### 57455 results for qubit oscillator frequency

Contributors: Rosenband, Till

Date: 2012-03-01

**oscillator** noise. In this context the squeezed states discussed by Andr...**qubits**, compared to the standard quantum limit (SQL). The most stable ...**qubits**, which are assumed not to decohere with one another....**frequency** corrections are φ E s t / 2 π T . Shaded in the background is...**qubits**, the protocol of Bu...**qubits** performance matches the analytical protocols. In the simulations...**qubits** can reduce clock instability, although the GHZ states yield no...**qubits** are required to improve upon the SQL by a factor of two....**oscillator** noise has an Allan deviation of 1 Hz....**qubits**, and improve upon the SQL variance by a factor of N -1 / 3 . For...**frequency** variance of the clock extrapolated to 1 second. For long-term...**frequency** is repeatedly corrected, based on projective measurements of...**qubits** yields improved clock stability compared to Ramsey spectroscopy...few-**qubit** clock protocols...**oscillator** decoheres due to flicker-**frequency** (1/f) noise. The **oscillator** ... The stability of several clock protocols based on 2 to 20 entangled atoms is evaluated numerically by a simulation that includes the effect of decoherence due to classical **oscillator** noise. In this context the squeezed states discussed by Andr\'{e}, S{\o}rensen and Lukin [PRL 92, 239801 (2004)] offer reduced instability compared to clocks based on Ramsey's protocol with unentangled atoms. When more than 15 atoms are simulated, the protocol of Bu\v{z}ek, Derka and Massar [PRL 82, 2207 (1999)] has lower instability. A large-scale numerical search for optimal clock protocols with two to eight **qubits** yields improved clock stability compared to Ramsey spectroscopy, and for two to three **qubits** performance matches the analytical protocols. In the simulations, a laser local **oscillator** decoheres due to flicker-**frequency** (1/f) noise. The **oscillator** **frequency** is repeatedly corrected, based on projective measurements of the **qubits**, which are assumed not to decohere with one another.

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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**, both the effective nonlinearity and the threshold become a non-trivial...**qubit**-cavity detuning for the **qubit** prepared in the ground state in the...**qubit** manipulation pulse was applied immediately before the start of the...**oscillator** Q....**qubit**-**oscillator** model with N l = 7 show the avoided crossings in the ...**qubit** and may be used to realize a high fidelity, latching readout whose...**qubit** junctions (lower and upper insets)....**qubit**-**oscillator** detuning. Moreover, the autoresonant threshold is sensitive...**oscillator** is strongly coupled to a quantized superconducting **qubit**, both...**qubit** energy levels were modeled as a Duffing nonlinearity....**qubit** state. (a) Color plot shows S | 1 versus **qubit** detuning. The dashed...**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 ... 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: Makhlin, Yuriy, Shnirman, Alexander

Date: 2003-12-22

**qubit**’s density matrix). The term in Fig. F:2ordera gives...**oscillations** of the solid lines are compensated by the dashed line from...**qubit**’s 2 × 2 density matrix ρ ̂ , exp - i L 0 t θ t , where L 0 is the...low-**frequency**, e.g. 1/f noise, motivated by recent experiments with superconducting...**oscillations** of the solid lines in the diagrams and assuming very slow...**frequency** domain, one constrains the **frequency** of the dashed line to be...**qubit** in Fig. F:qb at the degeneracy point, where the charge noise is ...**qubit**. The simplest Josephson charge **qubit** is the Cooper-pair box shown...low-**frequency** noise is equivalent to that of quadratic longitudinal coupling...**oscillations** under the influence of both low- and high-**frequency** fluctuations...high-**frequency** dashed line. The relaxation process in e also contributes...**qubit**...**qubits** by transverse low-frequency noise ... We analyze the dissipative dynamics of a two-level quantum system subject to low-**frequency**, e.g. 1/f noise, motivated by recent experiments with superconducting quantum circuits. We show that the effect of transverse linear coupling of the system to low-**frequency** noise is equivalent to that of quadratic longitudinal coupling. We further find the decay law of quantum coherent **oscillations** under the influence of both low- and high-**frequency** fluctuations, in particular, for the case of comparable rates of relaxation and pure dephasing.

