Analytic solutions to the two-state problem for a class of coupling potentials

Bambini, A.; Berman, P. R.

doi:10.1103/physreva.23.2496

Cited by 208 publications

(134 citation statements)

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“…The phenomenon of pulsed perturbations that return the full amplitude/occupation to the initial state has been studied in the context of atom-laser interactions. [29][30][31][32] In Figs. 4-6, we compare our semiclassical estimate ͑35͒ with results from numerical simulations of the exact quantum mechanical time FIG.…”

Section: ͑36͒mentioning

confidence: 99%

Double occupancy errors in quantum computing operations: Corrections to adiabaticity

et al. 2005

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We study the corrections to adiabatic dynamics of two coupled quantum dot spin qubits, each dot singly occupied with an electron, in the context of a quantum computing operation. Tunneling causes double occupancy at the conclusion of an operation and constitutes a processing error. We model the gate operation with an effective two-level system, where nonadiabatic transitions correspond to double occupancy. The model is integrable and possesses three independent parameters. We confirm the accuracy of Dykhne's formula, a nonperturbative estimate of transitions, and discuss physically intuitive conditions for its validity. Our semiclassical results are in excellent agreement with numerical simulations of the exact time evolution. A similar approach applies to two-level systems in different contexts.

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Section: ͑36͒mentioning

confidence: 99%

Double occupancy errors in quantum computing operations: Corrections to adiabaticity

et al. 2005

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“…On the other hand, the κ = 0.5 case is sensitive to the condition |Λ 1 | = |Λ 2 |. The filter function (20) with κ = 0.5 can also be achieved by using a constant detuning ∆ω and an asymmetric field coupling g(t) in the Hamiltonian (3), see [11].…”

Section: The Adiabatic Limitmentioning

confidence: 99%

Cavity field ensembles from non-selective measurements

Larson¹,

Stenholm²

2004

Journal of Modern Optics

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We continue our investigations of cavity QED with time dependent parameters. In this paper we discuss the situation where the state of the atoms leaving the cavity is reduced but the outcome is not recorded. In this case our knowledge is limited to an ensemble description of the results only. By applying the Demkov-Kunike level-crossing model, we show that even in this case, the filtering action of the interaction allows us to prepare a preassigned Fock state with good accuracy. The possibilities and limitations of the method are discussed and some relations to earlier work are presented.

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“…The coherence Bloch vector R ν is widely used in the theory of the magnetic resonance and characterizes the qudit behavior. In the case of the consistent field, as the expansion of the Rabi model, the solution (with the initial matrix elements ρ 1,1 (t = 0) = 1 and other ones are equal to zero) at resonance ω = H for the spin components of qubit or qutrit is the following: R = r B (sn(ωt|k) sin ht, − cn(ωt|k) sin ht, cos ht), (5) where r B = 3S/(S + 1) is the Bloch sphere radius. For higher spins, the direct calculation looks the same (5) only if k = 0.…”

Section: Master Equationmentioning

confidence: 99%

“…Such field modulation under the changing of the elliptic modulus k from 0 to 1 describes the whole class of field forms from trigonometric [4] (k = 0) to the exponentially impulse ones (k = 1) [5]. The elliptic functions cn(ωt|k) and sn(ωt|k) have a real period 4K/ω, while the function dn(ωt|k) has a period of half a duration.…”

Section: Introductionmentioning

confidence: 99%

Quantum speed limit time in a magnetic resonance

Ivanchenko

2017

Physics Letters A

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A visualization for dynamics of a qudit spin vector in a time-dependent magnetic field is realized by means of mapping a solution for a spin vector on the three-dimensional spherical curve (vector hodograph). The obtained results obviously display the quantum interference of precessional and nutational effects on the spin vector in the magnetic resonance. For any spin the bottom bounds of the quantum speed limit time (QSL) are found. It is shown that the bottom bound goes down when using multilevel spin systems. Under certain conditions the non-nil minimal time, which is necessary to achieve the orthogonal state from the initial one, is attained at spin S=2. An estimation of the product of two and three standard deviations of the spin components are presented. We discuss the dynamics of the mutual uncertainty, conditional uncertainty and conditional variance in terms of spin standard deviations. The study can find practical applications in the magnetic resonance, 3D visualization of computational data and in designing of optimized information processing devices for quantum computation and communication.

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Analytic solutions to the two-state problem for a class of coupling potentials

Cited by 208 publications

References 1 publication

Double occupancy errors in quantum computing operations: Corrections to adiabaticity

Double occupancy errors in quantum computing operations: Corrections to adiabaticity

Cavity field ensembles from non-selective measurements

Quantum speed limit time in a magnetic resonance

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