### 21982 results for qubit oscillator frequency

Contributors: D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, M.H. Devoret, C. Urbina, D. Esteve

Date: 2003-05-01

Top: Rabi **oscillations** of the switching probability p (5×104 events) measured just after a resonant microwave pulse of duration τ. Solid line is a fit used to determine the Rabi **frequency**. Bottom: test of the linear dependence of the Rabi **frequency** with Uμw.
...Electrical circuits can behave quantum mechanically when decoherence induced by uncontrolled degrees of freedom is sufficiently reduced. Recently, different nanofabricated superconducting circuits based on Josephson junctions have achieved a degree of quantum coherence sufficient to allow the manipulation of their quantum state with NMR-like techniques. Because of their potential scalability, these quantum circuits are presently considered for implementing quantum bits, which are the building blocks of the proposed quantum processors. We have operated such a Josephson **qubit** circuit in which a long coherence time is obtained by decoupling the **qubit** from its readout circuit during manipulation. We report pulsed microwave experiments which demonstrate the controlled manipulation of the **qubit** state....(A) Calculated transition **frequency** ν01 as a function of φ and Ng. (B) Measured center transition **frequency** (symbols) as a function of reduced gate charge Ng for reduced flux φ=0 (right panel) and as a function of φ for Ng=0.5 (left panel), at 15mK. Spectroscopy is performed by measuring the switching probability p (105 events) when a continuous microwave irradiation of variable **frequency** is applied to the gate before readout. Continuous line: best fits used to determine circuit parameters. Inset: Narrowest line shape, obtained at the saddle point (Lorentzian fit with a FWHM Δν01=0.8MHz).
... Electrical circuits can behave quantum mechanically when decoherence induced by uncontrolled degrees of freedom is sufficiently reduced. Recently, different nanofabricated superconducting circuits based on Josephson junctions have achieved a degree of quantum coherence sufficient to allow the manipulation of their quantum state with NMR-like techniques. Because of their potential scalability, these quantum circuits are presently considered for implementing quantum bits, which are the building blocks of the proposed quantum processors. We have operated such a Josephson **qubit** circuit in which a long coherence time is obtained by decoupling the **qubit** from its readout circuit during manipulation. We report pulsed microwave experiments which demonstrate the controlled manipulation of the **qubit** state.

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Contributors: J.R. Petta, A.C. Johnson, J.M. Taylor, A. Yacoby, M.D. Lukin, C.M. Marcus, M.P. Hanson, A.C. Gossard

Date: 2006-08-01

We demonstrate high-speed manipulation of a few-electron double quantum dot. In the one-electron regime, the double dot forms a charge **qubit**. Microwaves are used to drive transitions between the (1,0) and (0,1) charge states of the double dot. A local quantum point contact charge detector measures the photon-induced change in occupancy of the charge states. Charge detection is used to measure T1∼16ns and also provides a lower bound estimate for T2* of 400ps for the charge **qubit**. In the two-electron regime we use pulsed-gate techniques to measure the singlet–triplet relaxation time for nearly-degenerate spin states. These experiments demonstrate that the hyperfine interaction leads to fast spin relaxation at low magnetic fields. Finally, we discuss how two-electron spin states can be used to form a logical spin **qubit**....Microwave spectroscopy of a one-electron double dot. (a) Charge occupancy of the left dot, M, as a function of ε for several microwave **frequencies**. (b) One-half of the resonance peak splitting as a function of f for several values of VT. Solid lines are best fits to the experimental data using the theory outlined in the text. Inset: Two-level system energy level diagram. (c) Amplitude of the resonance, expressed as Mmax(τ)/Mmax(τ=5ns), as a function of chopped cw period, τ, with f=19GHz. Theory gives a best fit T1=16ns (solid line, see text). Inset: Single photon peak shown in a plot of M as a function of ε for τ=5ns and 1μs. (d) Power dependence of the resonance for f=24GHz. Widths are used to extract the ensemble-averaged charge dephasing time T2*. At higher microwave powers multiple photon processes occur. Curves are offset by 0.3 for clarity.
...Rabi **oscillation**...Spin **qubit**...Charge **qubit** ... We demonstrate high-speed manipulation of a few-electron double quantum dot. In the one-electron regime, the double dot forms a charge **qubit**. Microwaves are used to drive transitions between the (1,0) and (0,1) charge states of the double dot. A local quantum point contact charge detector measures the photon-induced change in occupancy of the charge states. Charge detection is used to measure T1∼16ns and also provides a lower bound estimate for T2* of 400ps for the charge **qubit**. In the two-electron regime we use pulsed-gate techniques to measure the singlet–triplet relaxation time for nearly-degenerate spin states. These experiments demonstrate that the hyperfine interaction leads to fast spin relaxation at low magnetic fields. Finally, we discuss how two-electron spin states can be used to form a logical spin **qubit**.

