### 57529 results for qubit oscillator frequency

Contributors: Ashhab, S.

Date: 2013-12-25

**qubit** and a single oscillator...**qubit**-oscillator correlation, we gain insight into the nature of the transition...multi-**qubit** case to that in the single-**qubit** case approaches N for all...**qubit**-**oscillator** correlations (which are finite only above the critical...**qubit**'s frequency; away from this limit one obtains a finite-width transition...**qubit** frequency Δ . One can see clearly that moving in the vertical direction...**qubit**-**oscillator** correlations change more slowly when the coupling strength...**qubit**, and a single harmonic **oscillator**. The system experiences a sudden...**qubit**-**oscillator** coupling strength is varied and increased past a critical...single-**qubit** case, whereas the other lines correspond to the multi-**qubit**...**oscillator** **frequency** ℏ ω 0 and the coupling strength λ , both measured...**oscillator**. For consistency with Ref. , we define it as...**qubits** now have a larger total spin (when compared to the single-**qubit**...**qubit** **frequency** Δ . One can see clearly that moving in the vertical direction...**oscillator** field and its squeezing and the **qubit**-**oscillator** correlation...**oscillator**'s **frequency** is much lower than the **qubit**'s **frequency**; away ...**qubit**’s reduced density matrix) and the correlation function C = σ z s...**qubit**-**oscillator** entanglement on the coupling strength just above the ...**qubit** state. Each one of these sets has a structure that is similar to...**qubit**, and a single harmonic oscillator. The system experiences a sudden...**qubit**-oscillator coupling strength is varied and increased past a critical...single-**qubit** case approaches N for all the lines as we approach the critical...single-**qubit** case is simple in principle. In the limit ℏ ω 0 / Δ → 0 , ... We consider the phase-transition-like behaviour in the Rabi model containing a single two-level system, or **qubit**, and a single harmonic **oscillator**. The system experiences a sudden transition from an uncorrelated state to an increasingly correlated one as the **qubit**-**oscillator** coupling strength is varied and increased past a critical point. This singular behaviour occurs in the limit where the **oscillator**'s **frequency** is much lower than the **qubit**'s **frequency**; away from this limit one obtains a finite-width transition region. By analyzing the energy-level structure, the value of the **oscillator** field and its squeezing and the **qubit**-**oscillator** correlation, we gain insight into the nature of the transition and the associated critical behaviour.

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Contributors: Saito, S., Meno, T., Ueda, M., Tanaka, H., Semba, K., Takayanagi, H.

Date: 2005-08-19

**frequency** f M W 1 of 10.25 GHz. (b) One-photon Rabi **oscillations** of P ...single-**frequency** microwave pulses. (a) Spectroscopic data of the **qubit**...**qubit** operation is performed by applying a microwave pulse to the **qubit**...**oscillations** by using single-**frequency** microwave pulses with each **frequency**...**oscillations** ∝ exp - t p / T d cos Ω R a b i t p . The Rabi **frequencies**...**qubit** at a distance of 20 μ m so that the **qubit** could be strongly driven...**qubit** transition energy ℏ ω q b ....**qubit** states when the sum of the two microwave frequencies or the difference...**qubit**...**frequencies** or the difference between them matches the **qubit** Larmor **frequency**...**qubit** measurement system. On-chip components are shown in the dashed box...**qubit**. Each set of the dots represents the resonant frequencies f r e ...**qubit** has been achieved by using two-frequency microwave pulses. We have...**qubit** Larmor frequency. We have also observed multi-photon Rabi oscillations...**oscillations**. (c) [(d)] Rabi **frequencies** as a function of V M W 1 , which...**oscillation** fits. Both the **qubit** Larmor **frequency** f q b and the microwave...**frequency** range of microwaves for controlling the **qubit** and offers a high...**qubit** Larmor frequency f q b . The **qubit** is thermally initialized to be...**qubit** and offers a high quality testing ground for exploring nonlinear...**qubit** has been achieved by using two-**frequency** microwave pulses. We have...**oscillations** stemming from parametric transitions between the **qubit** states...**qubit** with two-**frequency** microwave pulses....**qubit** Larmor frequency f q b and the microwave frequency f M W 1 are 10.25...**qubit** (inner loop) and a dc-SQUID (outer loop). The loop sizes of the **qubit** and SQUID are 10.2 × 10.4 μ m 2 and 12.6 × 13.5 μ m 2 , respectively...**oscillations** corresponding to one- to four-photon resonances by applying...**qubit** and the efficiency of the coupling between the **qubit** and the on-chip...two-**frequency** microwave pulses. (a) [(b)] Two-photon Rabi **oscillations** ... Parametric control of a superconducting flux **qubit** has been achieved by using two-**frequency** microwave pulses. We have observed Rabi **oscillations** stemming from parametric transitions between the **qubit** states when the sum of the two microwave **frequencies** or the difference between them matches the **qubit** Larmor **frequency**. We have also observed multi-photon Rabi **oscillations** corresponding to one- to four-photon resonances by applying single-**frequency** microwave pulses. The parametric control demonstrated in this work widens the **frequency** range of microwaves for controlling the **qubit** and offers a high quality testing ground for exploring nonlinear quantum phenomena.

