Storage and on-demand release of microwaves using superconducting resonators with tunable coupling

We present a system which allows to tune the coupling between a superconducting resonator and a transmission line. This storage resonator is addressed through a second, coupling resonator, which is frequency-tunable and controlled by a magnetic flux applied to a superconducting quantum interference device (SQUID). We experimentally demonstrate that the lifetime of the storage resonator can be tuned by more than three orders of magnitude. A field can be stored for 18 {\mu}s when the coupling resonator is tuned off resonance and it can be released in 14 ns when the coupling resonator is tuned on resonance. The device allows capture, storage, and on-demand release of microwaves at a tunable rate.Comment: 5 pages, 3 figure

Resonant and off-resonant microwave signal manipulation in coupled superconducting resonators

We present an experimental demonstration as well as a theoretical model of an integrated circuit designed for the manipulation of a microwave field down to the single-photon level. The device is made of a superconducting resonator coupled to a transmission line via a second frequency-tunable resonator. The tunable resonator can be used as a tunable coupler between the fixed resonator and the transmission line. Moreover, the manipulation of the microwave field between the two resonators is possible. In particular, we demonstrate the swapping of the field from one resonator to the other by pulsing the frequency detuning between the two resonators. The behavior of the system, which determines how the device can be operated, is analyzed as a function of one key parameter of the system, the damping ratio of the coupled resonators. We show a good agreement between experiments and simulations, realized by solving a set of coupled differential equations.Comment: 10 pages, 6 figure

Minoritetsspråklige elevers opplæringstilbud : hva karakteriserer minoritetsspråklige elevers opplæringstilbud i Norge og hvilke erfaringer fra den amerikanske utdanningssatsningen "No Child Left Behind" kan tilføres den norske utdanningspolitiske debatten?

Tema og problemområde: Temaet for oppgaven er minoritetsspråklige elevers opplæringstilbud. Ved å utdype de føringer som ligger i politiske dokumenter, samt ved å belyse forskning på området, ønsker jeg få svar på hva som karakteriserer minoritetsspråklige elevers opplæringstilbud i Norge. Jeg vil se på hvilke faktorer, både i og utenfor skolen, som innvirker på minoritetsspråklige elevers akademiske fungering. Videre vil jeg belyse den amerikanske utdanningssatsningen ”No Child Left Behind”, for å undersøke hvilke erfaringer fra utdanningssatsningen kan tilføres den norske debatten rundt minoritetsspråklige elevers opplæringstilbud. Formålet med oppgaven er å belyse den pågående utdanningspolitiske debatten rundt minoritetsspråklige elevers opplæringstilbud. Dette fører frem til følgende problemstilling: Hva karakteriserer minoritetsspråklige elevers opplæringstilbud i Norge og hvilke erfaringer fra den amerikanske utdanningssatsningen ”No Child Left Behind” kan tilføres den norske utdanningspolitiske debatten? For å besvare problemstillingen har jeg formulert fem delspørsmål: 1. Hva kjennetegner dagens utdanningspolitiske debatt om minoritetsspråklige elever i norsk skole? 2. Hvilket fokus har forskning rundt minoritetsspråklige elevers akademiske fungering? 3. Hva kjennetegner dagens opplæringstilbud for minoritetsspråklige elever i Norge? 4. Hva er ”No Child Left Behind” og hva er bakgrunnen for, og utfallet av, denne utdanningssatsningen? 5. Hvilke paralleller kan trekkes mellom norske og amerikanske utdanningsforhold? Metode: Den metodiske tilnærmingen i denne oppgaven er teoretisk. Litteraturstudie og dokumentanalyse benyttes som metode. Oppgaven tar utgangspunkt i eksisterende forskningslitteratur som er relativt ny, da bakgrunnen for problemstillingen er å belyse dagens utdanningspolitiske debatt om minoritetsspråklige elevers opplæringstilbud. I tillegg er noe eldre litteratur benyttet for å kunne gi et historisk tilbakeblikk. Forskningsbasert teori og analyse av politiske dokumenter benyttes både i forbindelse med norske og amerikanske utdanningsforhold. Kilder: Kildene jeg har brukt i oppgaven er både av nasjonal og internasjonal karakter. Den norske debatten belyses ved å anvende politiske dokumenter som stortingsmeldinger, lovverk, forskning og evalueringer av prosjekter gjennomført på oppdrag fra statlig hold, i hovedsak fra Kunnskapsdepartementet og Utdanningsdirektoratet. Vesentlig kilder her er Stortingsmelding nr. 16 (2006-2007), Stortingsmelding nr. 23 (2007-2008), Østberg-utvalgets mandat (2009), Rambølls evaluering av norsk som andrespråk (2005-2006), samt Opplæringsloven og lærerplanverket for Kunnskapsløftet. Når det gjelder forskning på området kan Cummins (1984; 2000), Baker (2006), Slavin & Cheung (2005), Bakken (2003; 2007) og Øzerk (1992; 2003; 2007) nevnes som vesentlige kilder. I forbindelse med amerikanske utdanningsforhold benytter jeg i stor grad evalueringer av ”No Child Left Behind”, gjennomført av U.S. Department of Education og Center of Education Policy. Videre kan McGuinn (2006) og Hess & Finn (2005) nevnes som sentrale kilder i forhold til beskrivelse av utdanningsprogrammet. Hovedkonklusjon: Ved gjennomgang av en rekke politiske dokumenter og forskning i forbindelse med minoritetsspråklige elevers opplæringstilbud, viser det seg at mange av de samme områdene vies oppmerksomhet i Norge og USA. Her kan nevnes fokus mot barnehagedeltagelse og tiltak som sikrer tidlig språkstimulering, tidlig innsats for å styrke grunnleggende ferdigheter, fokus på kompetansehevingstiltak for lærere og førskolelærere, samt økt grad av foreldresamarbeid. Til tross for at en rekke av disse satsningsområdene fremkommer i læreplanen, samt gjennom andre politiske dokumenter, synes det i norsk sammenheng å mangle systemer som operasjonaliserer tiltakene, ansvarliggjør skolene, samt stiller krav til og følger opp, de anbefalinger forskningen gir. Mange av erfaringene fra ”No Child Left Behind” som kan tilføres norske forhold, omhandler den amerikanske utdanningssatsningens struktur og måte å sette pedagogisk praksis i et system som sikrer et opplæringstilbud med forskningsforankring

