Univerzita Komenského v Bratislave

Fakulta matematiky, fyziky a informatiky

Matúš Rehák

Autoreferát dizertačnej práce

Spektroskopia feromagnetických a supravodivých nanoštruktúr

na získanie akademického titulu philosophiae doctor

v odbore doktorandského štúdia:

4.1.3. Fyzika kondenzovaných látok a akustika

Miesto a dátum:

Bratislava 2016

Dizertačná práca bola vypracovaná v dennej forme doktorandského štúdia na Katedre experimentálnej fyziky Fakulty matematiky, fyziky a informatiky Univerzity Komenského vBratislave.

Predkladateľ: Mgr. Matús Rehák Fakulta matematiky, fyziky a informatiky Univerzita Komenského v Bratislave Mlynská Dolina 842 48 Bratislava

Školiteľ: Prof. Miroslav Grajcar, DrSc. Fakulta matematiky, fyziky a informatiky Univerzita Komenského v Bratislave Mlynská Dolina 842 48 Bratislava

4.1.3. Fyzika kondenzovaných látok a akustika

Predseda odborovej komisie:Prof. RNDr. Peter Kúš, DrSc.

Katedra experimentálnej fyziky Fakulta matematiky, fyziky a informatiky UK

1 Introduction

Spectroscopy is a physical method useful for determining various properties

of wide range of samples. It is based on emission, absorption or scattering

of signal which is energy (frequency) dependent. Principle of each type is

shown in fig. 1.1. Emission spectroscopy is widely used in astronomy for anal-

yses of stars, gas clouds, etc. Using this method, it is possible to determine

composition of stellar objects from known transition energies/frequencies of

elements and compounds. Frequency of radiation ranges from microwave

to ultra-violet part of optical spectrum. Absorption spectroscopy found its

place, among other applications, in optical characterization of materials, e.g.

determining band-gap of semiconductors which can be found as the lowest

energy of photons absorbed by the sample. Other examples of absorption

and dispersion spectroscopic measurements are: nuclear magnetic resonance

(NMR), electron paramagnetic resonance (EPR) or ferromagnetic resonance

(FMR) experiments. Due to electronic instrumentation, in these types of

experiments frequency is usually fixed (resonance frequency of the cavity, in

which the sample is placed), so the sample is irradiated by single energy pho-

tons. However, the level splitting of the sample can be tuned by magnetic

field. These experiments, in most cases, use radiation in frequency bands

from 106 to 1011 Hz.

Figure 1.1: Principle of spectroscopic measurements.

Nowadays, storage capacities of PC hard-drives are getting larger, but it is

getting more difficult to store more and more information on a single mag-

netic chip. Researchers all over the world are trying to find other ways to

pack bits of information more densely in magnetic arrays. FMR spectroscopy

is a strong tool for characterization of wide range of ferromagnetic materials

3

which serve as a basis for these storage media.

Another demand in computer technology, besides aforementioned higher stor-

age capacities, is higher computational power. Semiconductor-based technol-

ogy will not be able to sustain progress in increasing of density of transistors

on a single chip, because quantum effects will be no more negligible when

transistor gates are placed too close to each other. Even though graphene

seems to be adequate replacement of silicon technology, its absence of band-

gap makes it inapplicable for this particular application and currently, there

is no modification which would eliminate this flaw while retaining its desired

properties. On the other hand, those quantum effects which are obstacle in

miniaturisation of silicon chips could be answer for increasing computational

power using alternative approach. Even though, first ”quantum computer”

has been sold [1], there are still disputes if it is really faster than classical

computer. Quantum computer with fully entangled quantum register1 has

not been developed, yet. To achieve this goal, it is important not only to

create quantum register with entangled qubits, but also completely new op-

erating electronics.

In the thesis, we study ferromagnetic storage media - permalloy nanodots and

also superconducting quantum bits and SQUIDs by means of spectroscopic

(transmission) measurements. These superconducting devices are further

used for some applications necessary for development of quantum computer

- parametric amplifier, sensitive microwave detector and single artificial atom

two-photon laser.

