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TitleTime-domain control of light-matter interaction with superconducting circuits
File Size3.6 MB
Total Pages117
Table of Contents
                            List of Figures
List of Tables
List of Symbols and Abbreviations
Introduction and Motivation
Theoretical background
	Josephson physics
		Josephson junction
		RCSJ model
		3 Josephson junction flux qubit
	Quantum harmonic oscillator
	Jaynes-Cummings model
	Dynamic and decoherence
Experimental setup
	Cryogenic setup
			Superconducting niobium resonator and antenna
			3 Josephson junction flux qubit and coupling junction
			Microwave input lines
			Microwave output line
			DC lines
	Room temperature setup
		Continuous wave spectroscopy
			Single tone continuous wave spectroscopy
			Two-tone continuous wave spectroscopy
		Pulsed wave spectroscopy and time-domain measurements
			Pulse generation
			Pulse detection
Measurement results
	Continuous wave spectroscopy
		Flux calibration
		High power continuous wave spectroscopy
		Photon number calibration
		Low power continuous wave spectroscopy
	Time-domain measurements
		ACQIRIS card measurements
			Pulsed two-tone spectroscopy
			Rabi oscillation measurements
		FPGA board measurements
			Rabi oscillation measurements
Conclusion and Outlook
Digital heterodyne IQ mixer calibration
	Mathematical calculations
	MATLAB code
Photon number calibration
Persönliche Erklärung
Document Text Contents
Page 1

Technische Fakultät Walther-Meißner- Bayerische
Universität für Institut für Akademie der
München Physik Tieftemperaturforschung Wissenschaften

Time-domain control

light-matter interaction

superconducting circuits

Diploma Thesis
Thomas Losinger

Advisor: Prof. Dr. Rudolf Gross
Garching, 2012-11-07

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


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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 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.


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


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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


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