Rabi model exactly solved

Rabi model looks very simple: it describes a two-level atom coupled to a monochromatic beam of light through dipole interactions. However, an exact solution is not found until recently. A paper [the preprint of which is here] in PRL reports such a solution. Exactly solvable models are always interesting, because they can offer insights in many areas that may seem irrelevant at first glance.

Braak’s unexpected full analytical solutions of the quantum Rabi model are, however, worthy of celebration [2]. In mathematics and physics there are many, not necessarily compatible, criteria for a model to be both integrable and solvable. Examples include Frobenius’ condition for integrability in differential systems and Liouville’s condition for integrability in dynamical systems [6]. In the realm of quantum physics, it has been assumed that the existence of invariant subspaces associated with conserved quantities, other than energy, might be a necessary condition, as is the case in the Jaynes-Cummings model. The quantum Rabi model possesses naturally an additional discrete symmetry, the parity, which was assumed for some time to be insufficient for yielding a solvable model. Braak has proved that this is not the case and has presented exact analytical solutions of the quantum Rabi model for all parameter regimes. This is a remarkable achievement that adds the model to the short list of integrable quantum systems. Furthermore, Braak is able to take advantage of this key result to propose an operational criterion of integrability, inspired by the case of the hydrogen atom.

Integrability is, following Braak, equivalent to the existence of quantum numbers that classify eigenstates uniquely. It does not presuppose the existence of a family of commuting operators. Surprisingly, he has been able to apply this novel integrability criterion to a more elaborate case, the generalized quantum Rabi model, where a term that allows tunneling between the two atomic states is added. For the latter, he was able to prove that the model is not integrable, because it has an additional symmetry that is broken. However, the model is exactly solvable, and Braak presents the solutions. These are important results advancing the mathematical aspects of the quantum Rabi model in terms of integrability and solvability. Moreover, we should not overlook that the quantum Rabi model is a key physical model describing the interaction of quantum light and matter. [http://physics.aps.org/viewpoint-for/10.1103/PhysRevLett.107.100401]

Revamp might may not work

The Standard Model has been very successful, but with loopholes many people try to revamp with traditional ideas. One such idea is the supersymmetry, which says that, a new symmetry might exist between bosons and fermions. To implement such symmetry, new particles have to be inserted in the architecture. Now it runs in deep trouble: no such particles have ever been detected in LHC, which is the most hopeful place to find them.

They come from the LHC Beauty (LHCb) experiment, one of the four main detectors situated around the collider ring at the European Organisation for Nuclear Research (Cern) on the Swiss-French border.

According to Dr Tara Shears of Liverpool University, a spokesman for the LHCb experiment: "It does rather put supersymmetry on the spot".

Continue reading the main story

“Start Quote

There's a certain amount of worry that's creeping into our discussions”

End Quote Dr Joseph Lykken Fermilab

The experiment looked at the decay of particles called "B-mesons" in hitherto unprecedented detail.

If supersymmetric particles exist, B-mesons ought to decay far more often than if they do not exist.

There also ought to be a greater difference in the way matter and antimatter versions of these particles decay.

The results had been eagerly awaited following hints from earlier results, most notably from the Tevatron particle accelerator in the US, that the decay of B-mesons was influenced by supersymmetric particles.

LHCb's more detailed analysis however has failed to find this effect. [http://www.bbc.co.uk/news/science-environment-14680570]

New design of transistors

These are of course seminal to future in electronics industry.

The team has created a two-layer GaAs/AlGaAs quantum well heterostructure, in which the wave function of one layer extends into the second to modulate the tunneling current between the layers. In this design, a voltage on the first quantum well causes that layer to be depleted of carriers, which changes the subband energy level in the well. As the subband energy approaches the top of the quantum well potential, the wave function extends further and further out toward the second layer. When the wave function overlaps the second layer, the tunneling current can increase as much as two orders of magnitude, a substantial degree of gating leverage.

Although the reported design only works at cryogenic temperatures, a different choice of materials, for example, graphene, may allow operation at more technologically relevant temperatures. – David Voss

Majorana fermions possibly in topological insulators

This is a wonderful short review of the work done in looking for those elusive fermions in condensed matter community. I'll almost utterly post it here.