1Only quantum computer with entangled quantum register can perform quantum al-gorithms, which in several cases (Shor’s [2] or Grover’s [3] algorithms) truly increase com-putational speed in comparison to classical computers.

4

Goals of the dissertation:

1. Spectroscopy of superconducting nanostructures.

2. Spectroscopy of ferromagnetic nanostructures.

3. Design, preparation and characterization of electrical devices based on

superconducting and ferromagnetic nanostructures (parametric ampli-

fiers, memories, microwave detectors, . . .).

4. Research in field of mesoscopic physics and quantum optics.

5

2 Results

2.1 FMR spectroscopy of permalloy thin film

Permalloy is a ferromagnetic alloy made of 80% of nickel and 20% of iron

(sometimes with addition of 5% of molybdenum). Because of its high perme-

ability (of order 105), low coercivity, low magnetostriction and high anisotropic

magnetoresistance, it is widely used for many applications like transformers,

relays, recording heads, loudspeakers or shielding. For applications such as

information storage media, permalloy memory cells are patterned from thin

films which properties may differ from bulk material [50]. 40 nm thin film of

permalloy was studied using FMR spectroscopy in a dielectric resonator and

its Landé g factor and effective saturation magnetization were determined

from positions of FMR peaks at different frequencies. All measurements of

ferromagnetic samples were carried out at room temperature. Results were

presented in article [P3]:The real and the imaginary part of the magnetic susceptibility of a sample

can be determined directly from the FMR measurements. In the figure 2.1,

the transmission amplitude and phase as a function of external magnetic

field are shown. Real part of the magnetic susceptibility (fig. 2.2 left) was

extracted from the detuning of the resonance frequency while the imaginary

part (fig. 2.2 right) was determined from the change of the quality factor

of the resonator. Two higher peaks are obviously of FMR origin, while the

smaller hysteretic one is due to domain structure change in the thin film.The permalloy thin film was also probed using broadband FMR technique.

In comparison to standard FMR, where frequency is fixed to frequency of

resonance peak(s) of resonator and external magnetic field is swept, the

broadband FMR allows one to probe sample in wide frequency range while

simultaneously sweeping external magnetic field. This way, it is possible to

get more information from single measurement. Unfortunately, it is more

prone to impedance mismatches and stability of the measurement system.

Usually measurement signal is weaker as well. It is due to used geometry - a

ferromagnetic sample is placed on top of a coplanar waveguide or stripline.

In these types of waveguides, coupling between a sample and a waveguide

6

Figure 2.1: Top panels: amplitude of transmitted signal through the dielec-tric resonator with permalloy thin film depending on external magnetic fieldand detuning from resonance frequency 2.822 GHz, which corresponds toTE01δ mode of the dielectric resonator. Bottom panels: Phase of the signal.Left panels depict measurements with increasing magnetic field, while rightpanels with decreasing.

Figure 2.2: Real (left panel) and imaginary (right panel) part of susceptibilityof permalloy thin film sample extracted from data shown in fig. 2.1.

is weak, because magnetic field decreases inversely proportional to distance

from the center conductor, while microwave cavities have modes with mag-

netic field spread in volume.For broadband FMR, coaxial cable (aluminium conductors and PTFE di-

electrics) with outer diameter 2.16 mm with small slot (see fig. 2.3, right

panel) connected to the network analyzer was used. The small slot allows us

to place samples in close vicinity of strong magnetic field of coaxial cable and

it does not change impedance substantially. This way, the reflections from

impedance mismatches are minimized and we were able to observe broadband

7

Figure 2.3: Left: Broadband FMR of 40 nm thick permalloy film. Toppanel: amplitude of transmitted signal, proportional to imaginary part ofmagnetic susceptibility of sample. Bottom panel: phase of transmitted sig-nal, proportional to real part of magnetic susceptibility of sample. Data werenormalized and filtered to eliminate effects caused by impedance mismatch,different transmission amplitude at different frequencies and fluctuation ofvoltages. Right top: the sample slot in coaxial cable for broadband FMR.Right bottom: Electric and magnetic fields in cross-section of coaxial cable(TEM mode).

permalloy spectrum with in-plane external static magnetic field applied, see

fig. 2.3. Measured curves correspond to Kittel resonance condition. More-

over, doubling of resonance curve, clearly visible in χimag, is effect of per-

pendicular spin waves1, see e.g. [52] for review of different types of spin

waves.

