### 57529 results for qubit oscillator frequency

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: 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: 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: 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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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: 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: unknown

Date: 2003-08-27

**qubit** in a lossy reservoir and demonstrate that the noise in a classical...**qubit** [6] inductively coupled to a (low frequency) classical oscillator...**qubit** by monitoring the noise level in its environment. We consider a ...**qubit** via environmental noise...**qubit** [6] inductively coupled to a (low **frequency**) classical **oscillator**...**frequency** **oscillator** at the resonance point (Φdc=0.00015Φ0) for the three...**qubit**...**frequency** **oscillator** at 300 MHz, as a function of the static magnetic ... We propose a method for characterising the energy level structure of a solid state **qubit** by monitoring the noise level in its environment. We consider a model persistent current **qubit** in a lossy reservoir and demonstrate that the noise in a classical bias field is a sensitive function of the applied field.

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Contributors: Wirth, T., Lisenfeld, J., Lukashenko, A., Ustinov, A. V.

Date: 2010-10-05

**qubit**. The **qubit** is controlled by microwave pulses which are applied via...**qubit** flux state....**qubit**. A capacitively shunted dc-SQUID is used as a nonlinear resonator...**oscillations** of the **qubit** for different driving powers, from bottom to...**qubit** state....**frequency** of 1.9 GHz. As the two **qubit** states differ by magnetic flux ...**qubit** state measurement time down to 25 microseconds, which is much faster...**qubit** measured for different driving powers of the **qubit** microwave driving...**qubit** microwave driving. As it is expected, the **frequency** of Rabi **oscillations**...**qubit** for future experiments. Fig. fig:3 (b) shows the same **frequency**...**qubits** using a single microwave line by employing frequency-division multiplexing...**qubits**, phase **qubit**, dispersive readout, SQUID...**frequency** applied to the SQUID vs. externally applied flux. The measurement...**oscillations** of the **qubit** measured for different driving powers of the...**qubit**. The pulsed microwave signal is applied via a cryogenic circulator...**qubit** itself. We verified this fact by measuring the same **qubit** with the...**qubits** using a single microwave line by employing **frequency**-division multiplexing...**qubit** changing its magnetic flux by approximately Φ 0 . (a) In the linear...**frequency** shift induced by the **qubit** is shown in detail in Fig. fig:3...**qubit** for different driving powers, from bottom to top: -18 dBm, -15 dBm...**qubit**...**qubit**. We detect the flux state of the **qubit** by measuring the amplitude...**frequency** of the SQUID resonator by 30 MHz due to the **qubit** changing its ... We present experimental results on a dispersive scheme for reading out a Josephson phase **qubit**. A capacitively shunted dc-SQUID is used as a nonlinear resonator which is inductively coupled to the **qubit**. We detect the flux state of the **qubit** by measuring the amplitude and phase of a microwave pulse reflected from the SQUID resonator. By this low-dissipative method, we reduce the **qubit** state measurement time down to 25 microseconds, which is much faster than using the conventional readout performed by switching the SQUID to its non-zero dc voltage state. The demonstrated readout scheme allows for reading out multiple **qubits** using a single microwave line by employing **frequency**-division multiplexing.

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Contributors: Schmidt, Thomas L., Nunnenkamp, Andreas, Bruder, Christoph

Date: 2012-11-09

**qubit**. The central MBSs γ 2 and γ 3 are tunnel-coupled ( t c ) to a topologically...single-**qubit** operations....**qubit** rotations....**qubit** state for a time t * = π / 4 Ω R . In the presence of damping, the...**frequency** | Ω R | in units of c = n p h g c 2 / L for μ = - 100 ϵ L and...**frequency** and damping, Ω R / Γ R , determines the fidelity of **qubit** rotations...**frequency** and damping determined numerically from Eq. ( eq:Dgamma2). Solid...single-**qubit** gate. Supplemented with one braiding operation, this gate...**frequency** is, as expected, exponentially suppressed in the length of the...**qubits** on which certain operations can be performed in a topologically...**qubit** rotations in microwave cavities...**frequency** Ω approaches the critical value | μ | , the prefactor 1 - Ω ...**oscillations** between adjacent Majorana bound states. These **oscillations** ... Majorana bound states have been proposed as building blocks for **qubits** on which certain operations can be performed in a topologically protected way using braiding. However, the set of these protected operations is not sufficient to realize universal quantum computing. We show that the electric field in a microwave cavity can induce Rabi **oscillations** between adjacent Majorana bound states. These **oscillations** can be used to implement an additional single-**qubit** gate. Supplemented with one braiding operation, this gate allows to perform arbitrary single-**qubit** operations.

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