### 57529 results for qubit oscillator frequency

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: Zhirov, O. V., Shepelyansky, D. L.

Date: 2007-10-10

**qubit** coupled to a quantum dissipative driven oscillator (resonator). ...**qubit** polarization with polarization angles θ φ defined in text (right...**qubit** synchronization is illustrated in a more clear way in Fig. fig2...**oscillator** with x = â + â / 2 , p = â - â / 2 i (left) and for **qubit** polarization...**qubit** with radiation suppression at **qubit** frequency Ω = 1.2 ω 0 and appearance...**frequency** of effective Rabi **oscillations** between quasi-degenerate levels...**oscillator** performs circle rotations in p x plane with **frequency** ω while...**qubit** radiation spectrum with appearance of narrow lines corresponding...**qubit** coupled to a driven dissipative oscillator...**qubit** exhibits tunneling between two orientations with a macroscopic change...**qubit** coupled to a driven **oscillator** with jumps between two metastable...**qubit** polarization phase φ vs. oscillator phase ϕ ( p / x = - tan ϕ ) ...**qubit** rotations become synchronized with the oscillator phase. In the ...**qubit** radiation ξ z t as function of driving power n p in presence of ...**qubit** polarization components ξ x and ξ z (full and dashed curves) on ...**qubit** frequency Ω / ω 0 for parameters of Fig. fig1; N f are computed...**qubit** **frequency** Ω / ω 0 for parameters of Fig. fig1; N f are computed...**qubit** polarization phase φ vs. **oscillator** phase ϕ ( p / x = - tan ϕ ) ...**qubit** rotations become synchronized with the **oscillator** phase. In the ...**qubit** with radiation suppression at **qubit** **frequency** Ω = 1.2 ω 0 and appearance...**oscillator** in two metastable states on the driving **frequency** ω (average...**qubit** coupled to a quantum dissipative driven **oscillator** (resonator). ...**qubit** (right) coupled by quantum tunneling (the angles are determined ... We study numerically the behavior of **qubit** coupled to a quantum dissipative driven **oscillator** (resonator). Above a critical coupling strength the **qubit** rotations become synchronized with the **oscillator** phase. In the synchronized regime, at certain parameters, the **qubit** exhibits tunneling between two orientations with a macroscopic change of number of photons in the resonator. The life times in these metastable states can be enormously large. The synchronization leads to a drastic change of **qubit** radiation spectrum with appearance of narrow lines corresponding to recently observed single artificial-atom lasing [O. Astafiev {\it et al.} Nature {\bf 449}, 588 (2007)].

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Contributors: Catelani, G., Schoelkopf, R. J., Devoret, M. H., Glazman, L. I.

Date: 2011-06-04

anharmonic **qubit**, such as the transmon and phase qubits. We start with...**qubit**, such as the transmon and phase **qubits**. We start with the the semiclassical...**qubit** controlled by a magnetic flux, see Eq. ( Hphi). (b) Effective circuit...**qubit** biased at Φ e = Φ 0 / 2 with E J / E L = 10 . The horizontal lines.../ 2 **qubit**-quasiparticle coupling in Eq. ( HTle) has a striking effect ...**qubit** sate. The results of Sec. sec:semi are valid for transitions between...**qubit** resonant frequency. In the semiclassical regime of small E C , the...the **qubit** states | - , | + are respectively symmetric and antisymmetric...**qubits**. The interaction of the **qubit** degree of freedom with the quasiparticles...**frequency** [cf. Eq. ( pl_fr)]...**qubit** frequency in the presence of quasiparticles....**frequency** is given by Eq. ( Gnn) with ϕ 0 = 0 and is independent of n ...**qubit** **frequency** in the presence of quasiparticles....**oscillations** of the energy levels are exponentially small, see Appendix...**qubit** resonant **frequency**. In the semiclassical regime of small E C , the...**qubit** properties in devices such as the phase and flux **qubits**, the split...**qubits**...**qubit** can be described by the effective circuit of Fig. fig1(b), with...**frequency** ω p , Eq. ( pl_fr)] and nearly degenerate levels whose energies...**qubit** decay rate induced by quasiparticles, and we study its dependence...**frequency** ω p , Eq. ( pl_fr), and give, for example, the rate Γ 1 0 . ... As low-loss non-linear elements, Josephson junctions are the building blocks of superconducting **qubits**. The interaction of the **qubit** degree of freedom with the quasiparticles tunneling through the junction represent an intrinsic relaxation mechanism. We develop a general theory for the **qubit** decay rate induced by quasiparticles, and we study its dependence on the magnetic flux used to tune the **qubit** properties in devices such as the phase and flux **qubits**, the split transmon, and the fluxonium. Our estimates for the decay rate apply to both thermal equilibrium and non-equilibrium quasiparticles. We propose measuring the rate in a split transmon to obtain information on the possible non-equilibrium quasiparticle distribution. We also derive expressions for the shift in **qubit** **frequency** in the presence of quasiparticles.

