### 62747 results for qubit oscillator frequency

Contributors: Averin, D. V.

Date: 2002-02-05

**qubit**, σ z and σ y , as required in the QND Hamiltonian ( 2). For discussion...**oscillations** avoiding the detector-induced dephasing that affects the ... **qubit**. The oscillations are represented as a spin rotation in the z -...**frequency** Δ . QND measurement is realized if the measurement frame (dashed...**qubit** structure that enables measurements of the two non-commuting observables...**oscillations** in an individual two-state system. Such a measurement enables...**frequency** Ω ≃ Δ ....**qubits** which combine flux and charge dynamics....**qubit**...**oscillations** of a **qubit**. The **oscillations** are represented as a spin rotation ... The concept of quantum nondemolition (QND) measurement is extended to coherent **oscillations** in an individual two-state system. Such a measurement enables direct observation of intrinsic spectrum of these **oscillations** avoiding the detector-induced dephasing that affects the standard (non-QND) measurements. The suggested scheme can be realized in Josephson-junction **qubits** which combine flux and charge dynamics.

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Contributors: Mandip Singh

Date: 2015-07-14

flux-**qubit** in the form of a cantilever. The net magnetic flux threading...superconducting-loop-**oscillator** when the intrinsic **frequency** is 10 kHz...flux-**qubit** and the mechanical degrees of freedom of the cantilever are...flux-**qubit**-cantilever turns out to be an entangled quantum state, where...superconducting-loop-**oscillator** with its axis of rotation along the z-axis... flux-qubit and the cantilever. An additional magnetic** flux** threading ...**frequency** (E/h) is ∼4×1011 Hz.
... flux-qubit-cantilever. A part of the** flux**-qubit (larger loop) is projected...**oscillator** is proposed, which consists of a flux-**qubit** in the form of ...flux-**qubit**-cantilever without a Josephson junction, is also discussed....flux-**qubit**-cantilever. A part of the flux-**qubit** (larger loop) is projected...**qubit**...**frequency** (E/h) is ∼3.9×1011 Hz.
... In this paper a macroscopic quantum **oscillator** is proposed, which consists of a flux-**qubit** in the form of a cantilever. The net magnetic flux threading through the flux-**qubit** and the mechanical degrees of freedom of the cantilever are naturally coupled. The coupling between the cantilever and the magnetic flux is controlled through an external magnetic field. The ground state of the flux-**qubit**-cantilever turns out to be an entangled quantum state, where the cantilever deflection and the magnetic flux are the entangled degrees of freedom. A variant, which is a special case of the flux-**qubit**-cantilever without a Josephson junction, is also discussed.

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Contributors: Whittaker, J. D., da Silva, F. C. S., Allman, M. S., Lecocq, F., Cicak, K., Sirois, A. J., Teufel, J. D., Aumentado, J., Simmonds, R. W.

Date: 2014-08-08

i n ≈ 4 , qubit lifetimes are relatively large across** the **full qubit ...**Qubits**...**oscillations** for **frequencies** near f 01 = 7.38 GHz. (b) Line-cut on-resonance...**qubit** anharmonicity, **qubit**-cavity coupling and detuning. A tunable cavity...a) Relative **qubit** anharmonicity** α r **versus **qubit** frequency ω 01 / 2 π ...is** the **qubit junction critical current, with** the **phase difference across the...**qubit** anharmonicity α r versus **qubit** **frequency** ω 01 / 2 π (design A )....**qubit** inductively coupled to a single-mode, resonant cavity with a tunable...minima....QB...**qubit** **frequency** change both Δ 01 and the ** qubit’s** anharmonicity α . In ...

