### 62772 results for qubit oscillator frequency

Contributors: Beaudoin, Félix, da Silva, Marcus P., Dutton, Zachary, Blais, Alexandre

Date: 2012-08-09

**qubits** have **frequencies** separated enough that they do not overlap during...**the** **second** **qubit**. The fidelity is extracted by injecting these unitaries...two-**qubit** operations in circuit QED. ϵ is the strength of the drive used...**qubit**-resonator and **qubit**-**qubit** interactions. We discuss in detail how...anticrossings in the qubit-resonator or qubit-qubit spectrum. They are...**qubit** or the resonator, with the significant disadvantage that such implementations...of the fidelity on qubit relaxation and dephasing is similar....**oscillator** with **frequency** ω r = 7.8 GHz. As explained in Section sec:...**qubit** at the red sideband **frequency** assuming the second **qubit** is in its...two-**qubit** operations in circuit QED. ϵ is **the** strength of **the** drive used...**qubit** frequency modulation...**oscillators** (see Section sec:Duffing) with E J 1 = 25 GHz, E J 2 = 35...**qubit** splitting is modulated at a **frequency** that lies exactly between ...**frequency** associated to the operating point φ i . This **frequency** is illustrated...coming from the spectator qubit (see Section sec:SB)....prepare qubit-qubit entangled states. The parameters of every pulses entering...**qubits** and microwave resonators. Up to now, these transitions have been...**qubit** frequency using a flux-bias line. Not only can first-order transitions...**oscillations** have been seen to be especially large for big relevant ε ...**eqn**:trace). The qubits are taken to be transmons, which are modelled as...**oscillations** of the **qubit** **frequency** using a flux-bias line. Not only can...**oscillations** in the Rabi **oscillations** that reduce the fidelity. These ...**qubit** transition **frequencies** in and out of resonance without crossing ...**second** **qubit** is excited. Blue dashed line: population transfer error 1...**qubit** at **the** red sideband frequency assuming **the** **second** **qubit** is in its ... Sideband transitions have been shown to generate controllable interaction between superconducting **qubits** and microwave resonators. Up to now, these transitions have been implemented with voltage drives on the **qubit** or the resonator, with the significant disadvantage that such implementations only lead to second-order sideband transitions. Here we propose an approach to achieve first-order sideband transitions by relying on controlled **oscillations** of the **qubit** **frequency** using a flux-bias line. Not only can first-order transitions be significantly faster, but the same technique can be employed to implement other tunable **qubit**-resonator and **qubit**-**qubit** interactions. We discuss in detail how such first-order sideband transitions can be used to implement a high fidelity controlled-NOT operation between two transmons coupled to the same resonator.

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Contributors: Saito, Keiji, Wubs, Martijn, Kohler, Sigmund, Hanggi, Peter, Kayanuma, Yosuke

Date: 2006-03-07

**qubit** and the oscillator, and can be written as...**qubit**, being independent of the frequency of the QED mode. Possible applications...**qubit** flip, the resulting dynamics is restricted to the states | ↑ , 2...**qubit** and the **oscillator**, and can be written as...**frequencies** Ω . The dashed line marks the Ω -independent, final probability...individual qubit-oscillator states for a coupling strength γ = 0.6 ℏ v...large **qubit**-oscillator coupling γ / ℏ Ω = 0.5 , reliable single-photon...**frequency** Ω = 0.5 v / ℏ ....**oscillator** **frequency**, P ↑ ↓ t resembles the standard LZ transition with...**frequency** Ω and the **qubit**-**oscillator** coupling γ are determined by the ...**qubit**, being independent of the **frequency** of the QED mode. Possible applications...**qubit**-**oscillator** entanglement....**qubit**-**oscillator** states for a coupling strength γ = 0.6 ℏ v and **oscillator**...**qubit** comes into resonance with the **oscillator** sometime during the sweep...**qubit** undergoing Landau-Zener transitions enabled by the coupling to a...**oscillator** **frequency** Ω , despite the fact that this is not the case for...**qubit** is in state | ↓ is depicted in Fig. fig:one-osc. It demonstrates...the **qubit** comes into resonance with the oscillator sometime during the...**qubit**-oscillator entanglement....**oscillations** that are typical for the tail of a LZ transition are averaged ... We study a **qubit** undergoing Landau-Zener transitions enabled by the coupling to a circuit-QED mode. Summing an infinite-order perturbation series, we determine the exact nonadiabatic transition probability for the **qubit**, being independent of the **frequency** of the QED mode. Possible applications are single-photon generation and the controllable creation of **qubit**-**oscillator** entanglement.

