Craig Savage: publications since 2004

We present an investigation of game-like simulations for physics teaching. We report on the effectiveness of the interactive simulation "Real Time Relativity" for learning special relativity. We argue that the simulation not only enhances traditional learning, but also enables new types of learning that challenge the traditional curriculum. Full abstract.

We present a study of student learning through the use of virtual reality. A software package is used to introduce concepts of special relativity to students in a game-like environment where users experience the eﬀects of travelling at near light speeds. From this new perspective, space and time are signiﬁcantly diﬀerent to that experienced in everyday life. The study explores how students have worked with this environment and how these students have used this experience in their study of special relativity. A mixed method approach has been taken to evaluate the outcomes of separate implementations of the package at two universities. Students found the simulation to be a positive learning experience and described the sub ject area as being less abstract after its use. Also, students were more capable of correctly answering concept questions relating to special relativity, and a small but measurable improvement was observed in the ﬁnal exam.

In 2009 we tried an experiment in our large core first year physics course: we introduced mastery learning. The basic idea behind mastery learning is that any student can learn anything well, but that it takes some students much longer than others. We should therefore let students proceed through a course at different speeds, while insisting that they totally master each section of the course before moving on. Full abstract.

The students have to get over 80% in each homework assignment before they are allowed to take the next one. They are, however, allowed to take different versions of each assignment multiple times until they reach this threshold. At the end, the weaker students would have covered less content than the strong ones, but they should have fully understood whatever they did. In the laboratory component, the students were assessed in each experiment against a set of lab mastery goals. The students could pass the lab component only if they have mastered each of these goals at least once.

Did it work? Logistically it worked very well, somewhat to our surprise. There were a number of striking unexpected benefits: students did more work, complained less about the workload, asked for help more often, and showed an improved ability to solve questions first time around. Gains in student conceptual understanding were much improved, but this may be due to other innovations introduced in the course. Examination performance, however, did not improve, even on the most basic material. Students could do the problems when given unlimited time and assistance from peers, but not in exam conditions.

Ultra-cold clouds of dimeric molecules can dissociate into quantum mechanically correlated constituent atoms that are either bosons or fermions. We theoretically model the dissociation of cigar shaped molecular condensates, for which this difference manifests as complementary geometric structures of the dissociated atoms. For atomic bosons beams form along the long axis of the molecular condensate. For atomic fermions beams form along the short axis. This directional beaming simplifies the measurement of correlations between the atoms through relative number squeezing.

Learning Special Relativity is a highly anticipated experience for first year students; however, the teaching and learning of Special Relativity are difficult tasks. Full abstract.

Learning Special Relativity is a highly anticipated experience for first year students; however, the teaching and learning of Special Relativity are difficult tasks. Special Relativity, while fundamentally and mathematically simple; has apparently bizarre implications and deals predominately with situations outside everyday experience. Understanding relativity requires one to accept that there is less that is absolute than was once believed and to accept a model of time and space that is strange and unfamiliar. As such, modifying everyday concepts of motion, time and space to develop accurate constructs of the theory of Special Relativity is extraordinarily difficult. While Special Relativity is often featured in introductory physics courses, Scherr (2001) indicates many students fail to develop fundamental concepts in Special Relativity even after advanced instruction. To address these issues there has broad variety of efforts to determine the conceptual misunderstandings and develop activities to address them.

Real Time Relativity (RTR) is a virtual reality simulation of Special Relativity. Giving learners real time control of how they explore and test the optical, spatial and time effects of near-light-speed motion in a realistic environment enables a constructivist approach, previously unavailable, for learning Special Relativity.

Given the hands-on nature of RTR, it has been incorporated into the experimental laboratories of first year physics courses at the University of Queensland and the Australian National University. These experiments enable students to explore relativistic effects without requiring a detailed understanding of the theoretical framework. RTR experiments have been developed with an active learning approach in which students learn by developing, testing and refining their constructs with their peers. The RTR system and experiments are currently being refined in a model inspired by the Physics Education Technology group at the University of Colorado and evaluated through a multimethods research approach. This paper outlines our current point in a continuing development and evaluation project.

We perform a theoretical analysis of atomic four-wave mixing via a collision of two Bose-Einstein condensates of metastable helium atoms, and compare the results to a recent experiment. We calculate atom-atom pair correlations within the scattering halo produced spontaneously during the collision. We also examine the expected relative number squeezing of atoms on the sphere. The analysis includes first-principles quantum simulations using the positive P-representation method. We develop a unified description of the experimental and simulation results.

We analyze the dynamics of quantum statistics in a harmonically trapped Bose-Einstein condensate, whose two-body interaction strength is controlled via a Feshbach resonance. From an initially non-interacting coherent state, the quantum field undergoes Kerr squeezing, which can be qualitatively described with a single mode model. To render the effect experimentally accessible, we propose a homodyne scheme, based on two hyperfine components, which converts the quadrature squeezing into number squeezing. The scheme is numerically demonstrated using a two-component Hartree-Fock-Bogoliubov formalism.

