Martin Sandberg - Academia.edu (original) (raw)

Papers by Martin Sandberg

We experimental study a high quality factor (Q-value) transmission line resonator terminated in a... more We experimental study a high quality factor (Q-value) transmission line resonator terminated in a superconducting quantum interference device (SQUID). Using an on-chip fast flux bias line we show that we can tune the frequency of such a resonator by hundreds of line widths on a time scale faster the photon lifetime of the resonator. Such a resonator could then be

We describe a circuit model for a flux-driven SQUID. This is useful for developing insight into h... more We describe a circuit model for a flux-driven SQUID. This is useful for developing insight into how these devices perform as active elements in parametric amplifiers. The key concept is that frequency mixing in a flux-pumped SQUID allows for the appearance of an effective negative resistance. In the three-wave, degenerate case treated here, a negative resistance appears only over a certain range of allowed input signal phase. This model readily lends itself to testable predictions of more complicated circuits.

Applied Physics Letters

We present a method to systematically locate and extract capacitive and inductive losses in super... more We present a method to systematically locate and extract capacitive and inductive losses in superconducting resonators at microwave frequencies by use of mixed-material, lumped element devices. In these devices, ultra-low loss titanium nitride was progressively replaced with aluminum in the inter-digitated capacitor and meandered inductor elements. By measuring the power dependent loss at 50 mK as the Al/TiN fraction in each element is increased, we find that at low electric field, i.e., in the single photon limit, the loss is two level system in nature and is correlated with the amount of Al capacitance rather than the Al inductance. In the high electric field limit, the remaining loss is linearly related to the product of the Al area times its inductance and is likely due to quasiparticles generated by stray IR radiation. At elevated temperature, additional loss is correlated with the amount of Al in the inductance, with a power independent TiN-Al interface loss term that exponent...

Applied Physics Letters

We have investigated the correlation between the microwave loss and patterning method for coplana... more We have investigated the correlation between the microwave loss and patterning method for coplanar waveguide titanium nitride resonators fabricated on Si wafers. Three different methods were investigated: fluorine- and chlorine-based reactive ion etches and an argon-ion mill. At high microwave probe powers the reactive etched resonators showed low internal loss, whereas the ion-milled samples showed dramatically higher loss. At single-photon powers we found that the fluorine-etched resonators exhibited substantially lower loss than the chlorine-etched ones. We interpret the results by use of numerically calculated filling factors and find that the silicon surface exhibits a higher loss when chlorine-etched than when fluorine-etched. We also find from microscopy that re-deposition of silicon onto the photoresist and side walls is the probable cause for the high loss observed for the ion-milled resonators

The light-matter interaction of multi-level transmons strongly coupled to a cavity and the extern... more The light-matter interaction of multi-level transmons strongly coupled to a cavity and the external drive field are measured over a wide frequency and power range. The transmons are fabricated from TiN capacitor plates with small Al/AlOx/Al shadow evaporated junctions. The long T1's of these devices, approximately 10 us, allow for a rich spectrum of doubly dressed states to be observed and modeled. Both single- and two-photon absorption features are identified as the drive power is increased. Quantitative agreement of the absorption spectra in both the weak and strong drive limits is obtained using the measured junction properties and the temperature.

Applied Physics Letters

We demonstrate single-photon counting at 1550nm with titanium-nitride (TiN) microwave kinetic ind... more We demonstrate single-photon counting at 1550nm with titanium-nitride (TiN) microwave kinetic inductance detectors. Full-width-at-half-maximum energy resolution of 0.4 eV is achieved. 0-, 1-, 2-photon events are resolved and shown to follow Poisson statistics. We find that the temperature-dependent frequency shift deviates from the Mattis-Bardeen theory, and the dissipation response shows a shorter decay time than the frequency response at low temperatures. We suggest that the observed anomalous electrodynamics may be related to quasiparticle traps or subgap states in the disordered TiN films. Finally, the electron density-of-states is derived from the pulse response

