### 57435 results for qubit oscillator frequency

Contributors: Hausinger, Johannes, Grifoni, Milena

Date: 2010-07-30

**oscillator** **frequency** approaches unity and goes beyond. In this regime ...**oscillator** **frequency** Ω , ε = l Ω . In this case we found that the levels...**qubit**-**oscillator** detuning. Furthermore, the dynamics is not governed anymore...**frequency** peaks coming from the two dressed **oscillation** **frequencies** Ω ...**Qubit**-oscillator system: An analytical treatment of the ultra-strong coupling...**qubit** for an **oscillator** at low temperature. We consider the coupling strength...**oscillations** **frequency** Ω j l . For l being not an integer those doublets...**qubit**-oscillator detuning. Furthermore, the dynamics is not governed anymore...**qubit** for an oscillator at low temperature. We consider the coupling strength...**qubit** ( ε / Ω = 0.5 ) at resonance with the oscillator Δ b = Ω in the ...**frequencies** through a variation of the coupling....**qubit** ( ε / Ω = 0.5 ) at resonance with the **oscillator** Δ b = Ω in the ...**frequency** range. The lowest **frequency** peaks originate from transitions...**qubit** tunneling matrix element $\Delta$ we are able to enlarge the regime...**oscillations**. With increasing time small differences between numerical...**oscillation** **frequency** Ω j 0 . Numerical calculations and VVP predict group...**oscillation** **frequencies** Ω j 1 and Ω j 2 influence the longtime dynamics...**qubit** ( ε / Ω = 0.5 ) being at resonance with the oscillator ( Δ b = Ω...**qubit** ( ε / Ω = 0.5 ) being at resonance with the **oscillator** ( Δ b = Ω ... We examine a two-level system coupled to a quantum **oscillator**, typically representing experiments in cavity and circuit quantum electrodynamics. We show how such a system can be treated analytically in the ultrastrong coupling limit, where the ratio $g/\Omega$ between coupling strength and **oscillator** **frequency** approaches unity and goes beyond. In this regime the Jaynes-Cummings model is known to fail, because counter-rotating terms have to be taken into account. By using Van Vleck perturbation theory to higher orders in the **qubit** tunneling matrix element $\Delta$ we are able to enlarge the regime of applicability of existing analytical treatments, including in particular also the finite bias case. We present a detailed discussion on the energy spectrum of the system and on the dynamics of the **qubit** for an **oscillator** at low temperature. We consider the coupling strength $g$ to all orders, and the validity of our approach is even enhanced in the ultrastrong coupling regime. Looking at the Fourier spectrum of the population difference, we find that many **frequencies** are contributing to the dynamics. They are gathered into groups whose spacing depends on the **qubit**-**oscillator** detuning. Furthermore, the dynamics is not governed anymore by a vacuum Rabi splitting which scales linearly with $g$, but by a non-trivial dressing of the tunneling matrix element, which can be used to suppress specific **frequencies** through a variation of the coupling.

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Contributors: Huang, Ren-Shou, Dobrovitski, Viatcheslav, Harmon, Bruce

