Pulsed coherent and squeezed driving of a spin-$S$ emitter as a deterministic source of Wigner-negative light

In the realm of quantum technology, light is not just a beam that illuminates a room; it is a delicate tool capable of carrying information in ways that classical physics cannot explain. For many advanced applications, such as building quantum computers or making ultra-precise measurements, scientists need light that behaves in a distinctly strange manner. This behavior is often described by a mathematical map called the Wigner distribution, which acts like a topographical chart for the light's quantum state. On this map, most ordinary light, like that from a laser pointer, looks like a smooth, positive hill. However, the most useful quantum states of light possess "negative" valleys on this map. These negative regions are a definitive signature that the light is behaving in a way that is impossible for classical objects, marking it as a resource for the next generation of technology. The challenge has always been how to create these negative states reliably. Historically, scientists have had to rely on luck, generating the light and then hoping a measurement confirms it worked, a process that is slow and inefficient.

A team of researchers at the University of Auckland has found a way to bypass this reliance on chance. They have demonstrated, through detailed computer simulations, that they can generate these valuable negative states of light on demand, using a method that is both deterministic and highly efficient. Their approach involves firing a short, controlled pulse of light at a tiny emitter, a single atom-like system that can exist in different energy states. By carefully shaping the pulse and the timing of the interaction, they can force the light leaving the emitter to transform into a state with deep negative valleys on its Wigner map. The researchers found that this method produces light with a level of quantum strangeness far greater than what was previously possible with continuous, steady streams of light. They showed that by adjusting the strength and shape of the incoming pulse, they could create specific, highly complex quantum states, including ones that resemble a single photon that has been shifted in space, or even more exotic forms that look like a superposition of two different squeezed states.

The study begins by looking at a simple two-level system, which acts like a basic switch that can be either on or off. When this system is hit with a pulse of coherent light, the researchers observed that the outgoing light could be tuned to exhibit strong negative features. They discovered that the amount of negativity is not a simple, steady increase as the pulse gets stronger; instead, it fluctuates in a complex pattern. By using optimization techniques to find the perfect combination of pulse width and timing, they identified a specific setup that produces a state very close to a displaced single-photon state. This is a significant finding because it suggests a reliable way to create a fundamental building block for quantum computing without needing to filter out unwanted results. The simulations showed that this optimal state has a negative volume, a measure of how much "quantumness" is present, that is more than five times larger than what was achieved in previous experiments using steady driving methods.

The researchers then expanded their investigation to more complex emitters, systems that can hold more than just two energy levels, similar to a dial with multiple settings rather than a simple switch. They found that driving these higher-spin systems with pulses of light produced even more dramatic results. As they increased the complexity of the emitter, the amount of negativity in the output light grew significantly. For a system with a spin of three-halves, the negative volume reached levels that far exceed any other deterministic method currently known. The shapes of these new states began to resemble patterns of multiple photons, suggesting that this technique could be used to deterministically generate states with specific numbers of particles, a capability that is currently very difficult to achieve.

In a second line of inquiry, the team replaced the standard coherent light pulses with pulses of squeezed light. Squeezed light is a special type of light where the uncertainty in one property is reduced at the expense of another, making it a powerful tool for precision. When they drove the simple two-level system with these squeezed pulses, the resulting light states looked like "Schrödinger cat" states, which are superpositions of two distinct quantum realities. These states are highly valued for their potential use in error-corrected quantum computing. The simulations revealed that the pulsed method again outperformed steady-state methods, producing states with much deeper negative valleys. The researchers were able to fine-tune the squeezing and the timing of the pulse to maximize this effect, finding a sweet spot where the generated state was almost identical to a theoretical squeezed cat state.

Perhaps the most surprising discovery came when they applied squeezed pulses to a spin-one emitter, a system with three energy levels. Here, the physics took a unique turn. The interaction between the squeezed light and the three-level system resulted in a state where the two-photon component was almost entirely missing. In the output light, the probability of finding exactly two photons was suppressed, while other numbers of photons remained. This phenomenon, which the researchers call "two-photon exclusion," creates a grid-like pattern in the quantum map that is reminiscent of a specific type of quantum error-correcting code known as a GKP state. These states are considered the holy grail for building robust quantum computers because they can protect information from noise. The simulations showed that the light generated in this way shares a high degree of similarity with these ideal GKP states, offering a potential new pathway to create them deterministically.

Throughout their work, the researchers emphasized that these results come from rigorous numerical simulations of a cascaded system, where light flows from a source, through an emitter, and into a capture cavity. They carefully modeled how the light pulses interact with the emitter and how the timing of the pulses affects the final state. They also explored how imperfections, such as light leaking out in the wrong direction or the emitter being slightly out of tune with the light, would affect the results. Their analysis showed that while these imperfections reduce the quality of the negative states, the core effect remains robust as long as the system is reasonably well-tuned. The study concludes that by moving from continuous driving to pulsed driving, and by utilizing emitters with different numbers of energy levels, it is possible to generate a wide array of highly non-classical light states. This work provides a theoretical blueprint for a deterministic source of Wigner-negative light, moving the field closer to the practical realization of quantum technologies that rely on these fragile and powerful states of matter.