**qubit**far detuned, biased at its maximum

**frequency**. The solid line is ...

**qubit**and cavity

**frequencies**and the dashed lines show the new coupled...

**qubits**....

**qubit**

**frequency**, at f 01 = 7.98 GHz, Ramsey

**oscillations**gave T 2 * = ...

**qubit**-cavity system, we show that dynamic control over the cavity

**frequency**...measure of the

**qubit**anharmonicity as shown later in Fig. Fig9....

**phase**

**qubit**(design A ) remains stable enough for operation (see text)...

**qubit**

**frequencies**. In order to capture the maximum dispersive

**frequency**...

**qubit**, and residual bus coupling for a system with multiple

**qubits**. With...

**qubit**evolutions and optimize state readout during

**qubit**measurements....

**frequency**of f c m a x = 7.07 GHz while sweeping the

**qubit**flux bias ...

**oscillation**decay time of T ' = 409 ns. (c) Ramsey

**oscillations**versus...

**oscillations**gave T ' = 727 ns, a separate measurement of

**qubit**energy...the

**qubit**flux bias is swept. Two different data sets (with the

**qubit**... GHz while sweeping

**the**qubit flux bias φ q . In

**both**cases, when the ...

**frequency**provides a way to strongly vary both the

**qubit**-cavity detuning...cavity (

**qubit**) (see text)....

**frequency**that allows for both microwave readout of tunneling and dispersive...resultant flux coupling of

**the**qubit bias coil, M q

**B**= 10.9 pH. The ... We describe a tunable-cavity QED architecture with an rf SQUID phase

**qubit**inductively coupled to a single-mode, resonant cavity with a tunable

**frequency**that allows for both microwave readout of tunneling and dispersive measurements of the

**qubit**. Dispersive measurement is well characterized by a three-level model, strongly dependent on

**qubit**anharmonicity,

**qubit**-cavity coupling and detuning. A tunable cavity

**frequency**provides a way to strongly vary both the

**qubit**-cavity detuning and coupling strength, which can reduce Purcell losses, cavity-induced dephasing of the

**qubit**, and residual bus coupling for a system with multiple

**qubits**. With our

**qubit**-cavity system, we show that dynamic control over the cavity

**frequency**enables one to avoid Purcell losses during coherent

**qubit**evolutions and optimize state readout during

**qubit**measurements. The maximum

**qubit**decay time $T_1$ = 1.5 $\mu$s is found to be limited by surface dielectric losses from a design geometry similar to planar transmon

**qubits**.

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Contributors: Serban, I., Solano, E., Wilhelm, F. K.

Date: 2007-02-28

between qubit and oscillator. Here ℏ Ω / k B T = 2 , κ / Ω = 0.025 and... seen by the qubit. The dephasing rate is also expected to diverge. The...**qubit** has been lost....**qubit** and **oscillator** or between **oscillator** and bath, corrections of the...**qubit** and the oscillator by means of their full Floquet state master equations...**qubit** and **oscillator**. Here ℏ Ω / k B T = 2 , κ / Ω = 0.025 and ℏ ν / k...through the qubit loop is Φ q and through the SQUID is Φ S .... of a qubit with one Josephson junction (phase γ , capacitance C q and...**qubit** quadratically coupled to its detector, a damped harmonic **oscillator**...effect after the qubit and the oscillator become entangled. The dephasing...**qubit** and **oscillator**. We also show that the pointer becomes measurable...states of the qubit split already during the transient motion of p ̂ t...**qubit** quadratically coupled to its detector, a damped harmonic oscillator...**qubit** with one Josephson junction (phase γ , capacitance C q and inductance...**qubit** and the **oscillator** by means of their full Floquet state master equations...**frequency** is at resonance with the harmonic **oscillator** — we have a continuum...**qubit** loop is Φ q and through the SQUID is Φ S ....**qubit** and oscillator. We also show that the pointer becomes measurable...**qubit** and the **oscillator** become entangled. The dephasing rate drops again...**frequencies** to the value obtained in the case without driving....**frequency** ν for different vales of κ ( Δ / Ω = 0.5 ). Here ℏ Ω / k B T...**qubit** states (c). Here ℏ Ω / k B T = 2 , Δ / Ω = 0.45 , κ / Ω = 0.025 ...**qubit** and explore several measurement protocols, which include a long-term...different qubit states (c). Here ℏ Ω / k B T = 2 , Δ / Ω = 0.45 , κ / ... we later approximate the qubit as a two-level system. The qubit used ...**qubits**...**oscillator** has the **frequency** Ω because it has not yet "seen" the **qubit**...about the qubit state, and has the advantage of avoiding decoeherence ... Motivated by recent experiments, we study the dynamics of a **qubit** quadratically coupled to its detector, a damped harmonic **oscillator**. We use a complex-environment approach, explicitly describing the dynamics of the **qubit** and the **oscillator** by means of their full Floquet state master equations in phase-space. We investigate the backaction of the environment on the measured **qubit** and explore several measurement protocols, which include a long-term full read-out cycle as well as schemes based on short time transfer of information between **qubit** and **oscillator**. We also show that the pointer becomes measurable before all information in the **qubit** has been lost.

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Contributors: Ginossar, Eran, Bishop, Lev S., Girvin, S. M.