We present a superconducting qubit design that is fabricated in a 2D geometry over a superconduct... more We present a superconducting qubit design that is fabricated in a 2D geometry over a superconducting ground plane to enhance the lifetime. The qubit is coupled to a microstrip resonator for readout. The circuit is fabricated on a silicon substrate using low loss, stoichiometric titanium nitride for capacitor pads and small, shadow-evaporated aluminum/aluminum-oxide junctions. We observe qubit relaxation and coherence times ($T_1$ and T_2T_2T2) of 11.7 pm\pmpm 0.2 mu\mumus and 8.7 pm\pmpm 0.3 mu\mumus, respectively. Calculations show that the proximity of the superconducting plane suppresses the otherwise high radiation loss of the qubit. A significant increase in T1T_1T_1 is projected for a reduced qubit-to-superconducting plane separation.

Applied Physics Letters

We present a superconducting transmon qubit circuit design based on large, coplanar capacitor pla... more We present a superconducting transmon qubit circuit design based on large, coplanar capacitor plates and a microstrip resonator. The microstrip geometry, with the ground plane on the back, enhances access to the circuit for state preparation and measurement relative to otherdesigns. The device is fabricated on a silicon substrate using low loss, stoichiometric titanium nitride for the capacitor plates and a single small aluminium/aluminium-oxide/aluminium junction. We observerelaxation and coherence times of 11.760.2ls and 9.660.5ls, respectively, using spin echo. Calculations show that the close proximity of the superconducting back-plane has the added advantage of suppressing the otherwise high radiation loss of the qubit.

Applied Physics Letters

We developed transmon qubits based on epitaxial tunnel junctions and interdigitated capacitors. T... more We developed transmon qubits based on epitaxial tunnel junctions and interdigitated capacitors. This multileveled qubit, patterned by use of all-optical lithography, is a step towards scalable qubits with a high integration density. The relaxation time T1 is .72-.86mu sec and the ensemble dephasing time T2 is slightly larger than T1. The dephasing time T2 (1.36mu sec) is nearly energy-relaxation-limited. Qubit spectroscopy yields weaker level splitting than observed in qubits with amorphous barriers in equivalent-size junctions. The qubit's inferred microwave loss closely matches the weighted losses of the individual elements (junction, wiring dielectric, and interdigitated capacitor), determined by independent resonator measurements.

We have investigated how the microwave loss in coplanar wave-guide titanium nitride resonators fa... more We have investigated how the microwave loss in coplanar wave-guide titanium nitride resonators fabricated on Si wafers is affected by the choice of etch method used to pattern the resonators. Three different etches has been investigated, one fluorine based reactive etch, one chlorine based reactive ion etch, and one argon ion mill. At high microwave probe powers, the two different reactive etches show low internal loss whereas the milled samples show dramatically higher loss. At single photon powers we observe that the fluorine etch resonators exhibit substantially lower loss than the chlorine etched resonators. In the single photon limit we observe loss tangents of 1.10-6 for the fluorine etched, 4.10-6 to 5.5.10-6 for the chlorine etch and 1.4.10-4 for the argon ion mill. We compare these results to numerically calculated filling factors and find that the chlorine etch Si surface has a higher loss tangent than the fluorine etched surface. We also find that re-deposition of Silicon...

Titanium Nitride (TiN) thin films, when optimally grown and processed, exhibit very low microwave... more Titanium Nitride (TiN) thin films, when optimally grown and processed, exhibit very low microwave loss at high and low power. We investigate reducing the loss by systematically removing Si substrate material from the gap region in TiN coplanar waveguides (CPWs) fabricated on intrinsic Si substrates. By exploiting the radial dependence of the etch rate in a parallel plate reactive ion etcher, otherwise identical CPWs with only the gaps etched to varying depth, i.e. trenched, were created in a single TiN film within a single processing step. The high power loss is similar for all resonators, < 2x10-7. However, when comparing the loss from all trench depths in the single photon regime at 50 mK we find that loss was reduced for the deeper trenches with the deepest reduced by a factor of 2. Predictions from finite-element analysis, with a reduced participation of lossy surface oxides in the deeper trenched CPW gaps, fit well to the measured reduction.

