### 21982 results for qubit oscillator frequency

Contributors: Hongjing Ma, Weiqing Liu, Ye Wu, Meng Zhan, Jinghua Xiao

Date: 2014-08-01

Spatial **frequencies** distributions...Ragged **oscillation** death...The phase synchronization domains (areas enclosed by the red lines) and the OD regions (black areas) in the parameter space of ε-δω for a ring of coupled Rossler systems with different **frequency** distributions: (a) G={1,2,3,4,5,6,7,8}, (b) G={1,4,3,6,2,8,5,7}, and (c) G={1,2,3,6,8,4,7,5}. N=8. The ragged OD sates are clear in (b) and (c) within a certain interval of δω indicated by two vertical dashed lines. In all three insets, the values of ωj are plotted for given ω0=0 and δω=N. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
...The bifurcation diagram and the largest Lyapunov exponent λ of the coupled Rossler **oscillators** versus the coupling strength ε with the same spatial arrangement of natural **frequencies** as in Fig. 1(a)–(c), respectively for δω=0.58. The bifurcation diagram is realized by the soft of XPPAUT [33] where the black dots are fixed points and the red dots are the maximum and minimum values of x1 for the stable periodic solution while the blue dots means the max/min values of x1 for the unstable periodical states. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
...The critical curves of OD domain from analysis in N coupled Landau–Stuart **oscillators** for different N’s: (a) N=2, (b) N=3, and (c)–(e) N=4 for G={1,2,3,4},G={1,2,4,3}, and G={1,3,2,4}, respectively. The ragged OD domain is clear in (d). The numerical results with points within the domains perfectly verify the analytical results.
...The OD regions in the parameter space of ε-δω for a ring of coupled Rossler systems with different **frequency** distributions: (a) G={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30}, (b) G={26,16,25,18,5,14,10,4,6,7,21,12,23,8,1,15,9,29,28,11,2,20,27,30,3,13,17,22,24,19}, and (c) G={19,22,18,13,10,28,7,15,17,8,30,12,26,11,20,9,27,21,25,6,29,1,23,5,3,24,16,14,4,2}. N=30. In all three insets, the values of ωj are plotted for given ω0=0 and δω=N.
...Coupled nonidentical **oscillators**...In this paper, the effect of spatial **frequencies** distributions on the **oscillation** death in a ring of coupled nonidentical **oscillators** is studied. We find that the rearrangement of the spatial **frequencies** may deform the domain of **oscillation** death and give rise to a ragged **oscillation** death in some parameter spaces. The usual critical curves with shape V in the parameter space of **frequency**-mismatch vs coupling-strength may become the shape W (or even shape WV). This phenomenon has been not only numerically observed in coupled nonidentical nonlinear systems, but also well supported by our theoretical analysis. ... In this paper, the effect of spatial **frequencies** distributions on the **oscillation** death in a ring of coupled nonidentical **oscillators** is studied. We find that the rearrangement of the spatial **frequencies** may deform the domain of **oscillation** death and give rise to a ragged **oscillation** death in some parameter spaces. The usual critical curves with shape V in the parameter space of **frequency**-mismatch vs coupling-strength may become the shape W (or even shape WV). This phenomenon has been not only numerically observed in coupled nonidentical nonlinear systems, but also well supported by our theoretical analysis.

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Contributors: Catherine Oikonomou, Frederick R Cross

