Search Results (65 total)

We measured what students perceive physicists to believe about physics and solving physics problems and how those perceptions differ from the students’ personal beliefs. In this study, we used a modified version of the Colorado Learning Attitudes about Science Survey which asked students to respond to each statement with both their personal belief and the response they thought a physicist would give. Students from three different types of university introductory physics courses were studied. Students who have not yet taken physics in college have a surprisingly accurate idea of what physicists believe about physics no matter what their high school background and what physics courses they choose to take in college. These ideas are largely unaffected by their college physics instruction. In contrast, students’ personal beliefs about physics differ with varying high school physics backgrounds and college physics courses in which they enroll, and these beliefs are affected by college physics instruction. Women have a larger difference between their reported personal beliefs and their perceptions of physicists’ beliefs than do men.

We report on a large-scale study of student learning of quantum tunneling in four traditional and four transformed modern physics courses. In the transformed courses, which were designed to address student difficulties found in previous research, students still struggle with many of the same issues found in other courses. However, the reasons for these difficulties are more subtle, and many new issues are brought to the surface. By explicitly addressing how to build models of wave functions and energy and how to relate these models to real physical systems, we have opened up a floodgate of deep and difficult questions as students struggle to make sense of these models. We conclude that the difficulties found in previous research are the tip of the iceberg, and the real issue at the heart of student difficulties in learning quantum tunneling is the struggle to build the complex models that are implicit in experts’ understanding but often not explicitly addressed in instruction.

We report on measurements of the excitation spectrum of a strongly interacting Bose-Einstein condensate. A magnetic-field Feshbach resonance is used to tune atom-atom interactions in the condensate and to reach a regime where quantum depletion and beyond mean-field corrections to the condensate chemical potential are significant. We use two-photon Bragg spectroscopy to probe the condensate excitation spectrum; our results demonstrate the onset of beyond mean-field effects in a gaseous Bose-Einstein condensate.

We report on the observation of controllable phase separation in a dual-species Bose-Einstein condensate with ⁸⁵Rb and ⁸⁷Rb. Interatomic interactions between the different components determine the miscibility of the two quantum fluids. In our experiments, we can clearly observe immiscible behavior via a dramatic spatial separation of the two species. Furthermore, a magnetic-field Feshbach resonance is used to change them between miscible and immiscible by tuning the ⁸⁵Rb scattering length. The spatial density pattern of the immiscible quantum fluids exhibits complex alternating-domain structures that are uncharacteristic of its stationary ground state.

We report on the creation and characterization of heteronuclear ⁴⁰K⁸⁷Rb Feshbach molecules in an optical dipole trap. Starting from an ultracold gas mixture of ⁴⁰K and ⁸⁷Rb atoms, we create as many as 25 000 molecules at 300 nK by rf association. Optimizing the association process, we achieve a conversion efficiency of 25%. We measure the temperature dependence of the rf association process and find good agreement with a phenomenological model that has previously been applied to Feshbach molecule creation by slow magnetic-field sweeps. We also present a measurement of the binding energy of the heteronuclear molecules in the vicinity of the Feshbach resonance and provide evidence for Feshbach molecules as deeply bound as 26 MHz.

Using a Feshbach resonance, we create ultracold fermionic molecules starting from a Bose-Fermi atom gas mixture. The resulting mixture of atoms and weakly bound molecules provides a rich system for studying few-body collisions because of the variety of atomic collision partners for molecules; either bosonic, fermionic, or distinguishable atoms. Inelastic loss of the molecules near the Feshbach resonance is dramatically affected by the quantum statistics of the colliding particles and the scattering length. In particular, we observe a molecule lifetime as long as 100 ms near the Feshbach resonance.

Some education researchers have claimed that we should not teach the Bohr model of the atom because it inhibits students’ ability to learn the true quantum nature of electrons in atoms. Although the evidence for this claim is weak, many have accepted it. This claim has implications for how to present atoms in classes ranging from elementary school to graduate school. We present results from a study designed to test this claim by developing a curriculum on models of the atom, including the Bohr and Schrödinger models. We examine student descriptions of atoms on final exams in transformed modern physics classes using various versions of this curriculum. We find that if the curriculum does not include sufficient connections between different models, many students still have a Bohr-like view of atoms rather than a more accurate Schrödinger model. However, with an improved curriculum designed to develop model-building skills and with better integration between different models, it is possible to get most students to describe atoms using the Schrödinger model. In comparing our results with previous research, we find that comparing and contrasting different models is a key feature of a curriculum that helps students move beyond the Bohr model and adopt Schrödinger’s view of the atom. We find that understanding the reasons for the development of models is much more difficult for students than understanding the features of the models. We also present interactive computer simulations designed to help students build models of the atom more effectively.