Photons are fundamental excitations of the electromagnetic field and can be captured in cavities.... more Photons are fundamental excitations of the electromagnetic field and can be captured in cavities. For a given cavity with a certain size, the fundamental mode has a fixed frequency f which gives the photons a specific "colour". The cavity also has a typical lifetime tau, which results in a finite linewidth delta f}. If the size of the cavity is

Physical Review Letters, 2007

We measure longitudinal dressed states of a superconducting qubit, the single Cooper-pair box, an... more We measure longitudinal dressed states of a superconducting qubit, the single Cooper-pair box, and an intense microwave field. The dressed states represent the hybridization of the qubit and photon degrees of freedom and appear as avoided level crossings in the combined energy diagram. By embedding the circuit in an rf oscillator, we directly probe the dressed states. We measure their

Physical review letters, 2014

We present measurements of a topological property, the Chern number (C_{1}), of a closed manifold... more We present measurements of a topological property, the Chern number (C_{1}), of a closed manifold in the space of two-level system Hamiltonians, where the two-level system is formed from a superconducting qubit. We manipulate the parameters of the Hamiltonian of the superconducting qubit along paths in the manifold and extract C_{1} from the nonadiabatic response of the qubit. By adjusting the manifold such that a degeneracy in the Hamiltonian passes from inside to outside the manifold, we observe a topological transition C_{1}=1→0. Our measurement of C_{1} is quantized to within 2% on either side of the transition.

Operation of transition edge sensors in a resistance locked loop Appl. Phys. Lett. 102, 023505 (2... more Operation of transition edge sensors in a resistance locked loop Appl. Phys. Lett. 102, 023505 (2013) Magnetic field resilient superconducting fractal resonators for coupling to free spins J. Appl. Phys. 112, 123905 Complex impedance, responsivity and noise of transition-edge sensors: Analytical solutions for two-and threeblock thermal models AIP Advances 2, 042110 Sub-micron normal-metal/insulator/superconductor tunnel junction thermometer and cooler using Nb Appl. Phys. Lett. 101, 112601 (2012) Frequency division multiplexing readout and simultaneous manipulation of an array of flux qubits

Physical Review Letters, 2014

We have generated frequency combs spanning 0.5 -20 GHz in superconducting /2-resonators at T=3 K... more We have generated frequency combs spanning 0.5 -20 GHz in superconducting /2-resonators at T=3 K. Thin films of niobium-titanium nitride enabled this development due to their low loss, high nonlinearity, low frequencydispersion, and high critical temperature. The combs nucleate as sidebands around multiples of the pump frequency. Selection rules for the allowed frequency emission are calculated using perturbation theory and the measured spectrum is shown to agree with the theory. The sideband spacing is measured to be accurate to 1 part in 10 8 . The sidebands coalesce into a continuous comb structure that has been observed to cover at least 6 octaves in frequency.

Thin Solid Films, 2013

The structural and electrical properties of Ti-N films deposited by reactive sputtering depend on... more The structural and electrical properties of Ti-N films deposited by reactive sputtering depend on their growth parameters, in particular the Ar:N 2 gas ratio. We show that the nitrogen percentage changes the crystallographic phase of the film progressively from pure α-Ti, through an α-Ti phase with interstitial nitrogen, to stoichiometric Ti 2 N, and through a substoichiometric TiN X to stoichiometric TiN. These changes also affect the superconducting transition temperature, T C , allowing, the superconducting properties to be tailored for specific applications. After decreasing from a T C of 0.4 K for pure Ti down to below 50 mK at the Ti 2 N point, the T C then increases rapidly up to nearly 5 K over a narrow range of nitrogen incorporation. This very sharp increase of T C makes it difficult to control the properties of the film from wafer-to-wafer as well as across a given wafer to within acceptable margins for device fabrication. Here we show that the nitrogen composition and hence the superconductive properties are related to, and can be determined by, spectroscopic ellipsometry. Therefore, this technique may be used for process control and wafer screening prior to investing time in processing devices.