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Contributors: Grajcar, M., Izmalkov, A., Il'ichev, E., Wagner, Th., Oukhanski, N., Huebner, U., May, T., Zhilyaev, I., Hoenig, H. E., Greenberg, Ya. S.

Date: 2003-03-31

**frequency** ω T . Then both amplitude v and phase shift χ (with respect...**qubit**, inductively coupled to a Nb LC tank circuit. The resonant properties...**the** **qubit** vs external flux. The dashed lines represent **the** classical potential...probing field to **the** **qubit**, and detects its response....**qubit**, which changes drastically as its flux states pass through degeneracy... **qubit** temperature has been verified [Fig. fig:Temp_dep(b)] to be **the**...**3JJ** **qubit**....** qubit’s** quantum properties, without using spectroscopy. In a range 50 ...

**oscillator**are sensitive to the effective susceptibility (or inductance...

**qubit**anticross [Fig. fig:schem(a)], with a gap of 2 Δ . Increasing ...

**qubit**states. Thus, the tank both applies the probing field to the

**qubit**...

**frequency**due to the change of the effective

**qubit**inductance by the tank...

**the**

**qubit**can adiabatically transform from Ψ l to Ψ r , staying in

**the**...

**qubit**...

**b**) Phase

**qubit**coupled to a tank circuit....

**qubit**vs external flux. The dashed lines represent the classical potential...saturation of

**the**effective

**qubit**temperature at 30 mK. (c) Full dip width...

**qubit**....

**qubit**temperature at 30 mK. (c) Full dip width at half the maximum amplitude...

**qubit**coupled to a tank circuit. ... We have observed signatures of resonant tunneling in an Al three-junction

**qubit**, inductively coupled to a Nb LC tank circuit. The resonant properties of the tank

**oscillator**are sensitive to the effective susceptibility (or inductance) of the

**qubit**, which changes drastically as its flux states pass through degeneracy. The tunneling amplitude is estimated from the data. We find good agreement with the theoretical predictions in the regime of their validity.

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

Date: 2009-10-23

**qubit** manipulation allows for much faster coherent operations....**oscillation** of the retrapping probability in one of the wells has a **frequency**...**qubit**. In the phase regime, the manipulation of the energy states is realized...phase qubit....**oscillation** **frequency** versus the normalized amplitude of the microwave...**qubit**, where the coherent evolution between the two flux states is induced... phase qubit by applying microwave pulses at 19 GHz. The oscillation frequency...**frequency** of the Larmor **oscillations**, the microwave-free **qubit** manipulation...**oscillation** and microwave-driven Rabi **oscillation** are rather similar. ...**oscillation** of the double SQUID manipulated as a phase **qubit** by applying...**oscillation** **frequency** changes from 540 MHz to 1.2 GHz by increasing the...**qubit**...**oscillation** **frequencies** versus amplitude of the short flux pulse (full...**qubit**. ... We report on two different manipulation procedures of a tunable rf SQUID. First, we operate this system as a flux **qubit**, where the coherent evolution between the two flux states is induced by a rapid change of the energy potential, turning it from a double well into a single well. The measured coherent Larmor-like **oscillation** of the retrapping probability in one of the wells has a **frequency** ranging from 6 to 20 GHz, with a theoretically expected upper limit of 40 GHz. Furthermore, here we also report a manipulation of the same device as a phase **qubit**. In the phase regime, the manipulation of the energy states is realized by applying a resonant microwave drive. In spite of the conceptual difference between these two manipulation procedures, the measured decay times of Larmor **oscillation** and microwave-driven Rabi **oscillation** are rather similar. Due to the higher **frequency** of the Larmor **oscillations**, the microwave-free **qubit** manipulation allows for much faster coherent operations.

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Contributors: Higgins, Kieran D. B., Lovett, Brendon W., Gauger, Erik M.