Date: 2012-07-19

**qubit** state measurement in circuit quantum electrodynamics...**qubit** and cavity are on resonance or far off-resonance (dispersive)....superconducting transmon qubits...**frequency** and amplitude. The region of bifurcation...**oscillator** with its set of transition **frequencies** depending on the state...**qubit** and cavity are strongly coupled. We focus on the parameter ranges...**qubit** decay** . **T 1** . **has** . **distinct influence on** the **lifetime of** the **QCS...**qubit** quantum state discrimination and we present initial results for ...**frequency**).... 4 transmon qubits transmonat 7.0** . **7.5** . **8.0** . **12.3** . **H z** . **All qubits...**oscillator**...**qubits** in the circuit quantum electrodynamics architecture, where the ...**oscillator** and we analyze the quantum and semi-classical dynamics. One...**oscillator** (Duffing **oscillator**) Duffing **oscillator**, constructed by making... the **qubit** is detuned from** the **cavity** . **ω q** . **ω c** . **2 π** . **2 g ). It is...disruptive to the **qubit** state and it is realized where** the **cavity and ... **qubit** (Fig. gino:chirp_figure). This selective dynamical mapping of** th**...**frequency**. For (b), if the state of one (‘spectator’) **qubit** is held constant...**frequency** response bifurcates, and the JC **oscillator** enters a region of...**frequency** and amplitude. Despite the presence of 4 **qubits** in the device...one **qubit**, see Fig. gino:fig:return. Such an asymmetric **qubit** dependent...**qubit** **frequency**. (c) Wave packet snapshots at selected times (indicated...anharmonic transmon....the **qubit** being detuned. Due to the interaction with the **qubit**, the cavity...**frequency** of panel (b) conditioned on the initial state of the **qubit**. ...**qubit** state q : (a) for the JC model, parameters as in Figs. gino:fig ... In this book chapter we analyze the high excitation nonlinear response of the Jaynes-Cummings model in quantum optics when the **qubit** and cavity are strongly coupled. We focus on the parameter ranges appropriate for transmon **qubits** in the circuit quantum electrodynamics architecture, where the system behaves essentially as a nonlinear quantum **oscillator** and we analyze the quantum and semi-classical dynamics. One of the central motivations is that under strong excitation tones, the nonlinear response can lead to **qubit** quantum state discrimination and we present initial results for the cases when the **qubit** and cavity are on resonance or far off-resonance (dispersive).

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Contributors: Shi, Zhan, Simmons, C. B., Ward, Daniel. R., Prance, J. R., Mohr, R. T., Koh, Teck Seng, Gamble, John King, Wu, Xian., Savage, D. E., Lagally, M. G.

Date: 2012-08-02

low-**frequency** noise processes are an important dephasing mechanism....**Qubit**...**oscillations** visible near δ t = 0 . The **oscillations** of interest appear...**qubit** states varies with external voltages, consistent with a decoherence...**qubit** in a double quantum dot fabricated in a Si/SiGe heterostructure ...**oscillation** **frequency** f for (a–c), respectively. As t is increased, the...**frequency** at more negative detuning (farther from the anti-crossing). ...**oscillation** **frequency** f for the data in (a–c), respectively. We obtain...**oscillations** at a given **frequency** decays with characteristic time T 2 ...**oscillations** of a charge **qubit** in a double quantum dot fabricated in a...**qubit**'s double-well potential). In the regime with the shortest T2*, applying ... Fast quantum **oscillations** of a charge **qubit** in a double quantum dot fabricated in a Si/SiGe heterostructure are demonstrated and characterized experimentally. The measured inhomogeneous dephasing time T2* ranges from 127ps to ~2.1ns; it depends substantially on how the energy difference of the two **qubit** states varies with external voltages, consistent with a decoherence process that is dominated by detuning noise(charge noise that changes the asymmetry of the **qubit**'s double-well potential). In the regime with the shortest T2*, applying a charge-echo pulse sequence increases the measured inhomogeneous decoherence time from 127ps to 760ps, demonstrating that low-**frequency** noise processes are an important dephasing mechanism.

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Contributors: Lisenfeld, Juergen, Mueller, Clemens, Cole, Jared H., Bushev, Pavel, Lukashenko, Alexander, Shnirman, Alexander, Ustinov, Alexey V.

