Effectiveness of interactive tutorials in promoting “which-path” information reasoning in advanced quantum mechanics

Research suggests that introductory physics students often have difficulty using a concept in contexts different from the ones in which they learned it without explicit guidance to help them make the connection between the different contexts. We have been investigating advanced students’ learning of quantum mechanics concepts and have developed interactive tutorials which strive to help students learn these concepts. Two such tutorials, focused on the Mach-Zehnder interferometer (MZI) and the double-slit experiment (DSE), help students learn how to use the concept of “which-path” information to reason about the presence or absence of interference in these two experiments in different situations. After working on a pretest that asked students to predict interference in the MZI with single photons and polarizers of various orientations placed in one or both paths of the MZI, students worked on the MZI tutorial which, among other things, guided them to reason in terms of which-path information in order to predict interference in similar situations. We investigated the extent to which students were able to use reasoning related to which-path information learned in the MZI tutorial to answer analogous questions on the DSE (before working on the DSE tutorial). After students worked on the DSE pretest they worked on a DSE tutorial in which they learned to use the concept of which-path information to answer questions about interference in the DSE with single particles with mass sent through the two slits and a monochromatic lamp placed between the slits and the screen. We investigated if this additional exposure to the concept of which-path information promoted improved learning and performance on the DSE questions with single photons and polarizers placed after one or both slits. We find evidence that both tutorials promoted which-path information reasoning and helped students use this reasoning appropriately in contexts different from the ones in which they had learned it.

Figure 1

Schematic description of the design used to investigate RQ1.a and RQ1.b. Abbreviations in the figure are undergraduate students (UG), graduate students (GS), and $N$ refers to the number of students. The timeline of chronological order is from left to right as depicted by the blue arrows. All of the questions were given as pretests, i.e., the DSE polarizer questions in both RQ1.a and RQ1.b were always given before students worked on the DSE QuILT, and the MZI polarizer questions in RQ1.a were given before students worked on the MZI QuILT.

Figure 2

Schematic description of the design used to investigate RQ2. UG, GS, and $N$ have the same meaning as in Fig. 1. The timeline of chronological order is from left to right as depicted by the blue arrow.

Figure 3

Basic MZI setup.

Figure 4

Basic DSE setup with single photons.

Figure 5

MZI setup with a vertical polarizer placed in the upper path.

Figure 6

DSE setup with a vertical polarizer placed after slit 1.

Figure 7

Double slit setup with the addition of a lamp (image reproduced with permission from a simulation developed by Klaus Muthsam, muthsam@habmalnefrage.de).