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Quantum Science and Technology

Phonon-induced non-equilibrium dynamics in a single solid-state spin

Ariel Norambuena, Diego Tancara, Vicente Chomalí-Castro, Daniel Castillo-Castro

Published Jul 16, 2025• 0 citations
Publisher

Abstract

Abstract The electron–phonon interaction is a cornerstone of condensed matter physics, playing a pivotal role in the properties of solid-state systems. When localized electronic states are coupled to lattice vibrations, phonons can induce memory effects. This study explores the non-equilibrium dynamics of a negatively charged silicon-vacancy center in diamond, analyzing the effects of both single phonon mode and structured phonon environment. Using numerical simulations and theoretical analysis, we employ trace distance as a metric to identify and understand memory effects in the transient dynamics and non-Markovian evolution. We systematically investigate the impact of longitudinal and transverse magnetic fields, phonon coupling strengths, Fock states, localized vibrations, and temperature on memory effects in this solid-state system. Our findings provide deeper insights into the interplay between electronic states and phonon environments, offering a comprehensive understanding of the conditions that govern the backflow of information in quantum solid-state devices.

DOI
10.1088/2058-9565/adf092

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Canadian Journal of Physics•Oct 30, 2026•0 citations
Abstract The electron–phonon interaction is a cornerstone of condensed matter physics, playing a pivotal role in the properties of solid-state systems. When localized electronic states are coupled to lattice vibrations, phonons can induce memory effects. This study explores the non-equilibrium dynamics of a negatively charged silicon-vacancy center in diamond, analyzing the effects of both single phonon mode and structured phonon environment. Using numerical simulations and theoretical analysis, we employ trace distance as a metric to identify and understand memory effects in the transient dynamics and non-Markovian evolution. We systematically investigate the impact of longitudinal and transverse magnetic fields, phonon coupling strengths, Fock states, localized vibrations, and temperature on memory effects in this solid-state system. Our findings provide deeper insights into the interplay between electronic states and phonon environments, offering a comprehensive understanding of the conditions that govern the backflow of information in quantum solid-state devices.
The electron-phonon interaction is one of the most fundamental mechanisms in condensed matter physics. Phonons can induce memory effects in solid-state platforms when localized electronic states interact with lattice vibrations in non-unitary dynamical maps. In this work, we demonstrate how single-mode and structured phonon environments can give rise to non-Markovian dynamics of an individual negatively charged silicon-vacancy center in diamond. Using trace distance as a quantifier via numerical simulations and theoretical calculations, we identify the physical conditions for emerging and understanding non-Markovian behavior in diverse scenarios. Most importantly, we investigate the influence of magnetic fields (longitudinal and transverse), phonon couplings, Fock states, and temperature to understand how these factors influence memory effects in this solid-state device.
Here we investigate the temperature-dependent non-Markovian dynamics of the SiV^- center in diamond, focusing on the roles of low- and high-frequency quasi-localized phonon modes. Low-frequency phonons exhibit stronger electron-phonon coupling, leading to long-lived dephasing rate, while high-frequency phonons induce rapid attenuation of oscillatory dephasing rate facilitating a persistent memory effect. The non-Markovianity measure N_C shows memory effects persisting at low temperatures but diminishing at high temperatures due to enhanced damping. The temperature dependence of N_C follows a monotonic decay, from which a transition temperature T_NM=110 K is determined. These results highlight the interplay between phonon activation and damping in shaping quantum coherence, offering insights for optimizing solid-state quantum systems.
Qubit coherence is an essential figure of merit for quantum information processing applications such as quantum computing, or quantum repeaters. Understanding the coherence properties of the underlying physical qubits that facilitate such applications is therefore are often limited by coupling to lattice phonons, which in turn constrains operation temperature. Here we study phonon induced electronic spin decoherence in group-IV vacancy centers in diamond. We begin by modeling the spin-phonon interaction and then employ the widely used Born-Markov approximation, highlighting its inconsistencies in this setting and its deviations from experimental observations. To close the gap between theoretical predictions and experimental results, we relax certain approximations, investigate their contributions to the predicted coherence times, and identify the dominant sources of discrepancy. We further demonstrate that experimentally measured electronic spin coherence dynamics are consistently captured within a non-Markovian framework, and we show how the magnetic field orientation influences the qubit coherence time.
Understanding the effect of vibrations on the relaxation process of individual spins is crucial for implementing nanosystems for quantum information and quantum metrology applications. In this work, we present a theoretical microscopic model to describe the spin-lattice relaxation of individual electronic spins associated to negatively charged nitrogen-vacancy centers in diamond, although our results can be extended to other spin-boson systems. Starting from a general spin-lattice interaction Hamiltonian, we provide a detailed description and solution of the quantum master equation of an electronic spin-one system coupled to a phononic bath in thermal equilibrium. Special attention is given to the dynamics of one-phonon processes below 1 K where our results agree with recent experimental findings and analytically describe the temperature and magnetic-field scaling. At higher temperatures, linear and second-order terms in the interaction Hamiltonian are considered and the temperature scaling is discussed for acoustic and quasilocalized phonons when appropriate. Our results, in addition to confirming a T5{T}^{5}T5 temperature dependence of the longitudinal relaxation rate at higher temperatures, in agreement with experimental observations, provide a theoretical background for modeling the spin-lattice relaxation at a wide range of temperatures where different temperature scalings might be expected.
Understanding the effect of vibrations in optically active nanosystems is crucial for successfully implementing applications in molecular-based electro-optical devices, quantum information communications, single photon sources, and fluorescent markers for biological measurements. Here, we present a first-principles microscopic description of the role of phonons on the isotopic shift presented in the optical emission spectrum associated to the negatively charged silicon-vacancy color center in diamond. We use the spin-boson model and estimate the electron-phonon interactions using a symmetrized molecular description of the electronic states and a force-constant model to describe molecular vibrations. Group theoretical arguments and dynamical symmetry breaking are presented in order to explain the optical properties of the zero-phonon line and the isotopic shift of the phonon sideband.
We investigate non-Markovian quantum memory in a negatively charged nitrogen-vacancy (NV) center strain-coupled to a quantized mechanical mode. From the spin-1 NV Hamiltonian and the C_3v spin--strain interaction, we derive an effective qubit--phonon model with transverse exchange and longitudinal phase-modulation couplings. The open dynamics is described by a GKSL master equation, and memory in the reduced qubit channel is characterized using trace-distance backflow for the orthogonal reference pair │±〉= (│0〉± │-1〉) / √2 and the Rivas--Huelga--Plenio (RHP) CP-divisibility criterion. At resonance, the reference-pair BLP backflow follows transverse > hybrid > longitudinal, whereas the extrapolated RHP quantity follows hybrid > transverse >> longitudinal. Adding g_z / ω_m = 0.10 to the transverse baseline g⊥ / ω_m = 0.20 reduces the reference-pair backflow by 8.61% while increasing the RHP quantity by approximately 78.65%. This opposite response is traced to the distinct roles of coherent exchange and longitudinal phase modulation in distinguishability recovery and full-channel CP-indivisibility. The same ordering contrast persists over the sampled detuning interval, whereas thermal occupation can modify the BLP hierarchy and induce isolated noninvertibility of the reduced dynamical map for some exchange-containing regimes. Numerical validation and convergence tests confirm the robustness of the principal resonance result and delineate the validity of the inverse-based RHP construction.