Date: 2009-09-18

**frequencies**. Each trace was recorded after adjusting the **qubit** bias to...**frequency** while the **qubit** was kept detuned. A π pulse was applied to measure...**qubit**-fluctuator system...the **qubit** in the excited state, P t , vs. driving frequency; (b) Fourier-transform...phase **qubit** circuit. (b) Probability to measure the excited **qubit** state...**the** **qubit** was kept detuned. A π pulse was applied to measure **the** energy...**oscillations**
...**qubits** often show signatures of coherent coupling to microscopic two-level...**frequency** of 7.805 GHz (indicated by a dashed line)....**qubits**, Josephson junctions, two-level
fluctuators, microwave spectroscopy...**qubit** and fluctuator v ⊥ and to the microwave field Ω q and Ω f v ....**qubit** in the excited state, P t , vs. driving **frequency**; (b) Fourier-transform...**qubit** levels....**qubit** as and and those of the TLF as and . Arrows indicate the couplings...** qubit’s** Rabi

**frequency**Ω q / h is set to 48 MHz....

**qubit**, in which we induce Rabi oscillations by resonant microwave driving...

**oscillations**observed experimentally....

**frequency**, revealing the coupling to a two-level defect state having a...

**the**

**qubit**loop. The

**qubit**state is controlled by an externally applied...levels

**in**

**the**

**qubit**....

**qubit**, in which we induce Rabi

**oscillations**by resonant microwave driving...

**qubit**is tuned close to the resonance with an individual TLF and the Rabi...

**frequency**components.

**Frequency**and visibility of each component depend...

**qubit**relative to the TLF’s resonance

**frequency**, which is indicated in...

**qubit**transition. In this work, we studied

**the**

**qubit**interacting with ...

**qubit**above or below the fluctuator's level-splitting. Theoretical analysis...

**qubit**circuit. (b) Probability to measure the excited

**qubit**state (color-coded...

**qubit**-TLF coupling), interesting 4-level dynamics are observed. The experimental...

**frequency**of order of the

**qubit**-TLF coupling), interesting 4-level dynamics...in the

**qubit**. (As the anharmonicity Δ / h ∼ 100 MHz in our circuit is...

**the**phase

**qubit**circuit (

**the**

**qubit**subspace) and disregard

**the**longitudinal ... Superconducting

**qubits**often show signatures of coherent coupling to microscopic two-level fluctuators (TLFs), which manifest themselves as avoided level crossings in spectroscopic data. In this work we study a phase

**qubit**, in which we induce Rabi

**oscillations**by resonant microwave driving. When the

**qubit**is tuned close to the resonance with an individual TLF and the Rabi driving is strong enough (Rabi

**frequency**of order of the

**qubit**-TLF coupling), interesting 4-level dynamics are observed. The experimental data shows a clear asymmetry between biasing the

**qubit**above or below the fluctuator's level-splitting. Theoretical analysis indicates that this asymmetry is due to an effective coupling of the TLF to the external microwave field induced by the higher

**qubit**levels.

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Contributors: Strauch, F. W., Dutta, S. K., Paik, Hanhee, Palomaki, T. A., Mitra, K., Cooper, B. K., Lewis, R. M., Anderson, J. R., Dragt, A. J., Lobb, C. J.

Date: 2007-03-02

**frequency**, and two-photon Rabi **frequency** are compared to measurements ...**frequency** Ω R , 01 of the one-photon 0 1 transition as function of microwave...**qubit**, scanned in **frequency** (vertical) and bias current (horizontal). ...**qubit** (current-biased Josephson junction) at high microwave drive power...**qubit** with Nb/AlOx/Nb tunnel junctions. Good agreement is found between...**oscillations** of the escape rate for I a c = 16.5 nA....**oscillations** have been observed in many superconducting devices, and represent...**oscillation** **frequency** Ω ̄ R , 01 as a function of the level spacing ω ...**qubit**...**qubits**) in a quantum computer. We use a three-level multiphoton analysis...phase qubit, scanned in frequency (vertical) and bias current (horizontal ... Rabi **oscillations** have been observed in many superconducting devices, and represent prototypical logic operations for quantum bits (**qubits**) in a quantum computer. We use a three-level multiphoton analysis to understand the behavior of the superconducting phase **qubit** (current-biased Josephson junction) at high microwave drive power. Analytical and numerical results for the ac Stark shift, single-photon Rabi **frequency**, and two-photon Rabi **frequency** are compared to measurements made on a dc SQUID phase **qubit** with Nb/AlOx/Nb tunnel junctions. Good agreement is found between theory and experiment.

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Contributors: Murch, K. W., Ginossar, E., Weber, S. J., Vijay, R., Girvin, S. M., Siddiqi, I.