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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...**qubit** state in this setup....**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...**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...**qubit**. In the 2D density plot Fig. fig:2DRabi, Rabi **oscillations** are ...**qubit** population P is plotted versus Δ t in Fig. fig:rabioscillationsa...**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** with Dispersive Readout...**qubit** state by coupling the **qubit** non-resonantly to a transmission line...**qubit**. In each panel the dashed lines correspond to the expected measurement...**oscillations** with Rabi pulse length Δ t , pulse **frequency** ω s and amplitude...**qubit** population P vs. Rabi pulse length Δ t (blue dots) and fit with ...**qubit**, a visibility in the population of the **qubit** excited state that ...**qubit** transition frequency ω a = ω s + 2 π ν R a m s e y ....**oscillations** in a superconducting **qubit**, a visibility in the population...**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: Chen, Yu, Sank, D., O'Malley, P., White, T., Barends, R., Chiaro, B., Kelly, J., Lucero, E., Mariantoni, M., Megrant, A.

Date: 2012-09-09

**qubits** can be read out simultaneously using **frequency** multiplexing on ...**qubit** in the ground state | g stays in the left well ( L ). (b) Readout...four-**qubit** sample. F B 1 - 4 are control lines for each **qubit** and R R ...**qubits** used in Ref. 6. In this experiment, we drove Rabi **oscillations** ...**qubit** to a separate lumped-element superconducting readout resonator, ...**qubit** flux bias, with no averaging. See text for details. fig.phase...**qubits** can be read out simultaneously using frequency multiplexing on ...**oscillations** for **qubits** Q 1 - Q 4 respectively, with the **qubits** driven...**frequencies** for the **qubit** in the left and right wells, marked by the dashed...**oscillations** in panels (a)-(d) compared to the multiplexed readout in ...**frequency** for maximum visibility. (b) Reflected phase as a function of...**qubit** Josephson junction. Each **qubit** is coupled to its readout resonator...**qubits**. Using a quantum circuit with four phase **qubits**, we couple each...**qubits**, a significant advantage for scaling up to larger numbers of **qubits**...**frequency**-multiplexed readout. Multiplexed readout signals I p and Q p...**qubit**’s | g ↔ | e transition and read out the **qubit** states simultaneously...**qubit** was projected onto the | g or the | e state....**qubit** | g ↔ | e transition frequency of 6-7 GHz), with loaded resonance...**qubits** Q 1 to Q 4 . We then drove each **qubit** separately using an on-resonance...**qubit** projective measurement, where a current pulse allows a **qubit** in ...**frequency** shifts as large as ∼ 150 kHz for the **qubit** between the two wells...**frequency** (averaged 900 times), for the **qubit** in the left ( L , blue) ...**qubit** chip. Reflected signals pass back through the circulator, through...**frequency**-multiplexed readout scheme for superconducting phase **qubits**....**qubits**, we couple each **qubit** to a separate lumped-element superconducting...**oscillations** measured simultaneously for all the **qubits**, using the same...**frequency**, with the **qubit** prepared first in the left and then in the right...**qubits** ... We introduce a **frequency**-multiplexed readout scheme for superconducting phase **qubits**. Using a quantum circuit with four phase **qubits**, we couple each **qubit** to a separate lumped-element superconducting readout resonator, with the readout resonators connected in parallel to a single measurement line. The readout resonators and control electronics are designed so that all four **qubits** can be read out simultaneously using **frequency** multiplexing on the one measurement line. This technology provides a highly efficient and compact means for reading out multiple **qubits**, a significant advantage for scaling up to larger numbers of **qubits**.

