Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation

Buca, Berislav; Booker, Cameron; Jaksch, Dieter

doi:10.48550/arxiv.2103.01808

Cited by 9 publications

(10 citation statements)

References 151 publications

(218 reference statements)

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“…In future work, we plan to apply our approach to many-body spin and bosonic systems where multistability and persistent oscillations have been experimentally observed in the thermodynamic limit. Exploring the underlying connection between emergent collective behaviors and topology in such systems with quantum synchronization [103,[113][114][115] are other interesting directions of the future studies. Importantly, our work provides an approach for proving presence of bistability in more general and widely studied quantum optical setups.…”

Section: Discussionmentioning

confidence: 99%

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Exact bistability and time pseudo-crystallization of driven-dissipative fermionic lattices

Alaeian¹,

Buča²

2022

Preprint

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The existence of bistability in quantum optical systems remains a intensely debated open question beyond the mean-field approximation. Quantum fluctuations are finite-size corrections to the mean-field approximation used because the full exact solution is unobtainable. Usually, quantum fluctuations destroy the bistability present on the mean-field level. Here, by identifying and using exact modulated semi-local dynamical symmetries in a certain quantum optical models of drivendissipative fermionic chains we exactly prove bistability in precisely the quantum fluctuations. Surprisingly, rather than destroying bistability, the quantum fluctuations themselves exhibit bistability, even though it is absent on the mean-field level for our systems. Moreover, the models studied acquire additional thermodynamic dynamical symmetries that imply persistent periodic oscillations in the quantum fluctuations, constituting pseudo-variants of boundary time crystals. Physically, these emergent operators correspond to finite-frequency and finite-momentum semi-local Goldstone modes. Our work therefore provides to the best of our knowledge the first example of a provably bistable quantum optical system.

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Section: Discussionmentioning

confidence: 99%

“…As may be explicitly checked, the semi-local dynamical symmetry satisfies [A, L µ ] = [A † , L µ ] = 0, ∀µ implying that it is a strong dynamical symmetry of the dissipative model [103,104]. This implies that the Lindblad master equation of the model has purely imaginary eigenvalues λ ±1 = ±∆, for pure imaginary ∆.…”

mentioning

confidence: 94%

Exact bistability and time pseudo-crystallization of driven-dissipative fermionic lattices

Alaeian¹,

Buča²

2022

Preprint

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“…For Lindblad dynamics with strong symmetries (i.e., existence of unitary S such that [S, H] = 0 and [S, O k ] = 0), the dimensionality of the Liouville subspace L ss is determined by the number of unique eigenvalues of S and subspaces with L ss ≥ 2 are known to be information preserving [35]. For all of these reasons we refer to the phenomenon involving multiple oscillating coherences as undergoing coherence synchronisation in general [36] and use the phrase phase synchronisation for models where the underlying dynamics exhibits a stable limit cycle and a neutral free phase. We note that the general theory of phase ordering of oscillating coherences remains an open problem.…”

mentioning

confidence: 99%

Role of Coherence and Degeneracies in Quantum Synchronisation

Solanki,

Jaseem,

Hajdušek

et al. 2021

Preprint

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Progress on the study of synchronisation in quantum systems has been largely driven by specific examples which resulted in several examples of frequency entrainment as well as mutual synchronisation. Here we study quantum synchronisation by utilising Liouville space perturbation theory. We begin by clarifying the role of centers, symmetries and oscillating coherences in the context of quantum synchronisation. We then analyse the eigenspectrum of the Liouville superoperator generating the dynamics of the quantum system and determine the conditions under which synchronisation arises. We apply our framework to derive a powerful relationship between energy conservation, degeneracies and synchronisation in quantum systems. Finally, we demonstrate our approach by analysing two mutually coupled thermal machines and the close relationship between synchronisation and thermodynamic quantities.

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“…Fragmentation, frustration and strictly local dynamical symmetries -The emerging theory of dynamical symmetries [4] has been successfully applied for calculating dynamics of various non-stationary systems, and thus has potential for explaining non-stationarity in fragmented systems. Systems for which this theory has been applied include isolated time crystals [29], Floquet time crystals [38,39], dissipative time crystals [4,11], synchronization [4,40,41], and, when further extended, quantum manybody scars (e.g. [42][43][44][45][46][47]).…”

mentioning

confidence: 99%

Out-of-Time-Ordered Crystals and Fragmentation

Buča

2021

Preprint

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Quantum many-body models with both Hilbert space fragmentation and non-stationarity have recently been identified. Hilbert space fragmentation does not immediately imply non-stationarity. However, strictly local dynamical symmetries directly imply non-stationarity. It is demonstrated here that these symmetries are equivalent to local fragmentation into spatially localized blocks. Using strictly local dynamical symmetries, a lower bound is given here for persistent oscillations of generalised out-of-time-ordered correlation functions (OTOCs). A novel notion of genuinely manybody continuous time translation symmetry breaking is provided by demanding non-trivial spatial modulation of the Fourier transform of the OTOC. Such non-trivial spatial-temporal dynamics stems from a perpetual backflow of quantum scrambling. Here we call systems with time-translation symmetry breaking in the OTOC, OTO crystals. This breaking cannot be realised by systems with a single effective degree of freedom (e.g. spin precession). Furthermore, the breaking is stable to all local unitary and dissipative perturbations. An XYZ Creutz ladder is presented as an example.

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Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation

Cited by 9 publications

References 151 publications

Exact bistability and time pseudo-crystallization of driven-dissipative fermionic lattices

Exact bistability and time pseudo-crystallization of driven-dissipative fermionic lattices

Role of Coherence and Degeneracies in Quantum Synchronisation

Out-of-Time-Ordered Crystals and Fragmentation

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