Quantum dark states lead to noise reduction benefit

While atomic clocks are already the most precise time measuring devices in the universe, physicists are working hard to further improve their accuracy. One solution is to exploit compressed spin states in clock atoms.

Spin-pressed states are entangled states in which particles in the system conspire to cancel out their intrinsic quantum noise. These states therefore offer great opportunities for quantum metrology since they allow more precise measurements. Yet squeezed spin states in desired optical transitions with little external noise have been difficult to prepare and maintain.

One particular way to generate a spin squeeze state, or squeeze, is to place the clock atoms in an optical cavity, a set of mirrors where light can bounce multiple times. In the cavity, atoms can synchronize their photon emissions and emit a burst of light much brighter than that of a single atom, a phenomenon called superradiance. Depending on how superradiance is used, it can lead to entanglement or, conversely, it can disrupt the desired quantum state.

In an earlier study, carried out as part of a collaboration between JILA and NIST fellows Ana Maria Rey and James Thompson, researchers found that multilevel atoms (with more than two internal energy states) offer unique opportunities to exploit superradiant emission by instead inducing atoms to cancel each other’s emissions and remain in darkness.

Now, reported in two new articles published in Physical Examination Letters And Physical examination A, Rey and his team discovered a method for not only creating dark states in a cavity, but, more importantly, rotating those states. Their findings could open up remarkable opportunities for generating entangled clocks, which could push the frontiers of quantum metrology in fascinating ways.

Ride in a dark state on a superradiant roller coaster

For several years, Rey and his team have been studying the possibility of exploiting superradiance by forming dark states inside a cavity. Because dark states are unique configurations in which the usual paths of light emission interfere destructively, these states do not emit light. Rey and his team showed that dark states could be realized when atoms prepared in certain initial states were placed inside a cavity.

Thus prepared, the quantum states could remain insensitive to the effects of superradiance or light emission in the cavity. Atoms could still emit light outside the cavity, but at a much slower rate than superradiance.

Former JILA postdoctoral researcher Asier Piñeiro Orioli, principal investigator of the previous study with Thompson and also a contributor to the two recently published studies, found a simple way to understand the emergence of a dark state in a cavity in terms of what they called a superradiant potential.

Rey says: “We can imagine superradiant potential as a roller coaster where atoms go up. As they move down the hill, they emit light collectively, but they can get stuck when they reach a valley. In the valleys, atoms form darkness. states and stop emitting light into the cavity.

In their previous work with Thompson, the JILA researchers found that dark states must be at least somewhat entangled.

“The question we wanted to address in the two new works is whether they can be both dark and highly entangled,” says first author Bhuvanesh Sundar, a former JILA postdoctoral researcher. “What’s exciting is that we not only found that the answer is yes, but that these types of compressed states are rather simple to prepare.”

Create highly entangled dark states

In the new studies, the researchers discovered two possible ways to prepare atoms in highly entangled spin states. One solution was to shine the atoms with a laser to energize them above their ground state, then place them in special points on the superradiant potential, also called saddle points. At the saddle points, the researchers let the atoms relax in the cavity by turning off the laser and, interestingly, the atoms reshape their noise distribution and are strongly compressed.

“Saddle points are valleys where the potential simultaneously has zero curvature and zero slope,” Rey says. “These are special points because the atoms are dark but on the verge of becoming unstable and therefore tend to reshape their noise distribution to become compressed.”

The other proposed method involved the transfer of superradiant states to dark states. Here, the team also found other special points where atoms are close to special “bright” points – not in a roller coaster valley, but at points with zero curvature – where the interaction between superradiance and an external laser generates spin compression. .

“What’s interesting is that the spin compression generated at these bright spots can then be transferred to a dark state where, after proper alignment, we can turn off the laser and preserve the compression,” adds Sundar.

This transfer works by first driving atoms into a valley of superradiant potential, then using lasers with appropriate polarizations (or directions of light oscillations) to coherently align the compressed directions, making the compressed states insensitive to superradiance.

The transfer from squeezed to dark states not only preserved the reduced noise characteristics of the squeezed states, but also ensured their survival in the absence of drive by an external laser, a crucial factor for practical applications in quantum metrology.

Even if the study published in Physical Examination Letters used a single polarization of laser light to induce spin compression, generating two compressed modes, the Physical examination A The paper took this simulation further by using both polarizations of the laser light, resulting in four spin compression modes (two modes for each polarization).

“In these two papers we considered multilevel atoms with many internal levels,” explains Piñeiro Orioli, “and having many internal levels is more difficult to simulate than having two levels, which is often studied in the literature So we developed a set of “Tools to solve these multi-level systems. We developed a formula to calculate the entanglement generated from the initial state. “

The results of these studies may have far-reaching implications for atomic clocks. By overcoming the limits of superradiance via the generation of dark entangled states, physicists store the entangled states using atoms as memory (allowing information to be retrieved from these states) or inject the entangled state into a sequence of clock or interferometer for quantum analysis. -improved measurements.