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Acta Physica Sinica

Metastable dynamics of Rydberg atomic system under electromagnetically induced transparency

Gang Xia, Yapeng Zhang, Jingwen Tang, Chunyan Li, Chun-Wang Wu, Jie Zhang, Yan‐Li Zhou

Published Jan 1, 2024• 1 citation
Publisher

Abstract

Open quantum system, coupled with an external bath is a key research field of quantum physics. Steady state is the state in which any initial state converges after a long time and is usually of the most interest. However, relatively speaking, the nonequilibrium dynamical processes of quantum many-body systems have been rarely studied. This is mainly due to the fact that quantum many-body systems generally have interactions, and the Hilbert space required for a complete description of their dynamical processes will grow exponentially with the number of particles increasing, and the computational difficulty will increase dramatically as well. Hence, it is a difficult problem to completely describe their dynamical processes completely. With the development of quantum technologies, the interest in the nonequilibrium dynamics of open quantum many-body systems is aroused. A common phenomenon is the metastable state, where the system initially relaxes into a long-lived state and then converges to the final stationary state for a longer time. In this paper, we establish a low-dimensional approximation to describe the metastability dynamics in Markovian open quantum system, based on the spectra of the Liouvillian super-operator. The separation of time scales implies a splitting in the spectrum, and this spectral division allows us to eliminate the fast decay modes by using the perturbation method, and then we establish the effective description in the low-lying eigenmodes subspace. Furthermore, we study the dynamics process of the Rydberg atomic system under electromagnetically induced transparency (EIT) conditions and find that the system can handle metastable dynamics if the atomic interactions are considered. We compare the effective dynamics in the subspace with the actual dynamics in the full space, and the results show that the effective dynamics works well on condition that the perturbation approximation holds. Our work provides a feasible idea and method for establishing an effective and simplified description of the dynamical process of open quantum many-body systems.

