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arXiv:2504.06579 · Journal of Statistical Mechanics Theory and Experiment

Coherence-decoherence interplay in quantum systems due to projective stochastic pulses: the case of Rabi oscillations

Sushanta Dattagupta, Shamik Gupta

Published Jul 1, 2025• 1 citation
arXivHTMLPDF

Abstract

Abstract The interplay of coherence and decoherence is played out in a three-level quantum system, in which the third level is incoherently coupled to the second one which itself is in coherent interaction with the first level. The study is based on a stochastic scenario in which the coherent, unitary evolution of the system is randomly interrupted by a Poisson-driven pulse sequence. In the absence of an external pulse, the system undergoes coherent, unitary evolution restricted to the subspace spanned by the first level (level 1) and the second level (level 2). The application of a pulse induces transitions between the second and the third level (level 3), thereby introducing non-unitary effects that perturb the otherwise isolated two-level dynamics. The pulses are assumed to have infinitesimal duration, with strengths modeled as random variables that are uncorrelated across different pulses. A representative model for the stochastically-averaged transition (super)operator mimicking the dynamics induced by the application of pulses allows for an analytical derivation of the matrix elements of the averaged density operator, especially, the element pertaining to the first level. When the system is initially in level 1, we obtain in particular the temporal behavior of the stay-put probability, that is, the probability P 1 ( t ) that the system is still in level 1 at time t. As a function of time, the quantity P 1 ( t ) exhibits a coherence-to-decoherence crossover behavior. At short times t ≪ 1 / λ , where λ is the average frequency at which pulses are applied to the system, coherent dynamics dominate. Consequently, P 1 ( t ) displays pronounced Rabi-like oscillations. At long times t ≫ 1 / λ , decoherence effects prevail, leading to an exponential decay of the form P 1 ( t ) − 1 / 3 ∼ exp ⁡ ( − λ t ) . The results are relevant in the context of well-established Rabi oscillations, applicable to molecular beams and magnetic resonance experiments, as well as in more contemporary frameworks including quantum information processing, quantum resetting protocols, and the theory of quantum trajectories.

DOI
10.1088/1742-5468/ade5f7

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A general coherent control scenario to suppress, or accelerate, tunneling of quantum states decaying into a continuum, is investigated. The method is based on deterministic, or stochastic, sequences of unitary pulses that affect the underlying interference phenomena responsible for quantum dynamics, without inducing decoherence, or collapsing the coherent evolution of the system. The influence of control sequences on the ensuing quantum dynamics is analyzed by using perturbation theory to first order in the control pulse fields and compared to dynamical decoupling (DD) protocols and sequences of pulses that collapse the coherent evolution and induce quantum Zeno (QZE) or quantum anti-Zeno effects (AZE). The analysis reveals a subtle interplay between coherent and incoherent phenomena and demonstrating that dynamics analogous to evolution due to QZE or AZE can be generated from stochastic sequences of unitary pulses when averaged over all possible realizations.
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Decoherence is a quantum-mechanical phenomenon severely limiting quantum information processing and storage capability in quantum computers. Decoherence refers to mechanisms that cause transfer of information from a quantum system to its bath. Typically, in theoretical and experimental considerations of different systems containing superconducting qubits, the coupling strength between a qubit and its bath has been assumed to be constant in time. In this case, many standard results in the dynamics of two-level systems follow. For example, due to decoherence, driven Rabi oscillations in a qubit have a characteristic decay time. In addition, the oscillations may take place at any phase. However, by considering time-dependent coupling to the bath, these phenomena may be absent. In this thesis, we demonstrate with numerical simulations of a time-dependent Lindblad master equation persistent Rabi oscillations in a qubit driven by a coherent drive tone. The persistent Rabi oscillations are induced by modulating the coupling of the qubit to the bath with a sinusoidal temporal shape. We observe that the temporal modulation enforces a limit cycle on the evolution of the dressed qubit state with a fixed phase relative to the phase of the sinusoidal modulation regardless of the initial state of the system. Through a synchronization-like phenomenon, the frequency of the Rabi oscillation adapts to match the frequency of the modulation. We determine the effect of different system parameters on the limit cycle and study how the amplitude of the persistent oscillation depends on the coupling modulation parameters. We also observe a similar effect in the freely evolving qubit precession. In addition, the qubit acts as a non-linear mixer, resulting in different linear combinations of the original modulation waveform appearing in the bath-induced Rabi oscillations. We also introduce a design for a physical system where our simulations can be verified experimentally.
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