2.2 Permalloy nanodots

Arrays of permalloy nanodisks were probed by means of FMR in the dielectric

resonator. The arrays were prepared by electron beam lithography process on

thinned resist and electron beam evaporation of sputtered permalloy layer,

1This type of spin waves is a standing wave of phase of magnetic dipoles precession indirection perpendicular to plane of sample.

8

Figure 2.4: Left: Real part of susceptibility of empty dielectric resonator(background measurement). There are two distinctive jumps (in both sweepdirections, red - sweep up, blue - sweep down) at +/-50 mT which are dueto the dielectric material from which the dielectric resonator is made. Topand bottom right: two different possible measurement geometries of staticand microwave magnetic fields.

followed by lift-off on low resistance silicon substrate [31][32], see scanning

electron microscope images in figures 2.5, 2.6 and 2.7. Three samples of

nanodot arrays are presented - with diameters 500 nm, 700 nm and 1000

nm, all of them with thickness 40 nm. The arrays had dimensions 0.1 mm x

0.1 mm and center-to-center distance between nanodots were approximately

2.5 times the nanodot diameter.

Figure 2.5: Left panel: Real part of magnetic susceptibility of an array of500 nm diameter nanodots (red - sweep up, blue - sweep down). There is asudden jump at +8 mT when sweeping up and -8 mT when sweeping down(jump at +/-50 mT is due to dielectric resonator). Right panel: SEM imageof the array.

During measurements, the samples were placed in dielectric resonator cavity

with static magnetic field parallel to plane of nanodot and microwave field

9

parallel to plane of nanodot and perpendicular to the static magnetic field

(see fig. 2.4, top right). Dielectric resonator was operated at resonance fre-

quency 2.82 GHz, which corresponds to TE01δ mode with maximal magnetic

field in the center of the cavity. Unfortunately, resonance on other modes

were not observed due to small interaction coupling between resonant mode

and the sample. This could be improved by increasing the area of the arrays

and the density of permalloy nanodots on the sample.

Figure 2.6: Left panel: Real part of magnetic susceptibility of an array of700 nm diameter nanodots (red - sweep up, blue - sweep down). There isa sudden jump at +/-11 mT in both sweeps (jump at +/-50 mT is due todielectric resonator). Right panel: SEM image of the array.

However, some resonances were observed at least on TE01δ mode of the di-

electric resonator on all three samples (besides parasitic resonances at +/-50

mT, see fig. 2.4). They show indeed interesting hysteresis. In first sam-

ple (500 nm diameter nanodots) spectrum, one jump appears when passing

through zero magnetic field at 8 mT or -8 mT in both directions. On the

other hand, 700 nm diameter sample has two jumps at +/-11 mT (in both

sweep directions). The last, 1000 nm diameter sample shows once again only

one jump, however, this time before passing through zero magnetic field at

+21 mT or -21 mT (in both sweep directions). This behaviour is completely

different in comparison to measured permalloy thin film. Jumps (resonances)

could correspond to either higher vortex modes (500 nm sample) or uniform

distribution modes (1000 nm sample, similar to ref. [37]), because resonance

fields lie in range of creation and annihilation fields of nanodots of these sizes

and uncommon hystereses support this presumption as well.Of course, from presented data, we are not able to determine resonance

frequencies of nanodots, because vortex state resonances are (almost) exter-

nal magnetic field independent and the samples were investigated at single

10

Figure 2.7: Left panel: Real part of magnetic susceptibility of an array of1000 nm diameter nanodots (red - sweep up, blue - sweep down). There isa sudden jump at -21 mT when sweeping up and +21 mT when sweepingdown (jump at +/-50 mT is due to dielectric resonator). Right panel: SEMimage of the array.

frequency (2.82 GHz). In publication [P3], we hit one of the higher order res-

onances of permalloy nanostructures. However, for systematic studies of their

FMR modes, broadband resonance FMR is more suitable [29][38][39][40][41][42].

