Reference.Variables.control

Variable "control" in MATLAB/Octave version of WavePacket

This global, structured(!) variable contains all information about control targets and related issues. Mainly used in qm_propa and/or qm_optimal, partly also in qm_matrix, qm_abncd.

Settable parameters

control.observe	Observables to be defined in qm_matrix (≥ V 5.3.0)
types	'amo' - additional multiplicative operators 'prj' - Populations from (mean values of) projectors onto eigenstates 'ovl' - Populations from (absolute squares of) overlaps with eigenstates (TDSE only!)
choices	cell vector of integer vectors selecting (one or several) of the 'amo' or 'prj' or 'ovl' type observables
labels	cell vector containing labels for the selected observables (can be empty for 'amo')
targets	integer vector selecting observables to serve as targets in (optimal) control Used in qm_abncd

control.plot	plot settings used for qm_propa and qm_optimal (≥ V 5.3.0)	default
uxy	Plot evolution of variables u(t), x(t), y(t) as figure 7	true
j12	Plot functionals j1, j2, jtotal as figure 8	true
psd	Plot power spectal density (PSD) and frequency resolved optical gating (FROG) as figure 9	true
mov	Create animation (movie) of variables u(t), x(t), y(t)	false

control.optimal	Specific information for optimal control used in qm_optimal	default
terminal	Which of the observables to be optimized (≥ V 5.3.0) Currently restricted to a single target; multi-target optimal control not yet implemented. Evaluated at terminal time; "running" targets (averages over time) not yet implemented	2
tolerance	Terminate iterations in OCT scheme when increment falls below this threshold	1e-3
max_iter	Maximum number of iterations in OCT scheme; default value is zero. Note that for max_iter=0 our function qm_optimal does essentially the same as qm_control, except for the difference of constant versus adaptive time-stepping	0
alpha	Penalty factor α to keep the laser fluence bounded Higher values of α favor minimization of the cost functional (laser fluence) Lower values of α favor maximization of the target functional See Fig 1d in work by Werschnik/Gross (2007)	1
eta	mixing coefficient η for optimal field in backward propagation	1
zeta	mixing coefficient ζ for optimal field in forward propagation	1
order	error order for calculations of optimal fields	1
prefactor	How to calculate the prefactor ⟨x(t),z(t)⟩ for fields when optimizing ⟨c,x(t)⟩² rather than ℜ⟨c,x(t)⟩ Either one of 'initial', 'current', or 'final' Option 'current' is most efficient, even though only 'final' is formally correct	'current'
fb_test	If set to true, testing only whether backward- and forward-propagation do really cancel each other for identical control field(s) u(t). Note that this is (numerically!) not trivial for LvNE with dissipation	false

control.lvne	Specific information for Liouville-von Neumann equation used in qm_abncd
order	tetradic ordering of vectorized density matrices (LvNE only). If not specified, columnwise ordering is used (which is MATLAB's default). If set to 'df', then diagonals first, followed by off-diagonals
temperature	temperature used for thermal equilibrium density matrix (LvNE only)

control.relax	Lindblad operators for relaxation used in qm_abncd (≥ V 5.3.0)
model	population relaxation model; one of 'fermi', 'einstein', 'constant', 'datafile', or 'none' where the latter one is the default. For model 'datafile', the rates are read from file 'relax.mat'
rate	specify one population relaxation rate (for models 'fermi', 'einstein', or 'constant')
upper	specify upper state pertaining to that rate (for model 'fermi' or 'einstein')
lower	specify lower state pertaining to that rate (for model 'fermi' or 'einstein')

control.depha	Lindblad operators for pure dephasing used in qm_abncd (≥ V 5.3.0)
model	pure dephasing model; one of 'gauss', 'constant', 'datafile', or 'none' where the latter one is the default. For model 'datafile', the rates are read from file 'depha.mat'.
rate	specify one pure dephasing rate (for models 'gauss' or 'constant')
upper	specify upper state pertaining to that rate (for model 'gauss')
lower	specify lower state pertaining to that rate (for model 'gauss')

Internal variables

Used in qm_propa and qm_optimal, mainly to log the time-depence of u, x, y. They will be saved to unformatted data files named ..._control.mat..._optimal.mat, respectively.

control.t	time discretization
n	number of time steps
delta	step size
steps	discretization points

Note that the discretization stored in control.t is essentially the same as that in time.main or time.sub when running qm_propa or qm_optimal, respectively.

control.u	(time-dependent!) control field(s)
dim	number of control fields
forward	control field(s) during forward propagation
backward	control field(s) during backward propagation
legends	legends for curve plots
shaping	prescribed pulse envelope/shape
previous	control field(s) from previous iteration step

control.x	(time-dependent!) state vectors
dim	number of state vector components
initial	state vector: initial value
equilib	state vector: equilibrium value
forward	state vector: during forward propagation
backward	state vector: during backward propagation
legends	legends for curve plots
previous	state vector from previous iteration step

control.y	(time-dependent!) observable(s)
dim	number of observables
equilib	observable(s): equilibrium value
forward	observable(s): during forward propagation
backward	observable(s): during backward propagation
legends	legends for curve plots

control.d	time derivative(s) of control field(s) (qm_optimal only)
forward	during forward propagation
backward	during backward propagation

control.j	control functionals (qm_optimal only)
target	target of control (to be maximized)
cost	cost/energy of control (to be minimized)
total	total functional, obtained as the difference f the two above
addup	total functional, obtained by adding up the increments (ideally equal to the above)

control.f	power spectral density: frequencies of control field(s) (qm_optimal only)
forward	during forward propagation

control.p	power spectral density: power of control field(s) (qm_optimal only)
forward	during forward propagation

control.g	frequency-resolved optical gating (FROG), aka GRENOUILLE: power of control field(s) (qm_optimal only)
forward	during forward propagation