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Contributors: Vierheilig, Carmen, Bercioux, Dario, Grifoni, Milena

Date: 2010-10-22

**qubit** dynamics is investigated. In particular, an analytic formula for...**qubit**’s evolution described by q t . This can be achieved within an effective...**qubit**, an intermediate nonlinear oscillator and an Ohmic bath. linearbath...**qubit** plus **oscillator** system (yellow (light grey) box) and accounts afterwards...**qubit** dynamics. The comparison of linear versus nonlinear case is done...**qubit** coupled to a nonlinear quantum **oscillator**, the latter coupled to...**oscillator** (red (dark grey) box). In the harmonic approximation the effective...**oscillator**. To determine the actual form of the susceptibility, we consider...**qubit**, an intermediate nonlinear **oscillator** and an Ohmic bath. linearbath...**qubit**, -the system of interest-, coupled to a nonlinear quantum **oscillator**...**qubit**, -the system of interest-, coupled to a nonlinear quantum oscillator...**frequency**, as shown in Fig. CompLorentz....**oscillator** within linear response theory in the driving amplitude. Knowing...**qubit** dynamics: In the first approach one determines the eigenvalues and...**qubit** coupled to a nonlinear quantum oscillator, the latter coupled to...**frequencies** with respect to the linear case. As a consequence the relative...**qubit** state we couple the **qubit** linearly to the oscillator with the coupling...**oscillator** and the Ohmic bath are put together, as depicted in Figure ...**qubit** dynamics. This composed system can be mapped onto that of a **qubit**...**qubit**-nonlinear **oscillator** system....**qubit**-nonlinear oscillator system....**qubit**'s population difference is derived. Within the regime of validity...**qubit** plus oscillator system (yellow (light grey) box) and accounts afterwards...**qubit** coupled to a dissipative nonlinear quantum oscillator: an effective...**qubit** state we couple the **qubit** linearly to the **oscillator** with the coupling...**qubit** dynamics. ... We consider a **qubit** coupled to a nonlinear quantum **oscillator**, the latter coupled to an Ohmic bath, and investigate the **qubit** dynamics. This composed system can be mapped onto that of a **qubit** coupled to an effective bath. An approximate mapping procedure to determine the spectral density of the effective bath is given. Specifically, within a linear response approximation the effective spectral density is given by the knowledge of the linear susceptibility of the nonlinear quantum **oscillator**. To determine the actual form of the susceptibility, we consider its periodically driven counterpart, the problem of the quantum Duffing **oscillator** within linear response theory in the driving amplitude. Knowing the effective spectral density, the **qubit** dynamics is investigated. In particular, an analytic formula for the **qubit**'s population difference is derived. Within the regime of validity of our theory, a very good agreement is found with predictions obtained from a Bloch-Redfield master equation approach applied to the composite **qubit**-nonlinear **oscillator** system.

