This is a my personal collection of programs for the SwissMicros DM42 pocket calculator which is based on the excellent Free42 simulator by Thomas Okken of the classic HP-42S calculator by Hewlett Packard.
Most of the programs are related to the requirements in atomic physics experiments but there is also some electronics and further completely unrelated stuff around.
Even though the programs should be mostly compatible with the original HP-42S they do make use of some of the convenience functions offered by Free42 and for graphical output the advanced capabilities of the DM42 platform are also partially relied on.
In the following we will quickly present each of the programs in the present collection.
This program calculates the energy difference f/MHz (in MHz) between the two
lowest hyperfine Zeeman levels, often denoted |1> and |2>, of Lithium-6 given
the applied magnetic field B/G (in Gauss) using the Breit-Wigner formula. It
is intended for use with the Solver application so it can also be used to
convert a frequency difference back into a magnetic field.
This is a collection of currently three programs for often needed calculations
with Gaussian beams selected by a menu system. Imax calculates the peak
intensity given the beam power and the waist size, and the Rayleigh length is
calculated by zR given waist and wavelength. Finally Focus is intended to
calculate the beam waist of a Gaussian beam that is focused by a lens.
Parameters are the WAIST size and its position Z0 of the incident beam, its
wavelength LAMBDA and the focal length F of the lens.
This is a simple converter program for capacitor values. It converts between
the nominal capacitance and the code number often printed on small capacitor
packages. Either enter the capacity (in Farad, e.g. 1ᴇ-7) and push →CODE or
give the code (e.g. 104) and push →VAL for the conversion.
This tool helps to quickly convert between setpoint voltages and the actual
magnetic fields created by three mutually orthogonal Helmholtz coil pairs. It
is intended for use from within the Solver application. The axis is chosen by
putting 1, 2 or 3 into Axis. Then, one starts by either giving the CMag/V
voltage or the B/G field and solves for the unknown. Internally each axis is
parameterized by a first order polynomial with the parameters ofst and
scale as local variables. Units are 'V' for ofst and 'V/(100 mG)' for
scale.
Based on CODATA 2018 this program is a collection of physical constants probably most useful for work in the field of atom-optics. It is implemented using the Free42 'FUNC' command to leave the stack unchanged and also includes some additional information on each constant (name and unit) in the ALPHA register which gets displayed.
This small tool converts between power in dBm, mW, Vpp (peak-to-peak
voltage) and Vrms (root-mean-square voltage). Enter the known numeric value
and the softkey corresponding to the initial unit. Then press the softkey of
the target unit and the converted value will be shown.
This program is intended for use with the Solver application and converts
between molecular binding energy E/Hz and effective scattering length a/a0,
given the masses (in amu) of the two atomic species involved and the finite
interaction range correction r0/a0. This range correction factor is related
to the C6 coefficient and can be determined with the C6-r0 helper program
(which is also intended for use with the Solver).
This collection of eight programs is to calculate the potential created by a pair laser beams forming a crossed FORT (far-off-resonance trap). The program is here presented in the files FORT_structure_overview.hp42s, giving only an annotated overview of the programs and sub-labels, and FORT_with_subprograms.hp42s which contains the detailed listings of all programs. Please look at both files for the details of the included programs and their individual inner workings.
The main frontend program is FORT. In the menu one defines the control voltages
H-VLT and V-VLT of the horizontal and vertical FORT lasers. These are
internally converted into laser powers. With these basic settings use CALC to
calculate the trap position, its frequencies and depth. The results are
accessed via G SAG (the gravitational sag atoms experience in the trap) and
FREQ (a summary of the three trapping frequencies). Use PLOT to plot a
vertical cut through the center of the trap on the display of the DM42. The
vertical zero position, the trap minimum and its maximum are indicated by
vertical and horizontal lines, respectively. On the second page of the menu the
atomic species can be selected (168Er, 174Yb, 7Li, 6Li) and the type of
trapping lasers (current options are 1 µm for a crossed FORT at 1064 and 1070
nm, and 1.5 µm for a FORT operating at 1550 nm) can be selected.
Finally, with PRNT a complete summary of the laser setup, the trap geometry
and a plot of the trap potential is printed to an IR printer such as the HP
82240A.
Plotting relies on the excellent DISPLAY program originally presented by
Bill in the SwissMicros
forum. This routine
is used for adding string output to the graphics output of the DM42. I here
use a slightly modified version of this program by encapsulating everything in
a 'FUNC 00' call to prevent any changes of the stack by the execution of
DISPLAY.
This program is based on the original HP-42S Owner´s manual PLOT routine. It is here expanded to also print out a frame around the plot with tic marks and labels. The program itself is not ready for use as-is. Rather, it served to develop the printing routines of the FORT program.
This program is for converting wavelengths, etc., between the wavelenth in
nm, the frequency in THz, the wavenumber in 1/cm, oscillation period in
fs, and the photon energy in eV and in J. Enter the known numeric value
and the softkey corresponding to the initial unit. Then press the softkey of
the target unit and the converted value will be shown.
This program serves the same purpose as 'B-F'. It calculates the energy difference (in MHz) between the two lowest hyperfine Zeeman levels, often denoted |1> and |2>, of Lithium-6 given the applied magnetic field (in Gauss). However, instead of using the Breit-Wigner formula it starts by formulating the Lithium ground state Hamiltonian which is then diagonalized and the difference of the two lowest eigenvalues gives the splitting energy.
The result is numerically equivalent to the Breit-Wigner expression. It is, however, much more computationally intensive, needs more time and memory but it was also a fun programming exercise. Internally the TRED2 and TQLI routines of 'Numerical Recipes' are used to do the heavy lifting.