Our measurement system is not sensitive enough to detect such resonances in

prepared samples, which could be estimated by comparison with broadband

FMR of permalloy thin film (dimensions: circle with diameter 5 mm, thick-

ness 40 nm). The arrays’ areas are roughly 20 times smaller than the area of

thin film sample and moreover, with center-to-center distance of nanodots 2.5

times the nanodot diameter, the nanodots fill only around 10% of substrate

(top) area. Thus, less than 200 times smaller signal (with similar measure-

ment settings) is expected, which is under the observable background noise.

To get above this level, larger and densely packed2 arrays are necessary.

2.3 Two coupled SQUIDs

Two mutually coupled SQUIDs embedded in current antinode of a supercon-

ducting coplanar waveguide resonator (SCPWR) with quality factor ≈ 9000

and resonance frequency of first mode 7.5 GHz (designed, without SQUIDs)

were studied. Ferromagnetic coupling between SQUIDs was achieved by

special design of electrodes [53][54] and realized by shadow evaporation tech-

nique. The sample was designed in the manner that the both SQUIDs con-

2But not too densely. If ferromagnetic nanostructures are placed too close one toanother, they start to interact via dipole interaction, which is in our case unwanted.

11

Figure 2.8: Top left: SEM image of 2 SQUIDs embedded in SCPWR. Bot-tom left: model of the device. Top right: simulated energy of the SQUIDsdepending on external magnetic flux. Bottom right: Second derivative of theenergy, which is proportional to measurable quantity - resonance frequencydetuning.

sist of three small junctions which determine the dynamics of the device, one

junction roughly twice bigger which serves as a coupling element to SCPWR

and a much bigger JJ which couples the SQUIDs together, see fig. 2.8.

Pair of SQUIDs can be found in four distinctive states: superconducting

currents in both loops flowing either cw or ccw or two states with currents

flowing in opposite directions. The currents are determined by properties of

JJs and by external magnetic flux. Because of ferromagnetic coupling of our

device, states with the currents flowing in same direction are preferred when

the external flux Φe ≈ Φ0/2. Simulated energy diagram and corresponding

measurable quantity - second derivative of energy in respect to external mag-

netic flux for parameters of our sample are shown in fig. 2.8. Even though

the antiferromagnetic state (ccw+cw) has higher energy than the ferromag-

netic states, it is stable (for measurably long periods of time) once reached.

Note that there are only 3 lines in the energy diagram. This is caused by

energy equivalence of two states - when left SQUID current is flowing cw

and right SQUID current is flowing ccw, and state with opposite directions

of currents.

12

Figure 2.9: Measured detuning of the resonance frequency of the two SQUIDssample depending on external magnetic flux. Left plot: Measurement in widerange of magnetic fluxes, periodical pattern is clearly visible. Right plot:Zoom into the area, where Φe = Φ0/2. All four states can be distinguished.

2.3.1 Characterization of the device

In the figure 2.9, transmission measurement results are shown - detuning of

the resonance frequency of the SCPWR caused by inductance of the mutually

coupled pair of SQUIDs as a function of applied external flux. Left figure

shows periodical pattern which is a result of gauge-invariance of supercon-

ducting phase. Transition from unstable (ferromagnetic, the lowest branch)

to stable state (ferromagnetic, the highest branch) always occur through one

of the metastable antiferromagnetic states. Measurements were carried out

at base temperature of our dilution refrigerator - 10 mK. Mismatch between

simulation and results is caused mainly by the fact, that one of the JJs

is short-circuited. This may have happened during lithographical process.

