### 21982 results for qubit oscillator frequency

Contributors: Xian-Ting Liang

Date: 2008-09-03

The evolutions of reduced density matrix elements ρ12 (below) and ρ11 (up) in SB and SIB models in low-**frequency** bath. The parameters are the same as in Fig. 1.
...The spectral density functions Johm(ω) (b) and Jeff(ω) (a) versus the **frequency** ω of the bath modes, where Δ=5×109Hz,λκ=1,ξ=0.01,Ω0=10Δ,T=0.01K,Γ=2.6×1011Hz.
...The evolutions of reduced density matrix elements of ρ12 (below) and ρ11 (up) in SIB model in medium-**frequency** bath in different values of Ω0, the other parameters are the same as in Fig. 1.
...Using the numerical path integral method we investigate the decoherence and relaxation of **qubits** in spin-boson (SB) and spin-intermediate harmonic **oscillator** (IHO)-bath (SIB) models. The cases that the environment baths with low and medium **frequencies** are investigated. It is shown that the **qubits** in SB and SIB models have the same decoherence and relaxation as the baths with low **frequencies**. However, the **qubits** in the two models have different decoherence and relaxation as the baths with medium **frequencies**. The decoherence and relaxation of the **qubit** in SIB model can be modulated through changing the coupling coefficients of the **qubit**-IHO and IHO-bath and the **oscillation** **frequency** of the IHO....The response functions of the Ohmic bath in (a) low and (c) medium **frequencies** and effective bath in (b) low and (d) medium **frequencies**. The parameters are the same as in Fig. 1. The cut-off **frequencies** for the two cases are taken according to Fig. 2.
...The sketch map on the low-, medium-, and high-**frequency** baths.
... Using the numerical path integral method we investigate the decoherence and relaxation of **qubits** in spin-boson (SB) and spin-intermediate harmonic **oscillator** (IHO)-bath (SIB) models. The cases that the environment baths with low and medium **frequencies** are investigated. It is shown that the **qubits** in SB and SIB models have the same decoherence and relaxation as the baths with low **frequencies**. However, the **qubits** in the two models have different decoherence and relaxation as the baths with medium **frequencies**. The decoherence and relaxation of the **qubit** in SIB model can be modulated through changing the coupling coefficients of the **qubit**-IHO and IHO-bath and the **oscillation** **frequency** of the IHO.

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Contributors: Xian-Ting Liang

Date: 2007-12-05

The response functions of the Ohmic bath and effective bath, where Δ=5×109Hz, λκ=1050, ξ=0.01, Ω0=10Δ, T=0.01K, Γ=2.6×1011, the lower-**frequency** and high-**frequency** cut-off of the baths modes ω0=11Δ, and ωc=100Δ.
...Using the numerical path integral method we investigate the decoherence and relaxation of **qubits** coupled to an Ohmic bath directly and via an intermediate harmonic **oscillator** (IHO). Here, we suppose the **oscillation** **frequencies** of the bath modes are higher than the IHO’s. When we choose suitable parameters the **qubits** in the two models may have almost same decoherence and relaxation times. However, the decoherence and relaxation times of the **qubit** in the **qubit**-IHO-bath model can be modulated through changing the coupling coefficients of the **qubit**-IHO and IHO-bath and the **oscillation** **frequency** of the IHO. ... Using the numerical path integral method we investigate the decoherence and relaxation of **qubits** coupled to an Ohmic bath directly and via an intermediate harmonic **oscillator** (IHO). Here, we suppose the **oscillation** **frequencies** of the bath modes are higher than the IHO’s. When we choose suitable parameters the **qubits** in the two models may have almost same decoherence and relaxation times. However, the decoherence and relaxation times of the **qubit** in the **qubit**-IHO-bath model can be modulated through changing the coupling coefficients of the **qubit**-IHO and IHO-bath and the **oscillation** **frequency** of the IHO.

