Resonator Spectroscopy¶

Note

This tutorial is applicable to all SHFQA+ Instruments.

Goals and Requirements¶

The goal of this tutorial is to demonstrate how to use the SHFQA+ to perform resonator spectroscopy measurement using the LabOne User Interface (UI) and Zurich Instruments Toolkit API.

Note

For zhinst-toolkit users, please find the example in https://github.com/zhinst/zhinst-toolkit/blob/main/examples/shfqa_sweeper.md, and the zhinst-toolkit documentation.

For LabOne Q users, please find the example in https://github.com/zhinst/laboneq/blob/main/examples/01_qubit_characterization/01_cw_resonator_spec_shfsg_shfqa_shfqc.ipynb and https://github.com/zhinst/laboneq/blob/main/examples/01_qubit_characterization/02_pulsed_resonator_spec_shfsg_shfqa_shfqc.ipynb, and the LabOne Q User Manual.

Preparation¶

Please follow the preparation steps in Connecting to the Instrument and connect the instrument in a loopback configuration as shown in Figure 1 or to a device under test.

Figure 1: SHFQA+ connection.

Tutorial¶

In this tutorial, we sweep frequency of output signal and measure the frequency response of the cable or the device under test.

LabOne UIzhinst-toolkit

This section shows how to use the LabOne UI to configure the instrument, run the measurement and monitor the measurement results.

Configure the instrument

Set center frequency and power range of input and output signals

Configure these parameters on the Input and Output Tab as in Figure 2 and in Table 1.

Table 1: Settings of QA Channel 1 on In/Out Tab
Parameter	Setting	Description
QA Channel Selection	All	Select All to display all QA Channels.
Cent Freq (Hz)	5 GHz	Set center frequency of the frequency sweep.
Signal Input 1 On	Enable	Enable the Signal Input 1.
Signal Input 1 Range (dBm)	0 dBm	Set power range of Signal Input 1 to 0 dBm. This setting allows the instrument to acquire a input signal with a power up to 0 dBm.
Signal Input 1 Input Path	RF	Set input path of Signal Input 1 to RF path.
Signal Output 1 On	Enable	Enable the Signal Output 1.
Signal Output 1 Range	0 dBm	Set power range of Signal Output 1 to 0 dBm. This setting allows the instrument to output a signal with a power up to 0 dBm.
Signal Output 1 Output Path	RF	Set output path of the Signal Output 1 to RF path.

Upload and compile measurement sequence

The measurement sequence is defined on the Sequence sub-tab of the Readout Pulse Generator tab, see Figure 3 and Table 2.

Figure 3: Configurations on Readout Pulse Generator Tab.

Table 2: Settings of QA Channel 1 on Readout Pulse Generator Tab.
Parameter	Setting	Description
QA Channel Selection	1	Select QA Channel 1.
Sub-Tab Display	Sequence	Select Sequence sub-tab and paste the sequence program below or load ziGenerator_functional_spectroscopy.seqc from the "Examples" library and modify it. The Waveform Viewer sub-tab displays readout envelope if it is uploaded.
Compile	Click "To Device"	Compile the sequence program by clicking "To Device".
Return	Disable	Disable return function.
Run/Stop	Disable	Disable Run/Stop.

Below is the the sequence program for the measurement. In the inner loop, the setSweepStep(OSC0, i) command sets frequency of digital oscillator 0 to i-th frequency in an array configured by configFreqSweep(OSC0, -500000000.0, 1000000.0) command, the setTrigger(value) command sets Sequencer Trigger 1 Output to high and then low to start integration, and waveform generation if pulsed waveform is desired, the playZero(samples) command define time to the next playZero(samples). The measurement is repeated 100 times by the outer loop.