Physical Review Letters, 2010

We report the observation of photon generation in a microwave cavity with a time-dependent bounda... more We report the observation of photon generation in a microwave cavity with a time-dependent boundary condition. Our system is a microfabricated quarter-wave coplanar waveguide cavity. The electrical length of the cavity is varied using the tunable inductance of a superconducting quantum interference device. It is measured in the quantum regime, where the temperature is significantly less than the resonance frequency (∼ 5 GHz). When the length is modulated at approximately twice the static resonance frequency, spontaneous oscillations of the cavity field are observed. Timeresolved measurements of the dynamical state of the cavity show multiple stable states. The behavior is well described by theory. Connections to the dynamical Casimir effect are discussed. PACS numbers: 85.25.Cp, 42.65.Lm, Photons, in contrast to electrons, do not directly interact with each other. However, effective interactions can be induced when photons interact with a nonlinear media. In many cases, these effective interactions result in so-called parametric processes which are very important in widespread technological applications and also in fundamental studies of quantum electrodynamics . In the optical regime, the effective nonlinearities are generally bulk properties of materials or plasmas. In the rf and microwave regime, they are often created by lumped-element electrical devices . These types of systems have been extensively studied both theoretical and experimentally.

Physical Review B, 2010

We study relaxation and dephasing in a strongly driven two-level system interacting with its envi... more We study relaxation and dephasing in a strongly driven two-level system interacting with its environment. We develop a theory which gives a straightforward physical picture of the complex dynamics of the system in terms of dressed states. In addition to the dressing of the energy diagram, we describe the dressing of relaxation and dephasing. We find a good quantitative agreement between the theoretical calculations and measurements of a superconducting qubit driven by an intense microwave field. The competition of various processes leads to a rich structure in the observed behavior, including signatures of population inversion.

Physica Scripta, 2009

... tunable superconducting resonator M Sandberg, F Persson, IC Hoi, CM Wilson and P Delsing Depa... more ... tunable superconducting resonator M Sandberg, F Persson, IC Hoi, CM Wilson and P Delsing Department of Microtechnology and Nanoscience, Chalmers University of Technology, Kemivägen 9, SE-41296 Gothenburg, Sweden E-mail: martin.sandberg@chalmers.se ...

We experimental study a high quality factor (Q-value) transmission line resonator terminated in a... more We experimental study a high quality factor (Q-value) transmission line resonator terminated in a superconducting quantum interference device (SQUID). Using an on-chip fast flux bias line we show that we can tune the frequency of such a resonator by hundreds of line widths on a time scale faster the photon lifetime of the resonator. Such a resonator could then be

We describe a circuit model for a flux-driven SQUID. This is useful for developing insight into h... more We describe a circuit model for a flux-driven SQUID. This is useful for developing insight into how these devices perform as active elements in parametric amplifiers. The key concept is that frequency mixing in a flux-pumped SQUID allows for the appearance of an effective negative resistance. In the three-wave, degenerate case treated here, a negative resistance appears only over a certain range of allowed input signal phase. This model readily lends itself to testable predictions of more complicated circuits.

Applied Physics Letters

We present a method to systematically locate and extract capacitive and inductive losses in super... more We present a method to systematically locate and extract capacitive and inductive losses in superconducting resonators at microwave frequencies by use of mixed-material, lumped element devices. In these devices, ultra-low loss titanium nitride was progressively replaced with aluminum in the inter-digitated capacitor and meandered inductor elements. By measuring the power dependent loss at 50 mK as the Al/TiN fraction in each element is increased, we find that at low electric field, i.e., in the single photon limit, the loss is two level system in nature and is correlated with the amount of Al capacitance rather than the Al inductance. In the high electric field limit, the remaining loss is linearly related to the product of the Al area times its inductance and is likely due to quasiparticles generated by stray IR radiation. At elevated temperature, additional loss is correlated with the amount of Al in the inductance, with a power independent TiN-Al interface loss term that exponent...

