Non-Markovian Quantum Limit for Driven Open Quantum Systems

Jay Gambetta, T. Askerud, Howard M. Wiseman

Non-Markovian evolution of an open quantum system can be ``unraveled'' into pure state trajectories generated by a non-Markovian stochastic (diffusive) Schr\"odinger equation, as introduced by Di\'osi, Gisin, and Strunz. Recently we have shown that such equations can be derived using the modal (hidden variable) interpretation of quantum mechanics. In this paper we generalize this theory to treat jumplike unravelings. To illustrate the jumplike behavior we consider a simple system: a classically driven (at Rabi frequency $\ensuremath{\Omega}$) two-level atom coupled linearly to a three mode optical bath, with a central frequency equal to the frequency of the atom, ${\ensuremath{\omega}}_{0}$, and the two side bands have frequencies ${\ensuremath{\omega}}_{0}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}$. In the large $\ensuremath{\Omega}$ limit we observed that the jumplike behavior is similar to that observed in this system with a Markovian (broad band) bath. This is expected as in the Markovian limit the fluorescence spectrum for a strongly driven two level atom takes the form of a Mollow triplet. However, the length of time for which the Markovian-like behavior persists depends upon which jumplike unraveling is used.

Carole Addis

Heinz‐Peter Breuer

Aritro Mukherjee

Quantum stochastic processes are widely used in describing open quantum systems and in the context of quantum foundations. Physically relevant quantum stochastic processes driven by multiplicative colored noise are generically non-Markovian and analytically intractable. Further, their Markovian limits are generically inequivalent when using either the Ito or Stratonovich conventions for the same quantum stochastic processes. We introduce a quantum noise homogenization scheme that temporally coarse-grains non-Markovian, colored-noise-driven quantum stochastic processes and connects them to their effective white-noise (Markovian) limits. Our approach uses a novel phase-space augmentation that maps the non-Markovian dynamics into a higher-dimensional Markovian system and then applies a controlled perturbative coarse-graining scheme in the characteristic time scales of the noise. This allows an explicit analytical algorithm to derive effective Markovian generators with renormalized coefficients and enables various physical constraints, such as causality, to be imposed on them. We thus resolve the Ito--Stratonovich ambiguity for multiplicative colored-noise-driven quantum stochastic processes, wherein we show that their consistent Markovian limit corresponds to the Stratonovich convention with renormalized coefficients as well as correction terms in Ito's convention. By assuming their Markovian limit unravels causal, completely positive and trace-preserving dynamics, we further characterize a physically relevant family of non-Markovian quantum stochastic processes driven by multiplicative colored~noise.

Roie Dann

Understanding how external driving and dissipation jointly influence the dynamics of open quantum systems is essential for advancing the study of non-equilibrium quantum phenomena and developing quantum technologies. The present study addresses the issue by exploring the behavior of open systems in driven optical setups coupled to a bosonic field. Starting from an exact non-Markovian master equation for linear systems, we extend the analysis to an ensemble of quantum emitters and validate the proposed solution. The analytical results unveil a range of intriguing phenomena, including pronounced non-Markovian corrections to the coherent driving and a collective cross-driving effect. These effects are experimentally accessible in platforms such as cavity QED, photonic crystals, and state-dependent optical lattices. In the Markovian limit, comparison with exact solutions reveal short-time non-Markovian effects that endure well beyond the environmental correlation decay time, alongside memory effects triggered by short laser pulses. These findings offer valuable insights into the dynamics of driven open systems, laying the groundwork for precise quantum state control.

Xinyu Zhao