Dissipation Stabilises Quantum Phase Transition in Driven Open Systems

Researchers demonstrate a phase transition stabilised by environmental dissipation, unlike conventional transitions occurring in equilibrium. Employing a driven spin-boson model with frequency-dependent bosonic loss, they observe a frozen spin dynamic emerging from renormalization by low-frequency modes, yielding a pure steady state.

The behaviour of quantum systems far from equilibrium presents a significant challenge to physicists, as interactions with the environment typically lead to a loss of quantum coherence. Researchers have now demonstrated a scenario where this environmental interaction – specifically, Markovian dissipation (energy loss to the surroundings occurring rapidly and randomly) – unexpectedly stabilises a quantum phase transition. This contrasts with the usual expectation that such dissipation destroys quantum behaviour. Naushad A. Kamar, Mostafa Ali, and Mohammad Maghrebi, all from Michigan State University, detail their findings in a paper entitled ‘Markovian dissipation can stabilise a (localisation) quantum phase transition’. Their work reveals that, in a driven spin-boson model with frequency-dependent dissipation, a transition to a frozen, localised state emerges not in the system’s lowest energy state, but within its dynamic, steady-state behaviour, potentially opening new avenues for quantum technologies.

Dissipation Stabilises Quantum Phase Transition in Driven-Dissipative Bose-Hubbard Model

Researchers have demonstrated a quantum phase transition within a driven-dissipative Bose-Hubbard model, establishing that Markovian dissipation can stabilise, rather than eliminate, quantum behaviour. This work challenges the conventional understanding that open quantum systems invariably exhibit classical behaviour due to environmental interactions, revealing a scenario where dissipation actively promotes quantum coherence at a critical point. The system investigated represents a variation of the spin-boson model, featuring a driven spin and bosons subject to frequency-dependent loss, effectively vanishing at low frequencies, providing a unique platform for exploring the interplay between coherence and decoherence.

The study focuses on the emergence of a localisation phase transition, a phenomenon where the system transitions from a delocalised state – where the spin freely moves – to a localised state where the spin dynamics effectively freeze. Unlike ground-state transitions observed in isolated systems, this transition manifests in the steady state of the driven-dissipative system, offering a distinct departure from traditional equilibrium physics and opening new avenues for exploring non-equilibrium phenomena. Crucially, the transition coincides with the system attaining a pure quantum state, a surprising result that challenges the expectation of increasing mixedness due to environmental interactions and suggests a novel mechanism for preserving quantum coherence.

Purity, a measure of quantum state mixedness – where a pure state has purity 1 and a completely mixed state has purity ( 1/N ) where N is the dimension of the Hilbert space – functions as an effective order parameter, signalling the transition point and providing a readily measurable indicator of the phase transition. Researchers meticulously analysed the steady state’s purity, revealing a dramatic decrease as the system approaches the critical point, indicating a loss of quantum coherence and confirming the transition to a localised phase. The purity exhibits power-law scaling with an exponent of approximately six, further characterising the transition and providing quantitative evidence supporting the identification of purity as a reliable order parameter.

The localisation is not simply a result of dissipation creating a ‘dark state’ – a zero-eigenvalue subspace where all dynamics cease – but rather arises from a complex interplay between the driven spin and the low-frequency bosonic modes. These modes induce the localisation, and the system’s behaviour differs from that of a simple dark state.

Numerical simulations were performed to investigate the transition and characterise its properties. Researchers plan to extend these simulations to larger system sizes to minimise finite-size effects and refine the estimated critical exponents. Investigating the robustness of this phase transition to variations in driving frequency and dissipation strength would further clarify its characteristics and identify the optimal conditions for achieving strong localisation. Exploring analogous phenomena in higher-dimensional systems and different physical platforms represents a promising avenue for expanding the scope of this research and assessing its generality.

This research provides a new perspective on the interplay between coherence and dissipation in open quantum systems. The ability to stabilise quantum coherence in the presence of dissipation is a crucial requirement for building robust quantum devices, and this research provides a promising pathway towards achieving this goal. Researchers envision that this phenomenon could be exploited to create novel quantum sensors, quantum memories, and quantum processors, all of which could benefit from the enhanced coherence provided by the dissipation-induced localisation.

Researchers believe that this work will stimulate further research in the field of non-equilibrium quantum physics, inspiring new theoretical models and experimental investigations. The findings challenge the conventional wisdom that dissipation always leads to decoherence, demonstrating that it can, under certain conditions, play a constructive role in preserving quantum coherence. This paradigm shift could lead to a deeper understanding of the fundamental principles governing quantum dynamics and pave the way for new breakthroughs in quantum science and technology.