// define which oscillator to use
const OSC0 = 0;

// set sequencer trigger output to 0
setTrigger(0);

// configure frequency sweep with a starting f of -500 MHz and a step of 1 MHz
configFreqSweep(OSC0, -500000000.0, 1000000.0);

// sweep oscillator frequency and repeat 100 times
for(var j = 0; j < 100; j++) {
    for(var i = 0; i < 1001; i++) {
        // self-triggering mode

        // define time from setting the oscillator frequency to sending
        // the spectroscopy trigger
        playZero(160);

        // set the oscillator frequency depending on the loop variable i
        setSweepStep(OSC0, i);
        resetOscPhase();

        // define time to the next iteration
        playZero(22448);

        // trigger the integration unit and pulsed playback in pulsed mode
        // set Sequencer Trigger Output 1 to high and then to low
        // make sure the trigger singnal in spectroscopy mode is set to sequencer trigger output 1
        setTrigger(1);
        setTrigger(0);
    }
}

Configure signal generation and data acquisition

Signal generation and data acquisition are defined on QA Setup Tab and QA Result logger Tab. The baseband readout signal is generated by a digital oscillator directly ("Continuous"), or by mixing the signal from the digital oscillator and a waveform envelop saved in the waveform memory ("Pulse"). The input signal after frequency down-conversion is integrated for 512 ns started 224 ns later after receiving a trigger from Sequencer 1 Trigger Output 1.

Figure 4: Configurations on QA Setup Tab.

Table 3: Settings of QA Channel 1 on QA Setup Tab, see details on
Parameter	Setting	Description
QA Channel Selection	1	Select QA Channel 1.
Application Mode	Spectroscopy	Use spectroscopy mode for resonator spectroscopy measurement. In spectroscopy mode, frequency sweep is done by sweeping the frequency of the digital oscillator.
Trigger Signal	Sequencer 1 Trigger Output 1	Select Sequencer 1 Trigger Output 1 as the trigger source to trigger both output pulse generation and integration. This selection matches the trigger setting written in the sequence program.
Integration Length (pts)	1048	Set the integration length in number of samples.
Integration Delay (s)	224n	Set the delay time after receiving a trigger before starting integration. This setting ensures only expected input signal is integrated. The internal delay from signal generation to integration is about 224 ns. Therefore integration delay is > 224 ns if the propagation delay from front panel signal output port to signal input port is not negligible.
Power Spectral Density	Disable	Disable the Power Spectral Density measurement function.
Digital Oscillator Amplitude	0.5	Set the amplitude factor of the digital oscillator to 0.5. The range of amplitude factor is from 0 to 1.
Waveform Mode	Continuous	Set the Waveform Mode to continuous, so the output waveform is continuous. Select "Pulse" and upload a .csv file with complex data for waveform envelope if pulsed output waveform is desired.

On the QA Result Logger Tab, it defines the source of the result, and how the result is averaged and displayed, see Figure 5 and Table 4. After configuration of all parameters, the QA Result Logger should be enabled to be ready to receive measurement results.

Figure 5: Configurations on QA Result Logger Tab.

Table 4: Settings of QA Channel 1 on QA Result Logger Tab.
Parameter	Setting	Description
QA Channel Selection	1	Select QA Channel 1.
Sub-Tab	Spectroscopy	Select Spectroscopy sub-tab to monitor measurement result when using the Spectroscopy mode.
Plot Type	Components	Select Components to display I, Q, amplitude or phase versus sample points. Select Dot Plot to display I versus Q with scattered dots.
Result Length (Sample)	1001	Set result length in number of samples. The number must match what is set in the sequence program.
Averages	100	Set number of averages. The number must match what is set in the sequence program.
Average Mode	Cyclic	Set the average mode to cyclic. This setting must match how the loop is configured in the sequence program.
Vertical Axis Groups	Add amplitude and phase	Select amplitude and phase to be displayed on the plot.
Run/Stop	Enable	Enable the result logger to receive and display measurement results.

Run the measurement

By clicking "Run/Stop" icon on the Readout Pulse Generation Tab, the measurement is started and finished in seconds.
Monitor the measurement result

The measurement result (complex data) is normalized by the integration length and displayed on the QA Result Tab, as shown in Figure 6. Select "Dot Plot" to display result in IQ (complex) plane.

Figure 6: Measurement results on the QA Result Logger Tab.

The tutorial starts with configuring the Sweeper, and is followed by sending out continuous or pulsed readout waveform and integrating the frequency down-converted signal, and is finished with power and phase plots calculated from integration results.

Connect the Instrument

Create a toolkit session to the data server and connect the Instrument with the device ID, e.g. 'DEV12001', see Connecting to the Instrument.

