### 57622 results for qubit oscillator frequency

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: Averin, Dmitri V., Rabenstein, Kristian, Semenov, Vasili K.

Date: 2005-10-27

**qubit** density matrix is nearly diagonal in the σ z basis, and the measurement...**qubit** which suppresses the effect of back-action dephasing on the **qubit**...**qubit**. The fluxons are periodically injected into the JTL by the generator...**oscillations**. The fluxon injection **frequency** f is matched to the **qubit**...**oscillation** **frequency** Δ : f ≃ Δ / π , so that the individual acts of measurement...**Qubits**...**qubit** oscillation frequency Δ : f ≃ Δ / π , so that the individual acts...**oscillation** dynamics. ... We suggest a new type of the magnetic flux detector which can be optimized with respect to the measurement back-action, e.g. for the situation of quantum measurements. The detector is based on manipulation of ballistic motion of individual fluxons in a Josephson transmission line (JTL), with the output information contained in either probabilities of fluxon transmission/reflection, or time delay associated with the fluxon propagation through the JTL. We calculate the detector characteristics of the JTL and derive equations for conditional evolution of the measured system both in the transmission/reflection and the time-delay regimes. Combination of the quantum-limited detection with control over individual fluxons should make the JTL detector suitable for implementation of non-trivial quantum measurement strategies, including conditional measurements and feedback control schemes.

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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: 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: 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: 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: 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: 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: 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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