### 62747 results for qubit oscillator frequency

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

Date: 2005-08-19

its transmission** to** the **qubit** and the efficiency of the coupling between...**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**...**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** 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 ...Then a **qubit** operation is performed by applying a microwave pulse** to** **the q**...**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...**qubit** has been achieved by using two-frequency microwave pulses. We have...**qubit** Larmor frequency. We have also observed multi-photon Rabi oscillations...**frequency** range of microwaves for controlling the **qubit** and offers a high...**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...fixes the **qubit** Larmor frequency f q b . The **qubit** is thermally initialized... is larger than the **qubit** transition energy ℏ ω q b ....**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...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: 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** Rabi frequency. This opens an additional noise channel, and we find...**qubit**, to first order, is insensitive to flux noise . The **qubit**-resonator...**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...**the** **qubit** energy detuning ε , **the** first-order **qubit**-resonator coupling...**qubit** experiences an **oscillating** field mediated by off-resonant driving...by **qubit** energy relaxation. The dotted line marks** the **position for the...**qubit** tunably coupled to a harmonic oscillator...**the** **qubit** flux detuning defined as = Φ + Φ 0 / 2 and Φ 0 = h / 2 e . The qub... the **qubit** and** the **oscillator. The **qubit** state is encoded in currents ...**qubit** experiences an oscillating field mediated by off-resonant driving...**the** **qubit**, appearing already at **moderate** **qubit**-resonator coupling g 1 ...**qubit** loop (blue arrow), while the mode of the harmonic **oscillator** is ...low-**frequency** noise in the coupling parameter causes a reduction of the...of **qubit** A, measured vs at = 0 . The driving field seen by the **qubit** contains...**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** (... the **qubit** and** the **harmonic oscillator. In addition, the two-photon **qubit**...**qubit** tunnel coupling is Δ = 5.4 . (b) Rabi frequency vs bias current ...**qubit** at large **frequency** detuning from the resonator while still staying...driving **the** **qubit**, appearing already at **moderate** **qubit**-resonator coupling...**qubit** **frequency** [see...**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**...**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: 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...measured **qubit**. The fluxons are periodically injected into the JTL by ...**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...combined qubit-resonator system, showing first-order red sideband transition...**qubits**. The terminations of the flux-bias lines for both **qubits** are visible...**qubit** and resonator.... of the** qubit** and cavity and roughly corresponds to κ + γ 1 / 2 , where...the qubits. The terminations of the flux-bias lines for both qubits are... qubits from the flux-bias lines....**frequency**. The sideband transitions are driven with a magnetic flux signal...**oscillations** can be explained by the separately measured loss of the **qubit**...**frequency**-modulated transmon **qubit**. The **qubit** contains a substantial asymmetry...**qubit**. This modulates the **qubit** splitting at a **frequency** near the detuning... qubit energy levels with negligible Joule heating** of** the refrigerator...**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...**oscillations** as a function of pulse duration vs. flux-drive **frequency**....of qubit-cavity layout and signal paths.... Qubit-state measurements were performed in the high-power limit . The qubits, labeled Q1 and Q2, were designed to be identical, with mutual...**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** 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

**oscillations** in an unbiased **qubit** dephased by the non-Gaussian noise with...**qubit** dynamics with noise which agree with the analytical results and ...**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**...**qubit** decoherence at long times t ≫ τ for ε = 0 and (a) Gaussian and (...of **qubit** dynamics with noise. Solid line is the exponential fit of the...**qubit** basis states fluctuating under the influence of noise v t ....**frequency** while the noise correlation time $\tau$ determines the time ...**diagram** of **qubit** basis states fluctuating under the influence of noise...**simulations** of **qubit** dynamics. Note different scales for γ in parts (a...**oscillations** in a **qubit** by low-**frequency** noise. Decoherence strength is...unbiased **qubit** dephased by the non-Gaussian noise with characteristic ...**qubit** by low-frequency noise. Decoherence strength is controlled by the...**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

**qubit** (blue) coupled to a dc-SQUID. The interaction is characterised ...**qubit** oscillations. This corroborates the underlying measurement relation...**oscillator** **frequency** Ω < 10 ω q b , for which the adiabatic approximation...coherent **qubit** oscillations at the degeneracy point ϵ = 0 . The full **qubit**-oscillator...**qubit** dynamics is obtained by recording the **oscillator** response to resonant...the **qubit**’s time evolution is rather coherent (see section sec:sn** on q**...**qubit**-osc-phase-spectrum(b). It reflects the **qubit** dynamics in terms of...from the **qubit** dynamics are visible at frequencies Ω ± ω q b . In order...fig:**qubit**-osc-phase-spectrum....**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** 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...of a **qubit** with finite coupling to** the **oscillator and a reference **qubit**...low-**frequency** **qubit** dynamics. Finally, we centre the clipped spectrum ...**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**-osc-phase-spectrum....**oscillations** with (angular) **frequency** ω q b . (b) Power spectrum ξ o u... fig:**qubit**-osc-phase-spectrum(b). It reflects the **qubit** dynamics in terms...**oscillator** (blue solid line). The sidebands stemming from the **qubit** dynamics...**qubit** with finite coupling to the **oscillator** and a reference **qubit** without...**qubit** to a harmonic oscillator with high frequency, representing a dc-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: Jerger, Markus, Poletto, Stefano, Macha, Pascal, Hübner, Uwe, Il'ichev, Evgeni, Ustinov, Alexey V.