Date: 2010-12-01

A phase-locking model for entrainment of peripheral **oscillators** to the cyclin–CDK **oscillator**. (a) Molecular mechanism of the Cdc14 release **oscillator**. The mitotic phosphatase Cdc14 is activated upon release from sequestration in the nucleolus. This release is controlled by a negative feedback loop in which Cdc14 release, promoted by the polo kinase Cdc5, activates APC-Cdh1, which then promotes Cdc5 degradation, allowing Cdc14 resequestration. This negative-feedback **oscillator** is entrained to the cyclin–CDK cycle at multiple points: by cyclin–CDK promotion of CDC5 transcription and Cdc5 kinase activation, and by cyclin–CDK inhibition of Cdh1 activity. (b) Schematic of multiple peripheral **oscillators** coupled to the CDK **oscillator** in budding yeast. As described above, coupling entrains such peripheral **oscillators** to cell cycle progression; peripheral **oscillators** also feed back on the cyclin–CDK **oscillator** itself. For example, major genes in the periodic transcription program include most cyclins, CDC20, and CDC5; Cdc14 directly promotes establishment of the low-cyclin–CDK positive feedback loop by activating Cdh1 and Sic1 as well as more indirectly antagonizing cyclin–CDK activity by dephosphorylating cyclin–CDK targets; the centrosome and budding cycles could communicate with the cyclin–CDK cycle via the spindle integrity and morphogenesis checkpoints. (c) **Oscillator** coupling ensures once-per-cell-cycle occurrence of events. Three hypothetical **oscillators** are shown: a master cycle in black, a faster peripheral cycle in blue, and a slower peripheral cycle in red. In the absence of phase-locking (top), the **oscillators** trigger events (colored circles) without a coherent phase relationship. In the presence of **oscillator** coupling (bottom), the peripheral **oscillators** are slowed or accelerated within their critical periods to produce a locked phase relationship, with events occurring once and only once within each master cycle.
...The cell cycle **oscillator**, based on a core negative feedback loop and modified extensively by positive feedback, cycles with a **frequency** that is regulated by environmental and developmental programs to encompass a wide range of cell cycle times. We discuss how positive feedback allows **frequency** tuning, how size and morphogenetic checkpoints regulate **oscillator** **frequency**, and how extrinsic **oscillators** such as the circadian clock gate cell cycle **frequency**. The master cell cycle regulatory **oscillator** in turn controls the **frequency** of peripheral **oscillators** controlling essential events. A recently proposed phase-locking model accounts for this coupling....Positive and negative feedback loops in the cyclin–CDK **oscillator**. (a) Inset: a negative feedback loop which can give rise to **oscillations**. Such an **oscillator** is thought to form the core of eukaryotic cell cycles, with cyclin–Cyclin Dependent Kinase (cyclin–CDK) acting as activator, Anaphase Promoting Complex-Cdc20 (APC-Cdc20) acting as repressor, and non-linearity in APC-Cdc20 activation preventing the system from settling into a steady state. Below is shown the cyclin–CDK machinery in eukaryotic cell cycles. CDKs, present throughout the cell cycle, require the binding of a cyclin subunit for activity. These cyclin partners can also determine the localization of the complex and its specificity for targets. At the beginning of the cell cycle, cyclin–CDK activity is low, and ramps up over most of the cycle. Early cyclins trigger production of later cyclins and these later cyclins then turn off the earlier cyclins, so that control is passed from one set of cyclin–CDKs to the next. The last set of cyclins to be activated, the G2/M-phase cyclins, initiate mitosis, and also initiate their own destruction by activating the APC-Cdc20 negative feedback loop. APC-Cdc20 targets the G2/M-phase cyclins for destruction, resetting the cell to a low-CDK activity state, ready for the next cycle. (b) Positive feedback is added to the **oscillator** in multiple ways. Left: a highly conserved but non-essential mechanism consists of ‘handoff’ of cyclin proteolysis from APC-Cdc20 to APC-Cdh1. Cdh1 is a relative of Cdc20 which activates the APC late in mitosis and into the ensuing G1. Cdh1 is inhibited by cyclin–CDK activity, resulting in mutual inhibition (which is logically equivalent to positive feedback). Middle: antagonism between cyclin–CDK and stoichiometric CDK inhibitors (CKIs) results in positive feedback. These loops stabilize high- and low-CDK activity states. Right: a double positive feedback loop comprising CDK-mediated inhibition of the Wee1 kinase (which inhibits CDK) and activation of the Cdc25 phosphatase (which activates CDK by removing the phosphorylation added by Wee1) is proposed to stabilize intermediate CDK activity found in mid-cycle, and an alternative stable state of high mitotic CDK activity.
... The cell cycle **oscillator**, based on a core negative feedback loop and modified extensively by positive feedback, cycles with a **frequency** that is regulated by environmental and developmental programs to encompass a wide range of cell cycle times. We discuss how positive feedback allows **frequency** tuning, how size and morphogenetic checkpoints regulate **oscillator** **frequency**, and how extrinsic **oscillators** such as the circadian clock gate cell cycle **frequency**. The master cell cycle regulatory **oscillator** in turn controls the **frequency** of peripheral **oscillators** controlling essential events. A recently proposed phase-locking model accounts for this coupling.

