### 21982 results for qubit oscillator frequency

Contributors: R. Zadoyan, D. Kohen, D.A. Lidar, V.A. Apkarian

Date: 2001-05-15

Molecular ro-vibronic coherences, joint energy-time distributions of quantum amplitudes, are selectively prepared, manipulated, and imaged in time–**frequency**-resolved coherent anti-Stokes Raman scattering (TFRCARS) measurements using femtosecond laser pulses. The studies are implemented in iodine vapor, with its thermally occupied statistical ro-vibrational density serving as initial state. The evolution of the massive ro-vibronic superpositions, consisting of 103 eigenstates, is followed through two-dimensional images. The first- and second-order coherences are captured using time-integrated **frequency**-resolved CARS, while the third-order coherence is captured using time-gated **frequency**-resolved CARS. The Fourier filtering provided by time-integrated detection projects out single ro-vibronic transitions, while time-gated detection allows the projection of arbitrary ro-vibronic superpositions from the coherent third-order polarization. A detailed analysis of the data is provided to highlight the salient features of this four-wave mixing process. The richly patterned images of the ro-vibrational coherences can be understood in terms of phase evolution in rotation–vibration–electronic Hilbert space, using time-circuit diagrams. Beside the control and imaging of chemistry, the controlled manipulation of massive quantum coherences suggests the possibility of quantum computing. We argue that the universal logic gates necessary for arbitrary quantum computing – all single **qubit** operations and the two-**qubit** controlled-NOT (CNOT) gate – are available in time-resolved four-wave mixing in a molecule. The molecular rotational manifold is naturally “wired” for carrying out all single **qubit** operations efficiently, and in parallel. We identify vibronic coherences as one example of a naturally available two-**qubit** CNOT gate, wherein the vibrational **qubit** controls the switching of the targeted electronic **qubit**....Diagrammatic representation of time-resolved CARS. Both time-circuit and Feynman diagram are illustrated for a non- overlapping sequence of P, S, P′ pulses, with central **frequency** of the S-pulse chosen to be outside the absorption spectrum of the B←X transition, to ensure that only the P(0,3) component of the third-order polarization is interrogated. In this dominant contribution, all three pulses act on bra (ket) state while the ket (bra) state evolves field free. Note, for the Feynman diagrams, we use the convention of Ref. [6], which is different than that of Ref. [5].
...The wavepacket picture associated with the evolution of the ket-state in the diagram of Fig. 1, for resonant CARS in iodine. The required energy matching condition for the AS radiation, Eq. (10b) of text, can only be met when the packet reaches the inner turning point of the B-surface. Once prepared, ϕ(3)(t) will **oscillate**, radiating periodically every time it reaches the inner turning point.
... Molecular ro-vibronic coherences, joint energy-time distributions of quantum amplitudes, are selectively prepared, manipulated, and imaged in time–**frequency**-resolved coherent anti-Stokes Raman scattering (TFRCARS) measurements using femtosecond laser pulses. The studies are implemented in iodine vapor, with its thermally occupied statistical ro-vibrational density serving as initial state. The evolution of the massive ro-vibronic superpositions, consisting of 103 eigenstates, is followed through two-dimensional images. The first- and second-order coherences are captured using time-integrated **frequency**-resolved CARS, while the third-order coherence is captured using time-gated **frequency**-resolved CARS. The Fourier filtering provided by time-integrated detection projects out single ro-vibronic transitions, while time-gated detection allows the projection of arbitrary ro-vibronic superpositions from the coherent third-order polarization. A detailed analysis of the data is provided to highlight the salient features of this four-wave mixing process. The richly patterned images of the ro-vibrational coherences can be understood in terms of phase evolution in rotation–vibration–electronic Hilbert space, using time-circuit diagrams. Beside the control and imaging of chemistry, the controlled manipulation of massive quantum coherences suggests the possibility of quantum computing. We argue that the universal logic gates necessary for arbitrary quantum computing – all single **qubit** operations and the two-**qubit** controlled-NOT (CNOT) gate – are available in time-resolved four-wave mixing in a molecule. The molecular rotational manifold is naturally “wired” for carrying out all single **qubit** operations efficiently, and in parallel. We identify vibronic coherences as one example of a naturally available two-**qubit** CNOT gate, wherein the vibrational **qubit** controls the switching of the targeted electronic **qubit**.