Applied Physics Letters

We have investigated the correlation between the microwave loss and patterning method for coplana... more We have investigated the correlation between the microwave loss and patterning method for coplanar waveguide titanium nitride resonators fabricated on Si wafers. Three different methods were investigated: fluorine- and chlorine-based reactive ion etches and an argon-ion mill. At high microwave probe powers the reactive etched resonators showed low internal loss, whereas the ion-milled samples showed dramatically higher loss. At single-photon powers we found that the fluorine-etched resonators exhibited substantially lower loss than the chlorine-etched ones. We interpret the results by use of numerically calculated filling factors and find that the silicon surface exhibits a higher loss when chlorine-etched than when fluorine-etched. We also find from microscopy that re-deposition of silicon onto the photoresist and side walls is the probable cause for the high loss observed for the ion-milled resonators

The light-matter interaction of multi-level transmons strongly coupled to a cavity and the extern... more The light-matter interaction of multi-level transmons strongly coupled to a cavity and the external drive field are measured over a wide frequency and power range. The transmons are fabricated from TiN capacitor plates with small Al/AlOx/Al shadow evaporated junctions. The long T1's of these devices, approximately 10 us, allow for a rich spectrum of doubly dressed states to be observed and modeled. Both single- and two-photon absorption features are identified as the drive power is increased. Quantitative agreement of the absorption spectra in both the weak and strong drive limits is obtained using the measured junction properties and the temperature.

Applied Physics Letters

We demonstrate single-photon counting at 1550nm with titanium-nitride (TiN) microwave kinetic ind... more We demonstrate single-photon counting at 1550nm with titanium-nitride (TiN) microwave kinetic inductance detectors. Full-width-at-half-maximum energy resolution of 0.4 eV is achieved. 0-, 1-, 2-photon events are resolved and shown to follow Poisson statistics. We find that the temperature-dependent frequency shift deviates from the Mattis-Bardeen theory, and the dissipation response shows a shorter decay time than the frequency response at low temperatures. We suggest that the observed anomalous electrodynamics may be related to quasiparticle traps or subgap states in the disordered TiN films. Finally, the electron density-of-states is derived from the pulse response

We present a superconducting qubit design that is fabricated in a 2D geometry over a superconduct... more We present a superconducting qubit design that is fabricated in a 2D geometry over a superconducting ground plane to enhance the lifetime. The qubit is coupled to a microstrip resonator for readout. The circuit is fabricated on a silicon substrate using low loss, stoichiometric titanium nitride for capacitor pads and small, shadow-evaporated aluminum/aluminum-oxide junctions. We observe qubit relaxation and coherence times ($T_1$ and T_2T_2T2) of 11.7 pm\pmpm 0.2 mu\mumus and 8.7 pm\pmpm 0.3 mu\mumus, respectively. Calculations show that the proximity of the superconducting plane suppresses the otherwise high radiation loss of the qubit. A significant increase in T1T_1T_1 is projected for a reduced qubit-to-superconducting plane separation.

Applied Physics Letters

We present a superconducting transmon qubit circuit design based on large, coplanar capacitor pla... more We present a superconducting transmon qubit circuit design based on large, coplanar capacitor plates and a microstrip resonator. The microstrip geometry, with the ground plane on the back, enhances access to the circuit for state preparation and measurement relative to otherdesigns. The device is fabricated on a silicon substrate using low loss, stoichiometric titanium nitride for the capacitor plates and a single small aluminium/aluminium-oxide/aluminium junction. We observerelaxation and coherence times of 11.760.2ls and 9.660.5ls, respectively, using spin echo. Calculations show that the close proximity of the superconducting back-plane has the added advantage of suppressing the otherwise high radiation loss of the qubit.

Applied Physics Letters

We developed transmon qubits based on epitaxial tunnel junctions and interdigitated capacitors. T... more We developed transmon qubits based on epitaxial tunnel junctions and interdigitated capacitors. This multileveled qubit, patterned by use of all-optical lithography, is a step towards scalable qubits with a high integration density. The relaxation time T1 is .72-.86mu sec and the ensemble dephasing time T2 is slightly larger than T1. The dephasing time T2 (1.36mu sec) is nearly energy-relaxation-limited. Qubit spectroscopy yields weaker level splitting than observed in qubits with amorphous barriers in equivalent-size junctions. The qubit's inferred microwave loss closely matches the weighted losses of the individual elements (junction, wiring dielectric, and interdigitated capacitor), determined by independent resonator measurements.