DOI
10.7498/aps.73.20240233

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Open quantum system, coupled with an external bath is a key research field of quantum physics. Steady state is the state in which any initial state converges after a long time and is usually of the most interest. However, relatively speaking, the nonequilibrium dynamical processes of quantum many-body systems have been rarely studied. This is mainly due to the fact that quantum many-body systems generally have interactions, and the Hilbert space required for a complete description of their dynamical processes will grow exponentially with the number of particles increasing, and the computational difficulty will increase dramatically as well. Hence, it is a difficult problem to completely describe their dynamical processes completely. With the development of quantum technologies, the interest in the nonequilibrium dynamics of open quantum many-body systems is aroused. A common phenomenon is the metastable state, where the system initially relaxes into a long-lived state and then converges to the final stationary state for a longer time. In this paper, we establish a low-dimensional approximation to describe the metastability dynamics in Markovian open quantum system, based on the spectra of the Liouvillian super-operator. The separation of time scales implies a splitting in the spectrum, and this spectral division allows us to eliminate the fast decay modes by using the perturbation method, and then we establish the effective description in the low-lying eigenmodes subspace. Furthermore, we study the dynamics process of the Rydberg atomic system under electromagnetically induced transparency (EIT) conditions and find that the system can handle metastable dynamics if the atomic interactions are considered. We compare the effective dynamics in the subspace with the actual dynamics in the full space, and the results show that the effective dynamics works well on condition that the perturbation approximation holds. Our work provides a feasible idea and method for establishing an effective and simplified description of the dynamical process of open quantum many-body systems.
We investigate the dynamics of a generic interacting many-body system under conditions of electromagnetically induced transparency (EIT). This problem is of current relevance due to its connection to nonlinear optical media realized by Rydberg atoms. In an interacting system the structure of the dynamics and the approach to the stationary state becomes far more complex than in the case of conventional EIT. In particular, we discuss the emergence of a metastable decoherence-free subspace, whose dimension for a single Rydberg excitation grows linearly in the number of atoms. On approach to stationarity this leads to a slow dynamics, which renders the typical assumption of fast relaxation invalid. We derive analytically the effective nonequilibrium dynamics in the decoherence-free subspace, which features coherent and dissipative two-body interactions. We discuss the use of this scenario for the preparation of collective entangled dark states and the realization of general unitary dynamics within the spin-wave subspace.
Quantum sensing based on Rydberg atoms is an emerging technology for electric-field measurement. Theoretical and numerical studies were generally limited by the many-body effect in atomic ensembles. In this work, we initially derived a many-body dynamic equation by incorporating the Rydberg- Rydberg interaction into the four-level optical Bloch equation. Particularly, we proposed a fast steady-state solution as an alternative to the transient one. As a result, we ingeniously replaced the computationally expensive matrix operations with a linearly iterative process, enabling rapid convergence within few steps while considering the Doppler frequency shift. This approach made it possible to simulate the interaction of 7000 atoms in less than a minute. Based on the many-body model, we investigated the phenomenon of electromagnetically induced transparency (EIT) and Autler- Townes (AT) splitting under varying atomic gas densities; and compared the numerical results with experimental data. The comparison revealed a relatively-low error of 4.59% for the EITAT simulation by the many-body model. Moreover, we found that the linear dynamic range of the quantum sensing shrinks when considering the many-body interaction.
By generalizing concepts from classical stochastic dynamics, we establish the basis for a theory of metastability in Markovian open quantum systems. Partial relaxation into long-lived metastable states-distinct from the asymptotic stationary state-is a manifestation of a separation of time scales due to a splitting in the spectrum of the generator of the dynamics. We show here how to exploit this spectral structure to obtain a low dimensional approximation to the dynamics in terms of motion in a manifold of metastable states constructed from the low-lying eigenmatrices of the generator. We argue that the metastable manifold is in general composed of disjoint states, noiseless subsystems, and decoherence-free subspaces.
Stochastic switching is a central phenomenon in dissipative many-body systems, offering a key probe of metastability across classical and quantum regimes. Here, we unravel the connection between switching dynamics and quantum metastability through the lens of spectral decomposition, quantum-jump simulations and the large deviation principles. By establishing a direct correspondence between classical fixed points and quantum metastable states, we distinguish trajectory-level, noise-induced metastability from spectrum-level, deterministic metastability in a Markovian open quantum system with bistability. The Liouvillian gap, the steady-state occupation ratio and the observed switching rates of the metastable states all exhibit exponential scaling with system size, giving rise to a quantum analogue of the Arrhenius law, with the inverse system size serving as an effective temperature. These results provide a unified picture of quantum bistability and clarify the relaxation processes of strongly interacting, dissipative quantum systems far from the thermodynamic limit.
We investigate the transient optical response property of an electromagnetically induced transparency (EIT) in a cold Rydberg atomic gas. We show that both the transient behavior and the steady-state EIT spectrum of the system depend strongly on Rydberg interaction. Especially, the response speed of the Rydberg-EIT can be five times faster (and even higher) than the conventional EIT without the Rydberg interaction. For comparison, two different theoretical approaches (i.e., two-atom model and many-atom model) are considered, revealing that Rydberg blockade effect plays a significant role for increasing the response speed of the Rydberg-EIT. The fast-responding Rydberg-EIT by using the strong, tunable Rydberg interaction uncovered here is not only helpful for enhancing the understanding of the many-body dynamics of Rydberg atoms but also useful for practical applications in quantum information processing by using Rydberg atoms.
We investigate the evolution of interacting Rydberg gases in the limit of strong noise and dissipation. Starting from a description in terms of a Markovian quantum master equation we derive effective equations of motion that govern the dynamics on a 'coarse-grained' timescale where fast dissipative degrees of freedom have been adiabatically eliminated. Specifically, we consider two scenarios which are of relevance for current theoretical and experimental studies—Rydberg atoms in a two-level (spin) approximation subject to strong dephasing noise as well as Rydberg atoms under so-called electromagnetically induced transparency (EIT) conditions and fast radiative decay. In the former case we find that the effective dynamics is described by classical rate equations up to second order in an appropriate perturbative expansion. This drastically reduces the computational complexity of numerical simulations in comparison to the full quantum master equation. When accounting for the fourth order correction in this expansion, however, we find that the resulting equation breaks the preservation of positivity and thus cannot be interpreted as a proper classical master rate equation. In the EIT system we find that the expansion up to second order retains information not only on the 'classical' observables, but also on some quantum coherences. Nevertheless, this perturbative treatment still achieves a non-trivial reduction of complexity with respect to the original problem.