Date: 2012-03-27

**qubit** design but with an **oscillating** voltage applied to the CPB bias gate... qubits. The criterion for the single term approximation to be valid is...**qubit** and **oscillator**, thus requiring a theoretical treatment beyond the...**qubit** and oscillator, thus requiring a theoretical treatment beyond the...the qubit frequency Ω with temperature. The upper inset shows the dependence...**qubit** thermometry of an oscillator....**qubit** dynamics in this regime, based on an **oscillator** correlation function...**qubit** thermometry: T i n is the temperature supplied to the numerical ...**oscillations** with **frequency** ( eqn:rho3) to it. The blue line is the data...**qubit** thermometry of an **oscillator**....**qubit** dynamics. We obtain a new expression for the ac Stark shift and ...**qubit** dynamics in this regime, based on an oscillator correlation function...**oscillations** are also shown as a reference (green). Left: the population...**oscillator** Hilbert space at a point where the dynamics have converged ... the** qubit**. These parameters can be achieved experimentally using the

**sam**...

**frequency**of the

**qubit**dynamics is still adequately captured by our single...

**qubit**dynamics is still adequately captured by our single term approximation...

**qubit**

**frequency**Ω with temperature. The upper inset shows the dependence...

**oscillator**on the

**qubit**. These parameters can be achieved experimentally...

**oscillator**represents a ubiquitous physical system. New experiments in...

**frequency**domain. The full numerical solution was Fourier transformed ...the

**dynamics analytically unwieldy, because the rational function...**

**qubit****qubit**dynamics are not greatly perturbed by the presence of the

**oscillator**... the

**dynamics are not greatly perturbed by the presence of the oscillator...of qubit thermometry: T i n is the temperature supplied to the numerical ... A quantum two level system coupled to a harmonic**

**qubit****oscillator**represents a ubiquitous physical system. New experiments in circuit QED and nano-electromechanical systems (NEMS) achieve unprecedented coupling strength at large detuning between

**qubit**and

**oscillator**, thus requiring a theoretical treatment beyond the Jaynes Cummings model. Here we present a new method for describing the

**qubit**dynamics in this regime, based on an

**oscillator**correlation function expansion of a non-Markovian master equation in the polaron frame. Our technique yields a new numerical method as well as a succinct approximate expression for the

**qubit**dynamics. We obtain a new expression for the ac Stark shift and show that this enables practical and precise

**qubit**thermometry of an

**oscillator**.

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Contributors: Wubs, Martijn, Kohler, Sigmund, Hanggi, Peter

Date: 2007-03-15

**the** **qubit** would be measured | ↑ . fig:photon_averages...**the** **qubit** would be measured in state | ↓ ; **the** dash-dotted blue curve ...**qubit**-**oscillator** coupling γ . Parameters: γ = 0.25 ℏ v and ℏ Ω 2 = 100...**oscillator** depend on the state of the **qubit**....**qubit** coupled to one oscillator, far outside **the** RWA regime: γ = ℏ Ω =...the qubit. In general not much can be said about this final state, but...**qubit** coupled to two cavities, we show that Landau-Zener sweeps of the...**oscillator** **frequency**. In Fig. fig:photon_averages we depict how for a...**qubit** coupled to two **oscillators**. Parameters: γ = 0.25 ℏ v and Ω 2 = 100...**qubit**-**oscillator** coupling, then the dynamics can very well be approximated...**oscillator** if the **qubit** would be measured in state | ↓ ; the dash-dotted...**qubit**-oscillator entanglement, with state-of-the-art circuit QED as a ...**qubit**-**oscillator** entanglement, with state-of-the-art circuit QED as a ...**oscillator** energies ℏ Ω 1 , 2 are much larger than the **qubit**-**oscillator**...**qubit** are well suited for the robust creation of entangled cavity states...**qubit** coupled to one **oscillator**, far outside the RWA regime: γ = ℏ Ω =... of a qubit coupled to two oscillators. Parameters: γ = 0.25 ℏ v and Ω...**qubit** may undergo Landau-Zener transitions due to its coupling to one ...**qubit**-oscillator coupling γ . Parameters: γ = 0.25 ℏ v and ℏ Ω 2 = 100...final qubit-two-oscillator state | ψ ∞ rather than merely the transition...**oscillator** **frequencies**, both inside and outside the regime where a rotating-wave... final qubit state is | ↑ . We call this dynamical selection rule the ...**qubit** coupled to two **oscillators**. Parameters: γ = 0.25 ℏ v , ℏ Ω 1 = 90...**oscillators**. We show that for a **qubit** coupled to one **oscillator**, Landau-Zener...state of the qubit....**qubit** coupled to two oscillators with large energies, and with detunings...**qubit** coupled to one oscillator, Landau-Zener transitions can be used ...**qubit** coupled to two **oscillators** with degenerate energies. Parameters: ... A **qubit** may undergo Landau-Zener transitions due to its coupling to one or several quantum harmonic **oscillators**. We show that for a **qubit** coupled to one **oscillator**, Landau-Zener transitions can be used for single-photon generation and for the controllable creation of **qubit**-**oscillator** entanglement, with state-of-the-art circuit QED as a promising realization. Moreover, for a **qubit** coupled to two cavities, we show that Landau-Zener sweeps of the **qubit** are well suited for the robust creation of entangled cavity states, in particular symmetric Bell states, with the **qubit** acting as the entanglement mediator. At the heart of our proposals lies the calculation of the exact Landau-Zener transition probability for the **qubit**, by summing all orders of the corresponding series in time-dependent perturbation theory. This transition probability emerges to be independent of the **oscillator** **frequencies**, both inside and outside the regime where a rotating-wave approximation is valid.

