Squeezed Photons Induce Normal and Superradiance in Multi-Atom Dicke Model

The interplay between light and matter forms the basis of many physical phenomena, and understanding how systems transition between different states of interaction remains a central challenge in quantum physics. Moorad Alexanian from the University of North Carolina Wilmington, along with colleagues, investigates this behaviour within a modified model of the Dicke model, a fundamental framework describing the collective interaction of atoms with a radiation field. Their work reveals how the system exhibits a quantum phase transition, moving between a normal state and a superradiant state where atoms collectively emit light, and demonstrates this transition occurs even with specific coupling terms between light and matter. This discovery advances our understanding of collective atomic behaviour and has implications for developing new technologies based on quantum optics and quantum information processing.

Dicke Model Dynamics and Quantum Phase Transitions

The Dicke model, a cornerstone of quantum optics and mechanics, describes how multiple two-level atoms collectively interact with light within an optical cavity. This simple yet powerful model exhibits a quantum phase transition at zero temperature, presenting a tractable system for understanding more complex many-body phenomena like superfluidity and superconductivity. Researchers investigate the Dicke model to gain insights into collective behaviours, and this work explores the model’s dynamics under various conditions to characterise the quantum phase transition and the resulting collective atomic behaviour.

Squeezed Photons and Collective Atomic Emission

Researchers investigated the quantum behaviour of multiple atoms interacting with light, specifically exploring the transition between normal and superradiant states, where atoms collectively emit light. They employed a theoretical framework centred on a modified Jaynes-Cummings model, a standard tool in quantum optics, extended to incorporate squeezed photons, light with altered quantum properties, and a system of interacting atoms. This model allows detailed examination of energy exchange between atoms and light, revealing conditions that promote collective emission. A key innovation involves mathematical transformations to simplify the complex interactions within the model.

Researchers used a unitary transformation, a technique that alters perspective without changing the underlying physics, to reshape the model’s energy equation into a more manageable form. This transformation, based on established principles, facilitated the identification of critical points where the system’s behaviour dramatically changes. The team then utilized a Bogoliubov transformation, a method for re-expressing quantum operators, to further diagonalize the equation and reveal the underlying quantum states. By adapting the techniques developed for the modified Jaynes-Cummings model, researchers explored how the interplay between co- and counter-rotating coupling terms, describing the direction of energy exchange, influences the transition between quantum phases.

The team meticulously mapped the conditions under which a quantum phase transition occurs, identifying critical points defined by the interplay of coupling strengths and atomic properties. To understand the emergence of superradiance, the collective emission of light, the researchers introduced a mathematical tool that shifts the quantum state of the system. This allowed them to calculate the excitation energy, the energy required to stimulate emission, and reveal how it changes as the system transitions into a superradiant phase. By carefully analysing this excitation energy, the team pinpointed the conditions necessary for achieving collective emission and understood the underlying quantum mechanisms driving the process. The results demonstrate how atomic and photonic properties dictate the system’s behaviour, offering insights into the fundamental principles governing light-matter interactions.

Dicke Model Exhibits Quantum Chaotic Transition

Results demonstrate a transition from quasi-integrable to quantum chaotic behaviour. The Dicke model, when considering a single two-level system, is known as the Rabi model. This work generalizes a recently introduced modified Jaynes-Cummings model for atoms with arbitrary spin, determining a normal/superradiance quantum phase transition in the Dicke model. The modified Jaynes-Cummings model involves an equation where energy differences between atomic states and the light field are defined. Applying a unitary transformation to this equation results in a simplified form, facilitating the identification of critical points.

Diagonalization is achieved via a Bogoliubov transformation of mathematical operators, further simplifying the equation. The quantum phase transition is characterised by a specific condition involving coupling constants. Two possible cases arise, each requiring a specific condition to avoid instability and maintain a single quantum phase. The existence of a differing quantum phase is associated with a change in a key variable. The Dicke model equation includes terms representing the frequencies of the light field and the atoms, and the interaction between them.

The interaction terms involve coupling constants describing the direction of energy exchange. Consequently, results from the previous section apply directly to the Dicke model with appropriate substitutions. For certain conditions, no phase transition occurs. However, a phase transition always exists provided the coupling constants are not equal. In the limit of a large number of atoms, no phase transition occurs under certain conditions.

The ground-state energy recovers results for the Rabi model and the Jaynes-Cummings model under specific conditions. Considering a mathematical tool on the Dicke model equation results in an excitation energy analogous to that of the modified Jaynes-Cummings model. The excitation energy reduces to the Rabi case and the Jaynes-Cummings case under specific conditions. The excitation energy exists in the limit of a large number of atoms with a negative and finite ratio.

Superradiance Transition Robust Across Atomic Spins

Conclusions. A modified Jaynes-Cummings model is generalised to the Dicke model of atoms with arbitrary spin and independent coupling terms. This model gives rise to a normal/superradiance quantum phase transition, as observed in previous publications concerning the Jaynes-Cummings and Rabi models. The research demonstrates that this transition occurs consistently across variations in atomic spin and coupling parameters. Future work will focus on exploring the dynamics of this phase transition and investigating the potential for utilising this system in quantum information processing. Further investigation will also examine the effects of dissipation and decoherence on the stability of the superradiant phase.