We report on the observation of ultracold heteronuclear Feshbach molecules. Starting with a ⁸⁷Rb Bose-Einstein condensate and a cold atomic gas of ⁸⁵Rb, we utilize previously unobserved interspecies Feshbach resonances to create up to 25 000 molecules. Even though the ⁸⁵Rb gas is nondegenerate, we observe a large molecular conversion efficiency due to the presence of a quantum degenerate ⁸⁷Rb gas; this represents a key feature of our system. We compare the molecule creation at two different Feshbach resonances with different magnetic-field widths. The two Feshbach resonances are located at 265.44±0.15   G and 372.4±1.3  G. We also directly measure the small binding energy of the molecules through resonant magnetic-field association.

We observe bright matter-wave solitons form during the collapse of ⁸⁵Rb condensates in a three-dimensional (3D) magnetic trap. The collapse is induced by using a Feshbach resonance to suddenly switch the atomic interactions from repulsive to attractive. Remnant condensates containing several times the critical number of atoms for the onset of instability are observed to survive the collapse. Under these conditions a highly robust configuration of 3D solitons forms such that each soliton satisfies the condition for stability and neighboring solitons exhibit repulsive interactions.

The Colorado Learning Attitudes about Science Survey (CLASS) is a new instrument designed to measure student beliefs about physics and about learning physics. This instrument extends previous work by probing additional aspects of student beliefs and by using wording suitable for students in a wide variety of physics courses. The CLASS has been validated using interviews, reliability studies, and extensive statistical analyses of responses from over 5000 students. In addition, a new methodology for determining useful and statistically robust categories of student beliefs has been developed. This paper serves as the foundation for an extensive study of how student beliefs impact and are impacted by their educational experiences. For example, this survey measures the following: that most teaching practices cause substantial drops in student scores; that a student’s likelihood of becoming a physics major correlates with their “Personal Interest” score; and that, for a majority of student populations, women’s scores in some categories, including “Personal Interest” and “Real World Connections,” are significantly different from men’s scores.

A novel atom-molecule conversion technique has been investigated. Ultracold ⁸⁵Rb atoms sitting in a dc magnetic field near the 155 G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field. There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy. We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the phase space density of the sample. This technique offers high conversion efficiencies without the necessity of crossing or closely approaching the Feshbach resonance and allows precise spectroscopic measurements. Efficiencies of 55% have been observed for pure Bose-Einstein condensates.

We investigate the production efficiency of ultracold molecules in bosonic ⁸⁵Rb and fermionic ⁴⁰K when the magnetic field is swept across a Feshbach resonance. For adiabatic sweeps of the magnetic field, our novel model shows that the conversion efficiency of both species is solely determined by the phase space density of the atomic cloud, in contrast with a number of theoretical predictions. In the nonadiabatic regime our measurements of the ⁸⁵Rb molecule conversion efficiency follow a Landau-Zener model.

The spontaneous dissociation of ⁸⁵Rb dimers in the highest lying vibrational level has been observed in the vicinity of the Feshbach resonance that was used to produce them. The molecular lifetime shows a strong dependence on magnetic field, varying by 3 orders of magnitude between 155.5 G and 162.2 G. Our measurements are in good agreement with theoretical predictions in which molecular dissociation is driven by inelastic spin relaxation. Molecule lifetimes of tens of milliseconds can be achieved within approximately a 1 G wide region directly above the Feshbach resonance.

We precisely measured the binding energy (ε_bind) of a molecular state near the Feshbach resonance in a ⁸⁵Rb Bose-Einstein condensate (BEC). Rapid magnetic-field pulses induced coherent atom-molecule oscillations in the BEC. We measured the oscillation frequency as a function of B field and fit the data to a coupled-channel model. Our analysis constrained the Feshbach resonance position [155.041(18) G], width [10.71(2) G], and background scattering length [-443(3)a₀] and yielded new values for the Rb interaction parameters. These results improved our estimate for the stability condition of an attractive BEC. We also found evidence for a mean-field shift to ε_bind.

Bose-Einstein condensation, or BEC, has a long and rich history dating from the early 1920s. In this article we will trace briefly over this history and some of the developments in physics that made possible our successful pursuit of BEC in a gas. We will then discuss what was involved in this quest. In this discussion we will go beyond the usual technical description to try and address certain questions that we now hear frequently, but are not covered in our past research papers. These are questions along the lines of: How did you get the idea and decide to pursue it? Did you know it was going to work? How long did it take you and why? We will review some our favorites from among the experiments we have carried out with BEC. There will then be a brief encore on why we are optimistic that BEC can be created with nearly any species of magnetically trappable atom. Throughout this article we will try to explain what makes BEC in a dilute gas so interesting, unique, and experimentally challenging.¹

A cooling process for optical dipole traps, rf-induced Sisyphus cooling in a circularly polarized far-off-resonance trap, is demonstrated. Cooling rates of up to ≈300 μK/s are observed without significant atom loss. The final temperature achieved was (a somewhat disappointing) 17 μK. Experimental studies and theoretical analysis of this cooling process were carried out, which explain that the temperature limit is due to an equilibrium between the small fraction of total thermal energy that is removed per Sisyphus cycle and the multiple photon recoils that are required to complete each cycle. Light-induced collisional loss made it difficult to operate under conditions where a larger fraction of the energy would be removed. A method for storing atoms in an optical trap with only a single confined spin state is also demonstrated.