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Contributors: Sun Jia-kui, Li Hong-juan, Jing-lin Xiao

Date: 2009-07-01

We study the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to the LO-phonon in a quantum dot with triangular bound potential by using the Pekar variational method. This system may be used as a two-level **qubit**. Our numerical results indicate that the **oscillation** period of the **qubit** is an increasing function of the confinement length, whereas it is a decreasing one of the electron-LO-phonon coupling constant. The influence of the confinement length on the **oscillation** period is dominant when the electron-LO-phonon coupling constant decreases, while the effect of the coupling constant on that is strong when the confinement length increases. Meanwhile, the **oscillating** period of the **qubit** and the electron probability density vary periodically with respect to the polar angle....**Qubit**...The relational curves of the **oscillation** period T of the **qubit** to the electron-LO-phonon coupling constant α and the polar angle θ.
...The **oscillation** period T changes with the confinement length l0 and the electron-LO-phonon coupling constant α.
...The relational curves of the **oscillation** period T to the confinement length l0 and the polar angle θ.
... We study the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to the LO-phonon in a quantum dot with triangular bound potential by using the Pekar variational method. This system may be used as a two-level **qubit**. Our numerical results indicate that the **oscillation** period of the **qubit** is an increasing function of the confinement length, whereas it is a decreasing one of the electron-LO-phonon coupling constant. The influence of the confinement length on the **oscillation** period is dominant when the electron-LO-phonon coupling constant decreases, while the effect of the coupling constant on that is strong when the confinement length increases. Meanwhile, the **oscillating** period of the **qubit** and the electron probability density vary periodically with respect to the polar angle.

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Contributors: Jonas Buchli, Ludovic Righetti, Auke Jan Ijspeert