Anyway, from the transmission data, we are able to reconstruct the energy

levels of the system and from fit determine real values of the JJs properties.These values slightly differ from those designed. Six nominally equal JJs

(see schematics in fig. 2.8) have the same values of critical current within

15%. Furthermore, it is most probable, that one of the JJ coupling SQUID

to SCPWR (bottom left or bottom right JJ in schematics in fig. 2.8) is

short-circuited, while the second has only 40% of designed area, thus only

40% of designed critical current. The biggest JJ (bottom JJ in schematics

in fig. 2.8), that couples two SQUIDs together has critical current 36 times

greater than the small JJs.

Numerical model of the device was based on the three JJ SQUID model

with two modifications. First, each of the JJs could have different EJ 3.

3We assumed this even though six of the JJs should be equal from design. However,

13

Figure 2.10: Left panel: Measurement procedure of the switching exper-iments. f1, f2, f3 are frequencies, which correspond to detuning of theSCPWR in the 3 distinctive (2 ferromagnetic and 1 antiferromagnetic) states.Right panel: Switching probabilities depending on length τ (x axis) and am-plitude (y axis) of the measurement pulse, top plot - unstable ferromagneticstate, middle - unstable antiferromagnetic state, bottom - stable ferromag-netic state.

Second, there were two conditions for the sum of the phases around the loop

of each SQUID, while external flux penetrating each loop was allowed to be

different within few percent. Then, the energy of the system was minimized

for different external magnetic fluxes φe = Φe/Φ0. It was important to look

not only for global minima, but also local minima, which correspond to the

metastable antiferromagnetic states.

Figure 2.11: Left plot: The same data as fig. 2.9, however the four states arenow color-coded. These colors corresponds to colors of data in the middle andthe right plot. Middle plot: Probability of ending in different states of thetwo SQUIDs system, when starting from the ferromagnetic (blue) state fordifferent magnetic fluxes. Right plot: Same as the middle plot, but insteadof starting from blue state, it starts from the red state.

due to lithography, these values in reality differ.

14

Between the aforementioned states, switching (jumping) is allowed and it

can be of classical (temperature activation) or quantum (qunatum tunneling)

nature. Characterization of the switching between the states was performed

using the procedure described in fig. 2.10. The probability of switching from

the unstable ferromagnetic state to the one of the antiferromagnetic state

and the stable ferromagnetic state is shown in figure 2.10. The switching

depends on length (time period during which the the switch can occur) and

the amplitude (deformation of potential energy landscape - decreasing the

barrier between minima) of the pulse. There are only three colorplots shown,

because the probability to switch into the second antiferromagnetic state is

equal to zero. This could be explained by the non-existence of the local

minimum at measured magnetic fluxes (0.55 − 0.85Φ0). However, this is not

the case when the other side of the degeneration point (Φe/Φ0 = 0.5) is

probed. Then, the system is able to enter the second antiferromagnetic state

while probability of entering the first antiferromagnetic state is very small,

however non-zero, see fig. 2.11.

This figure shows probability of switching from unstable ferromagnetic state

to the other states. In case Φe/Φ0 < 0.5 (figure 2.11 middle), the unstable

ferromagnetic state is the blue one , from which the measurement procedure

is started. Then, the external flux is changed during a time period τ = 1 µs

(including ramp up and down). Finally, measurement is carried out and

from the measurement, final state of the system is determined. The process

is repeated to accumulate sufficient statistics (1000). For Φe/Φ0 > 0.5 (figure

2.11 right) the unstable ferromagnetic state is the red one . The measurement

procedure was in this case repeated 4500 times.