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Contributors: Michael G. Tanner, David G. Hasko, David A. Williams

Date: 2006-04-01

Resonance response of the SET current to applied microwave **frequencies**, (a) over a large **frequency** range due to coupling with all device elements. (b) A resonance of interest believed to be associated with the IDQD. Central resonance peak is periodically split or suppressed with varying gate potential Vg2. The inset figure shows the response at Vg2=−9.5V (dashed line) and at Vg2=−8V plotted without offset for comparison. The feature repeats periodically as gate potential is increased further.
...**Qubit**...Differentiated SET current measured at 4.2K and zero source–drain bias as Vg1 is swept and Vg2 is incremented. Inset shows the main features: one main Coulomb **oscillation** indicated by the dashed line and subsidiary **oscillations** shown by the dotted lines.
... The fabrication methods and low-temperature electron transport measurements are presented for circuits consisting of a single-island single-electron transistor coupled to an isolated double quantum-dot. Capacitively coupled ‘trench isolated’ circuit elements are fabricated in highly doped silicon-on-insulator using electron beam lithography and reactive ion etching. Polarisation of the isolated double quantum-dot is observed as a function of the side gate potentials through changes in the conductance characteristics of the single-electron transistor. Microwave signals are coupled into the device for excitation of the polarisation states of the isolated double quantum-dot. Resonances attributed to an energy level splitting of the polarisation states are observed with an energy separation appropriate for quantum computation.

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Contributors: Xu-Chu Cai, Jun-Fang Liu

Date: 2011-04-01

Nonlinear **oscillator**...He’s **frequency** formulation is used to obtain the relationship between the **frequency** and amplitude of a nonlinear **oscillator**. The general approach is to choose two linear **oscillators**; in this paper, however, one linear **oscillator** and the Duffing **oscillator** are chosen as trial equations. The solution procedure is of utter simplicity, while the result is of high accuracy....He’s **frequency** formulation ... He’s **frequency** formulation is used to obtain the relationship between the **frequency** and amplitude of a nonlinear **oscillator**. The general approach is to choose two linear **oscillators**; in this paper, however, one linear **oscillator** and the Duffing **oscillator** are chosen as trial equations. The solution procedure is of utter simplicity, while the result is of high accuracy.

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Contributors: Xiufeng Cao, Qing Ai, Chang-Pu Sun, Franco Nori