The search for Majorana fermions is quickly becoming an obsession in the condensed-matter community. To understand the intense interest, I will begin with a practical definition: a Majorana fermion is a fermion that is its own antiparticle. While sophisticated particle physics experiments are testing for Majorana character in neutrinos propagating in three dimensions [1], solid state physicists are more interested in lower dimensional counterparts. The most interesting Majorana fermions that are predicted to appear in materials are zero-dimensional bound states confined to live on various types of topological defects [2]. In a paper published in Physical Review Letters, Pavan Hosur and collaborators from the University of California, Berkeley, predict that these bound states are found in the vortices of the superconductor Cu_xBi₂Se₃ [3] (Fig. 1). Once discovered, a set of zero-dimensional Majorana bound states (MBS) are predicted to exhibit exotic non-Abelian statistics when exchanged among each other. While of great fundamental interest, perhaps the biggest driving factor in the search is a well-regarded proposal for (topological) quantum computation, which uses this unique statistical property of the MBS to robustly process quantum information free from local sources of decoherence [4, 5].

....

Naively, this eliminates all fermions at play in conventional electronic systems from being Majorana. The key to getting around this obstacle is noting that one finds many different emergent fermionic vacua/ground states in electronic systems that are qualitatively different from the fundamental vacuum of spacetime. To illustrate this, consider a BCS superconductor ground state filled with a condensate of paired electrons. If we again scatter two electrons off each other, they can indeed bind into a Cooper pair and “annihilate” into the fermionic vacuum! However, if the vacuum is of s-wave character, the most common superconducting ground state, then the two electrons bound into the Cooper pair must have opposite spin and are thus not Majorana (the antiparticle of an electron with spin up, in this case, is one with spin down). The solution to this problem is manifest: we must find a way to get around the spin-quantum number. Currently, there are two primary mechanisms to do this: (i) the superconducting vacuum can have spin-triplet pairing, which pairs electrons with the same spin or (ii) the superconductivity can exist in the presence of spin-orbit coupling or some other mechanism which will remove the spin conservation. Solution (i) is the paradigm for the first proposals of the existence of MBS as quasiparticles of a fractional quantum Hall state which models a two-dimensional electron gas at filling ν=5/2 [6], and as vortex excitations in some theories of the unconventional superconducting state of Sr₂RuO₄ [7]. These proposals offer real material candidates for finding MBS, but experiments in both of these systems require utmost care in sample production and measurement precision. To date, MBS excitations have not been clearly distinguished in either of these systems. Recently, solution (ii), which was first implemented by Fu and Kane in topological insulator/superconductor heterostructures [8], has been garnering attention due to more inherent practicality. This has been followed up nicely with further predictions of MBS in low-dimensional spin-orbit-coupled heterostructures in proximity to s-wave superconductors [9].

The seminal proposal of Fu and Kane predicts that if the surface of a three-dimensional topological insulator is proximity-coupled to an s-wave superconductor, then vortex lines in the superconductor will trap MBS where the lines intersect the topological insulator surface [8]. This proposal requires two main ingredients: (i) a topological insulator and (ii) an s-wave superconductor that can effectively proximity-couple to the surface of the topological insulator. Despite all of the recent publicity about the discovery of three-dimensional topological insulators [10], finding a suitable topological insulator for these experiments is still a difficult task. The reason being that, as of yet, there are no topological insulator materials that are completely insulating in the bulk, despite intense experimental programs dedicated to this task. The most commonly studied topological insulators are variations of either Bi₂Se₃ or Bi₂Te₃ , in which it has been difficult to tune the bulk to a completely insulating state [11]. Thus, while many experiments have confirmed the robust nature and structure of the surface states, these materials, having bulk carriers, are not true topological insulators.

It is then natural to ask, What is a doped topological insulator good for? While one hopes that many of the topological phenomena of the true insulating state might be manifested in some form in a doped system, many questions still remain unanswered. However, Hosur et al. have made a striking prediction that MBS can still be realized in doped topological insulators under certain mild conditions [3]. A true insulating state is important in the Fu-Kane proposal because if the bulk contains low-energy states then the MBS can tunnel away from the surface and delocalize into the bulk, which effectively destroys the MBS. Hosur et al. circumvent this delocalization by requiring that the entire doped topological insulator become superconducting. They show that as long as the doping is not too large, vortices in superconducting topological insulators will bind MBS at the places where the vortex lines intersect the material surfaces. While this might seem like a big leap in complexity, experimental evidence already shows that, indeed, copper-doped Bi₂Se₃ is a superconductor below 3.8 K [12]. In this context, Hosur et al. make a strong prediction that vortex lines in superconducting Cu_xBi₂Se₃ can harbor MBS.

