[Paper Review] Dissipation-Induced Superradiance in a Non-Markovian Open Dicke Model

Orazio Scarlatella, Marco Schiró|arXiv (Cornell University)|Nov 28, 2016

Advanced Thermodynamics and Statistical Mechanics3 citations

TL;DR

This paper investigates the Dicke model coupled to a non-Markovian bath with a power-law spectral function, demonstrating that dissipation can induce a superradiant phase transition rather than suppress it—contrary to Markovian and thermal bath scenarios. The transition arises from low-frequency bath modes and persists at finite $ N $, indicating a genuine dissipative quantum phase transition with critical behavior governed by the bath's spectral exponent $ s $.

ABSTRACT

We consider the Dicke model, describing an ensemble of $N$ quantum spins interacting with a cavity field, and study how the coupling to a non-Markovian environment with power-law spectrum changes the physics of superradiant phase transition. Quite remarkably we find that dissipation can induce, rather than suppress, the ordered phase, a result which is in striking contrast with both thermal and Markovian quantum baths. We interpret this dissipation-induced superradiance as a genuine dissipative quantum phase transition that exists even at finite $N$ due to the coupling with the bath modes and whose nature and critical properties strongly depend on the spectral features of the non-Markovian environment.

Motivation & Objective

• To understand how non-Markovian, structured environments affect the superradiant phase transition in the Dicke model.
• To investigate whether dissipation can promote, rather than suppress, the ordered superradiant phase.
• To determine the existence and nature of a dissipative quantum phase transition at finite $ N $, beyond the mean-field limit.
• To explore the critical properties of the transition and their dependence on the bath's spectral function exponent $ s $.
• To contrast the non-Markovian scenario with previous results from Markovian or thermal baths, which typically suppress the superradiant phase.

Proposed method

• The Dicke Hamiltonian is coupled to a non-Markovian bath via a spectral function $ J_+( u) \propto \nu^s $, modeling structured electromagnetic environments.
• A mean-field treatment is applied to the Dicke model, leading to an effective quadratic bosonic theory with a shifted critical coupling $ \lambda_c^\infty(\kappa) = \lambda_c^\infty(0) + \delta\lambda/N $, where $ \delta\lambda $ depends on $ \omega_0, \omega_q $.
• Finite-$ N $ corrections are computed perturbatively using the retarded Green’s function $ \chi_b^R(t) $, which serves as a proxy for spin-spin correlations.
• The critical coupling shift $ \delta\lambda_c(N) = \lambda_c^N - \lambda_c^\infty $ is extracted and shown to scale with $ N $, confirming the finite-$ N $ transition.
• The system is mapped to a generalized spin-boson problem, linking the critical behavior to known universality classes (e.g., Kosterlitz-Thouless for $ s=1 $).
• The analysis is extended to include non-perturbative effects and potential external driving, with relevance to experimental platforms like circuit QED.

Experimental results

Research questions

• RQ1 Can a non-Markovian bath induce a superradiant phase transition rather than suppress it, contrary to the Markovian case?
• RQ2 What is the nature of the dissipative quantum phase transition at finite $ N $, and does it persist beyond the thermodynamic limit?
• RQ3 How do the critical properties of the transition depend on the spectral exponent $ s $ of the bath's power-law spectrum?
• RQ4 Is the finite-$ N $ transition related to the physics of the spin-boson model, and what universality class does it belong to?
• RQ5 How does the interplay between non-Markovian dissipation and external driving affect the emergence of non-equilibrium quantum phases?

Key findings

• Dissipation from a non-Markovian bath with power-law spectrum $ J_+(\nu) \propto \nu^s $ induces a superradiant phase transition, contrary to the suppressive effect of Markovian or thermal baths.
• The critical coupling for the superradiant transition shifts to lower values due to dissipation, with $ \lambda_c^\infty(\kappa) = \lambda_c^\infty(0) + \delta\lambda/N $, where $ \delta\lambda $ is positive or negative depending on $ \omega_0, \omega_q $.
• The finite-$ N $ phase transition exists only for $ s \leq 1 $, with critical behavior that depends strongly on $ s $, resembling the spin-boson problem.
• For $ s = 1 $, the transition belongs to the Kosterlitz-Thouless universality class; for $ s < 1 $, it is continuous with $ s $-dependent critical exponents.
• The transition is sharp at finite $ N $, indicating a genuine dissipative quantum phase transition in a thermodynamically large bath.
• The results suggest that non-Markovian baths can be engineered to stabilize and prepare non-equilibrium quantum many-body states, such as superradiant phases.