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Contributors: Dong-Qi Liu, Gang-Qin Liu, Yan-Chun Chang, Xin-Yu Pan

Date: 2014-01-01

Detection and manipulation of the **qubit**. (a) Fluorescence image of nanodiamond prepared on the CPW transmission line. NV S1 is circled. The inset is a photo of CPW with 20μm gaps fabricated on a silica glass. (b) CW ODMR spectrum for NV S1. The inset is energy levels of NV center. A 532nm laser is used to excite and initialize the NV center. Fluorescence is collected by a confocal microscope. (c) Rabi **oscillation** of NV S1. Rabi **oscillation** period is about 62ns. (d) Hahn echo and CPMG control pulse sequences. πx (πy) implies the direction of microwave magnetic fields parallel to x (y).
...Spectral density of the spin bath. (a) NV S1, (b) NV S2. All values of spectral density S(ω) of the spin bath are extracted from the CPMG data (blue points). Each blue data point represents a specific probed **frequency** ω=πn/t, in which n is the number of control pulses and t is the specific duration. The red points are the average values at a certain **frequency**. The mean spectral density is fit to the Lorentzian function (Eq. (3)) (green line). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
...Overcoming the spin **qubit** decoherence is a challenge for quantum science and technology. We investigate the decoherence process in nanodiamonds by Carr–Purcell–Meiboom–Gill (CPMG) technique at room temperature. We find that the coherence time T2 scales as nγ. The elongation effect of coherence time can be represented by a constant power of the number of pulses n. Considering the filter function of CPMG decoupling sequence as a δfunction, the spectrum density of noise has been reconstructed directly from the coherence time measurements and a Lorentzian noise power spectrum model agrees well with the experiment. These results are helpful for the application of nanodiamonds to nanoscale magnetic imaging....Characterization of lifetime of NV center spins. (a) Ramsey interference of NV S1 (circle) and NV S2 (diamond). The **oscillation** in Ramsey signal originates from the beating among different transitions corresponding to the host three 14N nuclear spin states. The **oscillation** **frequency** of Ramsey signal is equal to microwave detuning from spin resonance. Solid lines ~exp[−(t/T2⁎)m] fit the experimental data points, where m is a free parameter. (b) Comparison of Hahn echo coherence time T2 of NV S1 (circle) and NV S2 (diamond). The solid lines are fits to ~exp[−(t/T2)p], in which p is a fit parameter.
... Overcoming the spin **qubit** decoherence is a challenge for quantum science and technology. We investigate the decoherence process in nanodiamonds by Carr–Purcell–Meiboom–Gill (CPMG) technique at room temperature. We find that the coherence time T2 scales as nγ. The elongation effect of coherence time can be represented by a constant power of the number of pulses n. Considering the filter function of CPMG decoupling sequence as a δfunction, the spectrum density of noise has been reconstructed directly from the coherence time measurements and a Lorentzian noise power spectrum model agrees well with the experiment. These results are helpful for the application of nanodiamonds to nanoscale magnetic imaging.

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Contributors: Mina Amiri, Jean-Marc Lina, Francesca Pizzo, Jean Gotman

Date: 2016-01-01

Examples of a spike without HFOs (left) and a spike with HFOs (right), as defined with the Analytic Morse wavelet in the time–**frequency** domain.
...High **Frequency** **Oscillations**...Parameter selection for the Analytic Morse Wavelet; top: time–**frequency** presentation for different values of n (m=40), bottom: raw signal and filtered signal (80–250Hz). Blue lines represent HFO interval marked visually.
...Examples of detection errors. Left: HFO without isolated blob but having **oscillation** in the raw signal. Right: HFO without visible **oscillation** in the raw signal but representing an isolated peak. Blue lines show the HFO interval marked by reviewers.
...Time–**frequency**...To demonstrate and quantify the occurrence of false High **Frequency** **Oscillations** (HFOs) generated by the filtering of sharp events. To distinguish real HFOs from spurious ones using analysis of the raw signal. ... To demonstrate and quantify the occurrence of false High **Frequency** **Oscillations** (HFOs) generated by the filtering of sharp events. To distinguish real HFOs from spurious ones using analysis of the raw signal.

