##### Document Text Contents

Page 1

Technische Fakultät Walther-Meißner- Bayerische

Universität für Institut für Akademie der

München Physik Tieftemperaturforschung Wissenschaften

Time-domain control

of

light-matter interaction

with

superconducting circuits

Diploma Thesis

Thomas Losinger

Advisor: Prof. Dr. Rudolf Gross

Garching, 2012-11-07

Page 58

Time-domain control of light-matter interaction with superconducting circuits

46

Page 59

Time-domain control of light-matter interaction with superconducting circuits

4 Measurement results

As mentioned in the previous parts we study a superconducting resonator coupled to a flux qubit

and observe the response for continuous wave spectroscopy and time-domain measurements. As

we intend to observe quantum mechanical phenomena the sample is cooled down to very low

temperatures to neglect thermal population in the resonator as described in detail in section

3.1.2.1. Here we present the necessary measurements to characterize our system in the frequency-

and time-domain. We begin with a determination of the resonator modes followed by a flux

calibration. Afterwards we perform continuous wave single- and two-tone spectroscopy including

a photon number calibration. Finally we present pulsed wave spectroscopy and time-domain

measurements of the coupled qubit resonator system which were successfully performed in the

qubit group of the WMI for the first time.

4.1 Continuous wave spectroscopy

In this section we present all important measurements to characterize the coupled qubit-resonator

system in the frequency-domain. First we are interested in the modes of the resonator when the

sample is cooled down to approximately 50 mK. Therefore, we perform a wide range frequency

scan with the vector network analyzer (VNA) and search for peaks in the transmitted amplitude

in a single tone continuous wave spectroscopy (data not shown). Afterwards we perform a more

detailed scan on the peaks and fit a Lorentzian to the recorded data. In Figure 4.1 this is

visualized for the second harmonic and yields a resonance frequency of ω2/2π = 7.1057 GHz for

the resonator far detuned from the degeneracy point of the qubit. Taking into account the full

width half maximum (FWHM) κ2 = 831 kHz from the fit data we can estimate the quality factor

of our superconducting resonator Q2 = ω2/(2πκ2) ≈ 8500. By repeating this procedure for the

fundamental mode and the first harmonic we enumerate that the three experimentally accessible

modes have resonance frequencies given in Table 4.1. It is worth mentioning that the limited

amplifier bandwidth ranging from 4 to 8 GHz causes a low signal to noise ratio (SNR) of the

fundamental mode, making it challenging to record a clear spectrum such that the uncertainties

prevail the accuracy of the fit. We would like to mention that all three experimentally accessible

modes are affected by a mode-dependent phase drop as discussed on detail in section 2.2. Due

to the limited bandwidth we are not able to determine the mode ω3 which would not be affected

by a phase drop.

mode i frequency ωi/2π (GHz) κi (MHz) Qi (i+ 1) · ω0/2π (GHz)

0 (λ/2) 2.642 — — 2.642

1 (λ) 5.067 1.25 4054 5.284

2 (3λ/2) 7.106 0.831 8551 7.926

Table 4.1: The three experimentally accessible resonator modes with their center frequencies.

If we compare the second and fifth column, it turns out that the coupling junctions causes a

non-equidistant spacing of the modes.

47

Page 116

Time-domain control of light-matter interaction with superconducting circuits

104

Page 117

Time-domain control of light-matter interaction with superconducting circuits

C Persönliche Erklärung

Mit der Abgabe der Diplomarbeit versichere ich, dass ich die Arbeit selbständig verfasst und

keine anderen als die angegebenen Quellen und Hilfsmittel benutzt habe.

Ort, Datum, Unterschrift

105

Technische Fakultät Walther-Meißner- Bayerische

Universität für Institut für Akademie der

München Physik Tieftemperaturforschung Wissenschaften

Time-domain control

of

light-matter interaction

with

superconducting circuits

Diploma Thesis

Thomas Losinger

Advisor: Prof. Dr. Rudolf Gross

Garching, 2012-11-07

Page 58

Time-domain control of light-matter interaction with superconducting circuits

46

Page 59

Time-domain control of light-matter interaction with superconducting circuits

4 Measurement results

As mentioned in the previous parts we study a superconducting resonator coupled to a flux qubit

and observe the response for continuous wave spectroscopy and time-domain measurements. As

we intend to observe quantum mechanical phenomena the sample is cooled down to very low

temperatures to neglect thermal population in the resonator as described in detail in section

3.1.2.1. Here we present the necessary measurements to characterize our system in the frequency-

and time-domain. We begin with a determination of the resonator modes followed by a flux

calibration. Afterwards we perform continuous wave single- and two-tone spectroscopy including

a photon number calibration. Finally we present pulsed wave spectroscopy and time-domain

measurements of the coupled qubit resonator system which were successfully performed in the

qubit group of the WMI for the first time.

4.1 Continuous wave spectroscopy

In this section we present all important measurements to characterize the coupled qubit-resonator

system in the frequency-domain. First we are interested in the modes of the resonator when the

sample is cooled down to approximately 50 mK. Therefore, we perform a wide range frequency

scan with the vector network analyzer (VNA) and search for peaks in the transmitted amplitude

in a single tone continuous wave spectroscopy (data not shown). Afterwards we perform a more

detailed scan on the peaks and fit a Lorentzian to the recorded data. In Figure 4.1 this is

visualized for the second harmonic and yields a resonance frequency of ω2/2π = 7.1057 GHz for

the resonator far detuned from the degeneracy point of the qubit. Taking into account the full

width half maximum (FWHM) κ2 = 831 kHz from the fit data we can estimate the quality factor

of our superconducting resonator Q2 = ω2/(2πκ2) ≈ 8500. By repeating this procedure for the

fundamental mode and the first harmonic we enumerate that the three experimentally accessible

modes have resonance frequencies given in Table 4.1. It is worth mentioning that the limited

amplifier bandwidth ranging from 4 to 8 GHz causes a low signal to noise ratio (SNR) of the

fundamental mode, making it challenging to record a clear spectrum such that the uncertainties

prevail the accuracy of the fit. We would like to mention that all three experimentally accessible

modes are affected by a mode-dependent phase drop as discussed on detail in section 2.2. Due

to the limited bandwidth we are not able to determine the mode ω3 which would not be affected

by a phase drop.

mode i frequency ωi/2π (GHz) κi (MHz) Qi (i+ 1) · ω0/2π (GHz)

0 (λ/2) 2.642 — — 2.642

1 (λ) 5.067 1.25 4054 5.284

2 (3λ/2) 7.106 0.831 8551 7.926

Table 4.1: The three experimentally accessible resonator modes with their center frequencies.

If we compare the second and fifth column, it turns out that the coupling junctions causes a

non-equidistant spacing of the modes.

47

Page 116

Time-domain control of light-matter interaction with superconducting circuits

104

Page 117

Time-domain control of light-matter interaction with superconducting circuits

C Persönliche Erklärung

Mit der Abgabe der Diplomarbeit versichere ich, dass ich die Arbeit selbständig verfasst und

keine anderen als die angegebenen Quellen und Hilfsmittel benutzt habe.

Ort, Datum, Unterschrift

105