One method of calibrating the depth of an optical lattice in ultracold atom
experiments is to use very short lattice pulses and to observe the
interference pattern of a Bose-Einstein condensate after release from the
trap. In particular minima and maxima of the oscillation pattern as function
of either lattice beam intensity or pulse duration can be compared to
numerical calculations to determine the lattice depths. The program internally
assumes a lattice laser wavelenth of 532 nm (set in REG 01) and a mass of 174
amu (REG 02). The lattice depth (in units of the recoil energy) is set via the
s menu and the pulse duration (in µs) via t. To change those values, press
the corresponding softkey, enter the new value and confirm by pressing R/S.
Then, by pressing CALC the fractional population of the zero momentum ('k =
0') peak is calculated and displayed. Finally, with PLOT the DM42 plots for
the specified lattice depth s the development of the k = 0 and the |k| = 1
order peaks as function of the pulse duration. The minima and maxima of the k = 0
curve are labeled with their respective pulse durations. Press R/S to return
to the main menu.
Plotting relies on the excellent DISPLAY program originally presented by
Bill in the SwissMicros
forum. This routine
is used for adding string output to the graphics output of the DM42. I here
use a slightly modified version of this program by encapsulating everything in
a 'FUNC 00' call to prevent any changes of the stack by the execution of
DISPLAY.
Additionally, the helper program TQLI.hp42s for matrix diagonalization is required.
This simple program calculates the central density of a thermal gas in a
harmonic trap. Input parameters are the number of atoms N, their temperature
T (in K) and the atomic MASS in amu. Furthermore the trap frequencies (in
Hz) are expected to be stored in the 3x1 matrix TRAPF. The menu is
implemented as a standard VARMENU and the calculation is started by pressing
R/S.
This small tool converts from the color code of a resistor to its numerical resistance value. Just key in the colors one-by-one with the softkeys (use up and down to access all colors) and observe how the resister value slowly builds up.
This is the stock plotting program from chapter 10 of the HP-42S Owner´s manual for use with, e.g., an HP 82240A printer.
Seeing physical values with unnecessarily large or small exponents is prone to errors in the interpretation, therefore we usually use prefixes such as 'k', 'M', or 'µ'. The PREFIX program (implented as 'FUNC 00' to keep the stack in order) looks at the value in ST X, determines the most appropriate prefix, and adds the properly formatted number and its prefix character to the ALPHA register.
This package consists of three programs, the beam propagator BPROP, the cavity mode calculator CAVITY and the beam size plotter BPLOT.
At its heart the non-interactive program BPROB takes the variables WAIST,
Z0 and LAMBDA that define incident waist size, position and wavelength of
the Gaussian input beam, and calculated the beam parameters at the final
position POS. The beam is propagated through the optical system defined in
the matrix OSYS. The final radius is stored in RF and the complex output
beam parameter is retained in QO. The matrix OSYS defined pairs of beam
path elements (DIST, LENS, or MIRROR) and their parameters (distance, focal
length, or radius of curvature). See the end of PROPAG.hp42s
for some examples.
The beam plotter BPLOT works in close analogy to the original HP-42S DPLOT program and plots the size of the Gaussian beam as it traverses the optical system. The positions of the optical elements are indicated by vertical lines.
Finally, the cavity mode calculator CAVITY is for use with the Solver application and, given an optical system where the output of the last element can again be considered as the input of the same system, self-consistently finds the waist of the cavity mode. Note that the waist is assumed to be at position zero, that is coinciding with the input/output of the system.
This small program calculates the p-wave threshold energy (expressed as a
temperature in µK) for collisions between atoms with masses M1 and M2
(both in amu) and with a provided C6 coefficient. The menu system is a
standard VARMENU.
This set of two programs is to convert between the resistance of a typical 10 kΩ NTC thermistor and the actual temperature. The program R2T does the actual conversion between the resistance in ST X and the temperature in °C returned on the stack. The second program, T←→R, is a convenient frontend for use with the Solver application to quickly go back and forth between resistances and temperatures.
In the current version the NTC is assumed to be of type EC95F and the conversion is parameterized for the range 0 to 50°C as a third order polynomial.
This small tool, s←→T, is to determine the temperature of a cold atomic cloud
from the width of a Gaussian fit to a time-of-flight image. Necessary values
are the width s/μm (the 'sigma' width), the expansion time t/ms and the
atomic mass a/amu. The temperature is then given in T/μK. For maximal
flexibility the program is designed for the Solver application so that any
unknown parameter may be determined.
This is an implementation of the TQLI routine of Numerical recipes for the DM42. It is required for the HLi6 and LATTICE programs.
This is an implementation of the TRED2 routine of Numerical recipes for the DM42. It is required for the HLi6 program.
This is a small utility to convert between date/time in the usual notation and in UNIX time, that is the seconds since 1970/01/01. Alternatively, when FLAG 01 is set, the seconds since 1904/01/01 can also be calculated which is the convention used by LabView.
After so much physics and math a good cup of coffee is in order, preferably
made as a V60 drip coffee. But do you always remember the proper water
quantities and timings for the perfect cup? No? Fear not as now your DM42 (or
Free42 on your phone where it admittedly looks better) can give you a hand in
maintaining the perfect timing for all your pours. Everything starts by a
recipe which is stored in the matrix V60R it defines the names and the times
(in H.MMSS format) for each step. It provides the total elapsed time and the
time till the next step. There is even a preview of the upcoming step so that
you can better prep yourself.
My favorite method is the 4-6 method by Tetsu Kasuya. Find the recipe at the end of the V60.hp42s, use it as-is or take it as a base for your own approach.
And now, enjoy your coffee.
For any comments and/or bug reports please report to the author, schaefer@scphys.kyoto-u.ac.jp.