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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....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: 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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Contributors: A.R. Bosco de Magalhães, Adélcio C. Oliveira

Date: 2016-02-05

Nonlinear **oscillator**...Visibility dynamics in different timescales for initial state |Ψ2〉 and Γ=0. The timescale τp is associated to the decay of the envelope of the **oscillations** with characteristic time τr1. A very subtle increase in the amplitudes of the **oscillations** can be observed around t=τr2. The timescale of the fastest **oscillations** of the dynamics is τo.
...Visibility dynamics for initial state |Ψ2〉 and Γ varying from 0 to 0.1. For each value of Γ, the unit of time is chosen as the corresponding τp in (a), τr1 in (b), τr2 in (c), and τo in (d). For the majority of values of Γ investigated, the initial dynamics is flattened around t=2τp. Except for very small values of Γ, τr1 and τr2 are associated to partial revivals. When Γ increases, the number of fast initial **oscillations** decreases, but their characteristic durations are given by τo, which does not vary with Γ.
...Predictability dynamics in different timescales for initial state |Ψ2〉. The timescale τp is associated to the decay of the envelope of the **oscillations** with characteristic time τo. Revivals can be observed around the first multiples of τr.
...The structure of the entanglement dynamics of a **qubit** coupled to a quartic **oscillator** is investigated through the calculation of timescales of visibility and predictability, and their relation with the concurrence dynamics. This model can describe a Rydberg atom in a Kerr medium. A method based on the analysis of the different interference processes of the terms that compose the physical quantities studied is proposed, and timescales related to decay, revivals and fast **oscillations** under the decay envelope are computed. The method showed to be effective for the vast majority of cases studied, even when the timescales vary several orders of magnitude. The conditions for expansions in power series to give correct decay timescales are analyzed....Predictability dynamics in different timescales for initial state |Ψ1〉. The timescale τp is associated to the rise and decay of the **oscillations** with characteristic time τo. Revivals occur in the region around τr and its first multiples.
...Visibility dynamics in different timescales for initial state |Ψ2〉 and Γ=0.1. The timescale τp is associated to the rise and decay of the initial dynamics. Both τr1 and τr2 are related to partial revivals. There are no **oscillations** besides the revivals and the initial rise and decay; the timescale of their duration is given by τo.
... The structure of the entanglement dynamics of a **qubit** coupled to a quartic **oscillator** is investigated through the calculation of timescales of visibility and predictability, and their relation with the concurrence dynamics. This model can describe a Rydberg atom in a Kerr medium. A method based on the analysis of the different interference processes of the terms that compose the physical quantities studied is proposed, and timescales related to decay, revivals and fast **oscillations** under the decay envelope are computed. The method showed to be effective for the vast majority of cases studied, even when the timescales vary several orders of magnitude. The conditions for expansions in power series to give correct decay timescales are analyzed.

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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: Ludovic Righetti, Jonas Buchli, Auke Jan Ijspeert