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Contributors: Mandip Singh

Date: 2015-07-14

A contour plot indicating location of two-dimensional potential energy minima forming a symmetric double well potential when the cantilever equilibrium angle θ0=cos−1[Φo/2BxA], ωi=2π×12000 rad/s, Bx=5×10−2 T. The contour interval in units of **frequency** (E/h) is ∼4×1011 Hz.
...In this paper a macroscopic quantum **oscillator** is proposed, which consists of a flux-**qubit** in the form of a cantilever. The net magnetic flux threading through the flux-**qubit** and the mechanical degrees of freedom of the cantilever are naturally coupled. The coupling between the cantilever and the magnetic flux is controlled through an external magnetic field. The ground state of the flux-**qubit**-cantilever turns out to be an entangled quantum state, where the cantilever deflection and the magnetic flux are the entangled degrees of freedom. A variant, which is a special case of the flux-**qubit**-cantilever without a Josephson junction, is also discussed....A superconducting-loop-**oscillator** with its axis of rotation along the z-axis consists of a closed superconducting loop without a Josephson Junction. The superconducting loop can be of any arbitrary shape.
...A contour plot indicating location of a two-dimensional global potential energy minimum at (nΦ0=0, θn+=π/2) and the local minima when the cantilever equilibrium angle θ0=π/2, ωi=2π×12000 rad/s, Bx=5.0×10−2 T. The contour interval in units of **frequency** (E/h) is ∼3.9×1011 Hz.
...The potential energy profile of the superconducting-loop-**oscillator** when the intrinsic **frequency** is 10 kHz. (a) For external magnetic field Bx=0, a single well harmonic potential near the minimum is formed. (b) Bx=0.035 T. (c) For Bx=0.045 T, a double well potential is formed.
...A schematic of the flux-**qubit**-cantilever. A part of the flux-**qubit** (larger loop) is projected from the substrate to form a cantilever. The external magnetic field Bx controls the coupling between the flux-**qubit** and the cantilever. An additional magnetic flux threading through a dc-SQUID (smaller loop) which consists of two Josephson junctions adjusts the tunneling amplitude. The dc-SQUID can be shielded from the effect of Bx.
... In this paper a macroscopic quantum **oscillator** is proposed, which consists of a flux-**qubit** in the form of a cantilever. The net magnetic flux threading through the flux-**qubit** and the mechanical degrees of freedom of the cantilever are naturally coupled. The coupling between the cantilever and the magnetic flux is controlled through an external magnetic field. The ground state of the flux-**qubit**-cantilever turns out to be an entangled quantum state, where the cantilever deflection and the magnetic flux are the entangled degrees of freedom. A variant, which is a special case of the flux-**qubit**-cantilever without a Josephson junction, is also discussed.

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Contributors: Martijn Wubs, Sigmund Kohler, Peter Hänggi

Date: 2007-10-01

(Color online) Upper panel: adiabatic energies during a LZ sweep of a **qubit** coupled to two **oscillators**. Parameters: γ=0.25ℏv and Ω2=100ℏv, both as in Fig. 4; ℏΩ1=80ℏv. Lower panel: probability P↑→↑(t) that the system stays in the initial state |↑00〉 (solid), and corresponding exact survival final survival probability P↑→↑(∞) of Eq. (20) (dotted).
...(Color online) LZ dynamics of a **qubit** coupled to one **oscillator**, far outside the RWA regime: γ=ℏΩ=0.25ℏv. The red solid curve is the survival probability P↑→↑(t) when starting in the initial state |↑0〉. The dotted black line is the exact survival probability P↑→↑(∞) based on Eq. (16). The dashed purple curve depicts the average photon number in the **oscillator** if the **qubit** would be measured in state |↓〉; the dash-dotted blue curve at the bottom shows the analogous average photon number in case the **qubit** would be measured |↑〉.
...(Color online) Upper panel: adiabatic energies during a LZ sweep of a **qubit** coupled to two **oscillators** with large energies, and with detunings of the order of the **qubit**–**oscillator** coupling γ. Parameters: γ=0.25ℏv and ℏΩ2=100ℏv, as before; ℏΩ1=96ℏv. Lower panel: probability P↑→↑(t) that the system stays in the initial state |↑00〉 (solid), and corresponding exact survival final survival probability P↑→↑(∞) of Eq. (20) (dotted).
...(Color online) Upper panel: adiabatic energies during a LZ sweep of a **qubit** coupled to two **oscillators**. Parameters: γ=0.25ℏv, ℏΩ1=90ℏv, and Ω2=100ℏv. Viewed on this scale of **oscillator** energies, the differences between exact and avoided level crossings are invisible. Lower panel: for the same parameters, probability P↑→↑(t) that the system stays in the initial state |↑00〉 (solid), and corresponding exact survival final survival probability P↑→↑(∞) of Eq. (20) (dotted).
...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....(Color online) Sketch of adiabatic eigenstates during LZ sweep of a **qubit** that is coupled to one **oscillator**. Starting in the ground state |↑0〉 and by choosing a slow LZ sweep, a single photon can be created in the **oscillator**. Due to cavity decay, the one-photon state will decay to a zero-photon state. Then the reverse LZ sweep creates another single photon that eventually decays to the initial state |↑0〉. This is a cycle to create single photons that can be repeated.
... 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: J.F. Ralph, T.D. Clark, M.J. Everitt, H. Prance, P. Stiffell, R.J. Prance

