Quantum optics is a complex field where theoretical and experimental physicists collaborate on breakthroughs to explain phenomena at the subatomic level.
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Recently, Farokh Mivehvar from the University of Innsbruck has utilized the Dicke model, the most comprehensive model in quantum optics, to study the interaction of two groups of atoms in a quantized field.1 The novel study has enabled the observation of superradiant states, paving the way for high-performance superradiant lasers.
The Dicke Model and the Evolution of Quantum Optics
Superradiance, first conceptualized in 1954 by Dicke, describes the collective emission of light by a large group of atoms.2 Dicke's model involves a system of N two-level atoms, all initially in their excited states. When one atom spontaneously emits a photon, it triggers a cascade effect, causing all N atoms to decay and emit photons simultaneously.3
Dicke proposed that, by confining these atoms within a fraction of a wavelength, the emitted photons would be identical, leading to constructive interference and the generation of an electromagnetic field with an amplitude proportional to N and an energy density proportional to N2. This behavior contrasts with the independent decay of N isolated atoms, where light emission is incoherent and energy density scales linearly with N.
In 1973, Hepp and Lieb identified a distinct form of steady-state superradiance, in which a collection of atoms interacts with the quantized mode of a cavity. They investigated the thermal equilibrium characteristics of this interaction, employing the Dicke model as their framework.
They unveiled a continuous phase transition between two states: normal and superradiant. In the normal phase, the number of photons (denoted as n) does not increase with the number of atoms (N), whereas in the superradiant phase, n scales proportionally to N.
An Introduction to Cavity Quantum Materials
Quantum materials are intricate quantum many-body systems comprising multiple atomic species. Their low-energy behavior typically involves a complex interplay of several degrees of freedom, such as charge, spin, orbital, and lattice.
When exploring modifications to the emergent properties of quantum materials, an alternative approach arises through substituting a classical laser field with quantum-mechanical photon modes confined within a cavity [4].
In traditional cavity quantum electrodynamics (QED), emphasis is placed on the interaction between one or multiple emitters and the well-defined field mode of a cavity. This interaction becomes particularly noteworthy when a single dipole transition of the emitters strongly couples to the cavity, characterized by frequency ω. Such scenarios can be effectively described using a simple two-level model, where the light-matter interaction is quantified by a single coupling strength g.
The field of cavity quantum materials is still in its early stages, attracting researchers from diverse communities, including quantum materials science—particularly in two-dimensional systems—and quantum many-body physics. Cavity quantum materials hold promise as photonic platforms and can be integrated into photon-based quantum technologies.4
The strong electronic interactions inherent in quantum materials could facilitate efficient photonic interactions for two-photon quantum gates and enable the generation of nonclassical states of light.
Superradiance and Quantum Electrodynamics
The Dicke model has been efficaciously implemented utilizing cavity-assisted two-photon Raman transitions with both bosonic and fermionic atoms in low-lying atomic momentum or hyperfine states. Researchers are also keen on implementing Dicke-type models and exploring superradiance in waveguide-QED configurations and cavity quantum materials.4
The decay rate of an individual emitter is influenced by its surrounding radiative environment, a concept pivotal to cavity QED. By using highly reflective mirrors to confine a single optical mode, cavity QED creates a localized reservoir for the emitter, thereby enhancing its decay into the cavity.
In the context of "waveguide QED," where an atom interfaces with a propagating optical mode, the concept of one-dimensional (1D) baths becomes relevant.
The environment also shapes the collective decay of a group of excited emitters. Dicke superradiance exemplifies this phenomenon: a fully inverted collection of emitters synchronizes their decay, resulting in the emission of a brief, intense pulse of photons.5
Cutting-Edge Discoveries: Unconventional Dicke Model for Superradiant Lasers
Inspired by recent advancements in quantum-gas–cavity QED, Farokh Mivehvar, a theoretical physicist at the University of Innsbruck, introduced a novel variant of the Dicke model. This approach, named the "non-standard Dicke model," involves coupling two independent ensembles of spin-1/2 atoms to a single cavity mode, each with different coupling strengths.6
The research then focused on a specific scenario where the coupling strengths were opposite—equivalent to having equal coupling strengths under unitary transformation. This configuration led to various intriguing phenomena, primarily attributed to the conservation of the total spin within each ensemble individually.
The semi-classical approach uncovered the presence of multistable steady-state phases, notably a bistable superradiant regime. Within this bistable region were ±xFo-SR states, where the total spins of both atomic ensembles aligned in the same x direction, either positive or negative. Other superradiant phases were observed, characterized by the total spins of the two ensembles pointed in opposite x directions.
Mivehvar also identified initial states within the system’s multistable regimes, from which the subsequent nonequilibrium dynamics diverge from settling into any steady state. Rather than evolving towards a constant state, the system transitions into non-stationary states characterized by vibrational paths. This phenomenon is associated with the presence of competing fixed points. Full quantum-mechanical calculations also validated the coexistence of ±xFo-SR and ±xFi-SR states.
When the two coupling strengths, λ1 and λ2, differ, the Hamiltonian no longer maps unitarily to the standard Dicke model. Consequently, the system displays a broader range of steady-state and non-stationary phenomena. This is due to the conservation of the total spin in each ensemble, prompting the exploration of physics beyond the confines of the symmetric Dicke subspace.
In the general case, where λ1 is not equal to ±λ2, the system's dynamics become more intricate and diverse as different symmetry sectors interact. This complexity may lead to distinct critical behaviors and the emergence of multicritical points within the system.
Understanding these multicritical points is crucial for advancing our comprehension of the complex superradiant emission phenomena in quantum cavity models. The proposed model can be readily implemented in state-of-the-art experiments, offering a new avenue for investigating various nonequilibrium magnetic ordering and dynamical phenomena within cavity-QED experimental setups.
More from AZoOptics: Quantum Optics Experiments with Trapped Ions: Recent Advances
References and Further Reading
[1] Mivehvar, F. (2024). Conventional and Unconventional Dicke Models: Multistabilities and Nonequilibrium Dynamics. Physical Review Letters. doi.org/10.1103/PhysRevLett.132.073602
[2] Dicke, R. (1954). Coherence in spontaneous radiation processes. Physical review. doi.org/10.1103/PhysRev.93.99
[3] Kirton, P., et al. (2019). Introduction to the Dicke model: From equilibrium to nonequilibrium, and vice versa. Advanced Quantum Technologies. doi.org/10.1002/qute.201800043
[4] Schlawin, F., et al. (2022). Cavity quantum materials. Applied Physics Reviews. doi.org/10.1063/5.0083825
[5] Cardenas, S., et al. (2023). Many-body superradiance and dynamical mirror symmetry breaking in waveguide QED. Physical Review Letters. doi.org/10.1103/PhysRevLett.131.03360
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