Date: 2012-01-09

**Qubit**...We propose a strategy to demonstrate the transition from the quantum Zeno effect (QZE) to the anti-Zeno effect (AZE) using a superconducting **qubit** coupled to a transmission line cavity, by varying the central **frequency** of the cavity mode. Our results are obtained without the rotating wave approximation (RWA), and the initial state (a dressed state) is easy to prepare. Moreover, we find that in the presence of both qubitʼs intrinsic bath and the cavity bath, the emergence of the QZE and the AZE behaviors relies not only on the match between the **qubit** energy-level-spacing and the central **frequency** of the cavity mode, but also on the coupling strength between the **qubit** and the cavity mode....(Color online.) Contour plots of the normalized decay rate γ(τ)/γ0 of the **qubit** only in the cavity bath, versus the time interval τ between successive measurements, and the central **frequency** ωcav of the cavity mode. (a) The width of the cavity **frequency** is λ=10−4Δ, and accordingly the cavity quality factor Q=104. (b) The width of the cavity **frequency** λ=5×10−3Δ, corresponding to the cavity quality factor Q=2×103. The region 1⩽γ(τ)/γ0⩽1.05 is shown as light magenta. The QZE region corresponds to γ(τ)/γ01. Evidently, a transition from the QZE to the AZE is observed by varying the central **frequency** of the cavity mode at finite τ (τ>0.6Δ−1 when Q=104, and τ>2.6Δ−1 when Q=2×103).
...(Color online.) Time dependence of the probability for the **qubit** at its excited state. In the resonant case, the parameters are ωcav=Δ=100g and τ=0.1g−1. In the detuning case, the cavity mode **frequency** is varied to ωcav=80g. Note that the successive measurements slow down the decay rate of excited state in the resonant case, which is the QZE. While in the detuning case, the measurements speed up the **qubit** decay rate, which is the AZE.
...The normalized effective decay rate γ(τ)/γ0 of the **qubit** for two quality factors Q when τ=5Δ−1, in the presence of both the cavity bath and the low-**frequency** qubitʼs intrinsic bath.
...(Color online.) (a) Sketch of a **qubit** with the spontaneous dissipation rate γ coupled to a cavity with the loss rate κ via a coupling strength g. (b) and (c) schematically show the bath density spectrum of the **qubit** environment: (b) the Ohmic qubitʼs intrinsic bath (green dashed) and the Lorentzian cavity bath (red solid), (c) the low-**frequency** qubitʼs intrinsic bath (green dashed) and the Lorentzian cavity bath (red solid).
...(Color online.) (a) Superconducting circuit model of a **frequency**-tunable transmission line resonator, which is archived by changing the boundary condition, coupled with a **qubit**. (b) Superconducting circuit model (1) of the effective tunable inductors, which are consisted of a series array of SQUIDs (2).
... We propose a strategy to demonstrate the transition from the quantum Zeno effect (QZE) to the anti-Zeno effect (AZE) using a superconducting **qubit** coupled to a transmission line cavity, by varying the central **frequency** of the cavity mode. Our results are obtained without the rotating wave approximation (RWA), and the initial state (a dressed state) is easy to prepare. Moreover, we find that in the presence of both qubitʼs intrinsic bath and the cavity bath, the emergence of the QZE and the AZE behaviors relies not only on the match between the **qubit** energy-level-spacing and the central **frequency** of the cavity mode, but also on the coupling strength between the **qubit** and the cavity mode.

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Contributors: Václav Tesař

Date: 2014-01-01

Comparison of the **oscillation** in Fig. 17 and the basic **frequency** component L in Fig. 23. The replacement of the feedback channel loops by open areas for vortical flow made the feedback paths slightly shorter (and therefore the **frequency** higher)....Measured **oscillation** **frequency** with different feedback tube lengths of the **oscillator** shown in Fig. 7, plotted as a function of the supplied flow rate. Surprisingly, the **frequency** is neither proportional to the flow rate (as is usual in the constant Strouhal-number **oscillators**, e.g., Tesař et al., 2006) – nor constant (as in the **oscillators** with resonator channel (Tesař et al., 2013)).
...Efficient generation of sub-millimetre microbubbles was recently made possible by pulsating the flow of gas supplied into a parallel-exits aerator, using a fluidic **oscillator** for the purpose. Without moving parts, it can generate **oscillation** at high **frequency**, an important factor due to bubble natural **frequency** rapidly increasing with the desirable decrease of their size. This paper discusses development of an unusual **oscillator** – a part of an integral **oscillator**/aerator unit – capable of generating a particularly high driving **frequency**, in the kilohertz range, in a layout that promotes a strong third harmonic **frequency** of the basic **oscillation**....Fluidic **oscillator**...Results of measured dependence of **oscillation** **frequency** on the supplied flow rate in the layout shown in Figs. 20 and 12. Apart from basic **frequency** L, the output spectrum exhibited a much higher **frequency** component H.
...**Frequency** of generated **oscillation** plotted as a function of the air flow rate. Similarly as in Fig. 9 this dependence does not the fit the usual (constant Strouhal number) proportionality between **frequency** and flow rate.
...Basic data on the geometry of the **oscillator** used in the high-**frequency** experiments.
...Dependence of bubble natural **oscillation** **frequency** on the size – based on the measurements in Tesař (2013b). The line is fitted for constant value of **oscillation** Weber number We0.
... Efficient generation of sub-millimetre microbubbles was recently made possible by pulsating the flow of gas supplied into a parallel-exits aerator, using a fluidic **oscillator** for the purpose. Without moving parts, it can generate **oscillation** at high **frequency**, an important factor due to bubble natural **frequency** rapidly increasing with the desirable decrease of their size. This paper discusses development of an unusual **oscillator** – a part of an integral **oscillator**/aerator unit – capable of generating a particularly high driving **frequency**, in the kilohertz range, in a layout that promotes a strong third harmonic **frequency** of the basic **oscillation**.

