Controlling quantum critical dynamics of isolated systems

Campo, Adolfo del; Sengupta, K.

doi:10.1140/epjst/e2015-02350-4

Cited by 40 publications

(44 citation statements)

References 151 publications

(240 reference statements)

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“…A class of such dynamical phenomenon involve periodically driven quantum systems leading to multiple passages through their critical points during a drive cycle [18][19][20][21][22] . Such systems exhibit a wide class of dynamical phenomena which do not occur in their aperiodically driven counterparts.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, periodically driven integrable systems show a separate class of dynamical transitions which originates from the change in topology of their Floquet spectrum and leaves its imprint on temporal behavior of local correlation functions 24 . Such driven systems also exhibit the phenomenon of dynamics induced freezing 21,22,25,26 ; this phenomenon manifests itself in a near unity overlap of the system wavefunction after single or multiple drive period(s) with the initial wavefunction at t = 0. Such near-unity overlap signifying freezing occurs at specific discrete frequencies ω * and is therefore qualitatively different from the trivial freezing that occurs for ultrafast drive frequencies.…”

Section: Introductionmentioning

confidence: 99%

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Tuning towards dynamic freezing using a two-rate protocol

2016

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We study periodically driven closed quantum systems where two parameters of the system Hamiltonian are driven with frequencies ω1 and ω2 = rω1. We show that such drives may be used to tune towards dynamics induced freezing where the wavefunction of the state of the system after a drive cycle at time T = 2π/ω1 has almost perfect overlap with the initial state. We locate regions in the (ω1, r) plane where the freezing is near exact for a class of integrable and a specific non-integrable model. The integrable models that we study encompass Ising and XY models in d = 1, Kitaev model in d = 2, and Dirac fermions in graphene and atop a topological insulator surface whereas the non-integrable model studied involves the experimentally realized one-dimensional (1D) tilted Bose-Hubbard model in an optical lattice. In addition, we compute the relevant correlation functions of such driven systems and describe their characteristics in the region of (ω1, r) plane where the freezing is near-exact. We supplement our numerical analysis with semi-analytic results for integrable driven systems within adiabatic-impulse approximation and discuss experiments which may test our theory.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tuning towards dynamic freezing using a two-rate protocol

2016

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“…Previous research has shown that even when the spectral properties are available, the required control fields to guide the dynamics of a complex system involves highly nonlocal interactions. This understanding has been gained by analyzing critical quantum spin systems [77][78][79][80][81][82][83][84], see [3] for a review.…”

Section: Many-body Systems: Complexity Barriermentioning

confidence: 99%

Focus on Shortcuts to Adiabaticity

Campo

Kim

2019

New J. Phys.

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Shortcuts to Adiabaticity (STA) constitute driving schemes that provide an alternative to adiabatic protocols to control and guide the dynamics of classical and quantum systems without the requirement of slow driving. Research on STA advances swiftly with theoretical progress being accompanied by experiments on a wide variety of platforms. We summarize recent developments emphasizing advances reported in this focus issue while providing an outlook with open problems and prospects for future research.

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“…In addition, theoretical studies have shown that STA can be used to guide the evolution of many-body quantum systems that exhibit quantum critical behavior [30,31]. In this context, STA can be used to suppress excitation formation across a phase transition [32]. Implementing STA may require modifying the systems Hamiltonian with nonlocal interactions including high order terms [30,33].…”

Section: Introductionmentioning

confidence: 99%

Shortcuts to adiabaticity assisted by counterdiabatic Born–Oppenheimer dynamics

Duncan

Campo

2018

New J. Phys.

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Shortcuts to adiabaticity (STA) provide control protocols to guide the dynamics of a quantum system through an adiabatic reference trajectory in an arbitrary prescheduled time. Designing STA proves challenging in complex quantum systems when the dynamics of the degrees of freedom span different time scales. We introduce counterdiabatic Born-Oppenheimer dynamics (CBOD) as a framework to design STA in systems with a large separation of energy scales. CBOD exploits the Born-Oppenheimer approximation to separate the Hamiltonian into effective fast and slow degrees of freedom and calculate the corresponding counterdiabatic drivings for each sub-system. We show the validity of the CBOD technique via an example of coupled harmonic oscillators, which can be solved exactly for comparison, and further apply it to a system of two-charged particles.

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Controlling quantum critical dynamics of isolated systems

Cited by 40 publications

References 151 publications

Tuning towards dynamic freezing using a two-rate protocol

Tuning towards dynamic freezing using a two-rate protocol

Focus on Shortcuts to Adiabaticity

Shortcuts to adiabaticity assisted by counterdiabatic Born–Oppenheimer dynamics

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