Date: 2005-04-18

**qubit** and the resonator peak is barely visible. When the **qubit** energy ...**oscillations** of the **qubit** exhibit multiple stages of decay. New approaches...**qubit** decohered by many spins undergoing Rabi **oscillation** by a coherent...**qubit** decohered by many spins undergoing Rabi oscillation by a coherent...**qubit** exhibit multiple stages of decay. New approaches are established...**qubit** coupled to a spurious resonator is also studied, where we proposed...**qubit** dephased by 14 spins with and without a spurious resonator, which...**frequency** ω = 2 α . At high **frequency** the Fourier spectrum is dominated...**qubit** transition frequency. Here this situation is numerically simulated...**oscillation** of a **qubit** coupled to a spurious resonator is also studied...**oscillation**....**qubit** dephased and relaxed by a many-spin system. The parameters are the...**qubit**-spurious resonator system. In both graphs, the vertical axes are...**oscillations** of a **qubit** dephased and relaxed by a many-spin system. The...**qubits** have suggested the existence in the tunnel barrier of bistable ...**qubit** transition **frequency**. Here this situation is numerically simulated...**qubit** energy is detuned from the resonator at 9.95 GHz, the most visible...**qubit** under the direct influence of 1/f noise. In the graph of the Fourier...**oscillation** of one **qubit** coupled with 14 spins at T = 200 mK and T = 10...**Qubit** Rabi Oscillation Decohered by Many Two-Level Systems ... Recent experiments on Josephson junction **qubits** have suggested the existence in the tunnel barrier of bistable two level fluctuators that are responsible for decoherence and 1/f critical current noise. In this article we treat these two-level systems as fictitious spins and investigate their influence quantum mechanically with both analytical and numerical means. We find that the Rabi **oscillations** of the **qubit** exhibit multiple stages of decay. New approaches are established to characterize different decoherence times and to allow for easier feature extraction from experimental data. The Rabi **oscillation** of a **qubit** coupled to a spurious resonator is also studied, where we proposed an idea to explain the serious deterioration of the Rabi osillation amplitude.

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Contributors: Zueco, David, Reuther, Georg M., Kohler, Sigmund, Hänggi, Peter

Date: 2009-07-20

**Oscillator** **frequency** shift as function or the **qubit** splitting ϵ = ω + ...**qubit** splitting ϵ = ω + Δ for the spin state | ↓ obtained (a) within RWA...**qubit** state | ↓ ....**qubit**-**oscillator** coupling, we diagonalize the non-RWA Hamiltonian and ...**qubit** readout is possible. If several **qubits** are coupled to one resonator...**qubit**-**qubit** interaction of Ising type emerges, whereas RWA leads to isotropic...**qubits**....**Qubit**-oscillator dynamics in the dispersive regime: analytical theory ...**qubit**-oscillator coupling, we diagonalize the non-RWA Hamiltonian and ...**qubit** state | ↓ , where σ z | ↓ = - | ↓ . The results are depicted in ... We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation (RWA) in the coupling between the two-level system and the resonator. For a detuning sufficiently larger than the **qubit**-**oscillator** coupling, we diagonalize the non-RWA Hamiltonian and discuss the differences to the known RWA results. Our results extend the regime in which dispersive **qubit** readout is possible. If several **qubits** are coupled to one resonator, an effective **qubit**-**qubit** interaction of Ising type emerges, whereas RWA leads to isotropic interaction. This impacts on the entanglement characteristics of the **qubits**.

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Contributors: Simmonds, R. W., Lang, K. M., Hite, D. A., Pappas, D. P., Martinis, John M.

Date: 2004-02-18

**Qubits** from Junction Resonances...**qubits** show great promise for quantum computing, the origin of dominant...**frequency** resonators impacts the future of all Josephson **qubits** as well...**frequency** ω / 2 π and bias current I for a fixed microwave power. Data...diagram of qubit, showing qubit states and in cubic well at left. Measurement...**frequency**. Dotted vertical lines are centered at spurious resonances...**qubits** as well as existing Josephson technologies. We predict that removing...coupled qubit and resonant states for ω 10 ≃ ω r . Coupling strength ...**qubit**, showing **qubit** states and in cubic well at left. Measurement of...**qubits**, Josephson junction, decoherence...**qubit**, and show that their coherence amplitude is significantly degraded...**oscillation** **frequency** versus microwave amplitude. A linear dependence...**oscillations** for an improved phase **qubit**, and show that their coherence...**qubits**....junction qubit. Junction current bias I is set by I φ and microwave source...**oscillations**. ... Although Josephson junction **qubits** show great promise for quantum computing, the origin of dominant decoherence mechanisms remains unknown. We report Rabi **oscillations** for an improved phase **qubit**, and show that their coherence amplitude is significantly degraded by spurious microwave resonators. These resonators arise from changes in the junction critical current produced by two-level states in the tunnel barrier. The discovery of these high **frequency** resonators impacts the future of all Josephson **qubits** as well as existing Josephson technologies. We predict that removing or reducing these resonators through materials research will improve the coherence of all Josephson **qubits**.