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Contributors: Feng Liu, JiaFu Wang, Wei Wang

Date: 1999-05-31

(a) The SNR vs noise intensity D for fs=30,15, and 100 Hz, respectively. (b) The mean synaptic input Isyn(t) vs time for fs=30 Hz and D=0.15 and 6, respectively. (c) The SNR for various **frequencies** for the cases of D=0.5 and 5, respectively, in the case of I0i=0.8 and I1=0.11, and Jij∈[−4,20]. (d) The SNR vs signal **frequency** for D=0.5 and 5, respectively, for the case of I0i∈[0,1] and I1=0.072.
...Intrinsic **oscillations**...The 40 Hz **oscillation**...The **frequency** sensitivity...The **frequency** fi and the corresponding height H of the main peak in PSD of Isyn(t) vs (a) A for the case of I0i∈[0,3.5]; (b) M in the case of Jij∈[−5,10].
...The phenomena of **frequency** sensitivity in weak signal detection and the 40 Hz **oscillation** in a neuronal network have been interpreted based on the intrinsic **oscillations** of the system. There exists a most sensitive **frequency** range of 20–60 Hz, over which the signal-to-noise ratio has a large value. This results from the resonance between the subthreshold intrinsic **oscillation** and the periodic signal. The network can exhibit the synchronous 40 Hz **oscillation** only with constant bias, which is due to the intrinsic features of neurons and long-range interactions between them....I0i∈[0,2] and Jij∈[−1,10]. (a) The spatiotemporal firing pattern is plotted by recording the firing time tni defined by Xi(tni)>0 and Xi(tni−)**frequency** fi and the corresponding height H of the main peak in PSD of Isyn(t) for different coupling strength.
... The phenomena of **frequency** sensitivity in weak signal detection and the 40 Hz **oscillation** in a neuronal network have been interpreted based on the intrinsic **oscillations** of the system. There exists a most sensitive **frequency** range of 20–60 Hz, over which the signal-to-noise ratio has a large value. This results from the resonance between the subthreshold intrinsic **oscillation** and the periodic signal. The network can exhibit the synchronous 40 Hz **oscillation** only with constant bias, which is due to the intrinsic features of neurons and long-range interactions between them.

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Contributors: Weixiong Chen, Quanbin Zhao, Yingchun Wang, Palash Kumar Sen, Daotong Chong, Junjie Yan

