### 21982 results for qubit oscillator frequency

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: Erik Smedler, Per Uhlén

Date: 2014-03-01

**Frequency** modulation...Calcium (Ca2+) **oscillations** are ubiquitous signals present in all cells that provide efficient means to transmit intracellular biological information. Either spontaneously or upon receptor ligand binding, the otherwise stable cytosolic Ca2+ concentration starts to **oscillate**. The resulting specific oscillatory pattern is interpreted by intracellular downstream effectors that subsequently activate different cellular processes. This signal transduction can occur through **frequency** modulation (FM) or amplitude modulation (AM), much similar to a radio signal. The decoding of the oscillatory signal is typically performed by enzymes with multiple Ca2+ binding residues that diversely can regulate its total phosphorylation, thereby activating cellular program. To date, NFAT, NF-κB, CaMKII, MAPK and calpain have been reported to have **frequency** decoding properties....**Frequency** modulated Ca2+ **oscillations**. (A) A computer generated (in silico) **oscillating** wave with the parameters: period (T), **frequency** (f), full duration half maximum (FDHM), and duty cycle is depicted. (B) **Oscillating** wave **frequency** modulated by agonist concentration. (C) **Oscillating** wave **frequency** modulated by the different agonists X, Y, and Z. Three single cell Ca2+ recordings of a Fluo-4/AM-loaded neuroblastoma cell (D), HeLa cell (E), and cardiac cell (F) with the parameters T, f, FDHM, and duty cycle stated. Scale bars are 100s.
...**Frequency** decoders and host cells. Illustration showing the **frequencies** and periods that modulate the different **frequency** decoders and host cells.
...**Frequency** decoding ... Calcium (Ca2+) **oscillations** are ubiquitous signals present in all cells that provide efficient means to transmit intracellular biological information. Either spontaneously or upon receptor ligand binding, the otherwise stable cytosolic Ca2+ concentration starts to **oscillate**. The resulting specific oscillatory pattern is interpreted by intracellular downstream effectors that subsequently activate different cellular processes. This signal transduction can occur through **frequency** modulation (FM) or amplitude modulation (AM), much similar to a radio signal. The decoding of the oscillatory signal is typically performed by enzymes with multiple Ca2+ binding residues that diversely can regulate its total phosphorylation, thereby activating cellular program. To date, NFAT, NF-κB, CaMKII, MAPK and calpain have been reported to have **frequency** decoding properties.

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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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Contributors: Wei Xiao, Jing-Lin Xiao

Date: 2012-10-01

The period of **oscillation** T0 in a QR as a function of the transverse and longitudinal effective confinement lengths of the QR lp and lv.
...We study the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to LO-phonon in a quantum rod with a hydrogen-like impurity at the center by using the variational method of Pekar type. This quantum rod 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, the probability density of the electron **oscillates** in the quantum rod. It is found that the probability density and the **oscillation** period are individually increased and decreased due to the presence of the Coulomb interaction between the electron and the hydrogen-like impurity. The **oscillation** period is an increasing function of the ellipsoid aspect ratio and the effective confinement lengths of the quantum rod, whereas it is a decreasing one of the electron–phonon coupling strength....The period of **oscillation** T0 in a QR as a function of the electron–phonon coupling strength α and the Coulomb bound potential β.
...**Qubit**...The period of **oscillation** T0 in a QR as a function of the ellipsoid aspect ratio e′ and the electron–phonon coupling strength α.
... We study the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to LO-phonon in a quantum rod with a hydrogen-like impurity at the center by using the variational method of Pekar type. This quantum rod 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, the probability density of the electron **oscillates** in the quantum rod. It is found that the probability density and the **oscillation** period are individually increased and decreased due to the presence of the Coulomb interaction between the electron and the hydrogen-like impurity. The **oscillation** period is an increasing function of the ellipsoid aspect ratio and the effective confinement lengths of the quantum rod, whereas it is a decreasing one of the electron–phonon coupling strength.

