systematic effect must be accounted for in high-precision atom interferometry with light gratings.

An ion balance for ultra-high-precision atomic mass measurements.

We have developed the analog of a double-pan balance for determining the masses of single molecular ions from the ratio of their two cyclotron frequencies. By confining two different ions on the same magnetron orbit in a Penning trap, we balance out many sources of noise and error (such as fluctuations of the magnetic field). To minimize the systematic error associated with the Coulomb interaction between the two ions, they are kept about 1 millimeter apart from each other, resulting in fractional uncertainty below 1 x 10(-11). Such precision opens the door to numerous applications of mass spectrometry, including metrology, fundamental physics, and weighing chemical bonds.

Glory oscillations in the index of refraction for matter waves.

We have measured the index of refraction for sodium de Broglie waves in gases of Ar, Kr, Xe, and N2 over a wide range of sodium velocities. We observe glory oscillations--a velocity-dependent oscillation in the forward scattering amplitude. An atom interferometer was used to observe glory oscillations in the phase shift caused by the collision, which are larger than glory oscillations observed in the cross section. The glory oscillations depend sensitively on the shape of the interatomic potential, allowing us to discriminate among various predictions for these potentials, none of which completely agrees with our measurements.

The onset of matter-wave amplification in a superradiant Bose-Einstein condensate.

The interaction of short and strong laser pulses with an atomic Bose-Einstein condensate is found to generate patterns of recoiling atoms that are different from those seen in previous light-scattering experiments. This phenomenon can only be explained by optical stimulation, showing that the previous description of superradiance as atomic stimulation is incomplete and that matter-wave amplification in Bose-Einstein condensates is suppressed at short times. Our experiments clarify the nature of bosonic stimulation in the four-wave mixing of light and atoms.

Dispersion compensation for atom interferometry.

A new technique for maintaining high contrast in an atom interferometer is used to measure large de Broglie wave phase shifts. Dependence of an interaction induced phase on the atoms' velocity is compensated by applying an engineered counterphase. The counterphase is equivalent to a rotation, is precisely determined by a frequency, and can be used to measure phase shifts due to interactions of unknown strength. Phase shifts of 150 rad (5 times larger than previously possible) have now been measured in an atom beam interferometer, and we suggest that this technique can enable comparisons of atomic polarizability with precision of one part in 10,000.