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Contributors: Rabenstein, K., Sverdlov, V. A., Averin, D. V.

Date: 2004-01-26

**qubit** dynamics with noise which agree with the analytical results and ...**oscillations** in an unbiased **qubit** dephased by the non-Gaussian noise with...**qubit** dynamics with noise. Solid line is the exponential fit of the oscillation...**qubit** dynamics. Note different scales for γ in parts (a) and (b). Inset...**qubit** dynamics with noise. Solid line is the exponential fit of the **oscillation**...**oscillations** in a **qubit** by low-**frequency** noise. Decoherence strength is...**qubit** dephased by the non-Gaussian noise with characteristic amplitude...**qubit** by low-frequency noise. Decoherence strength is controlled by the...**qubit** decoherence at long times t ≫ τ for ε = 0 and (a) Gaussian and (...**qubit** basis states fluctuating under the influence of noise v t ....**frequency** while the noise correlation time $\tau$ determines the time ...**Qubit** decoherence by low-frequency noise ... We have derived explicit non-perturbative expression for decoherence of quantum **oscillations** in a **qubit** by low-**frequency** noise. Decoherence strength is controlled by the noise spectral density at zero **frequency** while the noise correlation time $\tau$ determines the time $t$ of crossover from the $1/\sqrt{t}$ to the exponential suppression of coherence. We also performed Monte Carlo simulations of **qubit** dynamics with noise which agree with the analytical results and show that most of the conclusions are valid for both Gaussian and non-Gaussian noise.

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Contributors: Strand, J. D., Ware, Matthew, Beaudoin, Félix, Ohki, T. A., Johnson, B. R., Blais, Alexandre, Plourde, B. L. T.

Date: 2013-01-03

**qubit**. The **qubit** contains a substantial asymmetry between its Josephson...**qubits** from the flux-bias lines....**qubits**. The terminations of the flux-bias lines for both **qubits** are visible...**qubit** and resonator....**frequency**. The sideband transitions are driven with a magnetic flux signal...**qubit** energy levels with negligible Joule heating of the refrigerator ...**oscillations** can be explained by the separately measured loss of the **qubit**...**frequency**-modulated transmon **qubit**. The **qubit** contains a substantial asymmetry...**qubit**-cavity layout and signal paths....**qubit**. This modulates the **qubit** splitting at a **frequency** near the detuning...**qubit**. This modulates the **qubit** splitting at a frequency near the detuning...**qubit** and resonator frequencies, leading to rates up to 85 MHz for exchanging...**qubit**-resonator system, showing first-order red sideband transition. (...**oscillations** as a function of pulse duration vs. flux-drive **frequency**....**oscillation** **frequency** Ω / 2 π extracted from the experimental linecuts...**oscillation** **frequency** from Eq. ( eq:H:t)....**oscillations** vs. drive **frequency**. Vertical white lines running through...**qubits**...**oscillation** **frequency** vs. flux drive amplitude (lower horizontal axis)...**Qubit**-state measurements were performed in the high-power limit . The **qubits**, labeled Q1 and Q2, were designed to be identical, with mutual ...**qubit** and cavity and roughly corresponds to κ + γ 1 / 2 , where γ 1 is...**qubit** and resonator **frequencies**, leading to rates up to 85 MHz for exchanging ... We demonstrate rapid, first-order sideband transitions between a superconducting resonator and a **frequency**-modulated transmon **qubit**. The **qubit** contains a substantial asymmetry between its Josephson junctions leading to a linear portion of the energy band near the resonator **frequency**. The sideband transitions are driven with a magnetic flux signal of a few hundred MHz coupled to the **qubit**. This modulates the **qubit** splitting at a **frequency** near the detuning between the dressed **qubit** and resonator **frequencies**, leading to rates up to 85 MHz for exchanging quanta between the **qubit** and resonator.