Date: 2003-10-20

Power spectral density for the low **frequency** **oscillator** at the resonance point (Φdc=0.00015Φ0) for the three spontaneous decay rates shown in Fig. 2: γ=0.005,0.05,0.5 per cycle. The other parameters are given in the text.
...(a) Close-up of the time-averaged (Floquet) energies of the single photon resonance (500 MHz), solid lines, with the time-independent energies given dotted lines. (b) The output power of the low **frequency** **oscillator** at 300 MHz, as a function of the static magnetic flux bias: γ=0.005 per cycle (solid line), γ=0.05 per cycle (crosses), γ=0.5 per cycle (circles). The other parameters are given in the text.
...We propose a method for characterising the energy level structure of a solid state **qubit** by monitoring the noise level in its environment. We consider a model persistent current **qubit** in a lossy reservoir and demonstrate that the noise in a classical bias field is a sensitive function of the applied field....Schematic diagram of persistent current **qubit** [6] inductively coupled to a (low **frequency**) classical **oscillator**. The insert graph shows the time-averaged (Floquet) energies as a function of the external bias field Φx1 for the parameters given in the text.
...Persistent current **qubit** ... We propose a method for characterising the energy level structure of a solid state **qubit** by monitoring the noise level in its environment. We consider a model persistent current **qubit** in a lossy reservoir and demonstrate that the noise in a classical bias field is a sensitive function of the applied field.

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Contributors: Alexander N. Korotkov

Date: 2005-03-01

We discuss an experimental proposal on quantum feedback control of a double-dot **qubit**, which seems to be within the reach of the present-day technology. Similar to the earlier proposal, the feedback loop is used to maintain the coherent **oscillations** in the **qubit** for an arbitrary long time; however, this is done in a significantly simpler way. The main idea is to use the quadrature components of the noisy detector current to monitor approximately the phase of **qubit** **oscillations**....Solid lines: synchronization degree D (and in-phase current quadrature 〈X〉) as functions of F for several values of the detection efficiency ηeff. Dashed and dotted lines illustrate the effects of the energy mismatch (ε≠0) and the **frequency** mismatch (Ω≠Ω0).
... We discuss an experimental proposal on quantum feedback control of a double-dot **qubit**, which seems to be within the reach of the present-day technology. Similar to the earlier proposal, the feedback loop is used to maintain the coherent **oscillations** in the **qubit** for an arbitrary long time; however, this is done in a significantly simpler way. The main idea is to use the quadrature components of the noisy detector current to monitor approximately the phase of **qubit** **oscillations**.

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Contributors: Yu.A. Pashkin, T. Yamamoto, O. Astafiev, Y. Nakamura, D.V. Averin, T. Tilma, F. Nori, J.S. Tsai

