### 62755 results for qubit oscillator frequency

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...**qubits** are quasi-degenerate, i.e., with **frequencies** much smaller than ...**qubit**-**qubit** entanglement. Both number state and coherent state preparations...**qubits** are much smaller than the oscillator frequency and the coupling...**oscillator** **frequency**, ω 0 ≪ ω , while the coupling between the **qubits** ... a single qubit....two-qubit case. Qualitative differences between the single-qubit and the...**frequencies** of **oscillation**, 2 Ω N ω and 2 2 Ω N ω . Since three new basis...**oscillator** state with the lowest of the S x states. Note the breakup in... of two-qubit TC model derived within the RWA is valid. At resonance, ...**qubit** system as a consequence of having only one Rabi **frequency** in the...that the two-qubit analytic formula matches well to the corresponding ...**oscillator**. For an **oscillator** of mass M and **frequency** ω the zero point...one-**qubit** and (b.) two-**qubit** probability dynamics, and (c.) shows that... (a.) one-qubit and (b.) two-qubit probability dynamics, and (c.) shows... for the single qubit case....**frequencies** of the **qubits** are much smaller than the **oscillator** **frequency**...**qubit** interacting with a common **oscillator** mode is extended beyond the...single-**qubit** case where only one Rabi **frequency** determines the evolution...single qubit case....multi-qubit cases are highlighted. In particular, we study the collapse...to the two-qubit case. Qualitative differences between the single-qubit...**qubit** interacting with a common oscillator mode is extended beyond the...**qubits**...**qubit**....two-qubit case (Fig. f.collapse_revival_double). The RWA fails to describe...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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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: 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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### 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: 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: 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: 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: Schmidt, Thomas L., Borkje, Kjetil, Bruder, Christoph, Trauzettel, Bjoern

Date: 2010-02-25

**oscillator** and the **qubit** leads to... **qubit** and oscillator operators contained in** the **EVM ( chi). As mentioned...**qubit** is realized as a Cooper pair box (CPB, yellow). Its state can be...**qubit**-**oscillator** system modulates the tunneling amplitude γ of the APC...**qubit** and **oscillator** operators contained in the EVM ( chi). As mentioned...**frequency**-dependent noise S ω = ∑ X S X ω X as a function of δ 1 and ω...oscillator and **qubit** properties....**qubits** close to the quantum regime and to measure their properties with...**qubit** using** an** electronic measurement in** an** atomic point contact (APC)...**qubit**-oscillator entanglement in nanoelectromechanical systems...**frequencies** of the system, ω = 0 , Ω , 2 Δ . The complete expression for...**qubit** in a nanoelectromechanical setup. The detection scheme involves ... and the **qubit** leads to...**qubit**. This setup could allow for the first observation of entanglement...**oscillator** and a **qubit**. This setup could allow for the first observation...a qubit and an oscillator coupled to an atomic point contact (APC). Electrons...**oscillation** of the nanomechanical resonator (NR, green) modulates the ...The qubit is realized as a Cooper pair box (CPB, yellow). Its state can...**oscillator** and **qubit** properties....**qubit** and an **oscillator** coupled to an atomic point contact (APC). Electrons...oscillator-**qubit** system. This allows for** the **detection of entanglement ... Experiments over the past years have demonstrated that it is possible to bring nanomechanical resonators and superconducting **qubits** close to the quantum regime and to measure their properties with an accuracy close to the Heisenberg uncertainty limit. Therefore, it is just a question of time before we will routinely see true quantum effects in nanomechanical systems. One of the hallmarks of quantum mechanics is the existence of entangled states. We propose a realistic scenario making it possible to detect entanglement of a mechanical resonator and a **qubit** in a nanoelectromechanical setup. The detection scheme involves only standard current and noise measurements of an atomic point contact coupled to an **oscillator** and a **qubit**. This setup could allow for the first observation of entanglement between a continuous and a discrete quantum system in the solid state.

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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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Contributors: Cao, Xiufeng, You, J. Q., Zheng, H., Nori, Franco

Date: 2010-01-26

**oscillation** **frequency** for the low-**frequency** noise is ω 0 > Δ , in spite...and the **qubit**, where the parameters of the low-frequency bath are α / ...**qubit**, where the parameters of the low-**frequency** bath are α / Δ 2 = 0.1...high-**frequency** one) and protect the coherence of the **qubit** by modulating...**qubit** energy towards higher energies (blue shift), while the ordinary ...high-**frequency** cutoff Ohmic bath shifts the **qubit** energy towards lower...**qubit**, we also investigate the quantum Zeno effect in two cases: low- ...**qubit** and the bath. In the horizontal axis, the time-interval τ is multiplied...**qubit** in either a low- or high-frequency bath: A non-markovian approach...**qubit** energy towards lower energies (red shift). In order to preserve ...**qubit** in either a low- or high-**frequency** bath modeling the **qubit** environment...**qubit** by modulating the dominant frequency of its environment....**qubit** in the low-**frequency** bath is longer than in the high-**frequency** noise...the **qubit** and the bath. The time-interval τ is multiplied by the **qubit**...low-**frequency** noise, the bath shifts the **qubit** energy towards higher energies...the **qubit** energy spacing Δ . (a) The case of weak interaction between ...**qubit** in either a low- or high-frequency bath modeling the **qubit** environment...**qubit**. The quantum Zeno effect only occurs in the high-**frequency** cutoff...**qubit** energy difference Δ . The curves in (a) correspond to the case of...**qubit**, where the parameters of the low-**frequency** Lorentzian-type spectrum...**oscillation** **frequency** is ω 0 < Δ , corresponding to a red shift. The shifting ... We use a non-Markovian approach to study the decoherence dynamics of a **qubit** in either a low- or high-**frequency** bath modeling the **qubit** environment. This approach is based on a unitary transformation and does not require the rotating-wave approximation. We show that for low-**frequency** noise, the bath shifts the **qubit** energy towards higher energies (blue shift), while the ordinary high-**frequency** cutoff Ohmic bath shifts the **qubit** energy towards lower energies (red shift). In order to preserve the coherence of the **qubit**, we also investigate the quantum Zeno effect in two cases: low- and high-**frequency** baths. For very frequent projective measurements, the low-**frequency** bath gives rise to the quantum anti-Zeno effect on the **qubit**. The quantum Zeno effect only occurs in the high-**frequency** cutoff Ohmic bath, after considering counter-rotating terms. For a high-**frequency** environment, the decay rate should be faster (without frequent measurements) or slower (with frequent measurements, in the Zeno regime), compared to the low-**frequency** bath case. The experimental implementation of our results here could distinguish the type of bath (either a low- or high-**frequency** one) and protect the coherence of the **qubit** by modulating the dominant **frequency** of its environment.

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