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Contributors: Meier, Florian, Loss, Daniel

Date: 2004-08-26

**frequency** is comparable to the coupling energy of micro-circuit and fluctuator...**oscillation** visibility. We also calculate the probability for Bogoliubov...**frequencies**, transitions to the second excited state of the superconducting...single-**frequency** **oscillations** with reduced visibility [Fig. Fig2(b)]....**Qubits**...single-**frequency** **oscillations** are restored. The fluctuator leads to a ...**oscillation** experiments....**oscillations** for a squbit-fluctuator system. The probability p 1 t to ...**oscillations** between quantum states of superconducting micro-circuits ...**frequencies** | b x | / h 100 M H z . We show next that, in this regime, ... Coherent Rabi **oscillations** between quantum states of superconducting micro-circuits have been observed in a number of experiments, albeit with a visibility which is typically much smaller than unity. Here, we show that the coherent coupling to background charge fluctuators [R.W. Simmonds et al., Phys. Rev. Lett. 93, 077003 (2004)] leads to a significantly reduced visibility if the Rabi **frequency** is comparable to the coupling energy of micro-circuit and fluctuator. For larger Rabi **frequencies**, transitions to the second excited state of the superconducting micro-circuit become dominant in suppressing the Rabi **oscillation** visibility. We also calculate the probability for Bogoliubov quasi-particle excitations in typical Rabi **oscillation** experiments.

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Contributors: Singh, Mandip

Date: 2014-07-01

flux-**qubit**-cantilever corresponds to a quantum entanglement between magnetic...**oscillation** ω i i.e. the **frequency** in absence of magnetic field. The external...**frequency** ( E / h ) is ∼ 4 × 10 11 Hz....**frequency** ( E / h ) is ∼ 3.9 × 10 11 Hz....**oscillator** is introduced that consists of a flux **qubit** in the form of ...flux-**qubit**-cantilever. When tunneling between wells is introduced the ...**oscillates** about an equilibrium angle θ 0 with an intrinsic **frequency** ...flux-**qubit**-cantilever interrupted by a single Josephson junction is...flux-**qubit**-cantilever. A part of the flux **qubit** (larger loop) is in the...flux-**qubit**-cantilever corresponds to a symmetric double well potential...**qubit** and the mechanical degrees of freedom of the cantilever are naturally...flux-**qubit**-cantilever to its ground state....**oscillation** **frequencies**, consider a flux-**qubit**-cantilever made of niobium...**frequencies** of the flux-**qubit**-cantilever are ω X ≃ 2 π × 7.99 × 10 10 ...**qubit** and the cantilever. An additional magnetic flux threading a DC-SQUID...**qubit** in the form of a cantilever. The magnetic flux linked to the flux...flux-**qubit**-cantilever is biased at a half of a flux quantum, Φ o / 2 ....**qubit**...**frequencies** are ω φ ≃ 2 π × 7.99 × 10 10 rad/s, ω δ = 2 π × 22384.5 ... In this paper a macroscopic quantum **oscillator** is introduced that consists of a flux **qubit** in the form of a cantilever. The magnetic flux linked to the flux **qubit** and the mechanical degrees of freedom of the cantilever are naturally coupled. The coupling is controlled through an external magnetic field. The ground state of the introduced flux-**qubit**-cantilever corresponds to a quantum entanglement between magnetic flux and the cantilever displacement.