Date: 2005-01-01

Probe current **oscillations** in the first (a) and the second (b) **qubit** when the system is driven non-adiabatically to the double-degeneracy point X for the case EJ1=9.1GHz and EJ2=13.4GHz. Right panels show the corresponding spectra obtained by Fourier transformation. Arrows and dotted lines indicate theoretically expected position of the peaks.
...EJ1 dependence of the spectrum components of Fig. 6. Solid lines: dependence of Ω+ε and Ω−ε obtained from Eq. (6) using EJ2=9.1GHz and Em=14.5GHz and varying EJ1 from zero to its maximum value of 13.4GHz. Dashed lines: dependence of the **oscillation** **frequencies** of both **qubits** in the case of zero coupling (Em=0).
...Schematic diagram of the two-coupled-**qubit** circuit. Black bars denote Cooper pair boxes.
...Probe current **oscillations** in the first (a) and the second (b) **qubit** when the system is driven non-adiabatically to the points R and L, respectively. Right panels show the corresponding spectra obtained by the Fourier transform. Peak position in the spectrum gives the value of the Josephson energy of each **qubit**, indicated by arrow. In both cases, the experimental data (open triangles and open dots) can be fitted to a cosine dependence (solid lines) with an exponential decay with 2.5ns time constant.
...We have analyzed and measured the quantum coherent dynamics of a circuit containing two-coupled superconducting charge **qubits**. Each **qubit** is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Two **qubits** are coupled electrostatically by a small island overlapping both Cooper pair boxes. Quantum state manipulation of the **qubit** circuit is done by applying non-adiabatic voltage pulses to the common gate. We read out each **qubit** by means of probe electrodes connected to Cooper pair boxes through high-Ohmic tunnel junctions. With such a setup, the measured pulse-induced probe currents are proportional to the probability for each **qubit** to have an extra Cooper pair after the manipulation. As expected from theory and observed experimentally, the measured pulse-induced current in each probe has two **frequency** components whose position on the **frequency** axis can be externally controlled. This is a result of the inter-**qubit** coupling which is also responsible for the avoided level crossing that we observed in the **qubits**’ spectra. Our simulations show that in the absence of decoherence and with a rectangular pulse shape, the system remains entangled most of the time reaching maximally entangled states at certain instances....Solid-state **qubits** ... We have analyzed and measured the quantum coherent dynamics of a circuit containing two-coupled superconducting charge **qubits**. Each **qubit** is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Two **qubits** are coupled electrostatically by a small island overlapping both Cooper pair boxes. Quantum state manipulation of the **qubit** circuit is done by applying non-adiabatic voltage pulses to the common gate. We read out each **qubit** by means of probe electrodes connected to Cooper pair boxes through high-Ohmic tunnel junctions. With such a setup, the measured pulse-induced probe currents are proportional to the probability for each **qubit** to have an extra Cooper pair after the manipulation. As expected from theory and observed experimentally, the measured pulse-induced current in each probe has two **frequency** components whose position on the **frequency** axis can be externally controlled. This is a result of the inter-**qubit** coupling which is also responsible for the avoided level crossing that we observed in the **qubits**’ spectra. Our simulations show that in the absence of decoherence and with a rectangular pulse shape, the system remains entangled most of the time reaching maximally entangled states at certain instances.

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Contributors: Weidong Xie, Bingxin Chu, Suqing Duan, Yan Xie, Weidong Chu, Ning Yang, Xian-Geng Zhao

Date: 2015-08-01

Time evolution of the reduced probability inversion P˜′1(2)−P˜1(2) in the coupling region for ΩR=Tc (a), ΩR>Tc (b), and ΩRoscillation with the same ΩR in each case is shown in gray line.
...Dependence of instantaneous tunneling currents on Rabi **frequency** ΩR and tunneling rate Tc at t=tp (a), t=1.25tp (b), t=1.5tp (c), and t=2tp (d).
...We couple the Rabi **oscillation** in a double quantum dot (DQD) with the quantum tunneling in another DQD by Coulomb interaction between the neighboring dots. Such a coupling leads to correlation of the Rabi **oscillating** electron and the quantum tunneling one, and gives a tendency of synchronizing them under appropriate Rabi **frequency** ΩR and tunneling rate Tc. The correlated **oscillation** is shown clearly in the tunneling current. As ΩR=Tc, the Rabi **oscillation** and the quantum tunneling reach their strongest correlation and the two electrons finish their complete transitions simultaneously. And then, a single optical signal accomplishes a gang control of two electrons. This result encourages superior design of two-**qubit** quantum gates based on correlated DQDs....Rabi **oscillation**...(a) Schematic representation of a four-dot structure with an electron in Rabi **oscillation** and another one in quantum tunneling. (b) Time-average current spectrum as functions of ℏω and ε3 for Tc=ΩR=0.4GHz. (c) Schematic diagrams of FLIP operation.
... We couple the Rabi **oscillation** in a double quantum dot (DQD) with the quantum tunneling in another DQD by Coulomb interaction between the neighboring dots. Such a coupling leads to correlation of the Rabi **oscillating** electron and the quantum tunneling one, and gives a tendency of synchronizing them under appropriate Rabi **frequency** ΩR and tunneling rate Tc. The correlated **oscillation** is shown clearly in the tunneling current. As ΩR=Tc, the Rabi **oscillation** and the quantum tunneling reach their strongest correlation and the two electrons finish their complete transitions simultaneously. And then, a single optical signal accomplishes a gang control of two electrons. This result encourages superior design of two-**qubit** quantum gates based on correlated DQDs.

