Readout and spectra
A spectrometer never sees a state vector. It sees the transverse magnetisation of each isotope, one channel at a time, oscillating at every frequency the spin system contains. This page explains how the NMR Analysis tab turns the circuit state into that spectrum, and what Readout() is for.
Readout(wires...)
A 90°y pulse on every listed spin, wrapped in an annotation named Readout. It turns z magnetisation into +x, which is what the receiver detects. Use it when your programme should end with an explicit readout pulse, and set the tab (or #settings NmrReadout "none") to acquire the state as it is, so the pulse is not applied twice.
#settings NmrReadout "none" Pulse(180, "x", 1) // invert the carbon Readout(0) // read the proton: its doublet appears with the -J/2 line
From density matrix to lines
The tab builds the density matrix ρ of the sample spins from the circuit state (a pseudo-pure state: the deviation part of a real ensemble that behaves like |ψ⟩). For the selected channel it then reads every single-quantum coherence of that isotope: an element ρij whose two basis states differ in exactly one spin of the channel. Each coherence is one line.
| Line property | Comes from |
|---|---|
| Frequency | The spin's offset δ·ν0 plus ±J/2 for every coupling partner: +J/2 when the partner is in |0⟩, −J/2 when it is in |1⟩. |
| Amplitude | The complex value of ρij, phased so that a spin in |0⟩ read out with a 90° pulse gives +1. |
| Sign | Positive for |0⟩, negative (an inverted line) for |1⟩; opposite signs within one doublet mean antiphase. |
| Shape | Real amplitudes give absorptive Lorentzians, imaginary ones dispersive: the phase of the coherence shows in the line shape. |
| Width | 1/(πT2) plus the line broadening set on the toolbar. |
Because the tab keeps the phase, a spin left along y instead of x shows a dispersive line, a spin along −x an inverted one, and a state with no transverse magnetisation on that isotope shows nothing at all. Entangled states appear as antiphase multiplets, exactly as they do on a real machine.
The two readout modes
| Mode | What is acquired | Use it when |
|---|---|---|
| 90° pulse, acquire | A 90°y pulse is applied to every spin of the channel, then ρ is read. | The programme ends in a z state, such as any ordinary circuit ending in |0⟩ and |1⟩ populations. |
| Acquire as is | ρ is read without any extra pulse. | The programme applied its own Readout() or leaves the spins transverse on purpose, such as after a spin echo or an INEPT transfer. |
The channel selector lists every isotope in the sample. Chloroform has a ¹H channel at 500 MHz and a ¹³C channel at 125.7 MHz (at 11.74 T); the same state gives a different spectrum on each.
FID and export
The FID view synthesises the time signal of the same lines, with a dwell time chosen from the spectral window and a length of three T2. Both the spectrum and the FID can be downloaded as CSV; the spectrum also as PNG. The CSV of the spectrum lists the phased line amplitudes below the trace so the numbers can be checked by hand.
Measuring instead
MEASURE collapses the state; an NMR acquisition does not. The tab maps a MEASURE gate to a readout pulse and an acquisition period on the pulse programme, which is the closest hardware equivalent, but the spectrum is always computed from the state before any collapse.