2.3.2 Microwave induced switching

Our two SQUIDs system was intended to use as a photon detector. There is a

huge demand for such devices working in microwave range, because it would

allow for observing new effects on low energy scales (1 GHz corresponds to

roughly 4 µeV ) in quantum optics and particle physics, as well as it would

find use in quantum computation. There has been a lot of efforts in this

area of research, however only a few attempts. Those were based on single

Josephson junction [55][56] or superconducting qubits coupled to microwave

cavities [57].To test capabilities of our device to switch the state under influence of mi-

15

Figure 2.12: Switching probability with ”help” by microwave field with fre-quency f (y-axis) biased by different external magnetic fluxes (x-axis). Toprow - probability of staying in unstable state (red state from figure 2.11),middle row - probability of switching to metastable state (green state fromfigure 2.11), bottom row - probability of switching to stable state (blue statefrom figure 2.11). Left column - wide range of frequencies and magneticfluxes. Right column - zoom to the area around Φ = 0.7Φ0, f = 6.88 GHz.

crowave photons, microwave signal was introduced to the input of SCPWR.

As it is shown in figure 2.12, our two SQUID device is sensitive to microwave

photons in narrow frequency band and this band changes with external mag-

netic flux4. These frequencies indeed correspond to resonance frequencies of

the SCPWR. It means, that during the 1 µs pulse, our device is tuned into

resonance with incoming microwave field and the field can enter the SCPWR

and contribute to switching probability.

Last part of measurements was power dependence of switching probability or

in other words, measurement of detector sensitivity. Figure 2.13 shows sev-

eral plots of switching probability against frequency of incoming microwave

photons (vertical slice from figure 2.12 at Φ/Φ0 = 0.69) for different number

of photons per unit of time. From microwave power and length of the pulse,

one can find out, that the onset of the detector’s sensitivity is at around

1000 photons (second graph, −112.5 dBm during 1 µs pulse). Almost 100%

sensitivity with only 10% dark count can be achieved at 10000 photons. In

4To better understand the plots, one can take through them a horizontal slice (f =const.) which corresponds to probabilities from figure 2.11, right plot. However, thepresence of microwave photons changes the shape of the graphs because it (for certainmagnetic fluxes) increases probability to switch the state of the device.

16

Figure 2.13: Switching probability due to incident microwave photons. Fromtop left to bottom right, power is increased in 2 dBm steps from −114.5 dBmto −104.5 dBm. Color-code matches the one from 2.9

comparison with infrared or visible light photon detectors, sensitivity might

seem very weak, however one must take into account, that the energy of

microwave photon is several orders of magnitude smaller and thus the mi-

crowave photon is much harder to ”catch”.

2.4 Two coupled superconducting flux qubits

Design of two ferromagnetically coupled flux qubits is similar to the design

of the two coupled SQUIDs mentioned in the previous chapter. Coupling

JJs (between qubits and also between qubits and SCPWR) are same as in

SQUID design, however, the three remaining JJs are smaller. Two of them

17

Figure 2.14: Transmission measurement of two flux qubit sample with twopairs of anti-crossings.

have same area while the last one has only 2/3 of it (see fig.1 in ref. [P4]).

Transmission measurements of the SCPWR with two qubits depicted in fig.

2.14 show presence of two pairs of anti-crossings, which is a sign of a quantum

mechanical behaviour of the system flux qubit - resonator. This is qualita-

tively different to the case of the SQUID sample. When the flux qubit is

tuned into resonance with SCPWR by the external magnetic flux (energy

level splitting of qubit corresponds to the resonance frequency of SCPWR),

two resonance peaks are observed simultaneously5, while in SQUIDs case,

only single peak is observed for each measurement (which one depends on

the state of the SQUIDs). The fact, that there are two different pairs of

anti-crossings is caused by slightly different properties of both qubits as well

as unequal mutual inductances between the biasing coil and qubits.

2.4.1 Parametric amplification

Josephson junctions and therefore also superconducting flux qubits are known

for their nonlinear behaviour. The strong nonlinearity of the aforementioned

pair of qubits was used for realization of parametric amplifier. Parametric

amplification effect occurs in nonlinear medium (in our case SCPWR with

embedded pair of flux qubits) pumped by strong microwaves with angular

frequency ωp. A weak signal (photons) with angular frequency ωs is mixed

with the pump by such a way that two pump photons and one signal pho-

ton transform into two signal photons with angular frequency ωs and one

5This peak doubling is due to interaction between qubit and SCPWR.

