Dynamical invariants of open quantum systems

Wu, Shunan; Zhang, X. Y.

doi:10.1103/physreva.92.062122

Cited by 9 publications

(3 citation statements)

References 33 publications

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“…This optimization has been performed so far by minimizing the excitation energy or maximizing the fidelity in perturbative schemes, e.g. in two-level systems (TLSs) [41][42][43][44] or for ion transport [45], using decoherence free subspaces [46,47], super-operator [48] and non-Hermitian invariants [49], and effective Hamiltonians [50].…”

Section: Introductionmentioning

confidence: 99%

Noise resistant quantum control using dynamical invariants

et al. 2018

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A systematic approach to design robust control protocols against the influence of different types of noise is introduced. We present control schemes which protect the decay of the populations avoiding dissipation in the adiabatic and nonadiabatic regimes and minimize the effect of dephasing. The effectiveness of the protocols is demonstrated in two different systems. Firstly, we present the case of population inversion of a two-level system in the presence of either one or two simultaneous noise sources. Secondly, we present an example of the expansion of coherent and thermal states in harmonic traps, subject to noise arising from monitoring and modulation of the control, respectively.

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Section: Introductionmentioning

confidence: 99%

Noise resistant quantum control using dynamical invariants

et al. 2018

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“…The invariant operator theory for timedependent harmonic oscillators is based on the construction of adiabatic invariants which were firstly introduced by Lewis and Riesenfeld [15,16] in describing their quantum features. The analysis of many oscillatory systems was fulfilled by introducing an invariant [13][14][15][16][17][18][19][20][21][22][23][24][25]. The dynamical invariant is also useful when we examine the entanglement for timedependent coupled oscillators based on the Schrödinger equation [14].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Invariant Applied on General Time-Dependent Three Coupled Nano-Optomechanical Oscillators

Hassoul

Benseridi

Choi

2021

Journal of Nanomaterials

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A quadratic invariant operator for general time-dependent three coupled nano-optomechanical oscillators is investigated. We show that the invariant operator that we have established satisfies the Liouville-von Neumann equation and coincides with its classical counterpart. To diagonalize the invariant, we carry out a unitary transformation of it at first. From such a transformation, the quantal invariant operator reduces to an equal, but a simple one which corresponds to three coupled oscillators with time-dependent frequencies and unit masses. Finally, we diagonalize the matrix representation of the transformed invariant by using a unitary matrix. The diagonalized invariant is just the same as the Hamiltonian of three simple oscillators. Thanks to such a diagonalization, we can analyze various dynamical properties of the nano-optomechanical system. Quantum characteristics of the system are investigated as an example, by utilizing the diagonalized invariant. We derive not only the eigenfunctions of the invariant operator, but also the wave functions in the Fock state.

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“…Floquet theory has seen a boom of interest in the last decades, specially due to its potential use in quantum simulation. Important advances in its extension to open quantum systems have also appeared recently [40,41,[44][45][46][47][48]. In particular, we call attention to Refs.…”

Section: Introductionmentioning

confidence: 99%

Lindblad-Floquet description of finite-time quantum heat engines

2018

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The operation of autonomous finite-time quantum heat engines rely on the existence of a stable limit cycle in which the dynamics becomes periodic. The two main questions that naturally arise are therefore whether such a limit cycle will eventually be reached and, once it has, what is the state of the system within the limit cycle. In this paper we show that the application of Floquet's theory to Lindblad dynamics offers clear answers to both questions. By moving to a generalized rotating frame, we show that it is possible to identify a single object, the Floquet Liouvillian, which encompasses all operating properties of the engine. First, its spectrum dictates the convergence to a limit cycle. And second, the state within the limit cycle is precisely its zero eigenstate, therefore reducing the problem to that of determining the steady-state of a time-independent master equation.To illustrate the usefulness of this theory, we apply it to a harmonic oscillator subject to a time-periodic work protocol and time-periodic dissipation, an open-system generalization of the Ermakov-Lewis theory. The use of this theory to implement a finite-time Carnot engine subject to continuous frequency modulations is also discussed.

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Dynamical invariants of open quantum systems

Cited by 9 publications

References 33 publications

Noise resistant quantum control using dynamical invariants

Noise resistant quantum control using dynamical invariants

Dynamical Invariant Applied on General Time-Dependent Three Coupled Nano-Optomechanical Oscillators

Lindblad-Floquet description of finite-time quantum heat engines

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