Algebraic theory of quantum synchronization and limit cycles under  dissipation

Buča, Berislav; Booker, Cameron; Jaksch, Dieter

doi:10.21468/scipostphys.12.3.097

Cited by 56 publications

(27 citation statements)

References 197 publications

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“…Crucially, these states are offdiagonal in the physical environmental (and many-body) eigenbasis of Q k (j) and therefore can store a qubit. This is reminiscent of noiseless subsystems [82][83][84] and other more exotic decoherence free structures [85,86]. However, in our case there is no clear distinction between the coherent system and decoherent environment because a dynamical ℓ−bit centered around site j spreads into other neighboring sites and has spatial overlap with neighboring dynamical ℓ−bits (i.e.…”

mentioning

confidence: 83%

Protecting coherence from environment via Stark many-body localization in a Quantum-Dot Simulator

Sarkar¹,

Buča²

2022

Preprint

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Semiconductor platforms are emerging as a promising architecture for storing and processing quantum information e.g., in quantum dot spin qubits. These setups have relatively low nuclear noise, but charge noise coming from many body interactions between the electrons is a major limiting factor with scalability for a useful quantum computer. Here we show how an electric field gradient, readily obtainable with semiconductor quantum dots, can be engineered to induce local quantum coherent dynamical ℓ−bits that have potential to be used as logical qubits. We take into account the full (interacting) electron and phonon dynamics, and analytically, from first principles without any approximation, show that these dynamical ℓ−bits are protected from all sources noise for exponentially long times provided only that the electron-phonon interaction is not completely non-local. Our work opens a new venue for passive quantum error correction and scaling of semiconductor quantum computers.

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confidence: 83%

Protecting coherence from environment via Stark many-body localization in a Quantum-Dot Simulator

Sarkar¹,

Buča²

2022

Preprint

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“…Third, the dissipation-induced non-thermalization proposed here is distinct from the dissipation-induced nonstationary dynamics of dissipative Hubbard models studied in Refs. [78,[159][160][161]. While dissipation in the previous works induces coherent oscillations in the dark space, here we utilize dissipation to distill the integrable dynamics of effectively non-interacting particles in the MHM.…”

Section: Dissipation-induced Non-thermalizationmentioning

confidence: 99%

Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $η$ pairing, weak ergodicity breaking, and partial integrability

Nakagawa¹,

Katsura²,

Ueda³

2022

Preprint

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We construct exact eigenstates of multicomponent Hubbard models in arbitrary dimensions by generalizing the η-pairing mechanism. Our models include the SU(N ) Hubbard model as a special case. Unlike the conventional two-component case, the generalized η-pairing mechanism permits the construction of eigenstates that feature off-diagonal long-range order and magnetic long-range order. These states form fragmented fermionic condensates due to a simultaneous condensation of multicomponent η pairs. While the η-pairing states in the SU(2) Hubbard model are based on the η-pairing symmetry, the exact eigenstates in the N -component system with N ≥ 3 arise not from symmetry of the Hamiltonian but from a spectrum generating algebra defined in a restricted Hilbert space. We exploit this fact to show that the generalized η-pairing eigenstates do not satisfy the eigenstate thermalization hypothesis and serve as quantum many-body scar states. This result indicates a weak breakdown of ergodicity in the N -component Hubbard models for N ≥ 3. Furthermore, we show that these exact eigenstates constitute integrable subsectors in which the Hubbard Hamiltonian effectively reduces to a non-interacting model. This partial integrability causes various multicomponent Hubbard models to weakly break ergodicity. We propose a method of harnessing dissipation to distill the integrable part of the dynamics and elucidate a mechanism of non-thermalization caused by dissipation. This work establishes the coexistence of off-diagonal longrange order and SU(N ) magnetism in excited eigenstates of the multicomponent Hubbard models, which presents a possibility of novel out-of-equilibrium pairing states of multicomponent fermions. These models unveil a unique feature of quantum thermalization of multicomponent fermions, which can experimentally be tested with cold-atom quantum simulators.

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“…However, generalizing the previously introduced notions of synchronization is challenging as phase space trajectories are ill defined concepts in the quantum regime. To overcome this challenge, synchronization measures in terms of the Husimi-Q or Wigner phase space distributions [8,11,51], explicit limit cycles of system observables [52,53], or informationtheoretical measures [54,55] have been proposed. In this work, we use a measure to quantify synchronization of two quantum systems j and j ′ that is based on their dimensionless quadratures as [56]…”

Section: A Synchronization and The Quantum Van Der Pol Oscillatormentioning

confidence: 99%