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.

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.

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.

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.

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.

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.

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.

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.

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.

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.