Protection of qubits by nonlinear resonances

Saini, Rakesh; Sehgal, R.; Jain, Sudhir R.

doi:10.1140/epjp/s13360-022-02561-6

Cited by 7 publications

(4 citation statements)

References 25 publications

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“…In the future, by adding nonlinear terms to incorporate interactions that allow the control of atomic states, these works could be useful for critical quantum metrology [ 75 ]. The control of states of multi-qubit systems [ 76 ] and their protection [ 77 ] belongs to the present theme in a rather compelling manner.…”

Section: Discussionmentioning

confidence: 99%

Quasi-integrability and nonlinear resonances in cold atoms under modulation

Gupta,

Jain,

Jain

2024

R. Soc. Open Sci.

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Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix Hamiltonian. The dynamics is shown to evolve on two coupled potential energy surfaces (PESs): one of them is binding, while the other one is scattering type. The dynamics is shown to be quasi-integrable with nonlinear resonances. The bounded dynamics with intermittent scattering at random moments presents a scenario reminiscent of Anderson and dynamical localization. We believe that a careful analytical investigation of a multi-component system that is classically non-integrable is relevant to many other fields, including quantum computation with multi-qubit systems.

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Section: Discussionmentioning

confidence: 99%

Quasi-integrability and nonlinear resonances in cold atoms under modulation

Gupta,

Jain,

Jain

2024

R. Soc. Open Sci.

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“…As discussed earlier, transition probability is intimately related to the time of transition from θ = 0 to θ = −π which becomes interesting in the context of any discussion of Zeno effect. In this case, it is simply calculated using (22):…”

Section: Time Of Transitionmentioning

confidence: 99%

“…However, the quantum fluctuations and tunneling across the separatrices which would enable the system to continue evolving. The tunneling probability is proportional to exp[−τ S I / ] where S I is the imaginary part of the action as the separatrix is crossed and τ is the inverse of the characteristic stability exponent along the unstable direction [21,22] found by the linearization process above.…”

Section: Critical Points and Their Stabilitymentioning

confidence: 99%

Qubit control using quantum Zeno effect: Action principle approach

Kumari,

Rajpoot,

Joshi

et al. 2022

Preprint

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We employ the stochastic path-integral formalism and action principle for continuous quantum measurements -the Chantasri-Dressel-Jordan (CDJ) action formalism [1, 2] -to understand the stages in which quantum Zeno effect helps control the states of a simple quantum system. The detailed dynamics of a driven two-level system subjected to repeated measurements unravels a myriad of phases, so to say. When the detection frequency is smaller than the Rabi frequency, the oscillations slow down, eventually coming to a halt at an interesting resonance when measurements are spaced exactly by the time of transition between the two states. On the other hand, in the limit of large number of repeated measurements, the dynamics organizes itself in a rather interesting way about two hyperbolic points in phase space whose stable and unstable directions are reversed. Thus, the phase space flow occurs from one hyperbolic point to another, in different ways organized around the separatrices. We believe that the systematic treatment presented here paves the way for a better and clearer understanding of quantum Zeno effect in the context of quantum error correction.

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“…Additional examples include the generation of NOON states in ultracold bosonic atoms [9,10], the efficacy of coherent control in driven [11][12][13][14] and kicked [15,16] systems, stability of quantum discrete breathers [17,18], and fragmentation of trapped Bose-Einstein condensates [19,20]. Furthermore, dynamical tunneling has been shown to play a crucial role in a variety of "engineered" systems [21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Tunneling in More than Two Degrees of Freedom

Keshavamurthy

2024

Entropy

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Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case presents several challenges. Specifically, in higher-dimensional phase spaces, multiple mechanisms for classical transport have significant implications for the evolution of initial quantum states. In this review, the importance of features on the Arnold web, a signature of systems with three or more DoF, to the mechanism of resonance-assisted tunneling is illustrated using select examples. These examples represent relevant models for phenomena such as intramolecular vibrational energy redistribution in isolated molecules and the dynamics of Bose–Einstein condensates trapped in optical lattices.

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Protection of qubits by nonlinear resonances

Cited by 7 publications

References 25 publications

Quasi-integrability and nonlinear resonances in cold atoms under modulation

Quasi-integrability and nonlinear resonances in cold atoms under modulation

Qubit control using quantum Zeno effect: Action principle approach

Dynamical Tunneling in More than Two Degrees of Freedom

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