Macroscopic mechanical objects and electromagnetic degrees of freedom can couple to each other through radiation pressure. Optomechanical systems in which this coupling is sufficiently strong are predicted to show quantum effects and are a topic of considerable interest. Devices in this regime would offer new types of control over the quantum state of both light and matter, and would provide a new arena in which to explore the boundary between quantum and classical physics. Experiments so far have achieved sufficient optomechanical coupling to laser-cool mechanical devices, but have not yet reached the quantum regime. The outstanding technical challenge in this field is integrating sensitive micromechanical elements (which must be small, light and flexible) into high-finesse cavities (which are typically rigid and massive) without compromising the mechanical or optical properties of either. A second, and more fundamental, challenge is to read out the mechanical element's energy eigenstate. Displacement measurements (no matter how sensitive) cannot determine an oscillator's energy eigenstate, and measurements coupling to quantities other than displacement have been difficult to realize in practice. Here we present an optomechanical system that has the potential to resolve both of these challenges. We demonstrate a cavity which is detuned by the motion of a 50-nm-thick dielectric membrane placed between two macroscopic, rigid, high-finesse mirrors. This approach segregates optical and mechanical functionality to physically distinct structures and avoids compromising either. It also allows for direct measurement of the square of the membrane's displacement, and thus in principle the membrane's energy eigenstate. We estimate that it should be practical to use this scheme to observe quantum jumps of a mechanical system, an important goal in the field of quantum measurement.

We present the results of theoretical and experimental studies of dispersively coupled (or "membrane in the middle") optomechanical systems. We calculate the linear optical properties of a high finesse cavity containing a thin dielectric membrane. We focus on the cavity's transmission, reflection, and finesse as a function of the membrane's position along the cavity axis and as a function of its optical loss. We compare these calculations with measurements and find excellent agreement in cavities with empty-cavity finesses in the range 10 4 -10 5 . The imaginary part of the membrane's index of refraction is found to be ∼ 10 −4 . We calculate the laser cooling performance of this system, with a particular focus on the less-intuitive regime in which photons "tunnel" through the membrane on a time scale comparable to the membrane's period of oscillation. Lastly, we present calculations of quantum nondemolition measurements of the membrane's phonon number in the low signal-to-noise regime where the phonon lifetime is comparable to the QND readout time.

A major goal in optomechanics is to observe and control quantum behavior in a system consisting of a mechanical resonator coupled to an optical cavity. Work towards this goal has focused on increasing the strength of the coupling between the mechanical and optical degrees of freedom; however, the form of this coupling is crucial in determining which phenomena can be observed in such a system. Here we demonstrate that avoided crossings in the spectrum of an optical cavity containing a flexible dielectric membrane allow us to realize several different forms of the optomechanical coupling. These include cavity detunings that are (to lowest order) linear, quadratic, or quartic in the membrane's displacement, and a cavity finesse that is linear in (or independent of) the membrane's displacement. All these couplings are realized in a single device with extremely low optical loss and can be tuned over a wide range in situ; in particular, we find that the quadratic coupling can be increased three orders of magnitude beyond previous devices. As a result of these advances, the device presented here should be capable of demonstrating the quantization of the membrane's mechanical energy.Nearly all optomechanical systems realized to date can be characterized by a linear relationship between the optical cavity's detuning ω(x) and the displacement of the mechanical element x.1 In the classical regime this "linear" optomechanical coupling has enabled powerful laser cooling and sensitive displacement readout of the mechanical element.2-7 As ω ≡ ∂ω/∂x increases this linear coupling becomes stronger, and it should become possible to observe quantum effects such as laser-cooling to the mechanical ground state, 8, 9 quantumlimited measurements of force and displacement, 10, 11 and the production of squeezed light. 12In the quantum regime, however, the form of the optomechanical coupling plays a crucial role in determining which phenomena are observable. For example, linear coupling provides a continuous readout of x, and so precludes a direct measurement of one of the most striking features associated with the quantum regime: the quantization of the mechanical oscillator's energy.1

We have measured the optical and mechanical loss of commercial silicon nitride membranes. We find that 50 nm-thick, 1 mm 2 membranes have mechanical Q > 10 6 at 293 K, and Q > 10 7 at 300 mK, well above what has been observed in devices with comparable dimensions. The near-IR optical loss at 293 K is less than 2 × 10 −4 . This combination of properties make these membranes attractive candidates for studying quantum effects in optomechanical systems.

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[This paper is part of the Focused Collection on Upper Division Physics Courses.] We review and extend existing frameworks on modeling to develop a new framework that describes model-based reasoning in introductory and upper-division physics laboratories. Constructing and using models are core scientific practices that have gained significant attention within K-12 and higher education. Although modeling is a broadly applicable process, within physics education, it has been preferentially applied to the iterative development of broadly applicable principles (e.g., Newton's laws of motion in introductory mechanics). A significant feature of the new framework is that measurement tools (in addition to the physical system being studied) are subjected to the process of modeling. Think-aloud interviews were used to refine the framework and demonstrate its utility by documenting examples of model-based reasoning in the laboratory. When applied to the think-aloud interviews, the framework captures and differentiates students' model-based reasoning and helps identify areas of future research. The interviews showed how students productively applied similar facets of modeling to the physical system and measurement tools: construction, prediction, interpretation of data, identification of model limitations, and revision. Finally, we document students' challenges in explicitly articulating assumptions when constructing models of experimental systems and further challenges in model construction due to students' insufficient prior conceptual understanding. A modeling perspective reframes many of the seemingly arbitrary technical details of measurement tools and apparatus as an opportunity for authentic and engaging scientific sense making.

In response to national calls to better align physics laboratory courses with the way physicists engage in research, we have developed an epistemology and expectations survey to assess how students perceive the nature of physics experiments in the contexts of laboratory courses and the professional research laboratory. The Colorado Learning Attitudes about Science Survey for Experimental Physics (E-CLASS) evaluates students' epistemology at the beginning and end of a semester. Students respond to paired questions about how they personally perceive doing experiments in laboratory courses and how they perceive an experimental physicist might respond regarding their research. Also, at the end of the semester, the E-CLASS assesses a third dimension of laboratory instruction, students' reflections on their course's expectations for earning a good grade. By basing survey statements on widely embraced learning goals and common critiques of teaching labs, the E-CLASS serves as an assessment tool for lab courses across the undergraduate curriculum and as a tool for physics education research. We present the development, evidence of validation, and initial formative assessment results from a sample that includes 45 classes at 20 institutions. We also discuss feedback from instructors and reflect on the challenges of large-scale online administration and distribution of results.

A thoughtful approach to designing and improving labs, particularly at the advanced level, is critical for the effective preparation of physics majors for professional work in industry or graduate school. With that in mind, physics education researchers in partnership with the physics faculty at the University of Colorado Boulder have overhauled the senior-level Advanced Physics Lab course. The transformation followed a three part process of establishing learning goals, designing curricula that align with the goals, and assessment. Similar efforts have been carried out in physics lecture courses at the University of Colorado Boulder, but this is the first systematic research-based revision of one of our laboratory courses. The outcomes of this effort include a set of learning goals, a suite of new lab-skill activities and transformed optics labs, and a set of assessments specifically tailored for a laboratory environment. While the particular selection of advanced lab experiments varies widely between institutions, the overall transformation process, the learning goals, and the assessments are broadly applicable to the instructional lab community.