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Contributors: Shevchenko, S. N., Omelyanchouk, A. N., Zagoskin, A. M., Savel'ev, S., Nori, F.

Date: 2007-12-12

**frequency** dependent on the perturbation amplitude. These serve as one ...**oscillations** from their classical Doppelganger....**qubit** in Fig. 4 of Ref. [...**qubit** states....**qubits** (current-biased Josephson junctions) this effect can be mimicked...**frequency**. The parameters used here are: η = 0.95 , E J / ℏ ω p = 300 ...**oscillations** in current-biased Josephson junctions: (a) and (b) show the...**qubits** provide a clear demonstration of quantum coherent behaviour in ...**frequency** in the classical case, in contrast to the positive Bloch-Siegert...**qubit** in state | 1 . Alternatively, instead of an RF readout pulse one...**oscillations** can be produced by the subharmonics of the resonant **frequency**...**qubit** (a) and its Josephson energy (b). The metastable states and can ...**qubit** is a current-biased Josephson junction (see Fig. scheme(a)), and...**frequency** and the amplitude of the **oscillations** respectively for ϵ = 2...**qubit**...**frequency** for relatively weak (a) and strong (b) driving. Different values ... Rabi **oscillations** are coherent transitions in a quantum two-level system under the influence of a resonant perturbation, with a much lower **frequency** dependent on the perturbation amplitude. These serve as one of the signatures of quantum coherent evolution in mesoscopic systems. It was shown recently [N. Gronbech-Jensen and M. Cirillo, Phys. Rev. Lett. 95, 067001 (2005)] that in phase **qubits** (current-biased Josephson junctions) this effect can be mimicked by classical **oscillations** arising due to the anharmonicity of the effective potential. Nevertheless, we find qualitative differences between the classical and quantum effect. First, while the quantum Rabi **oscillations** can be produced by the subharmonics of the resonant **frequency** (multiphoton processes), the classical effect also exists when the system is excited at the overtones. Second, the shape of the resonance is, in the classical case, characteristically asymmetric; while quantum resonances are described by symmetric Lorentzians. Third, the anharmonicity of the potential results in the negative shift of the resonant **frequency** in the classical case, in contrast to the positive Bloch-Siegert shift in the quantum case. We show that in the relevant range of parameters these features allow to confidently distinguish the bona fide Rabi **oscillations** from their classical Doppelganger.

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Contributors: Eugene Grichuk, Margarita Kuzmina, Eduard Manykin

Date: 2010-09-26

**qubit** simulates the behavior of electric field of
polarized light beam...**qubit** model has been designed as a
stochastic **oscillator** formed by a pair...**qubits** that is
exploited as a computation resource in one-way quantum
...**qubit** cluster, is designed, and system of equations for
network dynamics...one-**qubit**
gates are suggested. Changing of cluster entanglement degree...**oscillators** is
proposed for modeling of a cluster of entangled **qubits** ...**oscillators** with chaotically modulated limit cycle radii and
**frequencies**...**oscillators**...**qubit** model has been designed as a
stochastic oscillator formed by a pair ... A network of coupled stochastic **oscillators** is
proposed for modeling of a cluster of entangled **qubits** that is
exploited as a computation resource in one-way quantum
computation schemes. A **qubit** model has been designed as a
stochastic **oscillator** formed by a pair of coupled limit cycle
**oscillators** with chaotically modulated limit cycle radii and
**frequencies**. The **qubit** simulates the behavior of electric field of
polarized light beam and adequately imitates the states of two-level
quantum system. A cluster of entangled **qubits** can be associated
with a beam of polarized light, light polarization degree being
directly related to cluster entanglement degree. Oscillatory network,
imitating **qubit** cluster, is designed, and system of equations for
network dynamics has been written. The constructions of one-**qubit**
gates are suggested. Changing of cluster entanglement degree caused
by measurements can be exactly calculated.

