Intrinsic Dynamical Fluctuation Assisted Symmetry Breaking in Adiabatic Following

Zhang, Qi; Gong, Jiangbin; Oh, C. H.

doi:10.1103/physrevlett.110.130402

Cited by 4 publications

(6 citation statements)

References 33 publications

(27 reference statements)

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“…3 CNRS, Laboratoire des signaux et systèmes (L2S) Supélec, 3 rue Joliot-Curie, 91192 Gif-Sur-Yvette, France. 4 School of Engineering and Information Technology, University of New South Wales at ADFA, 2600 Canberra, Australia.…”

Section: Acknowledgementsmentioning

confidence: 99%

“…Adiabatic process is aimed at stabilizing a parameter-varying quantum system at its eigenstate. This process has many applications in the engineering of quantum systems [1,2,3,4,5], and in particular plays the fundamental role in adiabatic quantum computation (AQC) [6,7,8]. The adiabatic theorem [9,10] states that a system will undergo adiabatic evolution given that the system parameter varies slowly.…”

Section: Introductionmentioning

confidence: 99%

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Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem

Pan¹,

Zhang²,

Amini³

et al. 2015

EPJ Quantum Technol.

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Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure resembles the excitation energy or excess work performed in thermodynamics, which can be taken as the error of adiabatic approximation. We prove that under certain conditions, this error can be estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not linearly proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example in which the applicability of the adiabatic theorem is questionable.

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Section: Acknowledgementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem

Pan¹,

Zhang²,

Amini³

et al. 2015

EPJ Quantum Technol.

View full text Add to dashboard Cite

show abstract

“…Moreover, by substituting the hierarchically corrected wavefunction into the original Schrödinger equation, we may study possible corrections to the overall phase of the timeevolving quantum state [34,35]. Our approach can be directly applied to classical adiabatic processes and nonlinear quantum adiabatic evolution on the mean-field level [44][45][46][47][48][49]. For example, it is of considerable interest to apply our findings to assist in the control of adiabatic processes in both classical and quantum systems [50][51][52].…”

Section: Discussionmentioning

confidence: 99%

Hierarchical theory of quantum adiabatic evolution

Zhang¹,

Gong²,

Wu³

2014

New J. Phys.

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Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between non-degenerate instantaneous eigen-energy levels in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy levels. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians are constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The kth-order deviations are governed by a kth-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the kth-order. Two simple examples, the Landau-Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory.

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“…In that almost trivial case a(t) and b(t) can be easily found by solving the two first-order differential equations as suggested by Eqs. (11) and (12). If Eq.…”

Section: Differential Equationsmentioning

confidence: 99%

“…This issue is also of general interest because in Nature, slow and almost periodic modulation is often naturally introduced to a broad class of systems around us, by the slow periodic change of the four seasons. The common wisdom would say Yes to the question here, but caution must be taken because even in the domain of conventional quantum mechanics, new understandings of the physics of adiabatic following are still emerging [9][10][11][12][13][14]. Indeed, as shown by a recent study by us [15], the concept of adiabatic following with the instantaneous eigenstates of the system Hamiltonian is actually not necessarily true.…”

Section: Introductionmentioning

confidence: 99%

Piecewise adiabatic following: General analysis and exactly solvable models

Gong

Wang

2019

Phys. Rev. A

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The dynamics of a periodically driven system whose time evolution is governed by the Schrödinger equation with non-Hermitian Hamiltonians can be perfectly stable. This finding was only obtained very recently and will be enhanced by many exact solutions discovered in this work. The main concern of this study is to investigate the adiabatic following dynamics in such non-Hermitian systems stabilized by periodic driving. We focus on the peculiar behavior of stable cyclic (Floquet) states in the slow-driving limit. It is found that the stable cyclic states can either behave as intuitively expected by following instantaneous eigenstates, or exhibit piecewise adiabatic following by sudden-switching between instantaneous eigenstates. We aim to cover broad categories of non-Hermitian systems under a variety of different driving scenarios. We systematically analyze the sudden-switch behavior by a universal route. That is, the sign change of the critical exponent in our asymptotic analysis of the solutions is always found to be the underlying mechanism to determine if the adiabatic following dynamics is trivial or piecewise. This work thus considerably extends our early study on the same topic [Gong and Wang, Phys. Rev. A 97, 052126 (2018)] and shall motivate more interests in non-Hermitian systems.

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Intrinsic Dynamical Fluctuation Assisted Symmetry Breaking in Adiabatic Following

Cited by 4 publications

References 33 publications

Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem

Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem

Hierarchical theory of quantum adiabatic evolution

Piecewise adiabatic following: General analysis and exactly solvable models

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