Date: 2008-08-01

Typical convergence of an adaptive **frequency** **oscillator** (Eqs. (1)–(3)) driven by a harmonic signal (I(t)=sin(2πt)) and different coupling constants K. The coupling constant determines the convergence speed and the amplitude of **oscillations** around the **frequency** of the driving signal in steady state — the higher K the faster the convergence and the larger the **oscillations**.
...(a) Typical convergence of an adaptive **frequency** **oscillator** (Eqs. (1)–(3)) driven by a harmonic signal (I(t)=sin(2πt)). The **frequencies** converge in an oscillatory fashion towards the **frequency** of the input (indicated by the dashed line). After convergence it **oscillates** with a small amplitude around the **frequency** of the input. The coupling constant determines the convergence speed and the amplitude of **oscillations** around the **frequency** of the driving signal in steady state. In all figures, the top right panel shows the driving signals (note the different scales). (b)–(f) Non-harmonic driving signals. We depict representative results on the evolution of ωdωF=ω−ωFωF vs. time. The dashed line indicates the zero error between the intrinsic **frequency** ω and the base **frequency** ωF of the driving signals. (b) Square pulse I(t)=rect(ωFt), (c) Sawtooth I(t)=st(ωFt) (d) Chirp I(t)=cos(ωct) ωc=ωF(1+12(t1000)2). (Note that the graph of the input signal is illustrative only since the change in **frequency** takes much longer than illustrated.) (e) Signal with two non-commensurate **frequencies** I(t)=12[cos(ωFt)+cos(22ωFt)], i.e. a representative example how the system can evolve to different **frequency** components of the driving signal depending on the initial condition ωd(0)=ω(0)−ωF. (f) I(t) is the non-periodic output of the Rössler system. The Rössler signal has a 1/f broad-band spectrum, yet it has a clear maximum in the **frequency** spectrum. In order to assess the convergence we use ωF=2πfmax, where fmax is found numerically by FFT. The **oscillator** convergences to this **frequency**.
...(N=10000, K=0.1) — (a) The FFT (black line) of the Rössler signal (for t=[99800,100000]) in comparison with the distribution of the **frequencies** of the **oscillators** (grey bars, normalized to the number of **oscillators**) at time 105 s. The spectrum of the FFT has been discretized into the same bins as the statistics of the **oscillators** in order to allow for a good comparison with the results from the full-scale simulation. (b) Time-series of the output signal O(t) (bold line) vs the teaching signal T(t) (dashed line).
...We present a method to obtain the **frequency** spectrum of a signal with a nonlinear dynamical system. The dynamical system is composed of a pool of adaptive **frequency** **oscillators** with negative mean-field coupling. For the **frequency** analysis, the synchronization and adaptation properties of the component **oscillators** are exploited. The **frequency** spectrum of the signal is reflected in the statistics of the intrinsic **frequencies** of the **oscillators**. The **frequency** analysis is completely embedded in the dynamics of the system. Thus, no pre-processing or additional parameters, such as time windows, are needed. Representative results of the numerical integration of the system are presented. It is shown, that the **oscillators** tune to the correct **frequencies** for both discrete and continuous spectra. Due to its dynamic nature the system is also capable to track non-stationary spectra. Further, we show that the system can be modeled in a probabilistic manner by means of a nonlinear Fokker–Planck equation. The probabilistic treatment is in good agreement with the numerical results, and provides a useful tool to understand the underlying mechanisms leading to convergence....Adaptive **frequency** **oscillator**...The structure of the dynamical system that is capable to reproduce a given teaching signal T(t). The system is made up of a pool of adaptive **frequency** **oscillators**. The mean field produced by the **oscillators** is fed back negatively on the **oscillators**. Due to the feedback structure and the adaptive **frequency** property of the **oscillators** it reconstructs the **frequency** spectrum of T(t) by the distribution of the intrinsic **frequencies**.
...Coupled **oscillators**...**Frequency** analysis...(a) (N=1000, K=200) — T(t) is a non-stationary input signal (cf. text), in contrast to Figs. 4 and 5 the histogram of the distribution of the **frequency** ωi is shown for every 5 s, the grey level corresponds to the number of **oscillators** in the bins (note the logarithmic scale). The thin white line indicates the theoretical instantaneous **frequency**. Thus, it can be seen that the distribution tracks very well the non-stationary spectrum, however about 4% of the **oscillators** diverge after the cross-over of the **frequencies**. (b) This plots outlines the maximum tracking performance of the system for non-stationary signal. The input signal has a sinusoidal varying **frequency**. The **frequency** response of the adaptation is plotted (see text for details). As comparison we plot the first-order transfer function HK∞ and the vertical line indicates ωs=1. (c) The grey area shows the region where the **frequency** response of the adaptation is H>22. While for slower non-stationary signals the upper bound is a function of K, the bound becomes independent of K for ωs>1 (red dashed line).
... We present a method to obtain the **frequency** spectrum of a signal with a nonlinear dynamical system. The dynamical system is composed of a pool of adaptive **frequency** **oscillators** with negative mean-field coupling. For the **frequency** analysis, the synchronization and adaptation properties of the component **oscillators** are exploited. The **frequency** spectrum of the signal is reflected in the statistics of the intrinsic **frequencies** of the **oscillators**. The **frequency** analysis is completely embedded in the dynamics of the system. Thus, no pre-processing or additional parameters, such as time windows, are needed. Representative results of the numerical integration of the system are presented. It is shown, that the **oscillators** tune to the correct **frequencies** for both discrete and continuous spectra. Due to its dynamic nature the system is also capable to track non-stationary spectra. Further, we show that the system can be modeled in a probabilistic manner by means of a nonlinear Fokker–Planck equation. The probabilistic treatment is in good agreement with the numerical results, and provides a useful tool to understand the underlying mechanisms leading to convergence.