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### Temperature square dependence of the low **frequency** 1/f charge noise in the Josephson junction **qubits**

Contributors: Astafiev, O., Pashkin, Yu. A., Nakamura, Y., Yamamoto, T., Tsai, J. S.

Date: 2006-04-04

**qubit** dephasing during coherent oscillations. The coherent oscillations...**qubits**, we study temperature dependence of the 1/f noise and decay of ...**frequency** integration limit and the high **frequency** cutoff are taken to...**oscillations**. T^2 dependence of the 1/f noise is experimentally demonstrated...**oscillations** decay as exp - t 2 / 2 T 2 * 2 with...**frequency** 1/f noise and the quantum f noise recently measured in the Josephson...**qubits** off the electrostatic energy degeneracy point is consistently explained...**qubit** as an SET and measure the low **frequency** charge noise, which causes...**oscillations** measured at T = 50 mK and the dashed envelope exemplifies...**qubit** as an SET and measure the low frequency charge noise, which causes...**frequency** 1/f noise that is observed in the transport measurements....**oscillation** as a function of t away from the degeneracy point ( θ ≠ π ...**qubits**...**qubit** dephasing during coherent **oscillations**. The coherent **oscillations** ... To verify the hypothesis about the common origin of the low **frequency** 1/f noise and the quantum f noise recently measured in the Josephson charge **qubits**, we study temperature dependence of the 1/f noise and decay of coherent **oscillations**. T^2 dependence of the 1/f noise is experimentally demonstrated, which supports the hypothesis. We also show that dephasing in the Josephson charge **qubits** off the electrostatic energy degeneracy point is consistently explained by the same low **frequency** 1/f noise that is observed in the transport measurements.

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Contributors: Zorin, A. B.

Date: 2003-12-09

**frequency** ω r f ≈ ω 0 , the resonant **frequency** of the uncoupled tank circuit...**qubit** by Duty et al. . Their Al Cooper pair box had E c ≈ 0.8 Δ s c and...**frequency** ω 0 = 2 π × 100 MHz, L T / C T 1 / 2 = 100 Ω , k 2 Q β L = ...**qubit** state with the rf **oscillation** span ± π / 2 is preferable in either...**qubit** based on a superconducting single charge transistor inserted in ...radio-**frequency** readout of the **qubit**. (a) The resonance curves of the ...**qubit** whose value, as well as the produced **frequency** shift δ ω 0 , is ...**qubit** operation. In this basis, the Hamiltonian ( H0) is diagonal,...**oscillations** induced in the **qubit**. Recently, we proposed a transistor ...**qubit**. Another useful quantity is the Josephson inductance of the double...**frequency** of these **oscillations** is sufficiently low, ω r f ≪ Ω , they ...**qubit** dephasing and relaxation due to electric and magnetic control lines...**qubit** states by measuring the effective Josephson inductance of the transistor...**qubit**. Recently, we proposed a transistor configuration of the Cooper ...**qubit** in magic points producing minimum decoherence are given....**qubit** parameters are the same as in Fig. 2....**qubit** inductively coupled to a tank circuit by mutual inductance M . The...radio-**frequency** driven tank circuit enabling the readout of the **qubit** ...**qubit** calculated for the mean Josephson coupling E J 0 ≡ 1 2 E J 1 + E...**qubit** parameters (see caption of Fig. 2)....**frequency** Ω . Increase in amplitude of steady **oscillations** up to φ a ≈...**qubit** parameters (see caption of Fig. 2)....**qubit**....**oscillations** and has a small effect on the rise time of the response signal...**qubit** with radio frequency readout: coupling and decoherence ... The charge-phase Josephson **qubit** based on a superconducting single charge transistor inserted in a low-inductance superconducting loop is considered. The loop is inductively coupled to a radio-**frequency** driven tank circuit enabling the readout of the **qubit** states by measuring the effective Josephson inductance of the transistor. The effect of **qubit** dephasing and relaxation due to electric and magnetic control lines as well as the measuring system is evaluated. Recommendations for operation of the **qubit** in magic points producing minimum decoherence are given.