An initially stable ⁸⁵Rb Bose-Einstein condensate (BEC) was subjected to a carefully controlled magnetic field pulse near a Feshbach resonance. This pulse probed the strongly interacting regime for the BEC, with the diluteness parameter (na³) ranging from 0.01 to 0.5. Condensate number loss resulted from the pulse, and for triangular pulses shorter than 1 ms, decreasing the pulse length actually increased the loss, until very short time scales ( ∼10 μs) were reached. The observed time dependence is very different from that expected in traditional inelastic loss processes, suggesting the presence of new microscopic BEC physics.

We report extensions and corrections to the measurement of the Feshbach resonance in ⁸⁵Rb cold atom collisions reported earlier [J. L. Roberts et al., Phys. Rev. Lett. 81, 5109 (1998)]. In addition to a better determination of the position of the resonance peak [154.9(4) G] and its width [11.0(4) G], improvements in our techniques now allow the measurement of the absolute size of the elastic-scattering rate. This provides a measure of the s-wave scattering length as a function of magnetic field near the Feshbach resonance and constrains the Rb-Rb interaction potential.

The point of instability of a Bose-Einstein condensate (BEC) due to attractive interactions was studied. Stable ⁸⁵Rb BECs were created and then caused to collapse by slowly changing the atom-atom interaction from repulsive to attractive using a Feshbach resonance. At a critical value, an abrupt transition was observed in which atoms were ejected from the condensate. By measuring the onset of this transition as a function of number and attractive interaction strength, we determined the stability condition to be N|a| / a_ho  =  0.459±0.012±0.054, slightly lower than the predicted value of 0.574.

We investigate two-body loss in an optical dipole trap for ⁸⁷Rb atoms. In the presence of additional near-resonant light, such as from a magneto-optical trap during the trap loading, the two-body loss is strongly enhanced by long-range radiative escape. We suppressed this loss by a factor of 15 by adding a sideband to the optical dipole trap laser. This allows more atoms to be loaded into the optical dipole trap.

We have observed and characterized the dynamics of singly quantized vortices in dilute-gas Bose-Einstein condensates. Our condensates are produced in a superposition of two internal states of ⁸⁷Rb, with one state supporting a vortex and the other filling the vortex core. Subsequently, the state filling the core can be partially or completely removed, reducing the radius of the core by as much as a factor of 13, all the way down to its bare value of the healing length. The corresponding superfluid rotation rates, evaluated at the core radius, vary by a factor of 150, but the precession frequency of the vortex core about the condensate axis changes by only a factor of 2.

Bose-Einstein condensation has been achieved in a magnetically trapped sample of ⁸⁵Rb atoms. Long-lived condensates of up to 10⁴ atoms have been produced by using a magnetic-field-induced Feshbach resonance to reverse the sign of the scattering length. This system provides new opportunities for the study of condensate physics. The variation of the scattering length near the resonance has been used to magnetically tune the condensate self-interaction energy over a wide range, extending from strong repulsive to large attractive interactions. When the interactions were switched from repulsive to attractive, the condensate shrank to below our resolution limit, and after ∼5 ms emitted a burst of high-energy atoms.

Inelastic collision rates for ultracold ⁸⁵Rb atoms in the F  =  2, m_f  =  -2 state have been measured as a function of magnetic field. At 250 gauss (G), the two- and three-body loss rates were measured to be K₂  =  (1.87±0.95±0.19)×10^-14 cm³/s and K₃  =  (4.24_-0.29^+0.70±0.85)×10^-25 cm⁶/s, respectively. As the magnetic field is decreased from 250 G towards a Feshbach resonance at 155 G, the inelastic rates decrease to a minimum and then increase dramatically, peaking at the Feshbach resonance. Both two- and three-body losses are important, and individual contributions have been compared with theory.

We present a detailed experimental study of the physics involved in transferring atoms from a magneto-optical trap (MOT) to an optical dipole trap. The loading is a dynamical process determined by a loading rate and a density dependent loss rate. The loading rate depends on cooling and the flux of atoms into the trapping volume, and the loss rate is due to excited state collisions induced by the MOT light fields. From this study we found ways to optimize the loading of the optical dipole trap. Key ingredients for maximum loading are found to be a reduction of the hyperfine repump intensity, increased detuning of the MOT light, and a displacement of the optical dipole trap center with respect to the MOT. A factor of 2 increase in the number of loaded atoms is demonstrated by using a hyperfine repump beam with a shadow in it. In this way we load 8×10^{6 85}Rb atoms into a 1 mK deep optical dipole trap with a waist of 58 μm, which is 40% of the atoms initially trapped in the MOT.

The order parameter of a condensate with two internal states can continuously distort in such a way as to remove twists that have been imposed along its length. We observe this effect experimentally in the collapse and recurrence of Rabi oscillations in a magnetically trapped, two-component Bose-Einstein condensate of ⁸⁷Rb.