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Contributors: Gholamhossein Shahgoli, John Fielke, Jacky Desbiolles, Chris Saunders

Date: 2010-01-01

Average PTO power as a function of **oscillating** **frequency** for straight (♦: solid line) and bent leg (□: broken line) tines (**oscillation** angle β=+27°).
...Subsoiler draft signals with time for the control and the range of **oscillating** **frequencies**.
...Dominant **frequency** of draft signal over the **oscillating** **frequency** range.
...Proportion of cycle time for cutting and compaction phases versus **oscillating** **frequency** (**oscillation** angle β=+27°).
...Dominant **frequency** of torque signal over the **oscillating** **frequency** range.
...**Frequency**...Based on the published benefits of oscillatory tillage, a subsoiler was developed at the University of South Australia, which had two deep working oscillatory tines and could be fitted with four shallow leading tines for increased loosening efficiency. A series of field trials were conducted in a sandy-loam soil to determine the most efficient setting of the tine's oscillatory motion and to compare the effect of using straight or bentleg tines. The tines were **oscillated** with an amplitude at the tip of ±69mm and an **oscillation** angle of 27° using a forward speed of 3km/h. The **frequency** of **oscillation** was varied from 1.9 to 8.8Hz. Analysis showed that the underside of the **oscillating** tine pushed rearward on the soil during part of the **oscillation** cycle, this decreased the draft in comparison to rigid tillage from 25.8 to 9.3kN. Increasing **oscillation** **frequency**, increased the PTO power requirement from 2.5kW at 1.9Hz to 26.3kW at 8.8Hz. The peaks and troughs in draft and torque were able to be aligned with the various phases of the **oscillating** tillage. An optimum **oscillation** **frequency** of 3.3Hz (velocity ratio of 1.5) was observed for minimum power to operate the **oscillating** subsoiler. Whilst at this setting, the combined draft and PTO power was similar to the draft power of rigid tillage, but when considering the higher losses due to tractive efficiency and lower PTO power losses, the **oscillating** tillage would be expected to require around 27% less engine power than rigid tillage....**Oscillating** tine ... Based on the published benefits of oscillatory tillage, a subsoiler was developed at the University of South Australia, which had two deep working oscillatory tines and could be fitted with four shallow leading tines for increased loosening efficiency. A series of field trials were conducted in a sandy-loam soil to determine the most efficient setting of the tine's oscillatory motion and to compare the effect of using straight or bentleg tines. The tines were **oscillated** with an amplitude at the tip of ±69mm and an **oscillation** angle of 27° using a forward speed of 3km/h. The **frequency** of **oscillation** was varied from 1.9 to 8.8Hz. Analysis showed that the underside of the **oscillating** tine pushed rearward on the soil during part of the **oscillation** cycle, this decreased the draft in comparison to rigid tillage from 25.8 to 9.3kN. Increasing **oscillation** **frequency**, increased the PTO power requirement from 2.5kW at 1.9Hz to 26.3kW at 8.8Hz. The peaks and troughs in draft and torque were able to be aligned with the various phases of the **oscillating** tillage. An optimum **oscillation** **frequency** of 3.3Hz (velocity ratio of 1.5) was observed for minimum power to operate the **oscillating** subsoiler. Whilst at this setting, the combined draft and PTO power was similar to the draft power of rigid tillage, but when considering the higher losses due to tractive efficiency and lower PTO power losses, the **oscillating** tillage would be expected to require around 27% less engine power than rigid tillage.

