Dissipation-induced bistability in the two-photon Dicke model

Abstract

The Dicke model is a paradigmatic quantum-optical model describing the interaction of a collection of two-level systems with a single bosonic mode. Effective implementations of this model made it possible to observe the emergence of superradiance, i.e., cooperative phenomena arising from the collective nature of light-matter interactions. Via reservoir engineering and analogue quantum simulation techniques, current experimental platforms allow us not only to implement the Dicke model but also to design more exotic interactions, such as the two-photon Dicke model. In the Hamiltonian case, this model presents an interesting phase diagram characterized by two quantum criticalities: a superradiant phase transition and a spectral collapse, that is, the coalescence of discrete energy levels into a continuous band. Here, we investigate the effects of both qubit and photon dissipation on the phase transition and on the instability induced by the spectral collapse. Using a mean-field decoupling approximation, we analytically obtain the steady-state expectation values of the observables signaling a symmetry breaking, identifying a first-order phase transition from the normal to the superradiant phase. Our stability analysis unveils a very rich phase diagram, which features stable, bistable, and unstable phases depending on the dissipation rate. The Dicke model 1 describes the interaction of a collection of two-level systems with a single bosonic mode. In the thermodynamic limit, this model exhibits a superradiant phase transition at zero temperature 1-5. Namely, the ground-state number of photons changes non analytically from zero to finite values as the light-matter coupling strength is increased across a critical value. The relevance of the Dicke model to capture the physics of light-matter coupling near the critical point is the object of an ongoing debate. In particular, an obstacle to the observation of a superradiant phase transition arises due to the presence of the so-called diamagnetic term. In this regard, resolutions of gauge ambiguities have been recently proposed, such as employing modified unitary transformations or going beyond the two-level system description 6-9. It is possible, however, to circumvent this controversy entirely by using driven systems and bath engineering to simulate effective Hamiltonians. Thanks to this approach, it was possible to observe the superradiant phase transition in several platforms, in particular atomic systems in cavity 10-12 , and trapped ions 13,14. Other proposals have been put forward, using NV centers array 15 , or superconducting circuits 16. In general, the implementation of analogue quantum simulations 17,18 provides an ideal playground to test driven-dissipative physics in a controlled setting. Their experimental feasibility has motivated increasing research efforts devoted to the study of driven-dissipative quantum optical models, as it is known that noise and dissipation can drastically change the properties of the steady-state phase diagrams and the emergence of p...

Characterization of a Two-Photon Quantum Battery: Initial Conditions, Stability and Work Extraction

“…In addition, recent theoretical proposals have shown that it is possible to engineer, in both trapped ions [ 44 ] and flux qubit systems [ 45 ], the suppression of the conventional dipole coupling, linear in the quantum field radiation, in order to access the peculiar phenomenologies, such as super-radiance and spectral collapse, which are associated to the two-photon coupling (quadratic in the radiation field) [ 46 , 47 , 48 , 49 , 50 , 51 ]. These ideas have also recently been considered in the context of QBs by some of us, showing that two-photon coupling, once realized, can lead to an even greater (proportional to M instead of ) enhancement of the averaged charging power [ 52 ].…”

Characterization of a Two-Photon Quantum Battery: Initial Conditions, Stability and Work Extraction

“…In addition, recent theoretical proposals have shown that it is possible to engineer, in both trapped ions [44] and flux qubit systems [45], the suppression of the conventional dipole coupling, linear in the quantum field radiation, in order to access the peculiar phenomenologies, such as super-radiance and spectral collapse, which are associated to the two-photon coupling (quadratic in the radiation field) [46][47][48][49][50][51]. These ideas have also recently been considered in the context of QBs by some of us, showing that two-photon coupling, once realized, can lead to an even greater (proportional to M instead of √ M) enhancement of the averaged charging power [52].…”

Ultrafast charging in a two-photon Dicke quantum battery

“…Some recent proposals, based on trapped ions [50] or superconducting flux qubits [51] have suggested the possibility to suppress the dipole contribution, linear in the photon coupling, and to enhance the two-photon coupling. This configuration is predicted to lead to new and interesting physics, enhancing the visibility of a superradiant phase transition and hinting at a spectral collapse at high coupling [52][53][54][55][56][57].…”