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arXiv:2204.03267 · SciPost Physics

Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity

A. Chia, Wai‐Keong Mok, Changsuk Noh, L. C. Kwek

Published Sep 28, 2023• 6 citations
arXivHTMLPDF

Abstract

It is universally accepted that noise may bring order to complex nonequilibrium systems. Most strikingly, entirely new states not seen in the noiseless system can be induced purely by including multiplicative noise-an effect known as pure noise-induced transitions. It was first observed in superfluids in the 1980s. Recent results in complex nonequilibrium systems have also shown how new collective states emerge from such pure noise-induced transitions, such as the foraging behavior of insect colonies, and schooling in fish. Here we report such effects of noise in a quantum-mechanical system without a classical limit. We use a minimal model of a nonlinearly damped oscillator in a fluctuating environment that is analytically tractable, and whose microscopic physics can be understood. When multiplicative environmental noise is included, the system is seen to transition to a limit-cycle state. The noise-induced quantum limit cycle also exhibits other genuinely nonclassical traits, such as Wigner negativity and number-parity sensitive circulation in phase space. Such quantum limit cycles are also conservative. These properties are in stark contrast to those of a widely used limit cycle in the literature, which is dissipative and loses all Wigner negativity. Our results establish the existence of a pure noise-induced transition that is nonclassical and unique to open quantum systems. They illustrate a fundamental difference between quantum and classical noise.