Date: 2012-08-22

**qubit**-cavity detuning for the **qubit** prepared in the ground state in the...**qubit**, both the effective nonlinearity and the threshold become a non-trivial...**oscillator** Q....**the** **qubit**-oscillator model with N l = 7 show **the** avoided crossings in ...**qubit**-**oscillator** model with N l = 7 show the avoided crossings in the ...and **qubit** junctions (lower and upper insets)....**qubit** junctions (lower and upper insets)....**qubit** and may be used to realize a high fidelity, latching readout whose...**qubit**-**oscillator** detuning. Moreover, the autoresonant threshold is sensitive...**oscillator** is strongly coupled to a quantized superconducting **qubit**, both...**qubit** state. (a) Color plot shows S | 1 versus **qubit** detuning. The dashed... **qubit** state. (a) Color plot shows S | 1 versus **qubit** detuning. The dashed...**qubit**-cavity detuning for **the** **qubit** prepared in **the** ground state in **the**...**frequency** chirped excitation is applied to a classical high-Q nonlinear...**qubit**-oscillator detuning. Moreover, the autoresonant threshold is sensitive...**oscillators** (red) are shown. The arrows indicate the locations of avoided...**the** **qubit** energy levels were modeled as a Duffing nonlinearity. ... When a **frequency** chirped excitation is applied to a classical high-Q nonlinear **oscillator**, its motion becomes dynamically synchronized to the drive and large oscillation amplitude is observed, provided the drive strength exceeds the critical threshold for autoresonance. We demonstrate that when such an **oscillator** is strongly coupled to a quantized superconducting **qubit**, both the effective nonlinearity and the threshold become a non-trivial function of the **qubit**-**oscillator** detuning. Moreover, the autoresonant threshold is sensitive to the quantum state of the **qubit** and may be used to realize a high fidelity, latching readout whose speed is not limited by the **oscillator** Q.

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Contributors: Greenberg, Ya. S.

Date: 2003-03-04

**oscillations** in a phase **qubit**. The external source, typically in GHz range...**qubit** states, nevertheless the voltage across the tank **oscillates** with...**qubit** coupled to a dissipative tank circuit. The evolution of A exhibits...**qubit**). We explicitly account for the back action of a tank circuit and...**oscillations** with lower **frequency**. Deterministic case (a) together with...L...destroys the phase coherence between qubit states, nevertheless the voltage...**qubit** levels. The resulting Rabi **oscillations** of supercurrent in the **qubit**...speaking, consider qubit as having definite wave function. However, if...P...**qubit**. The external source, typically in GHz range, induces transitions...of qubit evolution as the coupling between the qubit and the tank is increased...loss-free qubit coupled to the dissipative tank circuit. The system is...loss-free **qubit** coupled to a loss-free tank circuit. Oscillations of A...**oscillates** with a high **frequency** which is about 10 GHz in our case. As...**qubit** loop. As is seen from the Fig. fig4a, A **oscillates** with Rabi **frequency**...case....**qubit** levels. The resulting Rabi oscillations of supercurrent in the **qubit**...**qubit**. Computer simulations...**oscillations** correspond to Rabi **frequency**....**oscillates** with gap **frequency**, while the **frequency** of A is almost ten ...**oscillates** also with Rabi **frequency** which is equal to 50 MHz in our case... to show the effect of qubit evolution as the coupling between the qubit... **qubit** coupled to a dissipative tank circuit Q T = 100 . The voltage across...**qubit** coupled to a loss-free tank circuit. **Oscillations** of A. Deterministic... A and B for **qubit** without dissipation....**qubit** without dissipation....**frequency**. Deterministic case (a) together with one realization (b) are...**oscillations** in MHz range can be detected using conventional NMR pulse...**oscillations** between quantum states in mesoscopic superconducting systems...**qubit**. Here we present the results of detailed computer simulations of ... Time-domain observations of coherent **oscillations** between quantum states in mesoscopic superconducting systems have so far been restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a method for direct observation of Rabi **oscillations** in a phase **qubit**. The external source, typically in GHz range, induces transitions between the **qubit** levels. The resulting Rabi **oscillations** of supercurrent in the **qubit** loop are detected by a high quality resonant tank circuit, inductively coupled to the phase **qubit**. Here we present the results of detailed computer simulations of the interaction of a classical object (resonant tank circuit) with a quantum object (phase **qubit**). We explicitly account for the back action of a tank circuit and for the unpredictable nature of outcome of a single measurement. According to the results of our simulations the Rabi **oscillations** in MHz range can be detected using conventional NMR pulse Fourier technique.

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