A team of physicists has uncovered a startling quantum behavior in a novel class of materials, revealing that the process of spontaneous emission does not always work as expected. By observing a quantum emitter placed within a photonic time crystal—a material whose optical properties are varied in time—researchers witnessed a substantial enhancement in the rate of light emission. More surprisingly, they also documented a completely new phenomenon: an atom in its low-energy ground state could spontaneously excite itself while simultaneously emitting a photon, a process that seemingly defies the standard understanding of energy conservation in light-matter interactions.
This discovery challenges long-held assumptions that have governed quantum electrodynamics for decades. For years, scientists have controlled spontaneous emission by altering the spatial environment around an emitter, but the advent of time-varying photonics has opened a new frontier. The new findings not only compel a reevaluation of fundamental theories but also introduce a powerful mechanism for manipulating light and matter. This work could pave the way for advancements in quantum information processing, advanced sensors, and highly efficient light sources by providing an entirely new toolkit for controlling quantum phenomena.
Understanding Photonic Time Crystals
Conventional photonic crystals are materials engineered with a spatially periodic structure, such as a lattice of holes or pillars, that controls the flow of light. These structures create “energy gaps,” which forbid photons of certain frequencies from propagating through the material. This principle is analogous to how semiconductors control the flow of electrons and is the basis for many modern optical technologies. Photonic time crystals, or PTCs, operate on a different principle. Instead of a periodic variation in space, their optical properties—primarily the refractive index—are modulated uniformly and periodically in time.
This temporal modulation causes any light wave traveling through the medium to be repeatedly reflected and refracted in time. The interference between these time-scattered waves gives rise to what are known as “momentum gaps.” Unlike energy gaps that block a range of frequencies, momentum gaps prevent light with a certain momentum from maintaining a stable energy, often causing its amplitude to grow exponentially. This unique property stems from the fact that, unlike spatial crystals, time crystals inherently break time-reversal symmetry, creating a rich and complex environment for light-matter interactions that can feature both loss and gain.
A Surprising Emission Process Observed
The core of the new research involved analyzing the behavior of a quantum emitter, such as an atom, embedded within a PTC. The established understanding of spontaneous emission, a cornerstone of quantum mechanics, dictates that an atom in a high-energy “excited” state will eventually decay to its low-energy “ground” state by releasing a photon. Scientists have long sought to control the rate of this decay, but the new experiment revealed behavior that went far beyond simple rate modification.
Using a theoretical framework based on classical light-matter interaction theory combined with Floquet analysis—a mathematical tool for handling time-periodic systems—the researchers made two profound discoveries. First, they confirmed that the spontaneous emission decay rate was substantially enhanced when the emission frequency was near the PTC’s momentum gap. This effect is partly due to the non-orthogonality of the system’s characteristic modes, or Floquet eigenmodes, which is a unique feature of these time-varying systems.
The second, more groundbreaking discovery was an entirely new process the team termed “spontaneous emission excitation.” In this counter-intuitive phenomenon, an atom already in its stable ground state was observed to spontaneously jump to an excited state while also emitting a photon. This appears to violate the simple expectation of energy decay, highlighting the unusual physics at play in nonequilibrium systems where energy can be drawn from the temporal modulation of the material itself.
Revisiting Foundational Theories
The observation of spontaneous excitation fundamentally challenges conventional theories that describe how light and matter interact. In typical, or equilibrium, systems, emission is a process of relaxation, where a system sheds excess energy to reach a more stable state. The work on PTCs demonstrates a nonequilibrium process where the time-varying nature of the crystal itself actively injects energy into the system, enabling pathways that would otherwise be forbidden.
The researchers found that the gain inherent in PTCs, resulting from the time modulation, creates what can be described as a negative photonic density of states. This is the key that unlocks the spontaneous excitation phenomenon. It necessitates a reevaluation of the foundational formulas, such as Fermi’s Golden Rule, which are typically used to calculate decay rates. The study successfully distinguishes between equilibrium and nonequilibrium emission processes, providing a more complete picture of quantum electrodynamics in dynamic environments. The findings suggest that the interplay of gain, loss, and unique modal structures in PTCs creates a far richer physical landscape than previously imagined.
Methodology of the Discovery
To arrive at their conclusions, the researchers modeled the interactions within the PTC by incorporating a dipole-induced current source into Maxwell’s equations, which govern electromagnetism. This allowed them to precisely quantify how the time-periodic modulation of the material’s permittivity influenced the quantum emitter. Their analysis accounted for the complex interplay of loss and gain regions in the system’s wave number-frequency space, which is critical for understanding its behavior.
A key factor in their analysis was the Petermann factor, a measure that quantifies the non-orthogonality of the Floquet eigenmodes in the PTC. They demonstrated that this factor directly amplifies both the spontaneous emission decay rate and the newly discovered spontaneous excitation rate. When the gain induced by the time modulation is engineered to exceed the system’s intrinsic losses, the PTC can even transition into a lasing state, producing a narrow-band, coherent emission of light. This theoretical work provides a clear roadmap for experimental verification and future device engineering.
Implications and Future Directions
New Frontiers in Quantum Technology
The ability to not only enhance but also fundamentally alter the nature of spontaneous emission opens powerful new avenues for technology. Controlling the emission and excitation of quantum emitters is central to building quantum computers, secure communication networks, and precision sensors. By engineering the temporal modulation of a PTC, scientists could potentially protect fragile quantum states from decaying, create on-demand single-photon sources with unprecedented efficiency, or develop novel quantum logic gates that harness these exotic nonequilibrium processes.
Engineering Light and Matter
This research brings the concept of engineering the local density of states (LDOS) in a time-periodic system much closer to practical realization. The LDOS essentially dictates the available pathways for an emitter to release its energy. By shaping the LDOS with time modulation, researchers can now access a vast parameter space that was previously unavailable. This could lead to hyper-efficient LEDs, novel types of lasers, and materials that can manipulate thermal radiation in surprising ways. The work also provides a new platform for studying other complex phenomena, such as the behavior of radiating particles moving at relativistic speeds or achieving highly efficient interactions between light and free electrons.