18

photon with angular frequency 2ωp − ωs (idler photon), while energy is con-

served. Detailed theoretical model of parametric amplification in SCPWR

with nonlinear elements can be found in ref. [58]. The parametric amplifier

has maximal gain of 20 dB and even though it has very narrow bandwidth

(of order 1 MHz), its working frequency is tunable around 7.5 GHz through

flux biasing. For more information about parametric amplifier based on non-

linearity of qubits, see author’s article [P4]:

2.4.2 Two-photon lasing

As known from quantum optics, a lot of interesting quantum mechanical

effects can be demonstrated in a system consisting of an atom and a quantized

electromagnetic field. In recent years, many of them have been realised

on artificial atoms (superconducting qubits) as well. To name a few: AC

Zeeman shift [64], electromagnetically induced transparency [65], resonance

fluorescence of an atom [66], Sisyphus cooling [67], Landau-Zener effect [68],

Lamb shift [69], AC Stark shift [70], single atom dressed-state lasing [63].

The last one, single atom dressed-state lasing was described for single photon

processes when probe frequency is equal to Rabi frequency of dressed-state

system. Two photon process was predicted by Hauss [62]. In this case,

the Rabi frequency is equal to twice the probe frequency. Observation of

two-photon lasing is summarized in author’s article [P9].

19

Conclusions

In the thesis, ferromagnetic permalloy thin film has been studied by means

of FMR spectroscopy. Its properties, namely Landé g factor, effective satura-

tion magnetization and hysteretic response were determined. Measurement

setup was also improved in a manner, that it was possible to detect FMR

signal in broad spectrum of frequencies and it was tested on permalloy thin

film. Unfortunately, this improvement has also a downside. For price of in-

creased frequency bandwidth, we paid with decreased detection accuracy.

Then permalloy nanostructures arrays - disks with diameters 500 nm, 700

nm and 1000 nm were probed by means of FMR (single frequency, 2.82 GHz)

showing non-trivial response.

Moreover, two superconducting nanostructures were investigated by trans-

mission measurements. The first sample consists of ferromagnetically coupled

pair of SQUIDs in superconducting coplanar waveguide resonator. Switch-

ing effects between SQUIDs’ states were described. This switching effect

was then utilized for sensitive detection of microwave photons in a coplanar

waveguide resonator. It was able to detect signal of around 10000 microwave

photons (corresponding to energy roughly 0.3 eV) in single-shot measure-

ment with probability 90% and dark count only around 10%.

Similarly, second sample - ferromagnetically coupled pair of flux qubits in

superconducting coplanar waveguide resonator was used for parametric am-

plification employing its large nonlinearity. Maximal gain of this narrow-band

magnetic-field tunable amplifier was found to be 20 dB.

This sample was also used to demonstrate an effect of single (artificial) atom

two-photon lasing and attenuation predicted by Hauss [62].

Most of these findings were published in peer-reviewed scientific journals.

20

List of publications[P1] M. Rehák, P. Neilinger, M. Grajcar, G. Oelsner, P. Macha, U. Hübner,E. Iľichev, Parametric amplification using nonlinearity of a qubit, APCOMProceedings 2013

[P2] P. Neilinger, M. Rehák, M. Gregor, M. Žemlička, T. Pleceník, M. Trgala,P. Ďurina, M. Grajcar, Periodic response of superconducting high qualityMgB2 resonator to magnetic field, APCOM Proceedings 2013

[P3] M. Rehák, P. Neilinger, M. Grajcar, J. Šoltýs, M. Precner, V. Cambel,FMR spectroscopy of permalloy thin films in dielectric resonator, Proceed-ings of conference of Slovak physicists 2013