We have investigated how the microwave loss in coplanar wave-guide titanium nitride resonators fa... more We have investigated how the microwave loss in coplanar wave-guide titanium nitride resonators fabricated on Si wafers is affected by the choice of etch method used to pattern the resonators. Three different etches has been investigated, one fluorine based reactive etch, one chlorine based reactive ion etch, and one argon ion mill. At high microwave probe powers, the two different reactive etches show low internal loss whereas the milled samples show dramatically higher loss. At single photon powers we observe that the fluorine etch resonators exhibit substantially lower loss than the chlorine etched resonators. In the single photon limit we observe loss tangents of 1.10-6 for the fluorine etched, 4.10-6 to 5.5.10-6 for the chlorine etch and 1.4.10-4 for the argon ion mill. We compare these results to numerically calculated filling factors and find that the chlorine etch Si surface has a higher loss tangent than the fluorine etched surface. We also find that re-deposition of Silicon...

Titanium Nitride (TiN) thin films, when optimally grown and processed, exhibit very low microwave... more Titanium Nitride (TiN) thin films, when optimally grown and processed, exhibit very low microwave loss at high and low power. We investigate reducing the loss by systematically removing Si substrate material from the gap region in TiN coplanar waveguides (CPWs) fabricated on intrinsic Si substrates. By exploiting the radial dependence of the etch rate in a parallel plate reactive ion etcher, otherwise identical CPWs with only the gaps etched to varying depth, i.e. trenched, were created in a single TiN film within a single processing step. The high power loss is similar for all resonators, < 2x10-7. However, when comparing the loss from all trench depths in the single photon regime at 50 mK we find that loss was reduced for the deeper trenches with the deepest reduced by a factor of 2. Predictions from finite-element analysis, with a reduced participation of lossy surface oxides in the deeper trenched CPW gaps, fit well to the measured reduction.

Photons are fundamental excitations of the electromagnetic field and can be captured in cavities.... more Photons are fundamental excitations of the electromagnetic field and can be captured in cavities. For a given cavity with a certain size, the fundamental mode has a fixed frequency f which gives the photons a specific "colour". The cavity also has a typical lifetime tau, which results in a finite linewidth delta f}. If the size of the cavity is

Physical Review Letters, 2007

We measure longitudinal dressed states of a superconducting qubit, the single Cooper-pair box, an... more We measure longitudinal dressed states of a superconducting qubit, the single Cooper-pair box, and an intense microwave field. The dressed states represent the hybridization of the qubit and photon degrees of freedom and appear as avoided level crossings in the combined energy diagram. By embedding the circuit in an rf oscillator, we directly probe the dressed states. We measure their

Physical review letters, 2014

We present measurements of a topological property, the Chern number (C_{1}), of a closed manifold... more We present measurements of a topological property, the Chern number (C_{1}), of a closed manifold in the space of two-level system Hamiltonians, where the two-level system is formed from a superconducting qubit. We manipulate the parameters of the Hamiltonian of the superconducting qubit along paths in the manifold and extract C_{1} from the nonadiabatic response of the qubit. By adjusting the manifold such that a degeneracy in the Hamiltonian passes from inside to outside the manifold, we observe a topological transition C_{1}=1→0. Our measurement of C_{1} is quantized to within 2% on either side of the transition.

Operation of transition edge sensors in a resistance locked loop Appl. Phys. Lett. 102, 023505 (2... more Operation of transition edge sensors in a resistance locked loop Appl. Phys. Lett. 102, 023505 (2013) Magnetic field resilient superconducting fractal resonators for coupling to free spins J. Appl. Phys. 112, 123905 Complex impedance, responsivity and noise of transition-edge sensors: Analytical solutions for two-and threeblock thermal models AIP Advances 2, 042110 Sub-micron normal-metal/insulator/superconductor tunnel junction thermometer and cooler using Nb Appl. Phys. Lett. 101, 112601 (2012) Frequency division multiplexing readout and simultaneous manipulation of an array of flux qubits