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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: 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.
...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.
...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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Contributors: D. Sugny, M. Ndong, D. Lauvergnat, Y. Justum, M. Desouter-Lecomte

Date: 2007-08-15

We examine the effect of dissipation on the laser control of a process that transforms a state into a superposed state. We consider a two-dimensional double well of a single potential energy surface. In the context of reactivity, the objective of the control is the localization in a given well, for instance the creation of an enantiomeric form whereas for quantum gates, this control corresponds to one of the transformation of the Hadamard gate. The environment is either modelled by coupling few harmonic **oscillators** (up to five) to the system or by an effective interaction with an Ohmic bath. In the discrete case, dynamics is carried out exactly by using the coupled harmonic adiabatic channels. In the continuous case, Markovian and non-Markovian dynamics are considered. We compare two laser control strategies: the Stimulated Raman Adiabatic Passage (STIRAP) method and the optimal control theory. Analytical estimations for the control by adiabatic passage in a Markovian environment are also derived....Dynamics controlled by f-STIRAP strategy for the preparation of the superposed state |R〉. Panels (a) and (b) show, respectively, the evolution of the localization in the right well for different values of λ and the Rabi **frequencies** of the different pulses. Rabi **frequencies** are in atomic units. The solid line of panel (b) corresponds to the Stokes pulse and the dashed one to the pump pulse. The total duration of the process is of the order of 4.5ps.
...**Qubit**...Half-live time τ1/2 in fs and the time τmax for which C(t) (Eq. (12)) vanishes for the two reference **frequencies** (Eq. (7)) and temperatures used in the simulations
...Robustness of the f-STIRAP process as a function of the peak Rabi **frequency** and the delay between the pulses for a total duration of 4.5ps of the overall field. Rabi **frequency** and delay are in atomic units. The upper and the lower part of the figure correspond, respectively, to λ=5×10−4 and λ=2×10−3.
... We examine the effect of dissipation on the laser control of a process that transforms a state into a superposed state. We consider a two-dimensional double well of a single potential energy surface. In the context of reactivity, the objective of the control is the localization in a given well, for instance the creation of an enantiomeric form whereas for quantum gates, this control corresponds to one of the transformation of the Hadamard gate. The environment is either modelled by coupling few harmonic **oscillators** (up to five) to the system or by an effective interaction with an Ohmic bath. In the discrete case, dynamics is carried out exactly by using the coupled harmonic adiabatic channels. In the continuous case, Markovian and non-Markovian dynamics are considered. We compare two laser control strategies: the Stimulated Raman Adiabatic Passage (STIRAP) method and the optimal control theory. Analytical estimations for the control by adiabatic passage in a Markovian environment are also derived.

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Contributors: A. Yoshimi, T. Inoue, T. Furukawa, T. Nanao, K. Suzuki, M. Chikamori, M. Tsuchiya, H. Hayashi, M. Uchida, N. Hatakeyama