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Contributors: Johansson, J., Saito, S., Meno, T., Nakano, H., Ueda, M., Semba, K., Takayanagi, H.

Date: 2005-10-17

**qubit**. The SQUID functions as a detector for the **qubit** state: the switching...**qubit** and then brought the **qubit** and the **oscillator** into resonance where...**qubit** dispersion around the gap of Δ = 2.1 GHz. (b) A close up of the...**qubit** LC oscillator system...**qubit** and **oscillator** manifests itself as the vacuum Rabi **oscillation** |...**frequency** components a 0 , , a 3 obtained from the fit as a function of...**oscillations** when a 2 ns long pulse with **frequency** ν e x = 4.35 GHz and...**frequency** Ω R until the shift pulse ends and the system returns to the...**qubit**–**oscillator** system showing the LC **oscillator** at ν r = 4.35 GHz and...**qubit** and a superconducting LC circuit acting as a quantum harmonic **oscillator**...**oscillations**: the **qubit** is **oscillating** between the excited state and the...**qubit**. The **qubit** is also enclosed by a larger loop containing on–chip ...**oscillator** between the vacuum state and the first excited state. We have...**qubit** and LC **oscillator** parameters (obtained from spectroscopy and **qubit**...**qubit** is oscillating between the excited state and the ground state and...**oscillator** [see Fig. fig1(b)] with resonance **frequency** ω r = 2 π ν r ...**oscillation** **frequency** when the LC circuit was not initially in the vacuum...**qubit** dephasing rate Γ φ = 0.1 GHz, **qubit** relaxation rate Γ e = 0.2 ...**qubit** signal in this region. After the MW pulses the **qubit** state is measured...**qubit** by Φ s h i f t , which, in turn, changes the operating point from...**qubit** and then brought the **qubit** and the oscillator into resonance where...**qubit** and the SQUID. The **qubit** dimension is 10.2 × 10.4 μ m 2 . (c) ...**oscillation** **frequency** is determined only by the system‘s intrinsic parameters...**qubit** is spatially separated from the rest of the circuitry. The **qubit**...**qubit** LC **oscillator** mutual inductance to be M = 5.7 pH. The current and...**qubit** brings the system from state 1 to 2 and the shift pulse changes ...**qubit** and a superconducting LC circuit acting as a quantum harmonic oscillator ... We have observed the coherent exchange of a single energy quantum between a flux **qubit** and a superconducting LC circuit acting as a quantum harmonic **oscillator**. The exchange of an energy quantum is known as the vacuum Rabi **oscillations**: the **qubit** is **oscillating** between the excited state and the ground state and the **oscillator** between the vacuum state and the first excited state. We have also obtained evidence of level quantization of the LC circuit by observing the change in the **oscillation** **frequency** when the LC circuit was not initially in the vacuum state.

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Contributors: Jerger, Markus, Poletto, Stefano, Macha, Pascal, Hübner, Uwe, Il'ichev, Evgeni, Ustinov, Alexey V.

