### 62747 results for qubit oscillator frequency

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

Date: 2009-07-20

**Oscillator** **frequency** shift as function or the **qubit** splitting ϵ = ω + ...**qubit** splitting ϵ = ω + Δ for the spin state | ↓ obtained (a) within RWA...**qubit** state | ↓ ....**qubit**-**oscillator** coupling, we diagonalize the non-RWA Hamiltonian and ...**qubit** readout is possible. If several **qubits** are coupled to one resonator...**qubit**-**qubit** interaction of Ising type emerges, whereas RWA leads to isotropic...**qubits**....**Qubit**-oscillator dynamics in the dispersive regime: analytical theory ...**qubit**-oscillator coupling, we diagonalize the non-RWA Hamiltonian and ...**of** the **qubit** state | ↓ ....**qubit** state | ↓ , where σ z | ↓ = - | ↓ . The results are depicted in ... We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation (RWA) in the coupling between the two-level system and the resonator. For a detuning sufficiently larger than the **qubit**-**oscillator** coupling, we diagonalize the non-RWA Hamiltonian and discuss the differences to the known RWA results. Our results extend the regime in which dispersive **qubit** readout is possible. If several **qubits** are coupled to one resonator, an effective **qubit**-**qubit** interaction of Ising type emerges, whereas RWA leads to isotropic interaction. This impacts on the entanglement characteristics of the **qubits**.

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Contributors: Hausinger, Johannes, Grifoni, Milena

Date: 2010-07-30

**oscillator** **frequency** approaches unity and goes beyond. In this regime ...**oscillator** **frequency** Ω , ε = l Ω . In this case we found that the levels...**qubit**-**oscillator** detuning. Furthermore, the dynamics is not governed anymore...**frequency** peaks coming from the two dressed **oscillation** **frequencies** Ω ...**Qubit**-oscillator system: An analytical treatment of the ultra-strong coupling...**qubit** for an **oscillator** at low temperature. We consider the coupling strength...**oscillations** **frequency** Ω j l . For l being not an integer those doublets...**qubit**-oscillator detuning. Furthermore, the dynamics is not governed anymore...**qubit** for an oscillator at low temperature. We consider the coupling strength...**qubit** ( ε / Ω = 0.5 ) at resonance with the oscillator Δ b = Ω in the ...**frequencies** through a variation of the coupling....**qubit** ( ε / Ω = 0.5 ) at resonance with the **oscillator** Δ b = Ω in the ...**frequency** range. The lowest **frequency** peaks originate from transitions...**qubit** tunneling matrix element $\Delta$ we are able to enlarge the regime...**oscillations**. With increasing time small differences between numerical...**oscillation** **frequency** Ω j 0 . Numerical calculations and VVP predict group...**oscillation** **frequencies** Ω j 1 and Ω j 2 influence the longtime dynamics...**qubit** ( ε / Ω = 0.5 ) being at resonance with the **oscillator** ( Δ b = Ω ... We examine a two-level system coupled to a quantum **oscillator**, typically representing experiments in cavity and circuit quantum electrodynamics. We show how such a system can be treated analytically in the ultrastrong coupling limit, where the ratio $g/\Omega$ between coupling strength and **oscillator** **frequency** approaches unity and goes beyond. In this regime the Jaynes-Cummings model is known to fail, because counter-rotating terms have to be taken into account. By using Van Vleck perturbation theory to higher orders in the **qubit** tunneling matrix element $\Delta$ we are able to enlarge the regime of applicability of existing analytical treatments, including in particular also the finite bias case. We present a detailed discussion on the energy spectrum of the system and on the dynamics of the **qubit** for an **oscillator** at low temperature. We consider the coupling strength $g$ to all orders, and the validity of our approach is even enhanced in the ultrastrong coupling regime. Looking at the Fourier spectrum of the population difference, we find that many **frequencies** are contributing to the dynamics. They are gathered into groups whose spacing depends on the **qubit**-**oscillator** detuning. Furthermore, the dynamics is not governed anymore by a vacuum Rabi splitting which scales linearly with $g$, but by a non-trivial dressing of the tunneling matrix element, which can be used to suppress specific **frequencies** through a variation of the coupling.

