Sequence Explorer¶

The menu selection Pulse Sequence ‣ Sequence Explorer… opens the Sequence Explorer. The Sequence Explorer provides tools to manage and edit both “Standard” tabular pulse sequences and textually-defined “Industrial”-type Pulse Sequences. This window/interface can be very difficult to use on a small screen, such as an iPhone, and is therefore often disabled (unavailable) if the screen is too small.

Sequence Selector¶

At the top left of the Sequence Explorer is a sequence category selection, and under it, a list of sequences that belong to the selected category. The sequences available in the regular Pulse Sequence menu appear in the category Standard. Other sequences appear under the category Industrial, and user-created sequences appear under the category User.

Standard sequences are stored internally in a JSON structure. The easies way to edit these sequences is with the normal Edit Sequence… Sequence Editor. The JSON can also be directly edited by by advanced users. By default the raw JSON is hidden, but can be displayed by checking the Show Raw Sequence checkbox in the upper right corner.

Industrial sequences are written in a pulse-sequence language very similar to the Bruker industry-standard NMR pulse sequence language. Indeed, some Bruker sequences can be simulated un-modified in SpinDrops.

User sequences can be of either form - either JSON or Industrial (Bruker-style).

Auto-Apply mode¶

When a sequence is selected from the list, it is shown in the Sequence Explorer, but not automatically loaded into the main SpinDrops simulation window. It is only displayed in the Sequence Explorer until the Apply button is clicked or when the checkbox Apply to Simulation is active, which enables automatic and immediate application of sequence selection or edits to the main SpinDrops simulation.

Industrial Sequence Language¶

The Industrial sequence language may look strange at first sight, but in reality is quite simple. The sequences are plain text files, and have three parts: an initial Definitions section, then the commands that generate pulses and delays, and finally a so-called Phase Programs section.

The language is very similar to the pulse language used by a well-known industrial NMR instrument manufacturer. Because of this, you can find a lot of example programs and ideas for pulse programs on the internet. However, be aware that the possibilities of a simulation software are somewhat different from an actual spectrometer, so not everything in the pulse programming is exactly the same.

The main difference in terms of the spin system is that in simulation we primarily look at a single, or a small number of spin systems, whereas in a real spectrometer, we’re interacting with a large number of similar spin systems with imperfect coupling to the experimental machinery. This means we can, in the simulator, specify exact starting states, and exact (and arbitrary) Hamiltonians – an impossibility for the experimentalist.

Definitions¶

Before using any pulses, it is possible (though not necessary) to specify some values and operators that can be used later in the description of the sequence. Usefully, we set some parameters to the time durations needed to achieve a certain pulse rotation, or time duration for certain relaxations or mixing periods. Also we can specify arbitrary Hamiltonians to be applied during certain time periods, or specify literal Propagators that can be applied to the state. All of these definitions (using the define statement) should be at the beginning of the pulse program:

define pulse ...
define delay ...
define channel ...
define propagator ...


Pulse Definition¶

define channel Hiso12 = 'pi*(J12*(2I1xI2x + 2I1yI2y + 2I1zI2z))'


Delay Definition¶

define delay mydelay

"mydelay = 1s"


Hamiltonian Channel Definition¶

This Isotropic Mixing sequence uses a special type of definition to associate a channel in the pulse sequence with a specific Hamiltonian in the simulation. Later use of this “channel” in the experiment will apply this Hamiltonian to the simulation. This example creates a isotropic mixing Hamiltonian between spins 1 and 2 on a new channel called Hiso12.

define channel Hiso12 = 'pi*(J12*(2I1xI2x + 2I1yI2y + 2I1zI2z))'


The define channel statement can be used to define a channel in terms of the Hamiltonian that will be in effect when the channel is actively “pulsing” (that is, when this channel’s Hamiltonian is added to the global system propagator Hamiltonian).

After the definition, a delay and the actual “pulsing” of the Hamiltonian are accomplished with the pulse program:

"d1=1/(2*cnst2)"                ; set the delay d1 to 1/(2*J12)

(d1) pulse(auto):Hiso12       ; pulse the Hiso12 channel for duration (d1)


Propagator Channel Definition¶

Another kind of definition is the propagator definition, it defines a special “channel” with an arbitrary propagator, rather than hamiltonian. In order to make the propagator non-instantaneous, for display purposes, a pseudo-Hamiltonian is internally calculated that, when applied for $$1 s$$, will have the same effect as the requested propagator. This example is a special case of the nop (no operation) propagator that does not affect the system state at all, it is the same as the identity operator:

define propagator nop = 'Id'        ; define the identity propagator

; To apply this propagator to the current state, make a 1-second pulse
; on it's channel:

1sp:nop


To use the nop propagator again, for example, in the definition of a spin-selective inverting notA channel, it is necessary to assign the expression to a name, within the definition string:

define propagator nop = 'nop=2*Ie'       ; define a 2x2 identity matrix
define propagator not = 'not=[0,1;1,0]'  ; define a 2x2 inversion matrix
define propagator notA = 'kron(not,nop)' ; define a 4x4 spinA not propagator

1sp:notA                               ; invert spin A in a 2-spin system


Pulse Lines¶

This is the “meat” of the pulse program, and it lies between the definitions and the first Exit. There are two main types of lines in this part of the pulse program:

• pulse/delay lines which take up time and create either pulses or delays,
• and calculation lines surrounded by double-quotes “”, which do not take up time but can alter values in the program.

These two types of lines may be interspersed. Here is an example program:

"d1=1/(2*cnst2)"     ; set delay to 1/(2*J12)

start,
p1          ; 90deg pulse
d1          ; delay
p2          ; 180deg pulse
d1          ; delay
exit


The first line sets the delay variable d1 to the value $$1/(2J_{12})$$. The value cnst2 is a special symbol that is set to the coupling J12 of the current simulation. If that value is 0, the pulse sequence becomes ill-defined.

Next there is a label start, which does nothing, but marks a place in the sequence where later looping commands (such as acquisition loops) could jump back to (see for example, the phase cycling experiments).

And finally, the line that starts with (d1) will create a delay of d1 in parallel with a pulse of automatic length (auto) on the Hiso12 channel – or in other words, the isotropic mixing Hamiltonian will be in effect for a time of d1 or $$1/(2J_{12})$$. Such pulses with automatic length will expand to fill the time of the line upon which it is specified – a time determined by the longest of the other elements which are active in parallel.

Preset Pulse Lengths¶

SpinDrops implicitly sets the maximum pulse amplitude to 10 Hz, although this completely unrealistic. Pulse durations (p1 - p31) are also automatically calculated for 90 and 180 degree pulses on the available spins. On a real spectrometer, you would use an experimental procedure to discover the pulse amplitude, and set these values accordingly. SpinDrops adopts the same convention as Bruker for the meanings of these pulse durations:

pulse duration meaning pulse on channel
p1 duration of 90° pulse on spin I1 f1 (this is the default when omitted)
p2 duration of 180° pulse on spin I1 f1 (this is the default when omitted)
p3 duration of 90° pulse on spin I2 f2
p4 duration of 180° pulse on spin I2 f2
p21 duration of 90° pulse on spin I3 f3
p22 duration of 180° pulse on spin I3 f3

Since these pulse durations are simply durations, is important to remember to send the pulse to the correct “channel” so that it affects the correct spin! This is done by appending a colon and the channel to the pulse, ie: p3:f2, or p22:f3.

Preset Durations¶

There are also a number of pre-calculated durations available for use in pulse programs. These are constants describing the spin system’s coupling parameters: $$J_{12}$$, $$J_{13}$$, and $$J_{23}$$. These are contained in the parameters:

delay duration meaning
cnst2 $$J_{12}$$
cnst4 $$J_{13}$$
cnst5 $$J_{23}$$

The value of these parameters will change whenever the corresponding Spin System parameters/sliders are changed using the System Parameters Window.

Shaped Pulses¶

Using shaped pulses in the advanced language is quite similar to on an actual spectrometer. Available pulses, and their names, can be seen in the Pulse Explorer Window. It is also possible to import shaped pulse files in either Bruker or Valerian format from there. There is a small difference from the normal industrial syntax to make setting the pulse names easier, it is done by assigning a pulse name to the corresponding sp parameter, as follows to set the name of the sp1 pulse file:

"sp1='Standard/sinc3_100.exc'"

start,
p1:sp1
exit


Exit¶

The exit command ends the pulse program execution. There can be multiple exit commands in the text file, but the first one will always be the end of the sequence. A pulse program does not need to have an exit, if there are no Phase Programs, since it just serves to separate the body of the sequence from their definition.

exit


Phase Programs¶

Phase Programs must be forgiven for their archaic name dating to an earlier era of computing terminology. What is meant here by “program” is simply a repeating sequences of phases. Values from this sequence can be referenced from pulses and acquisitions. When so referenced, they return the phase at the list’s current position, which of course starts at the first position and advances either explicitly or implicitly, depending on what is happening in the pulse sequence.

In the case of pulses, specifying a Phase Program along with a pulse determines what phase the pulse will have. The current position of all of the Phase Programs is implicitly advanced to the next element every time there is a go command. This automatic increment can be avoided by using the related command gonp used (which cryptically means “go with no phase increment”).

; phase programs
ph2 = 0 1 2 3