Date: 2012-05-29

**qubit**. The composite signal probes all resonators at the same time, storing...**oscillations**
...**qubit**, ω q and ω r are the angular resonance **frequencies** of the **qubit** ...**Qubits**...**qubits** using a **frequency** division multiplexing technique is demonstrated...**qubit** to be read out is sent through the common transmission line. The...**qubits**. Consequently, scaling up superconducting **qubit** circuits is no ...**qubits** far detuned from the resonances. (b) FDM readout of six flux **qubits**...**qubits** involved in the measurement. Here, we present a readout scheme ...**frequencies**. The local **oscillator** inputs of both mixers are fed from the...**qubit** and resonator leads to a state-dependent dispersive shift, Δ ω r...**qubits**....**oscillation** **frequency** versus power of the excitation tone; the error bars...**frequency** matches the transition between their ground and excited states...**qubits** on a chip....**qubits**. Here, we used individual microwave excitations for every **qubit**...**qubits** taken into account. The readout **frequency** of device #3 is shown...**qubits** using a frequency division multiplexing technique is demonstrated...**qubit**, ω q and ω r are the angular resonance frequencies of the **qubit** ...**qubit** manipulation signal is generated by a single microwave source for...**qubit**, **qubit** register, dispersive readout, **frequency** division
multiplexing...**qubits**. We discuss how this technique can be scaled up to read out hundreds...**oscillations** at three different powers for all **qubits**. The measured linear...**qubit**, **qubit** register, dispersive readout, frequency division
multiplexing...**qubit**, the instantaneous dispersive shift of the center **frequency** of the...**qubits** #2, 3 and 5. The **qubit** manipulation microwave excites **qubits** when...**qubits** is continuously and simultaneously monitored by the multi-tone ...**qubits**. Left plots: Rabi **oscillations** at several powers; traces are vertically ... An important desired ingredient of superconducting quantum circuits is a readout scheme whose complexity does not increase with the number of **qubits** involved in the measurement. Here, we present a readout scheme employing a single microwave line, which enables simultaneous readout of multiple **qubits**. Consequently, scaling up superconducting **qubit** circuits is no longer limited by the readout apparatus. Parallel readout of 6 flux **qubits** using a **frequency** division multiplexing technique is demonstrated, as well as simultaneous manipulation and time resolved measurement of 3 **qubits**. We discuss how this technique can be scaled up to read out hundreds of **qubits** on a chip.

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

Date: 2011-05-05

of a **qubit** with finite coupling to the oscillator and a reference **qubit**...**qubit** oscillations. This corroborates the underlying measurement relation...**qubit** oscillations at the degeneracy point ϵ = 0 . The full **qubit**-oscillator...**oscillator** **frequency** Ω < 10 ω q b , for which the adiabatic approximation...**qubit** dynamics is obtained by recording the **oscillator** response to resonant... **qubit**’s time evolution is rather coherent (see section sec:sn on **qubit**...**qubit** **oscillations**. This corroborates the underlying measurement relation...**oscillator** **frequency** Ω = 10 ω q b , which obviously represents a good ...**frequency** shift of the resulting harmonic **oscillator** (green) can be probed...**qubit** (blue) coupled to a dc-SQUID. The interaction is characterised by...**qubit** readout which provides the time evolution of a flux **qubit** observable...**qubit** to a harmonic **oscillator** with high **frequency**, representing a dc-SQUID...**qubit** dynamics is obtained by recording the oscillator response to resonant...**qubit** readout via nonlinear Josephson inductance...**frequency** window of size 2 Δ Ω centred at the **oscillator** **frequency** Ω ,...**qubit** with finite coupling to the oscillator and a reference **qubit** without...**qubit** **oscillations** at the degeneracy point ϵ = 0 . The full **qubit**-**oscillator**...**qubit** dynamics as long as the coefficient g 2 stays sufficiently small...**oscillations** with (angular) **frequency** ω q b . (b) Power spectrum ξ o u...**oscillator** **frequency** Ω . All other parameters are as in figure fig:**qubit**-osc-phase-spectrum...**oscillator** **frequency**, here chosen as Ω = 10 ω q b . The dissipative influence...**qubit** with finite coupling to the **oscillator** and a reference **qubit** without...**qubit**-oscillator interaction when Ω is small. This cubic dependence is...**qubit** to a harmonic oscillator with high frequency, representing a dc-SQUID...**qubit** dynamics are visible at frequencies Ω ± ω q b . In order to extract...**qubit** coupled to a SQUID as sketched in figure fig:setup. The SQUID ... We propose a generalisation of dispersive **qubit** readout which provides the time evolution of a flux **qubit** observable. Our proposal relies on the non-linear coupling of the **qubit** to a harmonic **oscillator** with high **frequency**, representing a dc-SQUID. Information about the **qubit** dynamics is obtained by recording the **oscillator** response to resonant driving and subsequent lock-in detection. The measurement process is simulated for the example of coherent **qubit** **oscillations**. This corroborates the underlying measurement relation and also reveals that the measurement scheme possesses low backaction and high fidelity.