Tunable superconducting resonators, subharmonic oscillations and manipulation of microwaves

In this thesis I present different types of manipulations of microwave fields using tunable superconducting resonators. A resonator is made tunable by adding one or more superconducting quantum interference devices, SQUIDs. The SQUID consists of a superconducting loop with two Josephson junctions and acts as a tunable nonlinear inductor. Modulation of the SQUID nonlinearity can be performed to induce different types of non-trivial oscillator dynamics. The first project I present is on subharmonic oscillations. Here, the SQUID in a tunable resonator is driven with an external signal at an integer multiple of the frequency w. When\ua0w is placed slightly below the first resonator mode, I show generation of radiation at w, which is known as frequency down-conversion. In my measurements, subharmonic oscillations have been detected from period doubling up to period quintupling. For the specific case of period tripling, theory is developed and I show good agreement between theory and experiments. The second project of the thesis is on a doubly tunable resonator. Here, I show creation of a superconducting resonator with two independently tunable boundary conditions. The idea with this system is to operate the resonator in a breathing or a translational mode and compare the two. For static dc magnetic flux the performance is very good. As a second step, I perform fast modulation of both SQUIDs to generate radiation. Even though some of the measurement results are promising, I also show some contradicting observations. These indicate that the actual modulation mechanism of the SQUID is not pumping of the magnetic flux in the SQUID loop as intended, but rather direct current driving of the SQUID. However, the system remains a promising idea for microwave manipulation and creation of interesting non-classical states. As a possible application of the doubly tunable resonator, I present a theory proposal on how to use it for measurements on relativistic effects. By using the tunability of the resonator boundary conditions, the resonator can simulate a space rocket and time dilation could be measured. However, due to the crosstalk problems in the doubly tunable resonator this experiment was never realized. Finally, I finish the thesis by presenting a design for a tunable microwave coupling. Papers E and F show a high on-off ratio for the coupler and demonstrate how it can be used for storage of microwave signals. Furthermore, the tunable coupler can be used to shape a microwave signal by tuning the strength of the coupling

Period-tripling subharmonic oscillations in a driven superconducting resonator

We have observed period-tripling subharmonic oscillations, in a superconducting coplanar waveguide resonator operated in the quantum regime, $k_B T \ll \hbar\omega$. The resonator is terminated by a tunable inductance that provides a Kerr-type nonlinearity. We detected the output field quadratures at frequencies near the fundamental mode, $\omega/2\pi \sim 5\,$GHz, when the resonator was driven by a current at $3\omega$ with an amplitude exceeding an instability threshold. The output radiation was red-detuned from the fundamental mode. We observed three stable radiative states with equal amplitudes and phase-shifted by $120^\circ$. The downconversion from $3\omega$ to $\omega$ is strongly enhanced by resonant excitation of the second mode of the resonator, and the cross-Kerr effect. Our experimental results are in quantitative agreement with a model for the driven dynamics of two coupled modes