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Contributors: Wallraff, A., Schuster, D. I., Blais, A., Frunzio, L., Majer, J., Girvin, S. M., Schoelkopf, R. J.

Date: 2005-02-27

**qubit** population P vs. pulse separation Δ t using the pulse sequence shown... to determine **the** **qubit** transition frequency ω a = ω s + 2 π ν R a m s...applying to **the** **qubit** microwave pulses of frequency ω s , which are resonant...**oscillating** at the detuning **frequency** Δ a , s = ω a - ω s ∼ 6 M H z decay...**oscillations** in the **qubit** population P vs. Rabi pulse length Δ t (blue...**qubit** population P vs. pulse separation Δ t using** the **pulse sequence shown...**oscillation** experiment with a superconducting **qubit** we show that a visibility...**qubit** we show that a visibility in the **qubit** excited state population ...**oscillations** in the **qubit** at a **frequency** of ν R a b i = n s g / π , where... φ will be reduced in any **qubit** read-out for which **the** timescale of **the**...**qubit**. In the 2D density plot Fig. fig:2DRabi, Rabi **oscillations** are ...**oscillation** **frequency** ν R a b i with the pulse amplitude ϵ s ∝ n s , see...**qubit** excited state population of more than 90 % can be attained. We perform...**qubit** population P is plotted versus Δ** t** in Fig. fig:rabioscillationsa...**Qubit** with Dispersive Readout...**qubit** state by coupling the **qubit** non-resonantly to a transmission line...**superconducting** **qubit**, a visibility in **the** population of **the** **qubit** excited...**qubit**. In each panel the dashed lines correspond to the expected measurement...**to **the **qubit**. In each panel** the **dashed lines correspond **to **the expected...**oscillations** with Rabi pulse length Δ t , pulse **frequency** ω s and amplitude...**oscillations** in a superconducting **qubit**, a visibility in the population... the **qubit** population P vs. Rabi pulse length Δ t (blue dots) and fit ...**qubit** coherence time is determined to be larger than 500 ns in a measurement...**oscillator** at **frequency** ω L O . The Cooper pair box level separation is ... In a Rabi **oscillation** experiment with a superconducting **qubit** we show that a visibility in the **qubit** excited state population of more than 90 % can be attained. We perform a dispersive measurement of the **qubit** state by coupling the **qubit** non-resonantly to a transmission line resonator and probing the resonator transmission spectrum. The measurement process is well characterized and quantitatively understood. The **qubit** coherence time is determined to be larger than 500 ns in a measurement of Ramsey fringes.

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

Date: 2010-10-05

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

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Contributors: Baur, M., Filipp, S., Bianchetti, R., Fink, J. M., Göppl, M., Steffen, L., Leek, P. J., Blais, A., Wallraff, A.

Date: 2008-12-23

the third qubit level ( ν - , f , ν + , f ) and between the dressed states...frequency to the qubit state-dependent resonance of the resonator under...**qubit** level ( ν - , f , ν + , f ) and between the dressed states ( ν -...**qubit**. The transition **frequency** from the first | e to the second excited...**qubit** resonance **frequencies** are extracted....6% of the qubit transition frequency ω g e ....**qubit** states and dispersive level shifts due to off-resonant drives....**oscillator** (LO) to an intermediate **frequency** at 300K and digitized with...stage, the qubit is coupled capacitively through C g to the resonator,... qubit anharmonicity . The qubit is strongly coupled to a coplanar waveguide...considerably larger **than **the qubit linewidth....**qubit**. The ground to first excited state transition of the **qubit** is strongly...**qubit** transition **frequency** ω g e ....**frequencies** (red dots) vs. drive power P d at a fixed drive **frequency** ...**frequency** and the Rabi **oscillation** **frequency** of the excited state population...**oscillation** experiments, lines as in (a). (c) Rabi **oscillation** measurements...**qubit** is coupled capacitively through C g to the resonator, represented...**qubit** coupled off-resonantly to a microwave transmission line resonator...**qubit** spectrum is probed with a weak tone. The corresponding transitions...**frequencies** of the Autler-Townes and Mollow spectral lines are in good...**frequency**. The **qubit** spectrum is then probed by sweeping a weak second...**qubit** ... We present spectroscopic measurements of the Autler-Townes doublet and the sidebands of the Mollow triplet in a driven superconducting **qubit**. The ground to first excited state transition of the **qubit** is strongly pumped while the resulting dressed **qubit** spectrum is probed with a weak tone. The corresponding transitions are detected using dispersive read-out of the **qubit** coupled off-resonantly to a microwave transmission line resonator. The observed **frequencies** of the Autler-Townes and Mollow spectral lines are in good agreement with a dispersive Jaynes-Cummings model taking into account higher excited **qubit** states and dispersive level shifts due to off-resonant drives.