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Contributors: unknown

Date: 2008-05-23

**qubits** in spin-boson (SB) and spin-intermediate harmonic oscillator (IHO...**frequencies**. However, the **qubits** in the two models have different decoherence...**qubit**-IHO and IHO-bath and the oscillation frequency of the IHO....**frequency** ω of the bath modes, where Δ=5×109Hz,λκ=1,ξ=0.01,Ω0=10Δ,T=0.01K...**qubit** in SIB model can be modulated through changing the coupling coefficients...**qubits** in the two models have different decoherence and relaxation as ...high-**frequency** baths....**qubits** in spin-boson (SB) and spin-intermediate harmonic **oscillator** (IHO...**qubits** coupled to low- and medium-frequency Ohmic baths directly and via...**frequencies** are investigated. It is shown that the **qubits** in SB and SIB...**frequencies**. The decoherence and relaxation of the **qubit** in SIB model ...**frequencies** for the two cases are taken according to Fig. 2....**frequencies** and effective bath in (b) low and (d) medium **frequencies**. ...**qubit**-IHO and IHO-bath and the **oscillation** **frequency** of the IHO....**qubits** in SB and SIB models have the same decoherence and relaxation as...low-**frequency** bath. The parameters are the same as in Fig. 1. ... Using the numerical path integral method we investigate the decoherence and relaxation of **qubits** in spin-boson (SB) and spin-intermediate harmonic **oscillator** (IHO)-bath (SIB) models. The cases that the environment baths with low and medium **frequencies** are investigated. It is shown that the **qubits** in SB and SIB models have the same decoherence and relaxation as the baths with low **frequencies**. However, the **qubits** in the two models have different decoherence and relaxation as the baths with medium **frequencies**. The decoherence and relaxation of the **qubit** in SIB model can be modulated through changing the coupling coefficients of the **qubit**-IHO and IHO-bath and the **oscillation** **frequency** of the IHO.

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Contributors: Gustavsson, Simon, Bylander, Jonas, Yan, Fei, Forn-Díaz, Pol, Bolkhovsky, Vlad, Braje, Danielle, Fitch, George, Harrabi, Khalil, Lennon, Donna, Miloshi, Jovi

