Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems

TL;DR

This paper introduces a hybrid discrete-continuous truncated Wigner approximation (DCTWA) for simulating driven, dissipative spin systems, improving accuracy and extending applicability to open quantum systems with quantum noise.

Contribution

The paper derives a rigorous hybrid phase space method embedding DTWA into a continuous framework, enabling systematic accuracy improvements and extension to open systems with noise.

Findings

Accurately models dissipative Rydberg atom dynamics

Provides a set of operator-differential mappings for spins

Extends DTWA to open quantum systems with noise

Abstract

We present a systematic approach for the semiclassical treatment of many-body dynamics of interacting, open spin systems. Our approach overcomes some of the shortcomings of the recently developed discrete truncated Wigner approximation (DTWA) based on Monte-Carlo sampling in a discrete phase space that improves the classical treatment by accounting for lowest-order quantum fluctuations. We provide a rigorous derivation of the DTWA by embedding it in a continuous phase space, thereby introducing a hybrid discrete-continuous truncated Wigner approximation (DCTWA). We derive a set of operator-differential mappings that yield an exact equation of motion (EOM) for the continuous SU(2) Wigner function of spins. The standard DTWA is then recovered by a systematic neglection of specific terms in this exact EOM. The hybrid approach permits us to determine the validity conditions and to gain detailed understanding of the quality of the approximation, paving the way for systematic improvements. Furthermore, we show that the continuous embedding allows for a straightforward extension of the method to open spin systems subject to dephasing, losses and incoherent drive, while preserving the key advantages of the discrete approach, such as a positive definite Wigner distribution of typical initial states. We derive exact stochastic differential equations for processes which cannot be described by the standard DTWA due to the presence of non-classical noise. We illustrate our approach by applying it to the dissipative dynamics of Rydberg excitation of one-dimensional arrays of laser-driven atoms and compare it to exact results for small systems.