### 25677 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....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.
...(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: 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 relational curves of the oscillation period T of the qubit to the electron-LO-phonon coupling constant α 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....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.
...Triangular bound potential quantum dot **qubit** ... 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: Kouichi Ichimura

Date: 2001-09-01

A simple **frequency**-domain quantum computer with ions in a crystal coupled to a cavity mode...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.
...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.
... 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: 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....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: Gholamhossein Shahgoli, John Fielke, Jacky Desbiolles, Chris Saunders

Date: 2010-01-01

...Experimental PTO torque signal variation over time with increasing frequencies.
...Average PTO power as a function of **oscillating** **frequency** for straight (♦: solid line) and bent leg (□: broken line) tines (**oscillation** angle β=+27°).
...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....Optimising oscillation **frequency** in oscillatory tillage...Dominant frequency of torque signal over the oscillating frequency range.
...Dominant frequency of draft signal over the oscillating frequency range.
...ANOVA st...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°).
...Dominan...Dominant **frequency** of torque signal over the **oscillating** **frequency** range.
...Synopsis of subsoiler tine motion parameters for different frequencies (a=±69mm, β=27°, V0=0.8m/s).
...To...**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: A Yahalom, R Englman

Date: 2000-07-24

Two-electron state amplitude in a dimer, with both molecules subject to a periodic force. After a full revolution the two electronic states each change their sign, leaving the total state invariant. **Frequencies**: ω1=1, ω2=1, G1=−100, G2=−200, G=40 (near adiabatic limit). Thick line: first, initially excited component. Medium thick line: second and third components. Thin line: fourth component.
...Two-electron state amplitudes in a dimer. The thick line shows the time dependent amplitude of the first (initially excited component), the thin line that of the second component in Eq. (5). **Frequencies**: ω1=1, ω2=4, G1=−40, G2=−80, G=16 (near adiabatic limit)
...The geometric and open path phases of a four-state system subject to time varying cyclic potentials are computed from the Schrödinger equation. Fast oscillations are found in the non-adiabatic case. For parameter values such that the system possesses degenerate levels, the geometric phase becomes anomalous, undergoing a sign switch. A physical system to which the results apply is a molecular dimer with two interacting electrons. Additionally, the sudden switching of the geometric phase promises to be an efficient control in two-**qubit** quantum computing....Non-adiabaticity effects in the real part of the initially excited component, as a function of time. The **frequencies** on the two dimers are ω1=1 and ω2=2. The values of the coupling parameters are as follows. Thick line: G1=−80, G2=−160, G=40 (near adiabatic limit). Thin line: G1=−8, G2=−16, G=4 (non-adiabatic case)
...The geometric and open path phases of a four-state system subject to time varying cyclic potentials are computed from the Schrödinger equation. Fast **oscillations** are found in the non-adiabatic case. For parameter values such that the system possesses degenerate levels, the geometric phase becomes anomalous, undergoing a sign switch. A physical system to which the results apply is a molecular dimer with two interacting electrons. Additionally, the sudden switching of the geometric phase promises to be an efficient control in two-**qubit** quantum computing....Non-adiabaticity effects in the real part of the initially excited component, as a function of time. The frequencies on the two dimers are ω1=1 and ω2=2. The values of the coupling parameters are as follows. Thick line: G1=−80, G2=−160, G=40 (near adiabatic limit). Thin line: G1=−8, G2=−16, G=4 (non-adiabatic case)
... The geometric and open path phases of a four-state system subject to time varying cyclic potentials are computed from the Schrödinger equation. Fast **oscillations** are found in the non-adiabatic case. For parameter values such that the system possesses degenerate levels, the geometric phase becomes anomalous, undergoing a sign switch. A physical system to which the results apply is a molecular dimer with two interacting electrons. Additionally, the sudden switching of the geometric phase promises to be an efficient control in two-**qubit** quantum computing.