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Contributors: M. Machida, T. Koyama

Date: 2007-10-01

On the basis of the theory for the capacitive coupling in intrinsic Josephson junctions (IJJ’s), we theoretically study the macroscopic quantum tunneling in the switching dynamics into the voltage states in IJJ. The effective action obtained by using the path integral formalism reveals that the capacitive coupling splits each of the lowest and higher quantum levels, which are given inside Josephson potential barrier of the single junction derived by dropping off the coupling, into levels composed of the number of junction (N). This level splitting can cause multiple low-**frequency** Rabi-**oscillations** and enhance the switching probability compared to the conventional Caldeira–Leggett theory. Furthermore, a possibility as a naturally built-in multi-**qubit** is discussed....The schematic figure for the projected quantum levels in IJJ composed of two junctions, the switching dynamics, and the transition between two quantum states caused by the irradiation of the microwave whose **frequency** is Ω2.
...Rabi-**oscillation**...The schematic figure for the quantum levels for IJJ, which are projected onto the potential barrier of the single Josephson junction without the coupling. The energy levels of the out-of-phase and the in-phase **oscillations** have the highest and the lowest eigen-energies, respectively.
... On the basis of the theory for the capacitive coupling in intrinsic Josephson junctions (IJJ’s), we theoretically study the macroscopic quantum tunneling in the switching dynamics into the voltage states in IJJ. The effective action obtained by using the path integral formalism reveals that the capacitive coupling splits each of the lowest and higher quantum levels, which are given inside Josephson potential barrier of the single junction derived by dropping off the coupling, into levels composed of the number of junction (N). This level splitting can cause multiple low-**frequency** Rabi-**oscillations** and enhance the switching probability compared to the conventional Caldeira–Leggett theory. Furthermore, a possibility as a naturally built-in multi-**qubit** is discussed.

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Contributors: Kouichi Ichimura

Date: 2001-09-01

A quantum computer where quantum bits (**qubits**) are defined in **frequency** domain and interaction between **qubits** is mediated by a single cavity mode is proposed. In this quantum computer, **qubits** can be individually addressed regardless of their positions. Therefore, randomly distributed systems in space can be directly employed as **qubits**. An application of nuclear spins in rare-earth ions in a crystal for the quantum computer is quantitatively analyzed....**Qubits** in solids...Schematic diagram of **qubits** addressed in a **frequency** domain. The ions whose 3H4(1)±
3
2–1D2(1) transitions are resonant with a common cavity mode are employed as **qubits**.
...Basic scheme of the concept of the **frequency**-domain quantum computer. The atoms are coupled to a single cavity mode. Lasers with **frequencies** of νk and νl are directed onto the set of atoms and interact with the kth and lth atoms selectively.
... A quantum computer where quantum bits (**qubits**) are defined in **frequency** domain and interaction between **qubits** is mediated by a single cavity mode is proposed. In this quantum computer, **qubits** can be individually addressed regardless of their positions. Therefore, randomly distributed systems in space can be directly employed as **qubits**. An application of nuclear spins in rare-earth ions in a crystal for the quantum computer is quantitatively analyzed.

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Contributors: Michael G. Tanner, David G. Hasko, David A. Williams

Date: 2006-04-01

Resonance response of the SET current to applied microwave **frequencies**, (a) over a large **frequency** range due to coupling with all device elements. (b) A resonance of interest believed to be associated with the IDQD. Central resonance peak is periodically split or suppressed with varying gate potential Vg2. The inset figure shows the response at Vg2=−9.5V (dashed line) and at Vg2=−8V plotted without offset for comparison. The feature repeats periodically as gate potential is increased further.
...**Qubit**...Differentiated SET current measured at 4.2K and zero source–drain bias as Vg1 is swept and Vg2 is incremented. Inset shows the main features: one main Coulomb **oscillation** indicated by the dashed line and subsidiary **oscillations** shown by the dotted lines.
... The fabrication methods and low-temperature electron transport measurements are presented for circuits consisting of a single-island single-electron transistor coupled to an isolated double quantum-dot. Capacitively coupled ‘trench isolated’ circuit elements are fabricated in highly doped silicon-on-insulator using electron beam lithography and reactive ion etching. Polarisation of the isolated double quantum-dot is observed as a function of the side gate potentials through changes in the conductance characteristics of the single-electron transistor. Microwave signals are coupled into the device for excitation of the polarisation states of the isolated double quantum-dot. Resonances attributed to an energy level splitting of the polarisation states are observed with an energy separation appropriate for quantum computation.