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Contributors: Wei, L. F., Liu, Yu-xi, Nori, Franco

Date: 2004-02-27

**qubits** without direct interaction can be effectively coupled by sequentially...**oscillator** with adjustable **frequency**. The coupling between any **qubit** and...**qubits**, located on the left of the dashed line, coupled to a large CBJJ...**qubit**-bus system. Here, C g k and 2 ε J k are the gate capacitance and...**qubit** and the bus can be controlled by modulating the magnetic flux applied...**qubits** and the bus. The dashed line only indicates a separation between...**qubit**. ζ k is the maximum strength of the coupling between the k th **qubit**...**qubits** via a current-biased information bus...**frequency** ω b . The detuning between the **qubit** and the bus energies is...**qubit** and the bus energies is ℏ Δ k = ε k - ℏ ω b . n = 0 , 1 is occupation...**qubit**. This tunable and selective coupling provides two-**qubit** entangled ... Josephson **qubits** without direct interaction can be effectively coupled by sequentially connecting them to an information bus: a current-biased large Josephson junction treated as an **oscillator** with adjustable **frequency**. The coupling between any **qubit** and the bus can be controlled by modulating the magnetic flux applied to that **qubit**. This tunable and selective coupling provides two-**qubit** entangled states for implementing elementary quantum logic operations, and for experimentally testing Bell's inequality.

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Contributors: Baur, M., Filipp, S., Bianchetti, R., Fink, J. M., Göppl, M., Steffen, L., Leek, P. J., Blais, A., Wallraff, A.

Date: 2008-12-23

**qubit** level ( ν - , f , ν + , f ) and between the dressed states ( ν -...**qubit** transition frequency ω g e ....**qubit** resonance **frequencies** are extracted....**qubit** to the **frequency** ω g e / 2 π ≈ 4.811 G H z , where it is strongly...**qubit** states and dispersive level shifts due to off-resonant drives....**qubit** state-dependent resonance of the resonator under **qubit** driving for...**oscillator** (LO) to an intermediate **frequency** at 300K and digitized with...**qubit**. The ground to first excited state transition of the **qubit** is strongly...**qubit** transition **frequency** ω g e ....**frequencies** (red dots) vs. drive power P d at a fixed drive **frequency** ...**frequency** and the Rabi **oscillation** **frequency** of the excited state population...**oscillation** experiments, lines as in (a). (c) Rabi **oscillation** measurements...**qubit** coupled off-resonantly to a microwave transmission line resonator...**qubit** is coupled capacitively through C g to the resonator, represented...**qubit** spectrum is probed with a weak tone. The corresponding transitions...**frequencies** of the Autler-Townes and Mollow spectral lines are in good...**frequency**. The **qubit** spectrum is then probed by sweeping a weak second...**qubit**...**qubit** linewidth....**qubit** anharmonicity . The **qubit** is strongly coupled to a coplanar waveguide ... We present spectroscopic measurements of the Autler-Townes doublet and the sidebands of the Mollow triplet in a driven superconducting **qubit**. The ground to first excited state transition of the **qubit** is strongly pumped while the resulting dressed **qubit** spectrum is probed with a weak tone. The corresponding transitions are detected using dispersive read-out of the **qubit** coupled off-resonantly to a microwave transmission line resonator. The observed **frequencies** of the Autler-Townes and Mollow spectral lines are in good agreement with a dispersive Jaynes-Cummings model taking into account higher excited **qubit** states and dispersive level shifts due to off-resonant drives.

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