Date: 2006-04-15

Nonlinear **oscillators** are widely used in biology, physics and engineering for modeling and control. They are interesting because of their synchronization properties when coupled to other dynamical systems. In this paper, we propose a learning rule for **oscillators** which adapts their **frequency** to the **frequency** of any periodic or pseudo-periodic input signal. Learning is done in a dynamic way: it is part of the dynamical system and not an offline process. An interesting property of our model is that it is easily generalizable to a large class of **oscillators**, from phase **oscillators** to relaxation **oscillators** and strange attractors with a generic learning rule. One major feature of our learning rule is that the **oscillators** constructed can adapt their **frequency** without any signal processing or the need to specify a time window or similar free parameters. All the processing is embedded in the dynamics of the adaptive **oscillator**. The convergence of the learning is proved for the Hopf **oscillator**, then numerical experiments are carried out to explore the learning capabilities of the system. Finally, we generalize the learning rule to non-harmonic **oscillators** like relaxation **oscillators** and strange attractors....Adaptive **frequency** **oscillator**...The left plot of this figure represents the evolution of ω(t) when the adaptive Hopf **oscillator** is coupled to the z variable of the Lorenz attractor. The right plot represents the z variable of the Lorenz attractor. We clearly see that the adaptive Hopf **oscillators** can correctly learn the pseudo-**frequency** of the Lorenz attractor. See the text for more details.
...Plots of the **frequency** of the **oscillations** of the Van der Pol **oscillator** according to ω. Here α=50. There are two plots, for the dotted line the **oscillator** is not coupled and for the plain line the **oscillator** is coupled to F=sin30t. The strength of coupling is ϵ=2. We clearly see basins of phase-locking, the main one for **frequency** of **oscillations** 30. The other major basins appear each 30n (dotted horizontal lines). We also notice small entrainment basins for some **frequencies** of the form 30pq. For a more detailed discussion of these results refer to the text.
...We show the adaptation of the Van der Pol **oscillator** to the **frequencies** of various input signals: (a) a simple sinusoidal input (F=sin(40t)), (b) a sinusoidal input with uniformly distributed noise (F=sin(40t)+uniform noise in [−0.5,0.5]), (c) a square input (F=square(40t)) and (d) a sawtooth input (F=sawtooth(40t)). For each experiment, we set ϵ=0.7 and α=100 and we show three plots. The right one shows the evolution of ω(t). The upper left graph is a plot of the **oscillations**, x, of the system, at the beginning of the learning. The lower graph shows the **oscillations** at the end of learning. In both graphs, we also plotted the input signal (dashed). In each experiment, ω converges to ω≃49.4, which corresponds to **oscillations** with a **frequency** of 40 rad s−1 like the input and thus the **oscillator** correctly adapts its **frequency** to the **frequency** of the input.
...**Frequency** spectra of the Van der Pol **oscillator**, both plotted with ω=10. The left figure is an **oscillator** with α=10 and on the right the nonlinearity is higher, α=50. On the y-axis we plotted the square root of the power intensity, in order to be able to see smaller **frequency** components.
...This figure shows the convergence of ω for several initial **frequencies**. The Van der Pol **oscillator** is perturbed by F=sin(30t), with coupling ϵ=0.7, α=50. We clearly see that the convergence directly depends on the initial conditions and as expected the different kinds of convergence correspond to the several entrainment basins of Fig. 7.
... Nonlinear **oscillators** are widely used in biology, physics and engineering for modeling and control. They are interesting because of their synchronization properties when coupled to other dynamical systems. In this paper, we propose a learning rule for **oscillators** which adapts their **frequency** to the **frequency** of any periodic or pseudo-periodic input signal. Learning is done in a dynamic way: it is part of the dynamical system and not an offline process. An interesting property of our model is that it is easily generalizable to a large class of **oscillators**, from phase **oscillators** to relaxation **oscillators** and strange attractors with a generic learning rule. One major feature of our learning rule is that the **oscillators** constructed can adapt their **frequency** without any signal processing or the need to specify a time window or similar free parameters. All the processing is embedded in the dynamics of the adaptive **oscillator**. The convergence of the learning is proved for the Hopf **oscillator**, then numerical experiments are carried out to explore the learning capabilities of the system. Finally, we generalize the learning rule to non-harmonic **oscillators** like relaxation **oscillators** and strange attractors.