Date: 2012-01-30

**qubit** tunnel coupling is Δ = 5.4 . (b) Rabi **frequency** vs bias current ...**qubit** and the oscillator. The **qubit** state is encoded in currents circulating...**qubit** energy detuning ε , the first-order **qubit**-resonator coupling strength...**qubit** Rabi frequency. This opens an additional noise channel, and we find...**qubit**, to first order, is insensitive to flux noise . The **qubit**-resonator...**qubit** frequency [see...**qubit** that is tunably coupled to a microwave resonator. We find that the...**qubit** Rabi **frequency**. This opens an additional noise channel, and we find...**qubit** experiences an **oscillating** field mediated by off-resonant driving...**qubit** tunably coupled to a harmonic oscillator...**qubit** A, measured vs at = 0 . The driving field seen by the **qubit** contains...**qubit**, appearing already at moderate **qubit**-resonator coupling g 1 and ...**qubit** experiences an oscillating field mediated by off-resonant driving...**qubit** loop (blue arrow), while the mode of the harmonic **oscillator** is ...**qubit** and the harmonic oscillator. In addition, the two-photon **qubit** (...low-**frequency** noise in the coupling parameter causes a reduction of the...**qubit** loop). The resonator **frequency** is around 2.3 and depends only weakly...**qubit** and the **oscillator**. The **qubit** state is encoded in currents circulating...**qubit** and the harmonic **oscillator**. In addition, the two-photon **qubit** (...**qubit** at large **frequency** detuning from the resonator while still staying...**qubit** **frequency** [see...**qubit** loop (blue arrow), while the mode of the harmonic oscillator is ...**frequency** of **qubit** A, measured vs at = 0 . The driving field seen by the...**frequencies** corresponding to the sum of the **qubit** and resonator **frequencies**...**qubit**+resonator ( + ) transitions are visible. (c) Flux induced in the...**oscillations** to decaying sinusoids, a few examples of Rabi traces for ... We have investigated the driven dynamics of a superconducting flux **qubit** that is tunably coupled to a microwave resonator. We find that the **qubit** experiences an **oscillating** field mediated by off-resonant driving of the resonator, leading to strong modifications of the **qubit** Rabi **frequency**. This opens an additional noise channel, and we find that low-**frequency** noise in the coupling parameter causes a reduction of the coherence time during driven evolution. The noise can be mitigated with the rotary-echo pulse sequence, which, for driven systems, is analogous to the Hahn-echo sequence.

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Contributors: Leyton, V., Thorwart, M., Peano, V.

Date: 2011-09-26

**qubit** states, and (b) the corresponding detector response A as a function...**oscillator** **frequency** Ω , where the coupling term is considered as a perturbation...**qubit**-detector coupling induces a global frequency shift of the response...**qubit** (black solid line). The blue dashed line indicates the response ...**frequency** ω e x for the same parameters as in Fig. fig2. fig4...**qubit**, which is based on resonant few-photon transitions in a driven nonlinear...**qubit**-detector setup, the **qubit**-resonator coupling typically will be required...**qubit** state....**qubit** for the same parameters as in a). fig3...**qubit** states....**oscillator**, but still smaller than Γ -1 , the **oscillator** is able to reliably...**frequency** ω e x . The parameters are the same as in Fig. fig2. fig5...**frequencies**. We show that this detection scheme offers the advantage of...**qubit** states is given by the **frequency** gap δ ω e x ≃ 2 g . Figure fig3...**Qubit** state detection using the quantum Duffing oscillator...**qubit** and is used as its detector. Close to the fundamental resonator **frequency**, the nonlinear resonator shows sharp resonant few-photon transitions...**qubit** bias), this coincides with the shifted one....**qubit** coupled to an Ohmically damped harmonic **oscillator**. This model can...**qubit** inductively coupled to a driven SQUID detector in its nonlinear ...**qubit** state, these few-photon resonances are shifted to different driving...**qubit**-detector coupling induces a global **frequency** shift of the response...**qubit** and is used as its detector. Close to the fundamental resonator ...**qubit** prepared in its ground state | ↓ (orange solid line) and in its ... We introduce a detection scheme for the state of a **qubit**, which is based on resonant few-photon transitions in a driven nonlinear resonator. The latter is parametrically coupled to the **qubit** and is used as its detector. Close to the fundamental resonator **frequency**, the nonlinear resonator shows sharp resonant few-photon transitions. Depending on the **qubit** state, these few-photon resonances are shifted to different driving **frequencies**. We show that this detection scheme offers the advantage of small back action, a large discrimination power with an enhanced read-out fidelity, and a sufficiently large measurement efficiency. A realization of this scheme in the form of a persistent current **qubit** inductively coupled to a driven SQUID detector in its nonlinear regime is discussed.

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