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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).
...(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.
...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....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.
...Adaptive **frequency** **oscillator**...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).
...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**.
...(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).
...**Frequency** analysis with coupled nonlinear **oscillators**...(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).
...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.
... 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: 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.
...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: T.P. Orlando, Lin Tian, D.S. Crankshaw, S. Lloyd, C.H. van der Wal, J.E. Mooij, F. Wilhelm

Date: 2002-03-01

Equivalent circuit of the linearized **qubit**–SQUID system. ϕm and ϕp are the two independent variables of a DC SQUID. ϕm correpsonds to the circulating current of the SQUID, and ϕp couples with the ramping current of the SQUID. The capacitances of the inner **oscillator** loop and the external **oscillator** loop are Cm=2CJ and Cp, the shunt capacitance outside the SQUID. Flux of the three loops, q=q0σz, ϕm, and ϕp, are chosen as independent variables in the calculation. Each of the inductances in the three loops interacts by mutual inductances as are indicated by the paired dots near the inductances.
...The SQUID used to measure the flux state of a superconducting flux-based **qubit** interacts with the **qubit** and transmits its environmental noise to the **qubit**, thus causing the relaxation and dephasing of the **qubit** state. The SQUID–**qubit** system is analyzed and the effect of the transmittal of environmental noise is calculated. The method presented can also be applied to other quantum systems....Engineering the quantum measurement process for the persistent current **qubit**...Equivalent circuit of the linearized **qubit**–SQUID system. ϕm and ϕp are the two independent variables of a DC SQUID. ϕm correpsonds to the circulating current of the SQUID, and ϕp couples with the ramping current of the SQUID. The capacitances of the inner oscillator loop and the external oscillator loop are Cm=2CJ and Cp, the shunt capacitance outside the SQUID. Flux of the three loops, q=q0σz, ϕm, and ϕp, are chosen as independent variables in the calculation. Each of the inductances in the three loops interacts by mutual inductances as are indicated by the paired dots near the inductances.
...The measuring circuit of the DC SQUID which surrounds the **qubit**. CJ and I0 are the capacitance and critical current of each of the junctions, and ϕi are the gauge-invariant phases of the junctions. The **qubit** is represented symbolically by a loop with an arrow indicating the magnetic moment of the |0〉 state. The SQUID is shunted by a capacitor Csh and the environmental impedance Z0(ω).
... The SQUID used to measure the flux state of a superconducting flux-based **qubit** interacts with the **qubit** and transmits its environmental noise to the **qubit**, thus causing the relaxation and dephasing of the **qubit** state. The SQUID–**qubit** system is analyzed and the effect of the transmittal of environmental noise is calculated. The method presented can also be applied to other quantum systems.

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Contributors: R. Taranko, T. Kwapiński