Date: 2016-09-01

Submerged steam jet condensation is widely applied in various fields because of its high heat transfer efficiency. Condensation **oscillation** is a major character of submerged steam turbulent jet, and it significantly affects the design and safe operation of industrial equipment. This study is designed to reveal the mechanism of the low-**frequency** pressure **oscillation** of steam turbulent jet condensation and determine its affected region. First, pressure **oscillation** signals with low **frequency** are discovered in the downstream flow field through **oscillation** **frequency** spectrogram and power analysis. The **oscillation** **frequency** is even lower than the first dominant **frequency**. Moreover, the critical positions, where the low-**frequency** pressure **oscillation** signals appear, move downstream gradually with radial distance and water temperature. However, these signals are little affected by the steam mass flux. Then, the regions with low-**frequency** pressure **oscillation** occurring are identified experimentally. The affected width of the low-**frequency** pressure **oscillation** is similar to the turbulent jet width. Turbulent jet theory and the experiment results collectively indicate that the low-**frequency** pressure **oscillation** is generated by turbulent jet vortexes in the jet wake region. Finally, the angular coefficients of the low-**frequency** affected width are obtained under different water temperatures. Angular coefficients, ranging from 0.2268 to 0.2887, decrease with water temperature under test conditions....**Frequency** spectrograms distribution along the axial direction (R/D=2).
...**Frequency** spectrograms of condensation **oscillation** [21].
...**Frequency** spectrograms under radial position of R/D=3.0 and R/D=4.0.
...Half affected width of pressure **oscillation**.
...Pressure **oscillation**...**Oscillation** power axial distribution for low **frequency** region.
... Submerged steam jet condensation is widely applied in various fields because of its high heat transfer efficiency. Condensation **oscillation** is a major character of submerged steam turbulent jet, and it significantly affects the design and safe operation of industrial equipment. This study is designed to reveal the mechanism of the low-**frequency** pressure **oscillation** of steam turbulent jet condensation and determine its affected region. First, pressure **oscillation** signals with low **frequency** are discovered in the downstream flow field through **oscillation** **frequency** spectrogram and power analysis. The **oscillation** **frequency** is even lower than the first dominant **frequency**. Moreover, the critical positions, where the low-**frequency** pressure **oscillation** signals appear, move downstream gradually with radial distance and water temperature. However, these signals are little affected by the steam mass flux. Then, the regions with low-**frequency** pressure **oscillation** occurring are identified experimentally. The affected width of the low-**frequency** pressure **oscillation** is similar to the turbulent jet width. Turbulent jet theory and the experiment results collectively indicate that the low-**frequency** pressure **oscillation** is generated by turbulent jet vortexes in the jet wake region. Finally, the angular coefficients of the low-**frequency** affected width are obtained under different water temperatures. Angular coefficients, ranging from 0.2268 to 0.2887, decrease with water temperature under test conditions.

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Contributors: Yu.P. Emelianova, A.P. Kuznetsov, I.R. Sataev, L.V. Turukina

Date: 2013-02-01

Trajectories on the phase torus. (a) resonant two-**frequency** regime with winding number w=1:2, (b) three-**frequency** regime.
...(Color online). Chart of the Lyapunov’s exponents for the system of three coupled phase **oscillators** (5) for Δ2=1. The color palette is given and decrypted under the picture. The numbers indicate the tongues of the main resonant two-**frequency** regimes. These regimes are explained in the description of Fig. 5.
...Rotation numbers ν1–2 and ν2–3 versus the **frequency** detuning Δ1 for the system (11). Values of the parameters are λ1=1.3,λ2=1.9,λ3=1.8,Δ2=1.5 and μ=0.32.
...Subdivision of the chain of four **oscillators** by clusters for the three types of the phase locked pair of **oscillators**. Parameters are chosen in such a way that the system of **oscillators** is near the point of the saddle–node bifurcation.
...Schematic representation of a system of three coupled self-**oscillators**.
...The problem of growing complexity of the dynamics of the coupled phase **oscillators** as the number of **oscillators** in the chain increases is considered. The organization of the parameter space (parameter of the **frequency** detuning between the second and the first **oscillators** versus parameter of dissipative coupling) is discussed. The regions of complete synchronization, quasi-periodic regimes of different dimensions and chaos are identified. We discuss transformation of the domains of different dynamics as the number of **oscillators** grows. We use the method of charts of Lyapunov exponents and modification of the method of the chart of dynamical regimes to visualize two-**frequency** regimes of different type. Limits of applicability of the quasi-harmonic approximation and the features of the dynamics of the original system which are not described by the approximate phase equations are discussed for the case of three coupled **oscillators**....Phase **oscillators** ... The problem of growing complexity of the dynamics of the coupled phase **oscillators** as the number of **oscillators** in the chain increases is considered. The organization of the parameter space (parameter of the **frequency** detuning between the second and the first **oscillators** versus parameter of dissipative coupling) is discussed. The regions of complete synchronization, quasi-periodic regimes of different dimensions and chaos are identified. We discuss transformation of the domains of different dynamics as the number of **oscillators** grows. We use the method of charts of Lyapunov exponents and modification of the method of the chart of dynamical regimes to visualize two-**frequency** regimes of different type. Limits of applicability of the quasi-harmonic approximation and the features of the dynamics of the original system which are not described by the approximate phase equations are discussed for the case of three coupled **oscillators**.