Physical Review Letters, 2014

We have generated frequency combs spanning 0.5 -20 GHz in superconducting /2-resonators at T=3 K... more We have generated frequency combs spanning 0.5 -20 GHz in superconducting /2-resonators at T=3 K. Thin films of niobium-titanium nitride enabled this development due to their low loss, high nonlinearity, low frequencydispersion, and high critical temperature. The combs nucleate as sidebands around multiples of the pump frequency. Selection rules for the allowed frequency emission are calculated using perturbation theory and the measured spectrum is shown to agree with the theory. The sideband spacing is measured to be accurate to 1 part in 10 8 . The sidebands coalesce into a continuous comb structure that has been observed to cover at least 6 octaves in frequency.

Thin Solid Films, 2013

The structural and electrical properties of Ti-N films deposited by reactive sputtering depend on... more The structural and electrical properties of Ti-N films deposited by reactive sputtering depend on their growth parameters, in particular the Ar:N 2 gas ratio. We show that the nitrogen percentage changes the crystallographic phase of the film progressively from pure α-Ti, through an α-Ti phase with interstitial nitrogen, to stoichiometric Ti 2 N, and through a substoichiometric TiN X to stoichiometric TiN. These changes also affect the superconducting transition temperature, T C , allowing, the superconducting properties to be tailored for specific applications. After decreasing from a T C of 0.4 K for pure Ti down to below 50 mK at the Ti 2 N point, the T C then increases rapidly up to nearly 5 K over a narrow range of nitrogen incorporation. This very sharp increase of T C makes it difficult to control the properties of the film from wafer-to-wafer as well as across a given wafer to within acceptable margins for device fabrication. Here we show that the nitrogen composition and hence the superconductive properties are related to, and can be determined by, spectroscopic ellipsometry. Therefore, this technique may be used for process control and wafer screening prior to investing time in processing devices.

Physical Review Letters, 2010

We report the observation of photon generation in a microwave cavity with a time-dependent bounda... more We report the observation of photon generation in a microwave cavity with a time-dependent boundary condition. Our system is a microfabricated quarter-wave coplanar waveguide cavity. The electrical length of the cavity is varied using the tunable inductance of a superconducting quantum interference device. It is measured in the quantum regime, where the temperature is significantly less than the resonance frequency (∼ 5 GHz). When the length is modulated at approximately twice the static resonance frequency, spontaneous oscillations of the cavity field are observed. Timeresolved measurements of the dynamical state of the cavity show multiple stable states. The behavior is well described by theory. Connections to the dynamical Casimir effect are discussed. PACS numbers: 85.25.Cp, 42.65.Lm, Photons, in contrast to electrons, do not directly interact with each other. However, effective interactions can be induced when photons interact with a nonlinear media. In many cases, these effective interactions result in so-called parametric processes which are very important in widespread technological applications and also in fundamental studies of quantum electrodynamics . In the optical regime, the effective nonlinearities are generally bulk properties of materials or plasmas. In the rf and microwave regime, they are often created by lumped-element electrical devices . These types of systems have been extensively studied both theoretical and experimentally.

Physical Review B, 2010

We study relaxation and dephasing in a strongly driven two-level system interacting with its envi... more We study relaxation and dephasing in a strongly driven two-level system interacting with its environment. We develop a theory which gives a straightforward physical picture of the complex dynamics of the system in terms of dressed states. In addition to the dressing of the energy diagram, we describe the dressing of relaxation and dephasing. We find a good quantitative agreement between the theoretical calculations and measurements of a superconducting qubit driven by an intense microwave field. The competition of various processes leads to a rich structure in the observed behavior, including signatures of population inversion.

Physica Scripta, 2009

... tunable superconducting resonator M Sandberg, F Persson, IC Hoi, CM Wilson and P Delsing Depa... more ... tunable superconducting resonator M Sandberg, F Persson, IC Hoi, CM Wilson and P Delsing Department of Microtechnology and Nanoscience, Chalmers University of Technology, Kemivägen 9, SE-41296 Gothenburg, Sweden E-mail: martin.sandberg@chalmers.se ...