[P4] M. Rehák, P. Neilinger, M. Grajcar, G. Oelsner, U. Hübner, E. Iľichev,H.-G. Meyer, Parametric amplification by coupled flux qubits, AppliedPhysics Letters 104, 162604 (2014)

[P5] M. Trgala, M. Žemlička, P. Neilinger, M. Rehák, M. Leporis, Š. Gaži,J. Greguš, T. Plecenik, T. Roch, E. Dobročka, M. Grajcar, SuperconductingMoC thin films with enhanced sheet resistance , Applied Surface Science312, p. 216–219 (2014)

[P6] P. Neilinger, M. Rehák, U. Hübner, E. Iľichev, M. Grajcar, Mach–Zehnderinterferometry in an artificial quantum two level system, APCOM Proceed-ings 2014

[P7] M. Žemlička, P. Neilinger, M. Rehák, M. Trgala, D. Manca, U. Hüb-ner, E. Iľichev, M. Grajcar, Transport properties of nanobridges created onmolybdenum carbide superconducting thin films, APCOM Proceedings 2014

[P8] M. Rehák, P. Neilinger, Žemlička, D. Manca, U. Hübner, E. Iľichev,M. Grajcar, Switching effect in SQUIDs coupled by josephson junction, AP-COM Proceedings 2014

[P9] P. Neilinger, M. Rehák, M. Grajcar, G. Oelsner, U. Hübner, E. Iľichev,H.-G. Meyer, Two-photon lasing by a superconducting qubit, Physical Re-view B 91, 104516 (2015)

[P10] M. Žemlička, P. Neilinger, M. Trgala, M. Rehák, D. Manca, M. Graj-car, P. Szabó, P. Samuely, Š. Gaži, U. Hübner, V. M. Vinokur, E. Iľichev,Finite quasiparticle lifetime in disordered superconductors , Physical Re-view B 92, 224506 (2015)

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[P11] P. Neilinger, M. Rehák, M. Grajcar, Estimation of effective temper-ature of an artificial quantum two-level system, APCOM Proceedings 2015

[P12] D. De Motte, A. R. Grounds, M. Rehák, A. Rodriguez Blanco, B. Lek-itsch, G. S. Giri, P. Neilinger, G. Oelsner, E. Iľichev, M. Grajcar, and W. K.Hensinger, Experimental system design for the integration of trapped-ion andsuperconducting qubit systems, pre-print, https://arxiv.org/pdf/1510.07298

[P13] P. Neilinger, S. N. Shevchenko, J. Bogár, M. Rehák, G. Oelsner, D.S. Karpov, O. Astafiev, M. Grajcar, E. Iľichev, Landau-Zener-Stuckelberg-Majorana lasing in circuit QED , pre-print https://arxiv.org/pdf/1603.00245

Conferences

[C1] Applied physics of condensed matter, 19-21 June 2013, Štrbské Pleso,Slovakia. Talk: Parametric amplification using nonlinearity of a qubit

[C2] Mesoscopic structures: fundamentals and applications, 23-29 June 2013Novosibirsk, Russia. Co-author of two contributions

[C3] 20th conference of Slovak physicists, 2-9 September, Bratislava, Slo-vakia. Poster: FMR spectroscopy of permalloy thin films in dielectric res-onator

[C4] 8th international conference in school format on vortex matter in nanos-tructured superconductors (VORTEX VIII), 21-26 September 2013, Rhodes,Greece. Poster: Parametric amplification using nonlinearity of supercon-ducting flux qubit

[C5] Applied physics of condensed matter, 25-27 June 2014, Štrbské Pleso,Slovakia. Talk: Switching effect in SQUIDs coupled by josephson junction

[C6] Topical research meeting on hybrid quantum systems, 16-18 December2014, Nottingham, United Kingdom. Talk: Experimental proposal for quan-tum hybrid system with trapped ions and superconducting qubits

[C7] 602. WE-Heraeus-Seminar: Microwaves Go Quantum, 17-20 November2015, Bad Honnef, Germany. Poster: Parametric amplification using nonlin-earity of superconducting flux qubit

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