Twin paradox with macroscopic clocks in superconducting circuits

We propose an implementation of a twin paradox scenario in superconducting circuits, with velocities as large as a few percent of the speed of light. Ultrafast modulation of the boundary conditions for the electromagnetic field in a microwave cavity simulates a clock moving at relativistic speeds. Since our cavity has a finite length, the setup allows us to investigate the role of clock size as well as interesting quantum effects on time dilation. In particular, our theoretical results show that the time dilation increases for larger cavity lengths and is shifted due to quantum particle creation.Comment: 6 pages, 3 figures. I. F. previously published as I. Fuentes-Guridi and I. Fuentes-Schulle

Period multiplication in a parametrically driven superconducting resonator

We report on the experimental observation of period multiplication in parametrically driven tunable superconducting resonators. We modulate the magnetic flux through a superconducting quantum interference device, attached to a quarter-wavelength resonator, with frequencies $n\omega$ close to multiples, $n=2,\,3,\,4,\,5$, of the resonator fundamental mode and observe intense output radiation at $\omega$. The output field manifests $n$-fold degeneracy with respect to the phase, the $n$ states are phase shifted by $2\pi/n$ with respect to each other. Our demonstration verifies the theoretical prediction by Guo et al. in PRL 111, 205303 (2013), and paves the way for engineering complex macroscopic quantum cat states with microwave photons

Microwave photon generation in a doubly tunable superconducting resonator

We have developed and tested a doubly tunable resonator, with the intention to simulate fast motion of the resonator boundaries in real space. Our device is a superconducting coplanar-waveguide half-wavelength microwave resonator, with fundamental resonant frequency ~5 GHz. Both of its ends are terminated by dc-SQUIDs, which serve as magnetic-flux-controlled inductances. Applying a flux to either SQUID allows tuning of the resonant frequency by approximately 700 MHz. By using two separate on-chip magnetic-flux lines, we modulate the SQUIDs with two tones of equal frequency, close to twice that of the resonator's fundamental mode. We observe photon generation, at the fundamental frequency, above a certain pump amplitude threshold. By varying the relative phase of the two pumps we are able to control the photon generation threshold, in good agreement with a theoretical model for the modulation of the boundary conditions. At the same time, some of our observations deviate from the theoretical predictions, which we attribute to parasitic couplings, resulting in current driving of the SQUIDs.Comment: 7 pages, 4 figure

Observation of Broadband Entanglement in Microwave Radiation from a Single Time-Varying Boundary Condition

Entangled pairs of microwave photons are commonly produced in the narrow frequency band of a resonator, which represents a modified vacuum density of states. We generate and investigate the entanglement of a stream of photon pairs, generated in a semi-infinite broadband transmission line, terminated by a superconducting quantum interference device (SQUID). A weak pump signal modulates the SQUID inductance, resulting in a single time-varying boundary condition, and we detect all four quadratures of the microwave radiation emitted at two different frequencies separated by 0.7\ua0GHz. Power calibration is done\ua0in\ua0situ, and we find positive logarithmic negativity and two-mode squeezing below the vacuum in the observed radiation, indicating entanglement

Nondegenerate parametric oscillations in a tunable superconducting resonator

We investigate nondegenerate parametric oscillations in a multimode superconducting microwave resonator that is terminated by a SQUID. The parametric effect is achieved by modulating magnetic flux through the SQUID at a frequency close to the sum of two resonator-mode frequencies. For modulation amplitudes exceeding an instability threshold, self-sustained oscillations are observed in both modes. The amplitudes of these oscillations show good quantitative agreement with a theoretical model. The oscillation phases are found to be correlated and exhibit strong fluctuations which broaden the oscillation spectral linewidths. These linewidths are significantly reduced by applying a weak on-resonance tone, which also suppresses the phase fluctuations. When the weak tone is detuned, we observe synchronization of the oscillation frequency with the frequency of the input. For the detuned input, we also observe an emergence of three idlers in the output. This observation is in agreement with theory indicating four-mode amplification and squeezing of a coherent input.Comment: 7 pages, 8 figure