Date: 2012-05-14

(a) Spin maser **oscillation** signal observed in a time span of 24 hours. (b) Transient pattern in the initial spin maser **oscillation**. (c) Steady state **oscillation** after the transient settled. The signals shown in the ordinates represent the beat between the spin detection signal and a 36.12 Hz fixed **frequency** reference signal for a lock-in amplifier.
...(a) Fourier spectrum obtained when the newly introduced current source was used for the **oscillator** operation. The measurement time was 3×104 seconds. (b) Fourier spectrum obtained when the previous current source was used for the **oscillator** operation. The measurement time was 1×104 seconds.
...Nuclear spin **oscillator**...We have constructed a 129Xe nuclear spin **oscillator** which executes a self-sustained **oscillation** through an external feedback loop with optical detection of nuclear spin. The **oscillator** is capable of operating at **frequencies** much lower than the conventional nuclear spin maser. A method for efficient optical detection of spin has been developed and applied to the nuclear spin **oscillator**, and the **frequency** characteristics of the **oscillator** at low **frequencies** has been investigated. The spin **oscillator** was operated at **frequencies** 2.5–36 Hz. The **frequency** performance of the **oscillator** is discussed in relation to a planned search for an atomic electric dipole moment taking advantage of the present **oscillator** scheme....Steady state **oscillations** observed at three low **frequencies**: (a) ν0=17.7 Hz, (b) ν0=8.9 Hz, (c) ν0=2.5 Hz. The strength of the static field adopted in the individual operations are indicated in the respective panels.
...**Frequency** precision...**Frequency** precision of the spin **oscillation**. The abscissa represents the standard deviation of the **frequency** ν determined by fitting a function ϕ(t)=2πνt+ϕ0 to the observed precession phases ϕ from t=0 to t=Tm. Solid, dotted and dashed lines are the presentation of three cases with power laws σν∝Tm−3/2, σν∝Tm−1, and σν∝Tm−1/2 respectively.
... We have constructed a 129Xe nuclear spin **oscillator** which executes a self-sustained **oscillation** through an external feedback loop with optical detection of nuclear spin. The **oscillator** is capable of operating at **frequencies** much lower than the conventional nuclear spin maser. A method for efficient optical detection of spin has been developed and applied to the nuclear spin **oscillator**, and the **frequency** characteristics of the **oscillator** at low **frequencies** has been investigated. The spin **oscillator** was operated at **frequencies** 2.5–36 Hz. The **frequency** performance of the **oscillator** is discussed in relation to a planned search for an atomic electric dipole moment taking advantage of the present **oscillator** scheme.

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Contributors: S. Filippov, V. Vyurkov, L. Fedichkin

Date: 2011-11-01

**Qubit** dynamics in Bloch ball picture. North pole corresponds to the excited (antisymmetric) energy eigenstate |1〉 and south pole corresponds to the ground (symmetric) state |0〉. Initially the electron is localized in one of the dots. Quality of Rabi **oscillations** Q=40. The effect of image charge potential: (a) K=0 and (b) K=0.4.
...Quality of **qubit** Rabi **oscillations** vs. distance to a metal surface. Centers of quantum dots are located 100nm apart. Lines and points correspond to analytical and numerical solutions, respectively.
...A charge-based **qubit** is subject to image forces originating in nearby metal gates. Displacement of charge in an **oscillating** **qubit** indispensably results in moving charges in metal. Therefore, Joule loss is one more source of **qubit** decoherence. We have estimated the quality of Rabi **oscillations** for a realistic double-quantum-dot as Q∼100. This kind of decoherence cannot be suppressed by lowering temperature as it is evoked by surface roughness scattering of electrons which is almost insensitive to temperature. Possibilities to avoid such a decoherence are briefly discussed. The effect of energy dissipation and image charge potential on **qubit** dynamics is studied by means of a specific local-in-time non-Markovian master equation....Quality of **qubit** Rabi **oscillations** vs. the distance between quantum dots. **Qubit** is located 50nm far from the metal surface. Lines and points correspond to analytical and numerical solutions, respectively.
...The moving charge in the **qubit** drags charges in metal that indispensably entails Joule loss: d is a double dot separation and D is a distance to the metal surface.
... A charge-based **qubit** is subject to image forces originating in nearby metal gates. Displacement of charge in an **oscillating** **qubit** indispensably results in moving charges in metal. Therefore, Joule loss is one more source of **qubit** decoherence. We have estimated the quality of Rabi **oscillations** for a realistic double-quantum-dot as Q∼100. This kind of decoherence cannot be suppressed by lowering temperature as it is evoked by surface roughness scattering of electrons which is almost insensitive to temperature. Possibilities to avoid such a decoherence are briefly discussed. The effect of energy dissipation and image charge potential on **qubit** dynamics is studied by means of a specific local-in-time non-Markovian master equation.