# Load the LabOne API and other necessary packages
from zhinst.toolkit import Session

DEVICE_ID = 'DEVXXXXX'
SERVER_HOST = 'localhost'

session = Session(SERVER_HOST)              ## connect to data server
device = session.connect_device(DEVICE_ID)  ## connect to device

Create a Sweeper and configure it

Python API SHFSweeper class is the core of the spectroscopy measurements. It defines all relevant parameters for frequency sweeping and sequencing. Toolkit wraps around the SHFSweeper and exposes an interface that is similar to the LabOne modules, meaning the parameters are exposed in a node tree like structure.

sweeper = session.modules.shfqa_sweeper
sweeper.device(device)
CHANNEL_INDEX = 0 # physical Channel 1

sweeper.sweep.start_freq(-500e6) # in units of Hz
sweeper.sweep.stop_freq(500e6) # in units of Hz
sweeper.sweep.num_points(1001)
sweeper.sweep.oscillator_gain(0.8) # amplitude scaling factor, 0 to 1
sweeper.sweep.use_sequencer = True # True (recommended): sequencer-based sweep; False: host-driven sweep

sweeper.average.integration_delay(224e-9) # internal delay is about 224 ns
sweeper.average.integration_time(10e-6) # in units of second
sweeper.sweep.wait_after_integration(1e-6) # waiting 1 us after integration before starting a new measurement
sweeper.average.num_averages(200)
sweeper.average.mode("sequential") # "sequential" or "cyclic" averaging

sweeper.rf.channel(CHANNEL_INDEX)
sweeper.rf.center_freq(5e9) # in units of Hz
sweeper.rf.input_range(0) # in units of dBm
sweeper.rf.output_range(0) # in units of dBm

with device.set_transaction():
    device.qachannels[CHANNEL_INDEX].input.on(1)
    device.qachannels[CHANNEL_INDEX].output.on(1)

All available settings of the Sweeper can be find using this command.

list(sweeper)

The sweep parameters are configured such that the offset frequency of output signal is linearly swept over 1001 points from -500 MHz to 500 MHz around the center frequency of 5 GHz with the input and output power range of 0 dBm and the oscillator gain of 0.8, the input signal is integrated for 10 μs after receiving an internal triggered, and the measurement is repeated 200 times at each offset frequency.

There are 2 sweeping modes, sequencer-based mode (default) and host-driven mode. The sequencer-based mode is recommended to achieve the highest sweep speed. In the sequencer-based mode, the frequency sweep is done by updating the frequency of the digital oscillator via the SeqC commands configFreqSweep and setSweepStep. This mode allows a fast resonator spectroscopy measurement with predicted cycle time of \(t_{\mathrm{settling\ time}} + t_{\mathrm{integration\ delay}} + t_{\mathrm{integration\ time}} + t_{\mathrm{wait\ after\ integration}}\), see Table 5. In the host-driven mode, the frequency sweep is done by updating the frequency of the digital oscillator via software, therefore measurement speed is limited by communication between instrument and host computer. Logarithmic or other non-linear frequency sweep is supported by the host-driven sweep mode only.

To get a better signal-to-noise ratio (SNR), the measurement is repeated, and the result is averaged. There are 2 ways for averaging, sequential and cyclic. In the sequential mode, measurement is repeated after each frequency step. In the cyclic mode, measurement is repeated after sweeping through all frequencies.

The output frequency of the signal is the sum of the center frequency and the offset frequency. The output power of the signal is determined by the output power range and the oscillator gain, se`` Inputs/Outputs Tab. The input range should be set properly to avoid input overflow and to reach the best SNR.

Please note that default values of Sweeper parameters listed in Table 5 depend on the zhinst version.

