Response to "Comment on 'A versatile thermoelectric temperature controller with 10 mK reproducibility and 100 mK absolute accuracy"' [Rev. Sci. Instrum. 80, 126107 (2009)]

The preceding comment by Sloman points out that the absolute accuracy of a temperature controller may be compromised by thermistor self-heating. We measured the self-heating of the thermistor used in our temperature controller, verifying a systematic error of nearly 200 mK. However, this error is reduced by over an order of magnitude with a slight change in our original circuit design. With this change, our controller does achieve an absolute temperature accuracy of 100 mK, limited mainly by the stated absolute accuracy of the thermistor used in the circuit

Interferometric measurement of the resonant absorption and refractive index in rubidium gas

We present a laboratory demonstration of the Kramers-Kronig relation between the resonant absorption and refractive index in rubidium gas. Our experiment uses a rubidium vapor cell in one arm of a simple Mach-Zehnder interferometer. As the laser frequency is scanned over an atomic resonance, the interferometer output is affected by variations of both the absorption and refractive index of the gas with frequency, all of which can be calculated in a straightforward manner. Changing the vapor density and interferometer phase produces a family of different output signals. The experiment was performed using a commercially available tunable diode laser system that was designed specifically for the undergraduate physics laboratory. As a teaching tool this experiment is reliable, fun, and instructive, while it also introduces the student to some sophisticated and fundamental physical concepts

A versatile thermoelectric temperature controller with 10 mK reproducibility and 100 mK absolute accuracy

We describe a general-purpose thermoelectric temperature controller with 1 mK stability, 10 mK reproducibility, and 100 mK absolute accuracy near room temperature. The controller design is relatively simple and could be readily modified for use in different experimental circumstances. We also describe a time-domain numerical model that allows one to characterize the stability and transient behavior of the system being controlled, even in the presence of elements with highly nonlinear responses

Crystal Growth in the Presence of Surface Melting: Novel Behavior of the Principal Facets of Ice

We present measurements of the growth rates of the principal facet surfaces of ice from water vapor as a function of supersaturation over the temperature range -2 C > T > -40 C. Our data are well described by a dislocation-free layer-nucleation model, parameterized by the attachment coefficient as a function of supersaturation \alpha(\sigma) = Aexp(-\sigma_0/\sigma). The measured parameters A(T) and \sigma_0(T) for the basal and prism facets exhibit a complex behavior that likely originates from structural changes in the ice surface with temperature, in particular the onset and development of surface melting for T > -15 C. From \sigma_0(T) we extract the terrace step energy \beta(T) as a function of temperature for both facet surfaces. As a basic property of the equilibrium ice surface, the step energy \beta(T) may be amenable to calculation using molecular dynamics simulations, potentially yielding new insights into the enigmatic surface structure of ice near the triple point

Measurements of Growth Rates of (0001) Ice Crystal Surfaces

We present measurements of growth rates of the (0001) facet surface of ice as a function of water vapor supersaturation over the temperature range $-2$ $\geq T\geq -40$ C. From these data we infer the temperature dependence of premelting on the basal surface and the effects of premelting on the ice growth dynamics. Over this entire temperature range the growth was consistent with a simple 2D nucleation model, allowing a measurement of the critical supersaturation $\sigma _{0}(T)$ as a function of temperature. We find that the 2D nucleation barrier is substantially diminished when the premelted layer is partially developed, as indicated by a reduced $\sigma _{0},$ while the barrier is higher both when the premelted layer is fully absent or fully developed

A low‐noise high‐speed diode laser current controller

We describe a new diode laser current controller which features low current noise, excellent dc stability, and the capacity for high‐speed modulation. While it is simple and inexpensive to construct, the controller compares favorably with the best presently available commercial diode laser current controllers

Creating long-lived neutral-atom traps in a cryogenic environment

We describe techniques for creating long-lived magneto-optical and magnetostatic traps for neutral atoms. These traps exist in a sealed cryogenic environment with a temperature near 4 K, where the background gas pressure can be extremely low. To date we have observed cesium magneto-optical traps with background-limited lifetimes in excess of 1 h, and magnetostatic traps with lifetimes of nearly 10 min. From these observations we use the known He-Cs van der Waals collision cross section to infer typical background gas pressures in our apparatus below 4×10^(-12) Torr. With hardware improvements we expect this pressure can be made much lower, extending the magnetostatic-trap lifetimes one to two orders of magnitude. Furthermore, with a cryogenic system one can use superconducting magnets and SQUID detectors to trap and to nondestructively sense spin-polarized atoms. With superconducting microstructures one can achieve very large magnetic-field gradients and curvatures, as high as ∼10^6 G/cm and ∼10^9 G/cm^2, respectively, for use in magnetic and magneto-optical traps

Absolute and differential measurement of water vapor supersaturation using a commercial thin-film sensor

We describe a technique for measuring the water vapor supersaturation of normal air over a temperature range of –40<~T<~0 °C. The measurements use an inexpensive commercial hygrometer which is based on a thin-film capacitive sensor. The time required for the sensor to reach equilibrium was found to increase exponentially with decreasing sensor temperature, exceeding 2 min for T = –30 °C; however, the water vapor sensitivity of the device remained high down to this temperature. After calibrating our measurement procedure, we found residual scatter in the data corresponding to an uncertainty in the absolute water vapor pressure of about ±15%. This scatter was due mainly to long-term drift, which appeared to be intrinsic to the capacitive thin-film sensor. The origin of this drift is not clear, but it effectively limits the applicability of this instrument for absolute measurements. We also found, however, that the high sensitivity of the thin-film sensor makes it rather well suited for differential measurements. By comparing supersaturated and saturated air at the same temperature we obtained a relative measurement uncertainty of about ±1.5%, an order of magnitude better than the absolute measurements

A basic lock-in amplifier experiment for the undergraduate laboratory

We describe a basic experiment for the undergraduate laboratory that demonstrates aspects of both, the science and the art of precision electronic measurements. The essence of the experiment is to measure the resistance of a small length of brass-wire to high accuracy using a simple voltage divider and a lock-in amplifier. By performing the measurement at different frequencies and different drive currents, one observes various random noise sources and systematic measurement effects