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Contributors: S.K. Ryu, Y.K. Kim, M.K. Kim, S.H. Won, S.H. Chung

Date: 2010-01-01

Behavior of periodically **oscillating** flame with large-scale **oscillation** for Vac=5kV, fac=20Hz, and U0=11m/s.
...**Oscillation** **frequency** in terms of AC **frequency** for U0=11.0m/s and Vac=5kV.
...Low **frequency**...Average amplitude of large-scale **oscillation** with AC **frequency** for U0=11.0m/s and Vac=5kV.
...The **oscillation** behavior of laminar lifted flames under the influence of low-**frequency** AC has been investigated experimentally in coflow jets. Various **oscillation** modes were existed depending on jet velocity and the voltage and **frequency** of AC, especially when the AC **frequency** was typically smaller than 30Hz. Three different **oscillation** modes were observed: (1) large-scale **oscillation** with the **oscillation** **frequency** of about 0.1Hz, which was independent of the applied AC **frequency**, (2) small-scale **oscillation** synchronized to the applied AC **frequency**, and (3) doubly-periodic **oscillation** with small-scale **oscillation** embedded in large-scale **oscillation**. As the AC **frequency** decreased from 30Hz, the **oscillation** modes were in the order of the large-scale **oscillation**, doubly-periodic **oscillation**, and small-scale **oscillation**. The onset of the **oscillation** for the AC **frequency** smaller than 30Hz was in close agreement with the delay time scale for the ionic wind effect to occur, that is, the collision response time. **Frequency**-doubling behavior for the small-scale **oscillation** has also been observed. Possible mechanisms for the large-scale **oscillation** and the **frequency**-doubling behavior have been discussed, although the detailed understanding of the underlying mechanisms will be a future study....**Oscillation**...Phase diagrams of HL and dHL/dt for various **oscillation** modes.
...Edge height of lifted flame together with **oscillation** amplitude with AC **frequency** for Vac=5kV and U0=11.0m/s.
... The **oscillation** behavior of laminar lifted flames under the influence of low-**frequency** AC has been investigated experimentally in coflow jets. Various **oscillation** modes were existed depending on jet velocity and the voltage and **frequency** of AC, especially when the AC **frequency** was typically smaller than 30Hz. Three different **oscillation** modes were observed: (1) large-scale **oscillation** with the **oscillation** **frequency** of about 0.1Hz, which was independent of the applied AC **frequency**, (2) small-scale **oscillation** synchronized to the applied AC **frequency**, and (3) doubly-periodic **oscillation** with small-scale **oscillation** embedded in large-scale **oscillation**. As the AC **frequency** decreased from 30Hz, the **oscillation** modes were in the order of the large-scale **oscillation**, doubly-periodic **oscillation**, and small-scale **oscillation**. The onset of the **oscillation** for the AC **frequency** smaller than 30Hz was in close agreement with the delay time scale for the ionic wind effect to occur, that is, the collision response time. **Frequency**-doubling behavior for the small-scale **oscillation** has also been observed. Possible mechanisms for the large-scale **oscillation** and the **frequency**-doubling behavior have been discussed, although the detailed understanding of the underlying mechanisms will be a future study.

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Contributors: Yun-Fei Liu, Jing-Lin Xiao

Date: 2008-09-01

The relational curve of the **oscillating** period T and the electron–LOP coupling constant α.
...**Qubit**...The relational curve of the **oscillating** period T and the confinement length R.
...In this paper, we study the influence of LO phonon (LOP) on the charge **qubit** in a quantum dot (QD), and find that the eigenenergies of the ground and first excited states are reduced due to the electron–LOP interaction. At the same time, the time evolution of the electron probability density is obtained, the dependence of the **oscillating** period on electron–LOP coupling constant is found, the relation of between the **oscillating** period and the confinement length of the QD is calculated. Finally, we consider the effects of the electron–LOP coupling constant on pure dephasing factor under considering the correction of electron–LOP interaction for the wave functions. Our results suggest that electron–LOP interaction has very important effects on charge **qubit**. ... In this paper, we study the influence of LO phonon (LOP) on the charge **qubit** in a quantum dot (QD), and find that the eigenenergies of the ground and first excited states are reduced due to the electron–LOP interaction. At the same time, the time evolution of the electron probability density is obtained, the dependence of the **oscillating** period on electron–LOP coupling constant is found, the relation of between the **oscillating** period and the confinement length of the QD is calculated. Finally, we consider the effects of the electron–LOP coupling constant on pure dephasing factor under considering the correction of electron–LOP interaction for the wave functions. Our results suggest that electron–LOP interaction has very important effects on charge **qubit**.

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