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Contributors: Ch. Wunderlich, Ch. Balzer

Date: 2003-01-01

Illustration of a linear ion trap including an axial magnetic field gradient. The static field makes individual ions distinguishable in **frequency** space by Zeeman-shifting their internal energy levels (solid horizontal lines represent **qubit** states). In addition, it mediates the coupling between internal and external degrees of freedom when a driving field is applied (dashed horizontal lines stand for vibrational energy levels of the ion string, see text).
...Rabi **oscillations** on the optical E2 transition S1/2-D5/2 in Ba + . A fit of the data (solid line) yields a Rabi **frequency** of 71.4 × 2πkHz and a transversal relaxation time of 100 μs (determined by the coherence time of the ir light used to drive the E2 resonance).
...Illustration of the coupled system ‘**qubit** ⊗ harmonic **oscillator**’ in a trap with magnetic field gradient. Internal **qubit** transitions lead to a displacement dz of the ion from its initial equilibrium position and consequently to the excitation of vibrational motion. In the formal description the usual Lamb–Dicke parameter is replaced by a new effective one (see text).
...This chapter discusses quantum measurements and new concepts for experiments with trapped ions. Quantum mechanics is a tremendously successful theory playing a central role in natural sciences even beyond physics, and has been verified in countless experiments, some of which were carried out with very high precision. Quantum theory predicts correlations between two or more quantum systems once an entangled state of these systems has been generated. The chapter introduces experiments with 171Yb+ ions demonstrating the precise manipulation of hyperfine states of single ions essentially free of longitudinal and transverse relaxation. A new concept for ion traps is described that allows for experiments requiring individual addressing of ions and conditional dynamics with several ions even with radiation in the radio **frequency** (rf) or microwave (mw) regime. It is shown how an additional magnetic field gradient applied to an electrodynamic trap individually shifts ionic **qubit** resonances making them distinguishable in **frequency** space. Thus, individual addressing for the purpose of single **qubit** operations becomes possible using long-wavelength radiation. At the same time, a coupling term between internal and motional states arises even when rf or mw radiation is applied to drive **qubit** transitions. Thus, conditional quantum dynamics can be carried out in this modified electrodynamic trap and in such a new type of trap all schemes originally devised for optical QIP in ion traps can be applied in the rf or mw regime, too....(a) Relevant energy levels and transitions in 138Ba + . (b) Schematic drawing of major experimental elements. OPO: Optical parametric **oscillator**; YAG: Nd:YAG laser; LD: laser diode; DSP: Digital signal processing system allows for real time control of experimental parameters; AOM: Acousto-optic modulators used as optical switches and for tuning of laser light; PM: Photo multiplier tube, serves for detection of resonance fluorescence. All lasers are **frequency** and intensity stabilized (not shown).
...Schematic drawing of the resonances of **qubits** j and j + 1 with some accompanying sideband resonances. The angular **frequency** vN corresponds to the Nth axial vibrational mode, and the **frequency** separation between carrier resonances is denoted by δω.
... This chapter discusses quantum measurements and new concepts for experiments with trapped ions. Quantum mechanics is a tremendously successful theory playing a central role in natural sciences even beyond physics, and has been verified in countless experiments, some of which were carried out with very high precision. Quantum theory predicts correlations between two or more quantum systems once an entangled state of these systems has been generated. The chapter introduces experiments with 171Yb+ ions demonstrating the precise manipulation of hyperfine states of single ions essentially free of longitudinal and transverse relaxation. A new concept for ion traps is described that allows for experiments requiring individual addressing of ions and conditional dynamics with several ions even with radiation in the radio **frequency** (rf) or microwave (mw) regime. It is shown how an additional magnetic field gradient applied to an electrodynamic trap individually shifts ionic **qubit** resonances making them distinguishable in **frequency** space. Thus, individual addressing for the purpose of single **qubit** operations becomes possible using long-wavelength radiation. At the same time, a coupling term between internal and motional states arises even when rf or mw radiation is applied to drive **qubit** transitions. Thus, conditional quantum dynamics can be carried out in this modified electrodynamic trap and in such a new type of trap all schemes originally devised for optical QIP in ion traps can be applied in the rf or mw regime, too.

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