We perform first-principles quantum simulations of dissociation of trapped, spatially inhomogeneous Bose-Einstein condensates of molecular dimers using the positive-P representation method. Specifically, we study spatial pair correlations of atoms produced in dissociation and analyze different correlation measures after time of flight. These include Glauber's density-density correlation and number-difference squeezing in spatial column densities which correspond to the experimental method of shot noise spectroscopy in absorption images. We find that the strength of the observable correlations may significantly degrade in systems with strong spatial inhomogeneity compared to the predictions of idealized uniform models. We show how binning of the signal can enhance the detectable correlations and lead to the violation of the classical Cauchy-Schwartz inequality.

Quasi-one dimensional outflow from a dilute gas Bose-Einstein condensate reservoir is a promising system for the creation of analogue Hawking radiation. We use numerical modeling to show that stable sonic horizons exist in such a system under realistic conditions, taking into account the transverse dimensions and three-body loss. We find that loss limits the achievable analogue Hawking temperatures, with sodium condensates allowing the highest temperatures. A condensate of 30,000 atoms, with transverse confinement frequency of 6800 × 2pi Hz, yields horizon temperatures of about 20 nK over a period of 50 ms. This is at least four times higher than for other atoms commonly used for Bose-Einstein condensates.

Real Time Relativity is a computer program that lets students fly at relativistic speeds though a simulated world populated with planets, clocks, and buildings. The counterintuitive and spectacular optical effects of relativity are prominent, while systematic exploration of the simulation allows the user to discover relativistic effects such as length contraction and the relativity of simultaneity. Full abstract.

We perform the first numerical three-dimensional studies of quantum field effects in the Bosenova experiment on collapsing condensates by E. Donley et al. [Nature 415, 39 (2002)] using the exact experimental geometry. In a stochastic truncated Wigner simulation of the collapse, the collapse times are larger than the experimentally measured values. We find that a finite temperature initial state leads to an increased creation of uncondensed atoms, but not to a reduction of the collapse time. A comparison of the time-dependent Hartree-Fock-Bogoliubov and Wigner methods for the more tractable spherical trap shows excellent agreement between the uncondensed populations. We conclude that the discrepancy between the experimental and theoretical values of the collapse time cannot be explained by quantum fluctuations or finite temperature effects.

Real Time Relativity is a computer program that allows the user to fly through a virtual world governed by relativistic physics. Full abstract.

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with non-opposite momenta. The net effect of this process -- which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion -- is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode-mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.

We have developed a relativistically-accurate computer graphics code and have used it to produce photo-realistic images and videos of scenes where special relativistic effects dominate, either in astrophysical contexts or in imaginary worlds where the speed of light is only a few metres per second. The videos have been integrated into our under-graduate teaching programme for several years. Recently we took the next step, encouraging undergraduate students to use the code to explore relativity, develop their own videos, and eventually package them together into Through Einstein's Eyes, a multimedia CD.

We show that the stability of three-dimensional Skyrmions in trapped Bose-Einstein condensates depends critically on scattering lengths, atom numbers, trap rotation and trap anisotropy. In particular, for the ⁸⁷Rb |F=1,m_f=-1>, |F=2,m_f=1> hyperfine states stability is sensitive to the scattering lengths at the level of their present experimental uncertainties. In a cigar shaped trap, we find stable Skyrmions with as few as 2 x10⁶ atoms, a number which scales with the inverse square root of the trap frequency. These can be stabilized against drift out of the trap by laser pinning.

We show that sound waves scattered from a hydrodynamic vortex may be amplified. Such superradiant scattering follows from the physical analogy between spinning black holes and hydrodynamic vortices. However a sonic horizon analogous to the black hole event horizon does not exist unless the vortex possesses a central drain, which is challenging to produce experimentally. In the astrophysical domain, superradiance can occur even in the absence of an event horizon: we show that in the hydrodynamic analogue, a drain is not required and a vortex scatters sound superradiantly. Possible experimental realization in dilute gas Bose-Einstein condensates is discussed.

We analyse quantum field models of the bosenova experiment, in which ⁸⁵Rb Bose-Einstein condensates were made to collapse by switching their atomic interactions from repulsive to attractive. Specifically, we couple the lowest order quantum field correlation functions to the Gross-Pitaevskii function, and solve the resulting dynamical system numerically. Comparing the computed collapse times with the experimental measurements, we find that the calculated times are much larger than the measured values. The addition of quantum field corrections does not noticeably improve the agreement compared to a pure Gross-Pitaevskii theory.

By direct comparison between experiment and theory, we show how the classical noise on a multi-state atom laser beam increases with increasing flux. Full abstract.

By direct comparison between experiment and theory, we show how the classical noise on a multi-state atom laser beam increases with increasing flux. The trade off between classical noise and flux is an important consideration in precision interferometric measurement. We use periodic 10 microsecond radio-frequency pulses to couple atoms out of an F=2 87Rb Bose-Einstein condensate. The resulting atom laser beam has suprising structure which is explained using three dimensional simulations of the five state Gross-Pitaevskii equations.

Publications 2004-now mainly cold atoms and relativistic optics

Publications 2004-now
mainly cold atoms and relativistic optics