Approximations of that type are obtained as a result of performing infinite summations of a certain class of diagrams. In the following, we will discuss how the adc procedure can be performed in the case of the dynamic self-energy part. In the preceding Chap. The respective adc matrices could then be incorporated within a common Dyson secular matrix allowing one to solve the Dyson equation in the form of a hermitian eigenvalue problem. The obvious advantage of these direct or non-Dyson schemes is the smaller size of the secular problem, being roughly half the size of a comparable Dyson formulation.
The price to be paid here is a higher complexity in the pt expansions of the secular matrix elements, which, however, is workable through the third-order adc 3 level.
As already anticipated in Chap. But what actually are these presumed intermediate states underlying the adc secular matrix? Being a wave-function approach, the new formulation overcomes certain limitations inherent to the propagator concept. Of the three sections of this chapter, Sect.
The equivalence of the direct adc approach and the eco - isr formulation rests on two common key features. While in the adc context these features could have been substantiated using diagrammatic arguments, the eco - isr concept established in the preceding chapter allows for a stringent formulation and rigorous proofs. This is the topic of the present chapter. The separability property will be treated in Sect. Finally, in Sect. Also, the adc and isr concepts in the design of practical approximation schemes Chaps.
In the following Chaps. By and large, the concepts developed for the electron propagator can be transferred to the case of the polarization propagator, but there are also important differences that need to be addressed. In this chapter, we present the polarization propagator, discuss its physical significance, and outline the pertaining diagrammatic perturbation expansion. This will be demonstrated in the following. Moreover, in analogy to Chap.
In this chapter, we will take a look at the famous random-phase approximation RPA to the polarization propagator. The computational benefit afforded by the rpa is rather modest, at least for atoms and molecules, as the resulting excitation energies and transition moments are only consistent through first order of perturbation theory. To some extent, the eom formulation is more general than the algebraic propagator approach since the former provides a genuine wave-function representation of the generalized excited states in terms of an extended set of ce states.
In this chapter, we briefly review the eom method, emphasizing here in particular its isr characteristics. For a more comprehensive presentation as well as references to the original literature, we refer to the cited review articles and to Ref. A direct connection to the algebraic propagator methods is established in Sect. Now, researchers at the Joint Quantum Institute JQI have demonstrated a new approach that enables different devices to repeatedly emit nearly identical single photons.
Single photons, which are an example of quantum light, are more than just really dim light. This distinction has a lot to do with where the light comes from. Many researchers are working on building reliable quantum light emitters so that they can isolate and control the quantum properties of single photons.
Topological order in 1D Cluster state protected by symmetry
Scientists can generate quantum light using a natural color-changing process that occurs when a beam of light passes through certain materials. In this experiment the team used silicon, a common industrial choice for guiding light, to convert infrared laser light into pairs of different-colored single photons.
They injected light into a chip containing an array of miniscule silicon loops. Under the microscope, the loops look like linked-up glassy racetracks. The light circulates around each loop thousands of times before moving on to a neighboring loop. The relatively long journey is necessary to get many pairs single photons out of the silicon chip.
Such loop arrays are routinely used as single photon sources, but small differences between chips will cause the photon colors to vary from one device to the next. Even within a single device, random defects in the material may reduce the average photon quality.
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This is a problem for quantum information applications where researchers need the photons to be as close to identical as possible. The team circumvented this issue by arranging the loops in a way that always allows the light to travel undisturbed around the edge of the chip, even if fabrication defects are present.
The loop layout essentially forces each photon pair to be nearly identical to the next, regardless of microscopic differences among the rings.
The central part of the chip does not contain protected routes, and so any photons created in those areas are affected by material defects. The researchers compared their chips to ones without any protected routes. They collected pairs of photons from the different chips, counting the number emitted and noting their color.