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### Temperature square dependence of the low **frequency** 1/f charge noise in the Josephson junction **qubits**

Contributors: Astafiev, O., Pashkin, Yu. A., Nakamura, Y., Yamamoto, T., Tsai, J. S.

Date: 2006-04-04

**qubits**, we study temperature dependence of the 1/f noise and decay of ...of qubit dephasing during coherent oscillations. The coherent oscillations...**oscillations**. T^2 dependence of the 1/f noise is experimentally demonstrated...**oscillations** decay as exp - t 2 / 2 T 2 * 2 with...**frequency** 1/f noise and the quantum f noise recently measured in the Josephson...**qubits** off the electrostatic energy degeneracy point is consistently explained...**frequency** independent in the measured **frequency** range (and usually do ...**qubit** as an SET and measure the low **frequency** charge noise, which causes...**oscillations** measured at T = 50 mK and the dashed envelope exemplifies...**qubit** as an SET and measure the low frequency charge noise, which causes...**frequency** 1/f noise that is observed in the transport measurements....**oscillation** as a function of t away from the degeneracy point ( θ ≠ π ...**qubits**...**qubit** dephasing during coherent **oscillations**. The coherent **oscillations** ... To verify the hypothesis about the common origin of the low **frequency** 1/f noise and the quantum f noise recently measured in the Josephson charge **qubits**, we study temperature dependence of the 1/f noise and decay of coherent **oscillations**. T^2 dependence of the 1/f noise is experimentally demonstrated, which supports the hypothesis. We also show that dephasing in the Josephson charge **qubits** off the electrostatic energy degeneracy point is consistently explained by the same low **frequency** 1/f noise that is observed in the transport measurements.

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Contributors: Shevchenko, S. N., Omelyanchouk, A. N., Zagoskin, A. M., Savel'ev, S., Nori, F.

Date: 2007-12-12

**frequency** dependent on the perturbation amplitude. These serve as one ...**oscillations** from their classical Doppelganger.... of the qubit in state | 1 . Alternatively, instead of an RF readout pulse...**qubit** in Fig. 4 of Ref. [...**qubit** states....**qubits** (current-biased Josephson junctions) this effect can be mimicked...Phase qubit (a) and its Josephson energy (b). The metastable states and...**frequency**. The parameters used here are: η = 0.95 , E J / ℏ ω p = 300 ...**oscillations** in current-biased Josephson junctions: (a) and (b) show the...**qubits** provide a clear demonstration of quantum coherent behaviour in ...**frequency** in the classical case, in contrast to the positive Bloch-Siegert...a phase qubit is a current-biased Josephson junction (see Fig. scheme(...**qubit** in state | 1 . Alternatively, instead of an RF readout pulse one...**oscillations** can be produced by the subharmonics of the resonant **frequency**...as qubit states....flux qubit in Fig. 4 of Ref. [...**qubit** (a) and its Josephson energy (b). The metastable states and can ...**frequency** and the amplitude of the **oscillations** respectively for ϵ = 2...**qubit** is a current-biased Josephson junction (see Fig. scheme(a)), and...**qubit**...**frequency** for relatively weak (a) and strong (b) driving. Different values...Superconducting phase qubits provide a clear demonstration of quantum ... Rabi **oscillations** are coherent transitions in a quantum two-level system under the influence of a resonant perturbation, with a much lower **frequency** dependent on the perturbation amplitude. These serve as one of the signatures of quantum coherent evolution in mesoscopic systems. It was shown recently [N. Gronbech-Jensen and M. Cirillo, Phys. Rev. Lett. 95, 067001 (2005)] that in phase **qubits** (current-biased Josephson junctions) this effect can be mimicked by classical **oscillations** arising due to the anharmonicity of the effective potential. Nevertheless, we find qualitative differences between the classical and quantum effect. First, while the quantum Rabi **oscillations** can be produced by the subharmonics of the resonant **frequency** (multiphoton processes), the classical effect also exists when the system is excited at the overtones. Second, the shape of the resonance is, in the classical case, characteristically asymmetric; while quantum resonances are described by symmetric Lorentzians. Third, the anharmonicity of the potential results in the negative shift of the resonant **frequency** in the classical case, in contrast to the positive Bloch-Siegert shift in the quantum case. We show that in the relevant range of parameters these features allow to confidently distinguish the bona fide Rabi **oscillations** from their classical Doppelganger.

