Population trapping in three-state quantum loops revealed by Householder reflections

Rangelov, Andon A.; Vitanov, Nikolay V.; Shore, Bruce W.

doi:10.1103/physreva.77.033404

Cited by 14 publications

(6 citation statements)

References 39 publications

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“…Allowing φ to take arbitrary values extends the concept of reflection by imprinting an arbitrary phase onto the component along |ψ , rather than a simple sign inversion. Householder reflections are widely used in classical data analysis and also constitute a powerful tool for coherent manipulation of quantum systems [21][22][23][24][25]. The core component of Grover's algorithm is a pair of coupled Householder reflections, which together form a single Grover operatorĜ:Ĝ…”

Section: Grover's Search Algorithmmentioning

confidence: 99%

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Scalable quantum search using trapped ions

Ivanov¹,

Ivanov²,

Linington³

et al. 2010

Phys. Rev. A

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We propose a scalable implementation of Grover's quantum search algorithm in a trapped-ion quantum information processor. The system is initialized in an entangled Dicke state by using simple adiabatic techniques. The inversion-about-average and the oracle operators take the form of single off-resonant laser pulses, addressing, respectively, all and half of the ions in the trap. This is made possible by utilizing the physical symmetrie of the trapped-ion linear crystal. The physical realization of the algorithm represents a dramatic simplification: each logical iteration (oracle and inversion about average) requires only two physical interaction steps, in contrast to the large number of concatenated gates required by previous approaches. This does not only facilitate the implementation, but also increases the overall fidelity of the algorithm.Comment: 6 pages, 2 figure

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Section: Grover's Search Algorithmmentioning

confidence: 99%

“…Householder reflections are widely used in classical data analysis and also constitute a powerful tool for coherent manipulation of quantum systems [22][23][24][25][26]. The core component of Grover's algorithm is a pair of coupled Householder reflections, which together form a single Grover operator Ĝ:…”

Section: Grover's Search Algorithmmentioning

confidence: 99%

Scalable quantum search using trapped ions

Ivanov¹,

Ivanov²,

Linington³

et al. 2010

Phys. Rev. A

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“…A way out of this problem comes from a similarity transformation streaming from the idea employed in [ 87 ],

where the matrix

reads

Thus, we can reduce the system to independent sub-systems, and allow for a simpler derivation of the trapping condition by fixing the rotation angle at

and further applying the shift transformation

The transformed Hamiltonian then reads

where the matrices

and

are given by

…”

Section: Multilevel Lics Systemmentioning

confidence: 99%

“…A way out of this problem comes from a similarity transformation streaming from the idea employed in [87],…”

Section: Multilevel Lics Systemmentioning

confidence: 99%

Multilevel Laser Induced Continuum Structure

Zlatanov

Vitanov

2021

Entropy

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Laser-induced-continuum-structure (LICS) allows for coherent control techniques to be applied in a Raman type system with an intermediate continuum state. The standard LICS problem involves two bound states coupled to one or more continua. In this paper, we discuss the simplest non-trivial multistate generalization of LICS which couples two bound levels, each composed of two degenerate states through a common continuum state. We reduce the complexity of the system by switching to a rotated basis of the bound states, in which different sub-systems of lower dimension evolve independently. We derive the trapping condition and explore the dynamics of the sub-systems under different initial conditions.

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“…(31). We consider a simplified version of the procedure, suited for our problem, for a detailed investigation of the system we refer the reader to [59]. The Hamiltonian of a three state system under cyclic excitation given in Fig.…”

mentioning

confidence: 99%

Chiral resolution based on laser-induced continuum structure

Zlatanov,

Vitanov

2021

Preprint

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In this paper we propose a chiral resolution technique based on laser-induced continuum structure (LICS). We show that the two enantiomers can have a different ionization profile based on implemented LICS excitation. We treat a cyclic excitation between two bound states and a continuum state and show how asymmetric ionization can be achieved based on different trapping of the enantiomers due to the additional coupling between the bound states. Alternatively, when multiple states are involved in the interaction we investigate a multilevel LICS strategy of asymmetric ionization based on dark-bright state trapping. In this latter case one of the enantiomers is trapped in a dark state, which is immune to ionization, while the other is driven in a bright state, from which the population leaks into the continuum.

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Population trapping in three-state quantum loops revealed by Householder reflections

Cited by 14 publications

References 39 publications

Scalable quantum search using trapped ions

Scalable quantum search using trapped ions

Multilevel Laser Induced Continuum Structure

Chiral resolution based on laser-induced continuum structure

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