DOI
10.21468/scipostphys.15.3.121

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It is universally accepted that noise may bring order to complex nonequilibrium systems. Most strikingly, entirely new states not seen in the noiseless system can be induced purely by including multiplicative noise-an effect known as pure noise-induced transitions. It was first observed in superfluids in the 1980s. Recent results in complex nonequilibrium systems have also shown how new collective states emerge from such pure noise-induced transitions, such as the foraging behavior of insect colonies, and schooling in fish. Here we report such effects of noise in a quantum-mechanical system without a classical limit. We use a minimal model of a nonlinearly damped oscillator in a fluctuating environment that is analytically tractable, and whose microscopic physics can be understood. When multiplicative environmental noise is included, the system is seen to transition to a limit-cycle state. The noise-induced quantum limit cycle also exhibits other genuinely nonclassical traits, such as Wigner negativity and number-parity sensitive circulation in phase space. Such quantum limit cycles are also conservative. These properties are in stark contrast to those of a widely used limit cycle in the literature, which is dissipative and loses all Wigner negativity. Our results establish the existence of a pure noise-induced transition that is nonclassical and unique to open quantum systems. They illustrate a fundamental difference between quantum and classical noise.
Quantum fluctuations are inherent in open quantum systems and they affect not only the statistical properties of the initial state but also the time evolution of the system. Using a generic minimal model, we show that quantum noise smooths the transition between a stationary and a dynamical phase corresponding to a limit cycle (LC) in the semiclassical mean-field approximation of a generic open quantum system. Employing truncated Wigner approximation, we show that the inherent quantum noise pushes the system to exhibit signatures of LCs for interaction strengths lower than the critical value predicted by the standard mean-field theory, suggesting a noise-induced emergence of temporal ordering. Our work demonstrates that the apparent crossover-like behavior between stationary phases brought by finite-size effects from quantum fluctuations also apply to transitions involving dynamical phases. To demonstrate this on a specific physical system, we consider a transversely pumped atom-cavity setup, wherein LCs have been observed and identified as continuous time crystals. We compare the oscillation frequencies of the LCs in the one-dimensional (1D) and two-dimensional regimes, and find that the frequencies have larger shot-to-shot fluctuations in 1D. This has an important consequence in the effectiveness of entrainment of LCs for a periodically driven pump intensity or light-matter coupling strength.
Abstract Recent experimental results point to the existence of coherent quantum phenomena in systems made of a large number of particles, despite the fact that for many-body systems the presence of decoherence is hardly negligible and emerging classicality is expected. This behaviour hinges on collective observables, named quantum fluctuations , that retain a quantum character even in the thermodynamic limit: they provide useful tools for studying properties of many-body systems at the mesoscopic level, in-between the quantum microscopic scale and the classical macroscopic one. We herein present the general theory of quantum fluctuations in mesoscopic systems, and study their dynamics in a quantum open system setting, taking into account the unavoidable effects of dissipation and noise induced by the external environment. As in the case of microscopic systems, decoherence is not always the only dominating effect at the mesoscopic scale: certain types of environment can provide means for entangling collective fluctuations through a purely noisy mechanism.
Nonequilibrium systems maintain spatiotemporal order through energy dissipation and entropy production. Here, we demonstrate this principle by engineering a quantum limit cycle that emerges from the interplay between a first-order absorbing-state phase transition and feedback mechanism coupling order and control parameters. The quantum limit cycle manifests dynamical correlations driven by multiplicative quantum noise and periodic traverses through tipping points, which act as a robust early-warning signal for state transitions. This periodic crossing results in the enhanced dynamical susceptibility and transient rise of long-range correlations near each tipping event and their subsequent disappearance away from it. These critical transitions are accompanied by a sharp increase in the energy dissipation rate, leading to a stepwise accumulation of dynamical entropy production over time. Our results provide a way for realizing dynamical fluctuations and long-range correlations in strongly interacting driven-dissipative open quantum systems.
Driven-dissipative quantum many-body systems have been the subject of many studies in recent years. They possess unique, novel classes of dissipation-stabilized quantum many-body phases including the limit cycle. For a long time it has been speculated if such a behavior, a recurring phenomenon in non-linear classical and quantum many-body systems, can be classified as a time crystal. However, the robustness of these periodic dynamics, against quantum fluctuations is an open question. In this work we seek the answer to this question in a canonical yet important system, i.e., a multi-mode cavity with self and cross-Kerr non-linearity, including the fluctuation effects via higher order correlations. Employing the Keldysh path integral, we investigate the Green's function and correlation of the cavity modes in different regions. Furthermore, we extend our analysis beyond the mean-field by explicitly including the effect of two-body correlations via the 2nd-cumulant expansion. Our results shed light on the emergence of dissipative phase transitions in open quantum systems and clearly indicate the robustness of limit-cycle oscillations in the presence of the quantum fluctuations.
We investigate the correspondence between classical noise and quantum environments. Although it is known that classical noise can be mapped to quantum environments for pure dephasing and infinite-temperature dissipation processes, we show how finite-temperature dissipation can be also described using classical noise by introducing auxiliary systems and conservation. Taking a two-level system as an example, we construct the so-called central spin model with its couplings fluctuating with the classical noise and then acquire its statistical-average dynamics which captures the dissipation beyond infinite temperature. By adjusting the number of auxiliary systems and their initial states, the noise-based model reproduces both Markovian and non-Markovian evolution. We also find that different quantities of the two-level system are governed by different model parameters, indicating that the constructed model is an effective simulator for specific observables rather than an equivalent form of a realistic open system. In addition, the model is also applicable to investigate topical mechanisms of open systems, e.g., negative temperatures and asymmetric equidistant quenches.
The introduction of nonlinearities in the Schrödinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear effects induced by subtracting a term proportional to Bohm’s quantum potential to the usual (linear) Schrödinger equation, which generates the so-called “classical” Schrödinger equation. Although a simple nonlinear transformation allows us to recover the well-known classical Hamilton–Jacobi equation, by combining a series of analytical results (in the limiting cases) and simulations (whenever the analytical treatment is unaffordable), we find an analytical explanation to why the dynamics in the nonlinear “classical” regime is still strongly nonclassical. This is even more evident by establishing a one-to-one comparison between the Bohmian trajectories associated with the corresponding wave function and the classical trajectories that one should obtain. Based on these observations, it is clear that the transition to a fully classical regime requires extra conditions in order to remove any trace of coherence, which is the truly distinctive trait of quantum mechanics. This behavior is investigated in three paradigmatic cases, namely, the dispersion of a free propagating localized particle, the harmonic oscillator, and a simplified version of Young’s two-slit experiment.