Table 5: Default values of Sweeper parameters.
Parameter	Description	Default Value for zhinst < 22.08	Default Value for zhinst >= 23.02
settling time	Waiting time after having set the new frequency until issuing the `setTrigger` command, which triggers the spectroscopy unit.	200 ns	80 ns
integration delay	Delay after the internal trigger arrives at the spectroscopy unit until the integration of the input signal starts.	0 ns	224 ns (zhinst-utils version ≥ 0.1.5)
envelope delay	Delay After the internal trigger arrives at the spectroscopy unit until the playback of the envelope waveform starts.	0 ns	0 ns
integration time	Time to integrate the input data.	1 ms	1 ms
wait after integration	Wait time after the end of the integration until the start of the next cycle.	72 ns	0 ns
predicted cycle time	Calculated duration of each cycle of the spectroscopy loop. Note that this property only applies in self-triggered mode, which is active when the trigger source is set to `None` and `use_sequencer` is `True`.	-	"settling time" + "integration delay" + "integration time" + "wait after integration" (read-only)

Run the measurement with continuous output waveform and plot the data
```
result = sweeper.run()
num_points_result = len(result["vector"])
print(f"Measured at {num_points_result} frequency points.")
sweeper.plot()
```
After executing sweeper.run(), all above parameters are updated, and a SeqC program is automatically generated, uploaded and compiled based on the sweep parameters, see in Figure 7. In the program, ConfigFreqSweep sets the start frequency and the frequency increment in units of Hz for a chosen oscillator, and setSweepStep sets the oscillator frequency. The oscillator phase is reset by resetOscPhase before each measurement. The trigger generated in the sequencer is used to start the integration, and the playZero sets the cycle duration. The measurement is repeated using the nested for loop according to the averaging mode. The measurement starts after enabling the sequencer.

Figure 7: Seqc program in the Readout Pulse Generator Tab.

The result returned from sweeper.run() is complex data \(E_{\mathrm{sweeper}}\) in units of Vrms. It is averaged and normalized by the integration length. The power \(P\) and phase \(\phi\) can be calculated as,

\[ \begin{equation}\tag{1} \begin{aligned} P & = 10\lg(\frac{|E_{\mathrm{sweeper}}|^2}{R}1000), \newline \phi & = \arctan\frac{\Im(E_{\mathrm{sweeper}})}{\Re(E_{\mathrm{sweeper}})}, \end{aligned} \end{equation} \]

where \(R\) is 50 \(\Omega\), 1000 is the conversion factor from W to mW. With sweeper.plot(), the power and phase are calculated and plotted, see Figure 8.

Figure 8: Measurement result with continuous waveform output.

Run the measurement with pulsed output waveform and plot the data

In contrast to continuous readout waveform generation, pulsed readout waveform generation requires an envelope data. Create a complex flat-top Gaussian envelope with 10 μs duration and 50 ns rise and fall time. Enable the pulsed mode by sweeper.envelope.enable(True) and upload the envelope to the waveform memory. This envelope can be displayed on the Waveform Viewer of the Readout Pulse Generator.

from scipy.signal import gaussian
import numpy as np

SAMPLING_FREQUENCY = 2e9 # in units of Hz
ENVELOPE_DURATION = 10.0e-6 # in units of second
ENVELOPE_RISE_FALL_TIME = 0.05e-6 # in units of second

rise_fall_len = int(ENVELOPE_RISE_FALL_TIME * SAMPLING_FREQUENCY)
std_dev = rise_fall_len // 10
gauss = gaussian(2 * rise_fall_len, std_dev)
complex_amplitude = (1 - 1j)/np.sqrt(2)
flat_top_gaussian = np.ones(int(ENVELOPE_DURATION * SAMPLING_FREQUENCY)) * complex_amplitude
flat_top_gaussian[0:rise_fall_len] = gauss[0:rise_fall_len] * complex_amplitude
flat_top_gaussian[-rise_fall_len:] = gauss[-rise_fall_len:] * complex_amplitude
sweeper.average.integration_delay(224e-9) # in units of second
sweeper.envelope.enable(True) # True: Pulsed mode; False: Continuous mode
sweeper.envelope.waveform(flat_top_gaussian) # upload envelope waveform

result = sweeper.run()
num_points_result = len(result["vector"])
print(f"Measured at {num_points_result} frequency points.")
sweeper.plot()

After executing sweeper.run(), all above parameters are updated, a SeqC program is automatically generated, uploaded and compiled based on the sweep parameters, see Figure 7, and the result is downloaded after the measurement is done. The power and phase are calculated, see in Figure 9. The result is consistent with measurement with continuous waveform output.