Real-time motion of open quantum systems: Structure of entanglement, renormalization group, and trajectories

Polyakov, Evgeny A.

doi:10.1103/physrevb.105.054306

Cited by 3 publications

(6 citation statements)

References 79 publications

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“…Therefore, we expect that near t = 0 the modes κ in k will appear at a high rate. But fast enough the highfrequency part of the quench spectrum will become decoupled [43,45], and we reach the Kotelnikov asymptocic rate t in k+1 − t in k ∝ τ = 1/B, see Fig. 3.…”

Section: A Forward Quantum Kotelnikov Samplingmentioning

confidence: 94%

“…Analogously to the classical spectral density eq. ( 4), the spectral density of the zero-point quantum noise (which coincides with the spectral density of the environment) J (ω) is also a Fourier transform [43,44]…”

Section: Bandlimited Quantum Noise Analogy To the Classical Kotelniko...mentioning

confidence: 99%

“…Analogously to the classical correlator eq. ( 3), we introduce the correlator of the zero-point quantum noise [43,44,58],…”

Section: Bandlimited Quantum Noise Analogy To the Classical Kotelniko...mentioning

confidence: 99%

“…In [44] we have implemented this approach in a numerical method and conjectured that the time domain should be employed in a properly formulated realtime renormalization group (RTRG). Such RTRG was proposed in [56] which was recently published as [43]. The present paper further develops this approach by taking into account the spectral properties of the quantum noise.…”

Section: Introductionmentioning

confidence: 99%

“…On the contrary, beyound the Markovian approximation, every excitation which is emitted by OQS can always be reabsorbed back (return to OQS) after a time interval t with some amplitude C q (t). This amplitude slowly decreases as a certain inverse power C q (t) ∝ t −p , p > 0 [43][44][45]. As a result, one fails to introduce the concept of full-fledged non-Markovian quantum jumps [46,47]: they appear to be never complete in finite time.…”

Section: Introductionmentioning

confidence: 99%

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Beyond The Fermi's Golden Rule: Discrete-Time Decoherence Of Quantum Mesoscopic Devices Due To Bandlimited Quantum Noise

Polyakov¹

2022

Preprint

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We are at the midst of second quantum revolution where the mesoscopic quantum devies are actively employed for technological purposes. Despite this fact, the description of their real-time dynamics beyond the Fermi's golden rule remains a formiddable theoretical problem. This is due to the rapid spread of entanglement within the degrees of freedom of the surrounding environment. This is accompanied with a quantum noise (QN) acting on the mesoscopic device. In this work we propose a possible way out: to exploit the fact that this QN is usually bandlimited. This is because its spectral density is often contained in peaks of localized modes and resonances, and may be constrained by bandgaps. Inspired by the Kotelnikov sampling theorem from the theory of classical bandlimited signals, we put forward and explore the idea that when the QN spectral density has effective bandwidth B, the quantum noise becomes a discrete-time process, with an elementary time step τ ∝ B −1 . After each time step τ , one new QN degree of freedom (DoF) gets coupled to the device for the first time, and one new QN DoF get irreversibly decoupled. Only a bounded number of QN DoFs are significantly coupled at any time moment. We call these DoFs the Kotelnikov modes. As a result, the real-time dissipative quantum motion has a natural structure of a discretetime matrix product state, with a bounded bond dimension. This yields a microscopically derived collision model. The temporal entanglement entropy appears to be bounded (area-law scaling) in the frame of Kotelnikov modes. The irreversibly decoupled modes can be traced out as soon as they occur during the real-time evolution. This leads to a novel bandlimited input-output formalism and to quantum jump Monte Carlo simulation techniques for real-time motion of open quantum systems. We illustrate this idea on a spin-boson model.

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Section: A Forward Quantum Kotelnikov Samplingmentioning

confidence: 94%

Section: Bandlimited Quantum Noise Analogy To the Classical Kotelniko...mentioning

confidence: 99%

“…Analogously to the classical correlator eq. ( 3), we introduce the correlator of the zero-point quantum noise [43,44,58],…”

Section: Bandlimited Quantum Noise Analogy To the Classical Kotelniko...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Beyond The Fermi's Golden Rule: Discrete-Time Decoherence Of Quantum Mesoscopic Devices Due To Bandlimited Quantum Noise

Polyakov¹

2022

Preprint

Self Cite

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Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics

Kang,

Nuomin,

Chowdhury

et al. 2024

Nat Rev Chem

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Efficient simulation of open quantum systems coupled to a reservoir through multiple channels

Nuomin,

Wu,

Zhang

et al. 2024

The Journal of Chemical Physics

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It is challenging to simulate open quantum systems that are connected to a reservoir through multiple channels. For example, vibrations may induce fluctuations in both energy gaps and electronic couplings, which represent two independent channels of system–bath couplings. Systems of this kind are ubiquitous in the processes of excited state radiationless decay. Combined with density matrix renormalization group (DMRG) and matrix product states (MPS) methods, we develop an interaction-picture chain mapping strategy for vibrational reservoirs to simulate the dynamics of these open systems, resulting in time-dependent spatially local system–bath couplings in the chain-mapped Hamiltonian. This transformation causes the entanglement generated by the system–bath interactions to be restricted within a narrow frequency window of vibrational modes, enabling efficient DMRG/MPS dynamical simulations. We demonstrate the utility of this approach by simulating singlet fission dynamics using a generalized spin-boson Hamiltonian with both diagonal and off-diagonal system–bath couplings. This approach generalizes an earlier interaction-picture chain mapping scheme, allowing for efficient and exact simulation of systems with multi-channel system–bath couplings using matrix product states, which may further our understanding of nonlocal exciton–phonon couplings in exciton transport and the non-Condon effect in energy and electron transfer.

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Real-time motion of open quantum systems: Structure of entanglement, renormalization group, and trajectories

Cited by 3 publications

References 79 publications

Beyond The Fermi's Golden Rule: Discrete-Time Decoherence Of Quantum Mesoscopic Devices Due To Bandlimited Quantum Noise

Beyond The Fermi's Golden Rule: Discrete-Time Decoherence Of Quantum Mesoscopic Devices Due To Bandlimited Quantum Noise

Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics

Efficient simulation of open quantum systems coupled to a reservoir through multiple channels

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