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Contributors: Xia, K., Macovei, M., Evers, J., Keitel, C. H.

Date: 2008-10-14

**qubits** are non-degenerate, and only afterwards render the two **qubits** degenerate...**qubits** via dynamic control of the transition frequencies...**oscillates** at twice the **frequency** of the population **oscillation**, since...**qubit** transition frequencies via the external bias flux in order to maximize...**in **the degenerate two-qubit system of about F = 0.94 is achieved. Finally... flux qubits interacting with each other through their mutual inductance...**qubit** transition **frequencies** around the optimum point. In the figure, ...the two qubits have a frequency difference Δ t = 0 = Δ 0 = 18 γ 0 . Applying...**oscillators**. As our main result, we achieve controlled robust creation...**qubits** interacting with each other through their mutual inductance and...**frequency** Ω 0 = 15 γ 0 and detuning δ = 0 , the symmetric state | s reaches...**frequency** and detuning required for SCRAP....two-**qubit** system....the two qubits are non-degenerate, and only afterwards render the two ...**qubit** transition **frequencies** via the external bias flux in order to maximize...control the qubit transition frequencies around the optimum point. In ...**oscillators**. We present different schemes using continuous-wave control...flux qubits coupled to each other through their mutual inductance M ...The two-qubit Hamiltonian H Q **in **two-level approximation and rotating ...that the two qubits become degenerate, Δ γ 0 t ≥ 160 = 0 . It can be seen...The two qubit transition frequencies are adjusted via time-dependent bias...**oscillate** between | a and | s due to the applied field. This **oscillation**...**oscillations** as a function of δ 0 . The maximum concurrence C is larger...**qubit** transition **frequencies** are adjusted via time-dependent bias fluxes...**qubits** have a **frequency** difference Δ t = 0 = Δ 0 = 18 γ 0 . Applying a...**oscillations** at **frequency** 2 2 Ω 0 , while the amplitude of the subsequent...**qubits** are operated around the optimum point, and decoherence is modelled ... Coherent control and the creation of entangled states are discussed in a system of two superconducting flux **qubits** interacting with each other through their mutual inductance and identically coupling to a reservoir of harmonic **oscillators**. We present different schemes using continuous-wave control fields or Stark-chirped rapid adiabatic passages, both of which rely on a dynamic control of the **qubit** transition **frequencies** via the external bias flux in order to maximize the fidelity of the target states. For comparison, also special area pulse schemes are discussed. The **qubits** are operated around the optimum point, and decoherence is modelled via a bath of harmonic **oscillators**. As our main result, we achieve controlled robust creation of different Bell states consisting of the collective ground and excited state of the two-**qubit** system.

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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...**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...linear **qubit**-oscillator coupling ( g 2 = 0 ), resonant driving, Ω = ω ...**qubit**-oscillator detuning and by considering also a coupling to the square... **qubit** operator σ x (solid line) and the corresponding purity (dashed)...**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** operator σ x (solid line) and the corresponding purity (dashed) ...**qubit**-oscillator Hamiltonian to the dispersive frame and a subsequent ...**oscillator** damping γ = ϵ , the conditions for the validity of the (Markovian...**qubit** decoherence during dispersive readout...**oscillator** coordinate, which is relevant for flux **qubits**. Analytical results...**qubit** decoherence under generalized dispersive readout, i.e., we investigate...**qubit** coupled to a resonantly driven dissipative harmonic **oscillator**. ...**qubit**-**oscillator** detuning and by considering also a coupling to the square...**qubit**-oscillator master equation in the original frame. ... 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: 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....15 qubits, and improve upon the SQL variance by a factor of N -1 / 3 ....**oscillator** noise has an Allan deviation of 1 Hz....more qubits, the protocol of Bu...**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...more qubits can reduce clock instability, although the GHZ states yield...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: 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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