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Contributors: Shahriar, M. S., Pradhan, Prabhakar

Date: 2002-12-19

**oscillation** from the plot in (a). (c) The time-dependence of the Rabi **frequency**. Inset: BSO as a function of the absolute phase of the field...**qubit** operations due to the Bloch-Siegert Oscillation...**frequency** is comparable to the Bohr **frequency** so that the rotating wave...low-**frequency** transitions. We present a scheme for observing this effect...**oscillation**. (b) The BSO **oscillation** (amplified scale) by itself, produced...**oscillation** is present with the Rabi **oscillation**. We discuss how the sensitivity...**Oscillation** (BSO): (a) The population of state | 1 , as a function of ... We show that if the Rabi **frequency** is comparable to the Bohr **frequency** so that the rotating wave approximation is inappropriate, an extra **oscillation** is present with the Rabi **oscillation**. We discuss how the sensitivity of the degree of excitation to the phase of the field may pose severe constraints on precise rotations of quantum bits involving low-**frequency** transitions. We present a scheme for observing this effect in an atomic beam.

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Contributors: Du, Lingjie, Yu, Yang

Date: 2010-12-13

**qubit** but also the systems with no crossover structure, e.g. phase **qubits**...**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...**qubits**. The interaction between **qubits** and electromagnetic fields can ...**qubit** population versus energy detuning and microwave amplitude. (a). ...**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 ...**qubit** states, leading to quantum interference in a microwave driven **qubit**...**qubits** and their environment. It also supplies a useful tool to characterize...**qubit** are identical with Fig. 4 (a)....**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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Contributors: Agarwal, S., Rafsanjani, S. M. Hashemi, Eberly, J. H.

Date: 2012-01-13

**qubit** case....**qubit** system is extended to the multi-**qubit** case. For a two-**qubit** system...single-**qubit** case where only one Rabi frequency determines the evolution...two-**qubit** analytic formula matches well to the corresponding numerical...**qubits** are quasi-degenerate, i.e., with **frequencies** much smaller than ...**qubits** are coupled to the **oscillator** so strongly, or are so far detuned...**oscillator**. For an **oscillator** of mass M and **frequency** ω the zero point...**oscillator** is allowed to be an appreciable fraction of the **oscillator** **frequency**. In this parameter regime, the dynamics of the system can neither...one-**qubit** and (b.) two-**qubit** probability dynamics, and (c.) shows that...**qubit**-**qubit** entanglement. Both number state and coherent state preparations...**frequencies** of the **qubits** are much smaller than the **oscillator** **frequency**...**qubit** interacting with a common **oscillator** mode is extended beyond the...two-**qubit** TC model derived within the RWA is valid. At resonance, the ...**qubits** are much smaller than the oscillator frequency and the coupling...two-**qubit** numerical evaluation, which comes from the ω - 2 ω beat note...**oscillator** **frequency**, ω 0 ≪ ω , while the coupling between the **qubits** ...**qubits** can be seen....two-**qubit** case. Qualitative differences between the single-**qubit** and the...two-**qubit** TC model beyond the validity regime of RWA. The regime of parameters...**qubit** interacting with a common oscillator mode is extended beyond the...**qubits**...**qubit**....**oscillator** state with the lowest of the S x states. Note the breakup in...two-**qubit** dynamics that are different from the single **qubit** case, including ... The Tavis-Cummings model for more than one **qubit** interacting with a common **oscillator** mode is extended beyond the rotating wave approximation (RWA). We explore the parameter regime in which the **frequencies** of the **qubits** are much smaller than the **oscillator** **frequency** and the coupling strength is allowed to be ultra-strong. The application of the adiabatic approximation, introduced by Irish, et al. (Phys. Rev. B \textbf{72}, 195410 (2005)), for a single **qubit** system is extended to the multi-**qubit** case. For a two-**qubit** system, we identify three-state manifolds of close-lying dressed energy levels and obtain results for the dynamics of intra-manifold transitions that are incompatible with results from the familiar regime of the RWA. We exhibit features of two-**qubit** dynamics that are different from the single **qubit** case, including calculations of **qubit**-**qubit** entanglement. Both number state and coherent state preparations are considered, and we derive analytical formulas that simplify the interpretation of numerical calculations. Expressions for individual collapse and revival signals of both population and entanglement are derived.

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