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

Date: 2012-05-10

**qubit**-**oscillator** coupling ( g 2 = 0 ), resonant driving, Ω = ω 0 , and...**oscillator** damping γ = 0.02 ϵ . The amplitude A = 0.07 ϵ corresponds to...**qubit**-oscillator coupling ( g 2 = 0 ), resonant driving, Ω = ω 0 , and...**oscillator** damping γ . The driving amplitude is A = 3.5 γ , such that ...**qubit**-**oscillator** coupling ( g 1 = 0 ), resonant driving at large **frequency**...**qubit**-**oscillator** Hamiltonian to the dispersive frame and a subsequent ...**qubit** expectation value σ x which exhibits decaying oscillations with ...**qubit** expectation value σ x which exhibits decaying **oscillations** with **frequency** ϵ . The parameters correspond to an intermediate regime between...**qubit**-oscillator detuning and by considering also a coupling to the square...**qubit** coupled to a resonantly driven dissipative harmonic oscillator. ...**qubit**-oscillator coupling ( g 1 = 0 ), resonant driving at large frequency...**qubit**-**oscillator** master equation in the original frame....**qubit**-oscillator Hamiltonian to the dispersive frame and a subsequent ...**qubit** operator σ x (solid line) and the corresponding purity (dashed) ...**oscillator** damping γ = ϵ , the conditions for the validity of the (Markovian...**qubit** decoherence during dispersive readout...**qubit** decoherence under generalized dispersive readout, i.e., we investigate...**oscillator** coordinate, which is relevant for flux **qubits**. Analytical results...**qubit**-oscillator master equation in the original frame....**qubit** coupled to a resonantly driven dissipative harmonic **oscillator**. ...**qubit**-**oscillator** detuning and by considering also a coupling to the square ... We study **qubit** decoherence under generalized dispersive readout, i.e., we investigate a **qubit** coupled to a resonantly driven dissipative harmonic **oscillator**. We provide a complete picture by allowing for arbitrarily large **qubit**-**oscillator** detuning and by considering also a coupling to the square of the **oscillator** coordinate, which is relevant for flux **qubits**. Analytical results for the decoherence time are obtained by a transformation of the **qubit**-**oscillator** Hamiltonian to the dispersive frame and a subsequent master equation treatment beyond the Markov limit. We predict a crossover from Markovian decay to a decay with Gaussian shape. Our results are corroborated by the numerical solution of the full **qubit**-**oscillator** master equation in the original frame.

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Contributors: Bertet, P., Chiorescu, I., Semba, K., Harmans, C. J. P. M, Mooij, J. E.

Date: 2004-05-03

**qubit**’s energy level population....**frequency** f 2 at the value f 2 * and measured Rabi **oscillations** (black...**oscillations** with high visibility (65%)....**oscillations**....**frequency** to the **qubit** resonance and measured the switching probability...**qubit** by resonant activation...**frequency** of the **qubit** and (insert) persistent-current versus external...**qubit** and (insert) persistent-current versus external flux. The squares...**qubit** state, which we detect by resonant activation. With a measurement...**frequency**. fig4...**oscillations** at a Larmor **frequency** f q = 7.15 ~ G H z (b) Switching probability...**qubit** by fitting the **qubit** “step" appearing in the SQUID’s modulation ...high-**frequency** side of the peak. Thus the plasma **oscillator** non-linearity...**qubit** loop (the scale bar indicates 1 ~ μ m ). Two layers of Aluminium...**frequency** on the **qubit** state, which we detect by resonant activation. ...**qubit** states in a time shorter than the **qubit**’s energy relaxation time...**qubit** were determined by fitting spectroscopic measurements with the above...**oscillation** measured by DC current pulse (grey line, amplitude A = 40 ...**qubit**. It relies on the dependency of the measuring Superconducting Quantum ... We present the implementation of a new scheme to detect the quantum state of a persistent-current **qubit**. It relies on the dependency of the measuring Superconducting Quantum Interference Device (SQUID) plasma **frequency** on the **qubit** state, which we detect by resonant activation. With a measurement pulse of only 5ns, we observed Rabi **oscillations** with high visibility (65%).