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Contributors: E. Il’ichev

Date: 2007-10-01

Dependence of the phase shift α on the two parameters ng and Φe. The **qubit** is irradiated by microwaves with a **frequency** of 8.0GHz. The periodic circular structure is due to the variation of the total interferometer-tank impedance caused by transitions from the lower to the upper energy band. The “crater ridges” (solid-line ellipse) correspond to all combinations of the parameters ng and Φe that give the same energy gap (8.0GHz) between the respective states [14].
...We present here recently obtained results with the theoretical and experimental investigations of charge-flux **qubits**. A charge-flux **qubit** consists of a single-Cooper-pair transistor closed by a superconducting loop. In this arrangement a **qubit** is effectively a tuneable two-level system. The **qubit** inductance was probed by a superconducting high-quality tank circuit. Under resonance irradiation, with a **frequency** of the order of the **qubit** energy level separation, change of the **qubit** inductance was observed. We have demonstrated that this effect is caused by the redistribution of the **qubit** level population. We have extracted from the measured data the energy gap of a **qubit** as a function of the quasicharge in the transistor island as well as the total Josephson phase difference across both junctions. The excitation of the **qubit** by one-, two-, and three-photon processes was detected. Quantitative agreement between theoretical predictions and experimental data was found. Relaxation as well as dephasing rates were reconstructed from the fitting procedure....Tank phase shift α dependence on gate parameter ng for different magnetic flux applied to the **qubit** loop . The data correspond to the flux Φ/Φ0=0.5, 0.53, 0.54, 0.56, 0.57. 0.61, 0.62, 0.65 (from bottom to top). For clarity, the upper curves are shifted.
...Superconducting **qubits**...Integrated design: Al **qubit** fabricated in the middle of the Nb coil (left-hand side), and single-Cooper-pair transistor (right-hand side).
...Left-hand side: tank phase shift α dependence on gate parameter ng without microwave power (lowest curve) and with microwave power at different excitation **frequencies**. The data correspond to the **frequency** of the microwave ΩMW/2π=8.9, 7.5, 6.0GHz (from top to bottom) [14]. Here the applied external magnetic flux was fixed Φdc=Φ0/2. For clarity, the upper curves are shifted. Right-hand side: energy gap Δ between the ground and upper states of the **qubit** determined from the experimental data for the case δ=π (Φdc=Φ0/2) [14]. The dots represent the experimental data, the solid line corresponds to the fit (cf. text).
...Calculated dependence of the tank voltage phase shift α on the phase difference δ. The curves correspond to the fixed **frequency** Ω/2π=7.05GHz with the different amplitude of the excitation (from bottom to top n˜g is: 0.1, 0.2, 0.4) [11]. For clarity, the upper curves are shifted.
... We present here recently obtained results with the theoretical and experimental investigations of charge-flux **qubits**. A charge-flux **qubit** consists of a single-Cooper-pair transistor closed by a superconducting loop. In this arrangement a **qubit** is effectively a tuneable two-level system. The **qubit** inductance was probed by a superconducting high-quality tank circuit. Under resonance irradiation, with a **frequency** of the order of the **qubit** energy level separation, change of the **qubit** inductance was observed. We have demonstrated that this effect is caused by the redistribution of the **qubit** level population. We have extracted from the measured data the energy gap of a **qubit** as a function of the quasicharge in the transistor island as well as the total Josephson phase difference across both junctions. The excitation of the **qubit** by one-, two-, and three-photon processes was detected. Quantitative agreement between theoretical predictions and experimental data was found. Relaxation as well as dephasing rates were reconstructed from the fitting procedure.

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