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arXiv:2401.09298 · Physical Review A

Dynamical signatures of non-Markovianity in a dissipative-driven qubit

Graziano Amati

Published May 22, 2024• 6 citations
arXivHTMLPDF

Abstract

We investigate signatures of non-Markovianity in the dynamics of a periodically driven qubit coupled to a dissipative bosonic environment. We propagate the dynamics of the reduced density matrix of the qubit by integrating the numerically exact hierarchical equations of motion. Non-Markovian features are quantified by comparing on an equal footing the predictions from diverse and complementary approaches to quantum dissipation. In particular, we analyze the distinguishability of quantum states, the decay of the volume accessible to the qubit on the Hilbert space, the negativity of the canonical rates in the generalized Lindblad equation, and the relaxation of the memory kernels in the Nakajima-Zwanzig generalized quantum master equation. We study the effects of controlled driving on the coherent dynamics of the system. We show that a suitable external field can offset the ergodic relaxation of time-correlation functions, increase distinguishability over time, and strengthen non-Markovian effects witnessed by the canonical dissipation channels. We furthermore observe the phenomenon of eternal non-Markovianity for sufficiently small system-bath coupling and we discuss how this can be enhanced by modulating the frequency of the external drive. This work provides a broad theoretical analysis of quantum dissipation in the framework of open quantum dynamics and quantum information.

DOI
10.1103/physreva.109.052433

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We investigate signatures of non-Markovianity in the dynamics of a periodically driven qubit coupled to a dissipative bosonic environment. We propagate the dynamics of the reduced density matrix of the qubit by integrating the numerically exact hierarchical equations of motion. Non-Markovian features are quantified by comparing on an equal footing the predictions from diverse and complementary approaches to quantum dissipation. In particular, we analyze the distinguishability of quantum states, the decay of the volume accessible to the qubit on the Hilbert space, the negativity of the canonical rates in the generalized Lindblad equation, and the relaxation of the memory kernels in the Nakajima-Zwanzig generalized quantum master equation. We study the effects of controlled driving on the coherent dynamics of the system. We show that a suitable external field can offset the ergodic relaxation of time-correlation functions, increase distinguishability over time, and strengthen non-Markovian effects witnessed by the canonical dissipation channels. We furthermore observe the phenomenon of eternal non-Markovianity for sufficiently small system-bath coupling and we discuss how this can be enhanced by modulating the frequency of the external drive. This work provides a broad theoretical analysis of quantum dissipation in the framework of open quantum dynamics and quantum information.
Understanding how external driving and dissipation jointly influence the dynamics of open quantum systems is essential for advancing the study of non-equilibrium quantum phenomena and developing quantum technologies. The present study addresses the issue by exploring the behavior of open systems in driven optical setups coupled to a bosonic field. Starting from an exact non-Markovian master equation for linear systems, we extend the analysis to an ensemble of quantum emitters and validate the proposed solution. The analytical results unveil a range of intriguing phenomena, including pronounced non-Markovian corrections to the coherent driving and a collective cross-driving effect. These effects are experimentally accessible in platforms such as cavity QED, photonic crystals, and state-dependent optical lattices. In the Markovian limit, comparison with exact solutions reveal short-time non-Markovian effects that endure well beyond the environmental correlation decay time, alongside memory effects triggered by short laser pulses. These findings offer valuable insights into the dynamics of driven open systems, laying the groundwork for precise quantum state control.
We study the dynamics of open quantum systems driven by an external time-periodic force. Combining Floquet theory and the time-convolutionless projection operator technique we derive a time-local quantum master equation which exactly takes into account the periodic driving, while treating the system-environment interaction within second order in the coupling strength without performing the Markov approximation. The resulting equation of motion for the reduced density matrix is called Floquet time-convolutionless master equation. Employing the example of the driven spin-boson system, we demonstrate that this master equation is capable of describing strong non-Markovian effects, while yielding the Floquet-Lindblad master equation in the Markovian limit. A characteristic feature of memory effects in such driven dissipative systems is the emergence of sharp peaks of the trace-distance based non-Markovianity measure as a function of the driving amplitude, which can be traced back to quasienergy crossings leading to almost decoherence-protected subspaces through a quasienergy-induced dissipative decoupling mechanism.
The reduced description of the quantum dynamic processes in the condensed phase environment leads to the equation of motion with a memory kernel. Such a memory effect, termed non-Markovianity, presents more complex dynamics compared to its memoryless or Markovian counterpart, and many chemical systems have been demonstrated through numerical simulations to exhibit non-Markovian quantum dynamics. Explicitly how the memory impacts the dynamic process remains largely unexplored. In this work, we focus on ways to separate the non-Markovian contributions from the dynamics and study the non-Markovian effects. Specifically, we developed a rigorous procedure for mapping the exact non-Markovian quantum propagator to the Lindblad form. Consequently, it allows us to extract the negative decay rate from the Lindbladian that is the signature of the non-Markovianity. By including or excluding the negative rate in the time evolution, we can decisively pinpoint the influence of non-Markovianity on the system's properties such as coherence, entanglement, and equilibrium state distribution. The understanding of such memory effects on the dynamic process suggests the possibility of leveraging non-Markovianity for quantum control.
The reduced dynamics of two interacting qubits coupled to two independent bosonic baths is investigated. The one-excitation dynamics is derived and compared with that based on the resolution of appropriate non-Markovian master equations. The Nakajima-Zwanzig and the time-convolutionless projection operator techniques are exploited to provide a description of the non-Markovian features of the dynamics of the two-qubit system. The validity of such approximate methods and their range of validity in correspondence to different choices of the parameters describing the system are brought to light.
We study the emergence of quantum memory effects in a spin-boson system at finite temperature driven by an external time-periodic force. Quantifying memory effects by the trace-distance based measure for non-Markovianity and performing numerical simulations employing the hierarchical equations of motion approach, we find a pronounced peak structure when plotting the non-Markovianity measure as a function of the driving amplitude. This distinctive feature is interpreted using Floquet theory and the Floquet-Lindblad master equation, associating the peaks with the degeneracies of the quasienergy spectrum which lead to a strong enhancement of the relaxation times of the system. These results suggest strategies for the efficient control of non-Markovianity in open quantum systems by periodic driving.
We describe temporally correlated noise processes that influence the idle evolution of a superconducting transmon qubit. To model the composite qubit-environment system we use quantum circuit theory, and we show how a circuit Hamiltonian can be derived for transverse noise affecting the qubit. Based on the time-convolutionless projection operator method, we construct a time-local master equation which, when transformed to its canonical Lindblad form, exhibits a decay rate that is negative at all times, corresponding to eternally non-Markovian dynamics. By expressing the solution of the master equation in the Kraus representation, we identify two crucial non-Markovian phenomena: periodic revivals of coherence, and the appearance of additional frequencies far from the qubit frequency in the precession of the qubit state. When a single qubit gate acts on the qubit state, these extra frequency terms rotate undesirably and they effectively act as the memory of the state prior to the rotation around the Bloch sphere.