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

Date: 2012-07-19

**qubit**, see Fig. gino:fig:return. Such an asymmetric **qubit** dependent response...**qubit** state measurement in circuit quantum electrodynamics...**qubit** and cavity are on resonance or far off-resonance (dispersive)....**oscillator** with its set of transition **frequencies** depending on the state...**qubit** and cavity are strongly coupled. We focus on the parameter ranges...**qubit** is detuned from the cavity ( ω q - ω c / 2 π ≈ 2 g ). It is followed...**qubit** frequency. (c) Wave packet snapshots at selected times (indicated...**qubit** quantum state discrimination and we present initial results for ...**qubit** state and it is realized where the cavity and **qubit** are strongly...**frequency**)....**oscillator**...**qubits** in the circuit quantum electrodynamics architecture, where the ...**qubit**. (d) The temporal evolution of the reduced density matrix | ρ m ...**qubit**, it is necessary to solve the coherent control problem...**oscillator** and we analyze the quantum and semi-classical dynamics. One...**oscillator** (Duffing **oscillator**) Duffing **oscillator**, constructed by making...**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...**qubit**; (c) for the model extended to one transmon **qubit** koch charge-insensitive...**qubit** **frequency**. (c) Wave packet snapshots at selected times (indicated...**qubit** being detuned. Due to the interaction with the **qubit**, the cavity...**qubits**...**frequency** of panel (b) conditioned on the initial state of the **qubit**. ...**qubit** decay times ( T 1 ), including a very long T 1 = 15 μ s indicating ... 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: Greenberg, Ya. S., Izmalkov, A., Grajcar, M., Il'ichev, E., Krech, W., Meyer, H. -G.

Date: 2002-08-07

**qubit** levels. The resulting Rabi oscillations of supercurrent in the **qubit**...**qubit**. According to the estimates for dephasing and relaxation times, ...**oscillations** in a phase **qubit**. The external source, typically in GHz range...**qubit**. The external source, typically in GHz range, induces transitions...**frequency** in MHz range....**qubit** in classical regime, when the hysteretic dependence of ground-state...**qubit**...**qubit** levels. The resulting Rabi **oscillations** of supercurrent in the **qubit**...**qubit**. Detailed calculation for zero and non-zero temperature are made...**qubit** coupled to a tank circuit....**oscillations** between quantum states in mesoscopic superconducting systems ... Time-domain observations of coherent **oscillations** between quantum states in mesoscopic superconducting systems were so far restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a new 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**. Detailed calculation for zero and non-zero temperature are made for the case of persistent current **qubit**. According to the estimates for dephasing and relaxation times, the effect can be detected using conventional rf circuitry, with Rabi **frequency** in MHz range.

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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

**qubit** lifetimes are relatively large across the full **qubit** spectrum with...**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...**qubit** inductively coupled to a single-mode, resonant cavity with a tunable...**qubit** anharmonicity α r versus **qubit** **frequency** ω 01 / 2 π (design A )....**qubit** flux bias is swept. Two different data sets (with the **qubit** reset...**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**...**qubit** anharmonicity as shown later in Fig. Fig9....**qubit** **frequencies**. In order to capture the maximum dispersive **frequency**...**qubit**, and residual bus coupling for a system with multiple **qubits**. With...**qubit** anharmonicity α r versus **qubit** frequency ω 01 / 2 π (design A )....**qubit** evolutions and optimize state readout during **qubit** measurements....**oscillation** decay time of T ' = 409 ns. (c) Ramsey **oscillations** versus...**qubit** is ...**qubit**) (see text)....**qubit** **frequenc**...**qubit** spectrum....**oscillations** gave T ' = 727 ns, a separate measurement of **qubit** energy...**frequency**, f c min ≈ 4.8 GHz. Notice in Fig. Fig6(a) that Rabi **oscillations**...**frequency** provides a way to strongly vary both the **qubit**-cavity detuning...**frequency** that allows for both microwave readout of tunneling and dispersive...**qubit** for various frequencies in order to excite the **qubit** transitions...**qubit** frequency change both Δ 01 and the **qubit**’s anharmonicity α . In ...**qubit** flux detuning near f 01 = 7.38 GHz. (d) Line-cut along the dashed ... 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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