Gaussian software harmonic osscialtor approximation

#GAUSSIAN SOFTWARE HARMONIC OSSCIALTOR APPROXIMATION LICENSE#
#GAUSSIAN SOFTWARE HARMONIC OSSCIALTOR APPROXIMATION FREE#

Enter displacement of harmonic oscillator along axis 0: 0 Enter harmonic oscillator eigenstate for axis 0: Enter the complex normalization 're im' for state 0: + Enter the number of superimposed states: Finally, specify the displacement of the eigenstate from the origin along each axis (probably you're just going to want to enter 0). In the example, we just have the ground state, so the coefficient is 1.0 + 0.0 i (which we enter as 1 0), and the eigenvalue is of course 0. if we were working in three dimensions, you need to give three numbers to describe a particular harmonic oscillator eigenstate). Next, specify the complex coefficient for each eigenstate, as well as the corresponding eigenvalue for each axis (i.e. After we enter the omega, we're asked to enter the number of superimposed states, which is just the number of harmonic oscillator eigenstates we sum over to get the initial state for this particular level. We do this by specifying a state for each level, giving the states in terms of harmonic oscillator eigenstates (this means we have to tell qsims what omega to use when generating the harmonic oscillator eigenstates-yes, you have to enter omega again, since you could conceivably want a different omega). Enter dx, or -omega to have dx calculated automatically: Finally, enter the length interval dx, or alternatively, if your potential is going to be roughly harmonic, enter -omega (where omega is the angular frequency of the harmonic potential) to have an optimal value for dx automatically calculated. Next, enter the number of grid points used in the discretization of the spatial wavefunction, for each dimension (hint: powers of two are good, as are products of powers of small prime numbers). Then, enter the number of motional degrees of freedom (e.g. Now we have to enter some simulation parameters. The mass is used when calculating the kinetic term in the Hamiltonian, and also in harmonic potentials. Next, enter the value of hbar (which is 1 in atomic units), and the mass of the atom.

#GAUSSIAN SOFTWARE HARMONIC OSSCIALTOR APPROXIMATION LICENSE#

See the GNU General Public License 2 (or any later version) for details.

#GAUSSIAN SOFTWARE HARMONIC OSSCIALTOR APPROXIMATION FREE#

qsims is free software,ДЄnd you are welcome to redistribute it under certain conditions. Qsims v0.4 Copyright (c) 2004 Travis Beals, Built Mar 2 2005 Upon launch, qsims displays a short blurb about the GNU General Public License, which is the license under which qsims is distributed. You can also use '-f filename' to read input from a file, '-p parameters' to use the parameters given on the command line, or '-h' for help. Launch qsims from the command line with the '-i' option to enter interactive mode. Just specify the appropriate values for hbar and other constants when asked. qsims is unit-agnostic-you are free to use whatever units you want with qsims. energy is given in Hartrees, lengths are specified in multiples of the Bohr Radius, time is in units of hbar / Hartree, and mass is multiples of the electron mass. The units used in this tutorial are 'atomic units', e.g. There are also time-dependent couplings between the levels, which would be generated by appropriate microwave pulses in an actual experiment. Physically, these Gaussian terms would be the result of an AC Stark Shift (or 'light shift') due to an 'addressing' laser focused on this particular atom. same in magnitude but opposite in sign to that experienced by |3>. |3> also is subject to a small Gaussian-shaped trapping potential, while |4> experiences a Gaussian anti-trapping potential (e.g. The atom experiences a state-dependent potential, with all states experiencing a harmonic trapping potential.

Specifically, the levels are m F=0 F=3 and F=4 (labeled |0> and |1>), and m F=1 F=4 and F=3 (labeled |3> and |4>), as shown in the figure on the right. The levels are a subset of the hyperfine sublevels of the 6 2S 1/2 state. In the simulation example, the atom has one degree of motional freedom, and four possible internal states ('levels'). This tutorial covers the following topics: This particular example is a simulation of a one-qubit gate-a 'flip' or NOT gate (equivalently, a rotation by pi about the X axis, in the Bloch sphere picture). Alkali atoms in optical lattices are one of the proposed methods of realizing a quantum computer. The example in this tutorial is a good approximation to a real physical situation, namely a Cesium-133 atom in an addressable optical lattice.

Gaussian software harmonic osscialtor approximation