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Contributors: Alberto Pretel, John H. Reina, William R. Aguirre-Contreras

Date: 2008-03-01

In all plots the decay rates κ/g=0.1, γr/g=4.35×10-2, and cavity factor Q=1400. The quantum dot excitonic Bohr **frequency** is assumed to be in resonance with the cavity field **frequency**, i.e., ωqd=ωc. The amplitude of the external laser field to the cavity decay rate ratio is fixed to I/κ=631. The coherence ρ01≡ρ(0,1) dynamics is plotted for: (a) Δωcl=0.4g; (b) Δωcl=g; (c) Δωcl=100g; (d) Δωcl=1000g. The cavity photons mean number is plotted in (e) and (f). We have used a logarithmic scale for the time axis and the values: (i) Δωcl=g; (ii) Δωcl=1000g, for the solid and dotted curves, respectively.
...Rabi **oscillations**...Within the density matrix formalism, we report on the quantum control of the excitonic coherences in quantum dots coupled to a single mode field resonant semiconductor cavity. We use an external classical laser field to drive the dynamical response of the excitonic states. Dissipation mechanisms associated with the cavity field and the excitonic states are explicitly included in the model. Our numerical simulations of the excitonic dynamics are in good agreement with recent experimental reports. Furthermore, we compute and show how to tailor such a dynamics in the presence of the laser field by means of controlling the detuning between the laser and the cavity field **frequencies**. The results are analyzed with a view to implementing quantum control of local **qubit** operations. ... Within the density matrix formalism, we report on the quantum control of the excitonic coherences in quantum dots coupled to a single mode field resonant semiconductor cavity. We use an external classical laser field to drive the dynamical response of the excitonic states. Dissipation mechanisms associated with the cavity field and the excitonic states are explicitly included in the model. Our numerical simulations of the excitonic dynamics are in good agreement with recent experimental reports. Furthermore, we compute and show how to tailor such a dynamics in the presence of the laser field by means of controlling the detuning between the laser and the cavity field **frequencies**. The results are analyzed with a view to implementing quantum control of local **qubit** operations.

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Contributors: Jing-Lin Xiao

Date: 2013-01-01

**Qubit**...We study the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron strongly coupled to LO-phonon in a quantum rod (QR) with a hydrogen-like impurity at the center by using variational method of Pekar type. This QR system may be used as a two-level quantum **qubit**. When the electron is in the superposition state of the ground and the first excited states, we obtained the time evolution of the electron probability density **oscillating** in the QR with a certain period. We then investigate the effects of the temperature and the hydrogen-like impurity on the time evolution of the electron probability density and the **oscillation** period. It is found that the electron probability density and the **oscillation** period increase (decrease) with increasing temperature in lower (higher) temperature regime. The electron probability density and the **oscillation** period decrease (increase) with increasing electron–phonon coupling strength when the temperature is lower (higher). Whereas they increase (decrease) with increasing Coulomb bound potential when the temperature is lower (higher)....The **oscillation** period T0 changes with the temperature T and Coulomb bound potential β.
...The **oscillation** period T0 changes with the temperature T and electron phonon coupling strength α .
... We study the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron strongly coupled to LO-phonon in a quantum rod (QR) with a hydrogen-like impurity at the center by using variational method of Pekar type. This QR system may be used as a two-level quantum **qubit**. When the electron is in the superposition state of the ground and the first excited states, we obtained the time evolution of the electron probability density **oscillating** in the QR with a certain period. We then investigate the effects of the temperature and the hydrogen-like impurity on the time evolution of the electron probability density and the **oscillation** period. It is found that the electron probability density and the **oscillation** period increase (decrease) with increasing temperature in lower (higher) temperature regime. The electron probability density and the **oscillation** period decrease (increase) with increasing electron–phonon coupling strength when the temperature is lower (higher). Whereas they increase (decrease) with increasing Coulomb bound potential when the temperature is lower (higher).

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