Date: 2012-05-29

**of** the **qubit** and resonator. We demonstrate FDM by measuring the maximum...and **qubit**, ω q and ω r are the angular resonance frequencies **of** the **qubit**...**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...**qubits**. Consequently, scaling up superconducting **qubit** circuits is no ...**qubits** far detuned from the resonances. (b) FDM readout of six flux **qubits**... **qubits**....**qubits** involved in the measurement. Here, we present a readout scheme ...three **qubits**. Left plots: Rabi oscillations at several powers; traces ...**frequencies**. The local **oscillator** inputs of both mixers are fed from the...**qubits**....**oscillation** **frequency** versus power of the excitation tone; the error bars...**frequency** matches the transition between their ground and excited states...of **qubits** #2, 3 and 5. The** qubit** manipulation microwave excites **qubits**... qubit manipulation signal is generated by a single microwave source for...**qubits** on a chip....**qubits** taken into account. The readout **frequency** of device #3 is shown...**qubits** using a frequency division multiplexing technique is demonstrated...anti-**crossings** between the **qubit** and the corresponding resonator. There...**long** as the **qubit** remains far detuned from the resonator. The amplitude...**qubit**, **qubit** register, dispersive readout, **frequency** division
multiplexing...three qubits. Here, we used individual microwave excitations for every qub...**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**. 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: Xian-Ting Liang

Date: 2008-09-03

**qubits** in spin-boson (SB) and spin-intermediate harmonic oscillator (IHO...**frequencies**. However, the **qubits** in the two models have different decoherence...**frequency** ω of the bath modes, where Δ=5×109Hz,λκ=1,ξ=0.01,Ω0=10Δ,T=0.01K...**qubit**-IHO and IHO-bath and the oscillation frequency of the IHO....**frequencies** for the two cases are taken according to Fig. 2.
...low-**frequency** bath. The parameters are the same as in Fig. 1.
...**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** 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 ... 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: 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...and **qubit** experiments: **qubit** dephasing rate Γ φ = 0.1 GHz, **qubit** relaxation...**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...**weak ****qubit** signal in this region. After** the **MW pulses the **qubit** state ...**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** and** the **detector SQUID enclosing it are** the **small square loops in...**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 ...**qubit** loop and two in** the **SQUID. The LC mode is indicated by** the **dashed...**qubit** and** the **SQUID. The **qubit** dimension is 10.2 × 10.4 μ m 2 . (c) ...**oscillation** **frequency** when the LC circuit was not initially in the vacuum...**oscillation** **frequency** is determined only by the system‘s intrinsic parameters...**qubit** LC oscillator mutual inductance to be M = 5.7 pH. The current and...**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** and a superconducting LC circuit acting as a quantum harmonic oscillator...the **qubit** and then brought the **qubit** and the oscillator into resonance ... 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: Bennett, Douglas A., Longobardi, Luigi, Patel, Vijay, Chen, Wei, Averin, Dmitri V., Lukens, James E.

Date: 2008-11-14

**qubit** using pulsed microwaves and rapid flux pulses. The modified rf SQUID...**oscillation's** waveform is compared to analytical results obtained for ...**frequencies** of the Rabi **oscillations** that correspond to these microwave... rf SQUID qubit and the readout magnetometer, (c) a cross section of the...our qubit is large enough to cause a measurable effect. If the flux noise...**Qubits**...**frequency** flux noise....**frequency**); 0 V ’s (no detuning), 0.1 V ∘ ’s (0.21 n s -1 ), 0.45 V ’s...in our qubit is large enough to cause a measurable effect. If the flux...investigating superconducting phase qubits . In general these gaps do ...**Qubits** \and Flux **Qubit** \and SQUIDs...**oscillations** for detunings going from top to bottom of 0.094, 0.211, 0.328...**oscillations**. The line is a fit to Eq. fin for δ = 0 averaged over quasi-static...it appears that the qubit is coupled strongly to a two level fluctuator...decoherence in the qubit, one would expect a resonance in the microwave...**qubit** and the readout magnetometer, (c) a cross section of the wafer around...**frequency** flux noise and is consistent with independent measurement of...**oscillations** is dominated by the lifetime of the excited state and low...**oscillates** in time, demonstrating the phenomenon of Rabi **oscillations**,...**oscillations** when δ = 0 and the microwave **frequency**, f x r f = 17.9 G ...**qubit** in terms of Ω ....**qubits** . Ω , the **frequency** of the **oscillations** for δ = 0 , is ideally...**frequency** ... We report measurements of coherence times of an rf SQUID **qubit** using pulsed microwaves and rapid flux pulses. The modified rf SQUID, described by an double-well potential, has independent, in situ, controls for the tilt and barrier height of the potential. The decay of coherent **oscillations** is dominated by the lifetime of the excited state and low **frequency** flux noise and is consistent with independent measurement of these quantities obtained by microwave spectroscopy, resonant tunneling between fluxoid wells and decay of the excited state. The **oscillation's** waveform is compared to analytical results obtained for finite decay rates and detuning and averaged over low **frequency** flux noise.

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