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Contributors: Kim, Mun Dae

Date: 2008-09-02

**oscillating** field it is shown that the high fidelity of the CNOT gate ... qubits. (b) Occupation probabilities of | ρ ρ ' states during Rabi-type...coupled-**qubit** states with the initial state, | ψ 0 = | 00 + | 10 / 2 for...**Qubits**...two-**qubit** **oscillation** deviates seriously from the Rabi **oscillation** and...**oscillations** of occupation probability of coupled-**qubit** states with the...**oscillating** field amplitude for any given values of **qubit** energy gap and...**oscillation**. Here, the unit of all numbers is GHz....**qubit** energy gap ω 0 . For small ω 0 and large J the **oscillations** are ... **qubit** energy gap ω 0 / 2 π =4GHz, and Rabi frequency Ω 0 / 2 π = 600 ...that the target qubit flips for a specific state of control qubit such...**oscillating** field with the resonant **frequency** ω = ω 0 < ω 1 ....values of qubit energy gap and coupling strength between qubits. While... qubits, where ρ , ρ ' ∈ 0 1 . E s s ' with s , s ' ∈ are shown as thin...coupled-**qubit** oscillation driven by an oscillating field. When the period...**qubit** energy gap ω 0 . For small ω 0 and large J the oscillations are ...**qubit** energy gap ω 0 / 2 π =4GHz, and Rabi **frequency** Ω 0 / 2 π = 600 MHz...coupled-**qubit** **oscillation** driven by an **oscillating** field. When the period...**qubit** energy gap in experiments....**oscillation** for strongly coupled **qubits**. While the P 00 ( P 01 ) is reversed...**oscillation**, we show that the controlled-NOT (CNOT) gate operation can...two-qubit oscillation deviates seriously from the Rabi oscillation and...**oscillations**, while for a sufficiently strong coupling it can be done ...**qubits**, where ρ , ρ ' ∈ 0 1 . E s s ' with s , s ' ∈ are shown as thin...to shift the qubits slightly away from the degeneracy point to detect ... We study the coupled-**qubit** **oscillation** driven by an **oscillating** field. When the period of the non-resonant mode is commensurate with that of the resonant mode of the Rabi **oscillation**, we show that the controlled-NOT (CNOT) gate operation can be demonstrated. For a weak coupling the CNOT gate operation is achievable by the commensurate **oscillations**, while for a sufficiently strong coupling it can be done for arbitrary parameter values. By finely tuning the amplitude of **oscillating** field it is shown that the high fidelity of the CNOT gate can be obtained for any fixed coupling strength and **qubit** energy gap in experiments.

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Contributors: Hoffman, Anthony J., Srinivasan, Srikanth J., Gambetta, Jay M., Houck, Andrew A.

