Phase and Frame in QUA

This page will discuss the concepts of frame and phase, how they affect the OPX's output, and the APIs that relates to them, namely, the reset_frame(), reset_if_phase(), and the reset_global_phase() commands.

Every time we use the play() command on a specific element, the output pulse will have a lab (total) phase calculated from several separate contributions:

\[\phi_L = \overbrace{\overbrace{\overbrace{\omega_{UC} \cdot t}^{\mbox{upconveter phase}} + \overbrace{\omega_{IF} \cdot t}^{\mbox{intermediate phase}}}^{\mbox{global phase}} + \overbrace{\phi_F}^{\mbox{frame}}}^{\mbox{lab phase}}\]

\[\phi_L = \phi_{UC} + \phi_{IF} + \phi_F = \phi_G + \phi_F\]

• The global phase associated with the rotating frame of the element, based on its frequency (upconveter frequency + intermediate frequency) and time passed from the beginning of the sequence \(t\).
• The frame phase, \(\phi_F\), which is the phase within the rotating frame.

Note

The phase from the upconverter can be zero if there is no upconverter being used. It can come from an external LO source or from the MW-FEM upconverters.

Generally, the OPX ensures that the phase is coherent for all the elements within a program. This specifically implies that pulses from different elements with the same frequencies will be phase matched. This is true even if the frequencies are updated during runtime, for example, using update_frequency().

Global Phase

There are a few ways in which the global phase associated with an element can be changed. Using the command reset_if_phase() we effectively define a constant phase \(\tilde{\phi} = \tilde{\omega_{IF}} \cdot \tilde{t}\), where \(\tilde{\omega_{IF}}\) and \(\tilde{t}\) are the intermediate frequency of the element and the time in which the command reset_if_phase() was applied. From that point forward the phase \(\tilde{\phi}\) is subtracted from the global phase of the element.

Note

This means that the intermediate phase after the reset_if_phase() command will be \(\phi_{IF} = \omega_{IF} \cdot t - \tilde{\omega_{IF}} \cdot \tilde{t}\), where \(\tilde{\omega_{IF}}\) and \(\tilde{t}\) are defined according to the last reset_if_phase() command used in the sequence. The same \(\tilde{\phi}\) will be subtracted even if the intermediate frequency is later changed. It is not possible to set \(\tilde{t}\) back to zero after the reset_if_phase() command is used.

Using reset_global_phase() would also subtract the phase associated with the MW-FEM upconverter, in addition to the intermediate phase. For any element which is not using the MW-FEM, reset_global_phase() is equivalent to reset_if_phase()

Another command that will change the global phase is update_frequency(). When using the flag keep_phase=True, the phase of the pulse will be continuous through the frequency change, as can be seen in figure 1 indicated by the first dashed black line. The phase continuity results in a change to the global phase, \(\phi_G\). This change, however, is not tracked similarly to the phase change caused by reset_if_phase(), so if we update to the frequency with the flag keep_phase=False afterward, the global phase will be reevaluated from the beginning of the sequence (or the last phase reset), as can be seen in figure 1 indicated by the second dashed black line.

Note

Phase behavior of update_frequency

By default keep_phase=False, in this case the phase of the signal \(\omega_{IF}t\) after the frequency has been updated will change according to the rule:

\[ \omega_1 t_0 \rightarrow \omega_2 (t_0+\Delta t) \]

where \(\omega_1\), \(\omega_2\) are the frequencies before and after the transition, \(\Delta t\) is the sampling rate and \(\rightarrow\) signifies a transition from the sample \(t_0\) to the next.

To maintain a continuous phase through the transition, use keep_phase=True. This will update the phase according to the rule:

\[ \omega_1 t_0 \rightarrow \omega_1 t_0 + \omega_2 \Delta t. \]

Fig. 1: The phase behavior when using update_frequency(), with the flag keep_phase = True and keep_phase = False. The black dashed line indicates when update_frequency() was used. The blue signal is the reference signal, and all operations are performed on the orange signal.

Frame Phase

The frame phase is constant in relation to the element's global phase, i.e., the phase in the rotating frame. At the beginning of a sequence, the frame phase is defined as \(\phi_F=0\), and using the commands frame_rotation() and frame_rotation_2pi(), we can control \(\phi_F\). The frame phase is separate from the global phase and is not affected by the element's frequency. Using the command reset_frame() we set the frame phase back to zero, \(\phi_F=0\).

Note

Resetting the global phase will not reset the frame phase. So if we want to reset the lab phase of an element to zero, we need to use both reset_global_phase() and reset_frame().

Fig. 2: Simulation of the OPX output showing, a frame_rotation_2pi(0.5, element) - first dashed line, a reset_frame(element) - second dashed line, and reset_if_phase(element) - third dashed line. The blue signal is the reference signal, and all operations are performed on the orange signal.

Further Examples

QUA code examples illustrating these concepts can be found in our GitHub Repository