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Contributors: Jürgen Audretsch, Felix E. Klee, Thomas Konrad

Date: 2007-01-29

Comparison between simulated evolution of a **qubit's** Rabi **oscillations** and processed measurement signal for p¯=0.5, Δp=0.1 and τ=TR/16. Dashed curve: |c1|2 over time (in units of the Rabi period TR) in the presence of weak measurements. Dotted curve: |c1|2 over time in the absence of measurements. The solid curve corresponds to the evolution of the estimate g based on the measurement results.
...We present a new scheme to detect and visualize **oscillations** of a single quantum system in real time. The scheme is based upon a sequence of very weak generalized measurements, distinguished by their low disturbance and low information gain. Accumulating the information from the single measurements by means of an appropriate Bayesian estimator, the actual **oscillations** can be monitored nevertheless with high accuracy and low disturbance. For this purpose only the minimum and the maximum expected **oscillation** **frequency** need to be known. The accumulation of information is based on a general derivation of the optimal estimator of the expectation value of a Hermitian observable for a sequence of measurements. At any time it takes into account all the preceding measurement results....Power spectrum of |c1|2 in the presence of measurements. It assumes its maximum at the **frequency** ΩR of the undisturbed Rabi **oscillations**.
... We present a new scheme to detect and visualize **oscillations** of a single quantum system in real time. The scheme is based upon a sequence of very weak generalized measurements, distinguished by their low disturbance and low information gain. Accumulating the information from the single measurements by means of an appropriate Bayesian estimator, the actual **oscillations** can be monitored nevertheless with high accuracy and low disturbance. For this purpose only the minimum and the maximum expected **oscillation** **frequency** need to be known. The accumulation of information is based on a general derivation of the optimal estimator of the expectation value of a Hermitian observable for a sequence of measurements. At any time it takes into account all the preceding measurement results.

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Contributors: Peihao Huang, Hang Zheng

Date: 2010-11-19

Diagrammatic sketch of a **qubit** coupled with structured environments. The environment in the 1st case consists of a two level system coupled to a bath. The environment in 2nd case is a damped harmonic **oscillator**.
...(1st case) P(t) as a function of time for the on-resonance case (ΔA=ΔB), where the decoherence is enhanced with T. Inset (a): Fourier analysis of P(t). One can see that two **frequencies** are dominating the dynamics and the peaks locate at ΔA±g0. Inset (b): The effective spectral density Jeff(ω). Here, it is not πJeff(ΔA) but πJeff(ΔA±g0) indicates the damping rate γA.
...The dynamics of a **qubit** in two different environments are investigated theoretically. The first environment is a two level system coupled to a bosonic bath. And the second one is a damped harmonic **oscillator**. Based on a unitary transformation, we find that the decoherence of the **qubit** can be reduced with increasing temperature T in the first case, which agree with the results in Ref. [8], whereas, it cannot be reduced with T in the second case. In both cases, the **qubit** dynamics are changed substantially as the coupling increases or finite detuning appears....(2nd case) P(t) as a function of time, where the decoherence is enhanced with T. Inset (a): Fourier analysis of the main plot. One sees that two **frequencies** are dominating the dynamics and the splitting of the peaks increases with temperature. Inset (b): The effective spectral density Jeff(ω). The square, triangle and circle points correspond to the dominant **frequencies** of P(t) in different temperatures, respectively. One can see that smaller Jeff’s, which characterize long time dynamics, are almost the same for three different temperatures. This is the reason why the damping rate of P(t) is almost not changing with different temperatures.
... The dynamics of a **qubit** in two different environments are investigated theoretically. The first environment is a two level system coupled to a bosonic bath. And the second one is a damped harmonic **oscillator**. Based on a unitary transformation, we find that the decoherence of the **qubit** can be reduced with increasing temperature T in the first case, which agree with the results in Ref. [8], whereas, it cannot be reduced with T in the second case. In both cases, the **qubit** dynamics are changed substantially as the coupling increases or finite detuning appears.

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