Date: 2011-08-12

**qubit** starts in the g 10 - 00 = 0 state and is simulataneously moved to...single **qubit** gate errors in one **qubit** while a second **qubit** is driven....the **qubit**-cavity coupling is tuned through zero....**qubit** **frequency** and coupling strength are functions of the control voltages...**oscillations** approximately the same for the lower **qubit**-cavity coupling...different **qubit**-cavity coupling strengths and a fixed dressed **qubit** frequency...constant **qubit** frequency, the **qubit**-cavity coupling strength, g 10 - 00...**qubit** **frequency**. This subspace accounts for any dispersive shifts due ...**oscillations** for three different **qubit**-cavity coupling strengths and a...**qubit** transition **frequencies**, it is necessary to find the control subspace...**qubit** can be incorporated into quantum computing architectures....the **qubit** while moving along the 7.5 G H z contour in Fig. 1. The dressed qu...**qubit** to the cavity while keeping the **qubit** **frequency** fixed. Since the...**frequency** response of the **qubit** while moving along the 7.5 G H z contour...**oscillations** at three different points on the constant **frequency** contour...**qubit** coupled to a superconducting coplanar waveguide resonator with a...**qubit** being in the excited state as a function of delay following a π ...**qubit** transition can be turned off by a factor of more than 1500. We show... **qubit**....**qubit**-cavity coupling strength. Rabi oscillations are measured for several...**qubit** **frequency**, the **qubit**-cavity coupling strength, g 10 - 00 , changes...**qubit** can still be accessed in the off state via fast flux pulses. We ... **qubit** to the cavity while keeping the **qubit** frequency fixed. Since the...**qubit**-cavity coupling strength. Rabi **oscillations** are measured for several...**Qubit** with Dynamically Tunable **Qubit**-cavity Coupling...**qubit** **frequency** of 7.5 G H z . Panels (a), (b), and (c) correspond to ...**qubit** gate errors in one **qubit** while a second **qubit** is driven. ... We demonstrate coherent control and measurement of a superconducting **qubit** coupled to a superconducting coplanar waveguide resonator with a dynamically tunable **qubit**-cavity coupling strength. Rabi **oscillations** are measured for several coupling strengths showing that the **qubit** transition can be turned off by a factor of more than 1500. We show how the **qubit** can still be accessed in the off state via fast flux pulses. We perform pulse delay measurements with synchronized fast flux pulses on the device and observe $T_1$ and $T_2$ times of 1.6 and 1.9 $\mu$s, respectively. This work demonstrates how this **qubit** can be incorporated into quantum computing architectures.

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Contributors: Du, Lingjie, Yu, Yang

Date: 2010-12-13

between a **qubit** and an electromagnetic system (such as the environment...**qubit** are identical **with **Fig. 4 (a)....**qubit** but also the systems with no crossover structure, e.g. phase **qubits**...of a flux **qubit**. The dotted curve represents the strong driving field ...**oscillation** induced interference. (a) describes the transition from state...**frequency** of the bath. In addition, we demonstrate the relaxation can ...**oscillation**, resulting respectively from the multi- or single-mode interaction...**qubit**. The dotted curve represents the strong driving field A cos ω t ...**qubit** and an electromagnetic system (such as the environment bath or a...**with **the **qubit**. (b). Quantum tunnel coupling exists between states | 0...**qubits**. The interaction between **qubits** and electromagnetic fields can ...**oscillation**, Rabi **oscillation** induced interference involves more complicated...**qubit**, with more controllable parameters including the strength and position...**qubit**. (b). Quantum tunnel coupling exists between states | 0 and | 1 ...final **qubit** population versus energy detuning and microwave amplitude....**qubit** states, leading to quantum interference in a microwave driven **qubit**...**qubit** are identical with Fig. 4 (a)....**qubits** and their environment. It also supplies a useful tool to characterize...**qubits** ... We study electromagnetically induced interference at superconducting **qubits**. The interaction between **qubits** and electromagnetic fields can provide additional coupling channels to **qubit** states, leading to quantum interference in a microwave driven **qubit**. In particular, the interwell relaxation or Rabi **oscillation**, resulting respectively from the multi- or single-mode interaction, can induce effective crossovers. The environment is modeled by a multi-mode thermal bath, generating the interwell relaxation. Relaxation induced interference, independent of the tunnel coupling, provides deeper understanding to the interaction between the **qubits** and their environment. It also supplies a useful tool to characterize the relaxation strength as well as the characteristic **frequency** of the bath. In addition, we demonstrate the relaxation can generate population inversion in a strongly driving two-level system. On the other hand, different from Rabi **oscillation**, Rabi **oscillation** induced interference involves more complicated and modulated photon exchange thus offers an alternative means to manipulate the **qubit**, with more controllable parameters including the strength and position of the tunnel coupling. It also provides a testing ground for exploring nonlinear quantum phenomena and quantum state manipulation, in not only the flux **qubit** but also the systems with no crossover structure, e.g. phase **qubits**.

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