Date: 2013-01-01

Current-composed quantity Q(t) (solid lines) and the far-removed **qubit** QD occupancy, n3 (dashed lines), as a function of time for the horizontal **qubit**-detector connection, U13=U24=0, 2 or 4, respectively. μL=−μR=20, ΓL=5, ΓR=10, U12=U34=5 and the other parameters are the same as in Fig. 2. The lines for U13=U24=2 (4) are shifted by −1 (−2) for better visualisation.
...We investigate theoretically the dynamics of a charge **qubit** (double quantum dot system) coupled electrostatically with the double-dot detector. The **qubit** charge oscillations and the detector current are calculated using the equation of motion method for appropriate correlation functions. In order to find the best detector performance (i.e. the detector current signal follows as well as possible the **qubit** charge oscillations) we consider different **qubit**-detector geometries. The optimal setup was found for the **qubit** lying parallel to the detector quantum dots for which we observed very good detector performance together with weak decoherence of the system. It is also shown that the asymptotic detector current (flowing in response to the limited in time **qubit**-detector interaction) fully reproduces the **qubit** dynamics....The sketch of the **qubit**-detector systems discussed in the text. Double quantum dot (1 and 4) between the left and right electron reservoirs stands for the **qubit** charge detector. **Qubit** is represented by two coupled quantum dots (2 and 3) occupied by a single electron. Straight black (zig-zag red) lines correspond to the tunnel matrix elements V14, V23 (Coulomb interactions, e.g. U14, U24) between the appropriate states. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
...We investigate theoretically the dynamics of a charge **qubit** (double quantum dot system) coupled electrostatically with the double-dot detector. The **qubit** charge **oscillations** and the detector current are calculated using the equation of motion method for appropriate correlation functions. In order to find the best detector performance (i.e. the detector current signal follows as well as possible the **qubit** charge **oscillations**) we consider different **qubit**-detector geometries. The optimal setup was found for the **qubit** lying parallel to the detector quantum dots for which we observed very good detector performance together with weak decoherence of the system. It is also shown that the asymptotic detector current (flowing in response to the limited in time **qubit**-detector interaction) fully reproduces the **qubit** dynamics....The asymptotic pulse-induced current I(τ) against the time interval (pulse length) τ – for details see the text – and the charge occupation of the far-removed **qubit** QD, n3, (dashed lines) for the **qubit**-detector system schematically shown in Fig. 1b. The upper (bottom) panel corresponds to ΓL=5, ΓR=10 (ΓL=5, ΓR=1). μL=−μR=20 and the other parameters are the same as in Fig. 2. The current lines are multiplied by −2 for better visualisation.
...The sketch of the **qubit**-detector systems discussed in the text. Double quantum dot (1 and 4) between the left and right electron reservoirs stands for the **qubit** charge detector. Qubit is represented by two coupled quantum dots (2 and 3) occupied by a single electron. Straight black (zig-zag red) lines correspond to the tunnel matrix elements V14, V23 (Coulomb interactions, e.g. U14, U24) between the appropriate states. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
...Dynamics of a charge **qubit** coupled with a double-dot detector...Current-composed quantity Q(t) (solid lines) and the charge occupation of the far-removed **qubit** QD, n3, (dashed lines) as a function of time for the **qubit**-detector system schematically shown in Fig. 1b. The upper (bottom) panel corresponds to (ΓL,ΓR)=(5,1) ((ΓL,ΓR)=(5,10)). The other parameters are: μL=−μR=2 or μL=−μR=20, ε1,2,3,4=0, U24=5, U14=50, n2(t<10)=0, n3(t<10)=1. The lines for μL=−μR=20 are shifted by −1 for better visualisation.
...Upper panel: Current-composed quantity Q(t) (solid lines) and the far-removed **qubit** QD occupancy, n3, (dashed lines) as a function of time for different **qubit**-detector connections shown in Fig. 1d (U12=5), Fig. 1c (U12=U24=5) and Fig. 1b (U24=5)—the upper, middle and lower curves, respectively. The bottom panel depicts the corresponding left (solid lines) and right (dashed lines) currents, IL(t), IR(t), flowing in the system for the above three **qubit**-wire connections. μL=−μR=2, ΓL=5, ΓR=10 and the other parameters are the same as in Fig. 2. The lines in the upper panel for U12=U24=5 and for U24=5 are shifted by −1 and −2, respectively, and by −0.15 and −0.3 in the bottom panel. Note different scales in the vertical axis of both panels.
... We investigate theoretically the dynamics of a charge **qubit** (double quantum dot system) coupled electrostatically with the double-dot detector. The **qubit** charge **oscillations** and the detector current are calculated using the equation of motion method for appropriate correlation functions. In order to find the best detector performance (i.e. the detector current signal follows as well as possible the **qubit** charge **oscillations**) we consider different **qubit**-detector geometries. The optimal setup was found for the **qubit** lying parallel to the detector quantum dots for which we observed very good detector performance together with weak decoherence of the system. It is also shown that the asymptotic detector current (flowing in response to the limited in time **qubit**-detector interaction) fully reproduces the **qubit** dynamics.

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