### 57622 results for qubit oscillator frequency

Contributors: Poletto, S., Chiarello, F., Castellano, M. G., Lisenfeld, J., Lukashenko, A., Cosmelli, C., Torrioli, G., Carelli, P., Ustinov, A. V.

Date: 2008-09-08

**oscillation** **frequency** ω 0 depends on the amplitude of the manipulation...**qubit** is measured as a function of Φ x and Φ c fluxes and the switching...**qubits**. An other advantage of this type of **qubit** is its insensitivity ...**oscillation** **frequencies** for the corresponding pulse amplitudes....**qubit** is thus initialized in the chosen potential well. Next, the barrier...**qubit** initialization in the left or right well, and Φ x 1 equal to Φ 0...**oscillation** **frequency** could be tuned between 6 and 21 GHz by changing ...**oscillation** **frequencies** for different values of Φ c (open circles). Excellent...**oscillation** **frequency** as shown in Fig. fig:4(a). In Fig. fig:5, we plot...**oscillation** **frequency**, and (b) for different potential symmetry by detuning...**qubit** flux state is done by applying a bias current ramp to the dc SQUID...**qubit** by manipulating its energy potential with a nanosecond-long pulse...**oscillations** of a tunable superconducting flux **qubit** by manipulating its...**qubit** manipulation at which the **qubit** potential has a shape as indicated...**qubit** circuit. (b) The control flux Φ c changes the potential barrier ...**oscillate** at a **frequency** ranging from 6 GHz to 21 GHz, tunable via the...**qubit**....**qubit** initially prepared in the state, and for (a) different pulse amplitudes...**oscillation** **frequency**, as shown in Fig. fig:4(b), is consistent with ...**qubit** manipulated without microwaves ... We experimentally demonstrate the coherent **oscillations** of a tunable superconducting flux **qubit** by manipulating its energy potential with a nanosecond-long pulse of magnetic flux. The occupation probabilities of two persistent current states **oscillate** at a **frequency** ranging from 6 GHz to 21 GHz, tunable via the amplitude of the flux pulse. The demonstrated operation mode allows to realize quantum gates which take less than 100 ps time and are thus much faster compared to other superconducting **qubits**. An other advantage of this type of **qubit** is its insensitivity to both thermal and magnetic field fluctuations.

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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: 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: 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: 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: 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: 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: 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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