Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2004.01948

Time development of a driven three-level lambda system: A case study

James P. Lavine
View original source ↗Read source document ↗Export metadata ↓

Abstract

How does a driven system with many energy levels approach its steady state? Insights are gained by studying a system with three energy levels when the ground state is excited by a laser. The time-dependent occupation probabilities of the three energy levels show students how the system develops in time. The occupation probabilities come from the numerical solution of the Liouville-von Neumann equations for the density operator matrix elements when relaxation is included. A combination of the Interaction Picture, the Rotating Wave Approximation, and the assumption of resonance permit the eigenvalues of the Liouville-von Neumann equations to be found numerically and in closed-form in certain limits. The two methods are complementary and help students understand time-dependent systems. In addition, the eigenvalues allow the short-time and the long-time occupation probabilities to be connected to the relaxation parameters and the magnitude of the laser's electric field. Thus, this model three-level system illuminates how a driven system behaves over time and provides guidance for students studying time-dependent systems.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

James P. Lavine. 2022-07-30. Time development of a driven three-level lambda system: A case study. https://arxiv.org/abs/2004.01948

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Evolution of IBM's Quantum Information Software Kit (Qiskit): A Review of its Applications

Quantum computing is being increasingly adopted for solving classically intractable problems across various domains. However, the availability of accessible and scalable software frameworks remains essential for practical experimentation and adoption. IBM's open-source quantum computing toolkit 'Qiskit' has become a key player in this space by offering tools for circuit design, simulation, hardware execution, and domain-specific applications. This survey provides a systematic review of how Qiskit has evolved and what it has contributed to several critical fields including cryptography and cybersecurity, image and signal processing, climate science and energy applications, and finance. We show how Qiskit facilitates hybrid classical-quantum workflows and enables the deployment of algorithms on physical quantum hardware through error mitigation and modular integration approaches. Our exploration covers several key applications, including quantum key distribution, climate simulation, and quantum-enhanced portfolio optimization, while providing practical insights into their implementation. This work also covers the framework's technical structure and current limitations associated with scalability and reproducibility. By bringing together developments that have been scattered across different areas, this work serves as a reference point for researchers and practitioners who want to understand or contribute to Qiskit-enabled quantum computing.

quant-ph↗
arXiv2026

Extending the Handover-Iterative VQE to Challenging Strongly Correlated Systems: $N_2$ and Fe-S Cluster

Accurately describing strongly correlated electronic systems remains a central challenge in quantum chemistry, as electron-electron interactions give rise to complex many-body wavefunctions that are difficult to capture with conventional approximations. Classical wavefunction-based approaches, such as the Semistochastic Heat-bath Configuration Interaction (SHCI) and the Density Matrix Renormalization Group (DMRG), currently define the state of the art, systematically converging toward the Full Configuration Interaction (FCI) limit, but at a rapidly increasing computational cost. Quantum computing algorithms promise to alleviate this scaling bottleneck by leveraging entanglement and superposition to represent correlated states more compactly. We introduced the Handover-Iterative Variational Quantum Eigensolver (HI-VQE) as a practical quantum computing algorithm with an iterative "handover" mechanism that dynamically exchanges information between quantum and classical computers, even using Noisy Intermediate-Scale Quantum (NISQ) computers. In this work, we extend the HI-VQE to benchmark two prototypical strongly correlated systems, the nitrogen molecule $N_2$ and iron-sulfur (Fe-S) cluster, which serve as stringent tests for both classical and quantum electronic-structure methods. By comparing HI-VQE results against Heat-bath Configuration Interaction (HCI) benchmarks, we assess its accuracy, scalability, and ability to capture multireference correlation effects. Achieving quantitative agreement on these canonical systems demonstrates a viable pathway toward quantum-enhanced simulations of complex bioinorganic molecules, catalytic mechanisms, and correlated materials.

quant-ph↗
arXiv2026

Phonon-limited detection thresholds for genetically encoded fluorescent-protein spin-qubit relaxometry of neural radicals

The demonstration that enhanced yellow fluorescent protein hosts an optically addressable spin-1 qubit in its metastable triplet state raises the prospect of genetically encoded quantum sensing at molecular length scales. We develop a detection-limit theory for using this fluorescent-protein spin qubit (FPSQ) to sense paramagnetic neural signaling radicals by spin relaxometry. We derive the transition-resolved Redfield relaxation matrix of the zero-field-split triplet coupled to a diffusing radical bath, establish the regime in which it collapses to a single exponential, and validate it against Lindblad simulations and nitrogen-vacancy benchmarks. Propagating the effects of photon shot noise, photobleaching-grounded photon budget, and finite measurement bandwidth, we find that the native room-temperature sensor falls short of physiological sensitivity by six to eight orders of magnitude with the bottleneck being the phonon-limited intrinsic $\Tone$. Analyzing the underlying direct and two-phonon Raman processes, we show that room-temperature relaxation is Raman-dominated by $\sim\!720\!:\!1$ and that, because the Raman coefficient scales as $v^{-10}$ with sound velocity, a $\sim\!2\times$ stiffening of the chromophore environment recovers $\Tone\sim\SI{100}{\micro\second}$, sufficient for micromolar sensing. Nanomolar sensing is obstructed by a direct-process ceiling of \SI{79}{\micro\second} that vibronic decoupling alone cannot breach. We obtain quantitative design rules, identify photon yield as a co-equal bottleneck, and propose a frequency-resolved protocol for chemical specificity.

quant-ph↗