Mittal adds that this device has one additional advantage over other single photon sources. The team says that this finding could open up a new avenue of research, which unites quantum light with photonic devices having built-in protective features. Magnets, whether in the form of a bar, horseshoe or electromagnet, always have two poles. But some physics theories predict the existence of single-pole magnets—a situation akin to electric charges, which come in either positive or negative chunks.
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One particular incarnation—called the Yang monopole after its discoverer—was originally predicted in the context of high-energy physics, but it has never been observed. The result, which provides another example of using cold quantum gases to simulate other areas of physics , was reported in the June 29 issue of Science. To detect the Yang monopoles in their quantum gas, Spielman, Sugawa and coworkers manipulated the internal compass needles that all atoms carry—a quantum property called spin—using radio waves and microwaves to rotate the needles in specific ways.
In this case, the size and direction of the deflection matched predictions for the curvature created by a Yang monopole. To test that the deflections were indeed due to the monopole and not another source, researchers sent the atoms on a different journey, one that attempted to avoid the space-bending singularity created by the monopole. Researchers playing with a cloud of ultracold atoms uncovered behavior that bears a striking resemblance to the universe in microcosm.
In several sets of experiments, Eckel and his colleagues rapidly expanded the size of a doughnut-shaped cloud of atoms, taking snapshots during the process. The growth happens so fast that the cloud is left humming, and a related hum may have appeared on cosmic scales during the rapid expansion of the early universe—an epoch that cosmologists refer to as the period of inflation.
The work brought together experts in atomic physics and gravity, and the authors say it is a testament to the versatility of the Bose-Einstein condensate BEC —an ultracold cloud of atoms that can be described as a single quantum object—as a platform for testing ideas from other areas of physics. Prior studies mimicked black holes and searched for analogs of the radiation predicted to pour forth from their shadowy boundaries. The first and most direct analogy involves the way that waves travel through an expanding medium. During that expansion, space itself stretched any waves to much larger sizes and stole energy from them through a process known as Hubble friction.
In one set of experiments, researchers spotted analogous features in their cloud of atoms. They imprinted a sound wave onto their cloud—alternating regions of more atoms and fewer atoms around the ring, like a wave in the early universe—and watched it disperse during expansion. Unsurprisingly, the sound wave stretched out, but its amplitude also decreased. The math revealed that this damping looked just like Hubble friction, and the behavior was captured well by calculations and numerical simulations.
In a second set of experiments, the team uncovered another, more speculative analogy. For these tests they left the BEC free of any sound waves but provoked the same expansion, watching the BEC slosh back and forth until it relaxed. In a way, that relaxation also resembled inflation. Some of the energy that drove the expansion of the universe ultimately ended up creating all of the matter and light around us. In the BEC, the energy of the expansion was quickly transferred to things like sound waves traveling around the ring.
Some early guesses for why this was happening looked promising, but they fell short of predicting the energy transfer accurately. So the team turned to numerical simulations that could capture a more complete picture of the physics. What emerged was a complicated account of the energy conversion: After the expansion stopped, atoms at the outer edge of the ring hit their new, expanded boundary and got reflected back toward the center of the cloud. There, they interfered with atoms still traveling outward, creating a zone in the middle where almost no atoms could live.
Atoms on either side of this inhospitable area had mismatched quantum properties, like two neighboring clocks that are out of sync.here
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The situation was highly unstable and eventually collapsed, leading to the creation of vortices throughout the cloud. These vortices, or little quantum whirlpools, would break apart and generate sound waves that ran around the ring, like the particles and radiation left over after inflation. Some vortices even escaped from the edge of the BEC, creating an imbalance that left the cloud rotating. Unlike the analogy to Hubble friction, the complicated story of how sloshing atoms can create dozens of quantum whirlpools may bear no resemblance to what goes on during and after inflation.
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But Ted Jacobson, a coauthor of the new paper and a physics professor at the University of Maryland specializing in black holes, says that his interaction with atomic physicists yielded benefits outside these technical results.