To understand the prediction, we begin with the Fu-Kane proximity effect scenario, as mentioned above, with a vortex line stretched between two surfaces. MBS are trapped where each end of the vortex line meets the topological insulator surface (see Fig. 1). If we tune the bulk chemical potential to lie in the conduction band, as opposed to the nominal insulating gap, then the MBS on each end of the vortex line could tunnel through the bulk and hybridize with the state on the opposite end. This is prevented in Hosur et al.’s work by inducing a superconducting gap in the entire bulk so that the MBS remain trapped. If the superconducting state were homogeneous, then the MBS would be trapped on the ends of the vortex line for any doping level. However, the superconducting order parameter varies rapidly near the vortex core, which is essentially a thin tube of normal metal (doped topological insulator) containing bound states with energies that lie below the nominal superconducting gap. It is easiest for the MBS to tunnel through the “mini-gap” region in the vortex core, and in fact, Hosur et al. go on to show that there is a critical chemical potential level where a vortex-core bound state becomes gapless and the MBS can easily tunnel through the vortex line to annihilate. Beyond this critical doping, the vortex line re-enters a gapped phase, but the MBS are absent. See Fig. 1 for an illustration of this process. The critical chemical potential can be calculated solely from low-energy information about the Fermi surface, and depends on the orientation of the vortex line with respect to the crystal structure. It is estimated that vortex lines oriented along the c axis of Cu_xBi₂Se₃ are just on the trivial side of the transition, while vortices perpendicular to the c axis should be well within the nontrivial regime and should trap MBS.

Physics and Physicists: So I Am Your Academic Advisor?

Physics and Physicists: So I Am Your Academic Advisor?

What is the standard model ?

The standard model, as it is usually called, tries to encompass all possible interactions including production and annihilation of somewhat elusive elementary particles that are supposed to partly make up the universe. The following quantity explains it without words:

Back now

You know, on the world there are some undercivilized areas, where no connections to certain websites are possible due to something called the 'great fire wall'. I had been in one of such shit areas days. And this misfortune will go on in the coming six months. I need to commute between where I am and that culturally barren area.

Microwaves to entangle trapped ions

This is definitely a very important step toward practical quantum computing. Rather than using laser, which are not easy to set up as required, these groups [The work is described in Nature 476 181 and Nature 476 185.] use microwaves that can created by just alternating currents, to entangle ion spins.

However, entangling two trapped ions had required a pair of carefully aligned ultraviolet laser beams – which cannot be produced easily on an integrated circuit. To entangle two pairs of ions, two pairs of laser beams were needed and so on. A practical quantum computer would need a processor containing thousands or even millions of qubits, so scientists have long sought a way to manipulate many trapped ions without large numbers of laser beams.

In 2001 Christof Wunderlich and a colleague of the University of Hamburg had the idea of replacing the lasers with microwave and radio sources, which can be produced and controlled much more easily. Such radiation had previously been used in other trapped-ion experiments, but using it to implement quantum logic operations was a highly revolutionary suggestion. This is because the type of interaction required for quantum logic is usually very weak for this radiation. However, the researchers suggested adding a magnetic field gradient to stimulate the interaction.

Unfortunately, the need to use states that are sensitive to static magnetic fields makes the quantum states vulnerable to the magnetic noise found all around us, and the technique proved problematic. In 2008 physicists at the Ion Storage Group at the National Institute for Standards and Technology (NIST) in Boulder, Colorado, proposed eliminating the static magnetic-field gradient and using instead the oscillating field produced by the microwave source itself. The benefit being that the quantum states used in this scheme are less vulnerable to magnetic noise and more robust.

Both research groups now report significant advances in the journal Nature. Wunderlich's group, now at the University of Siegen, together with colleagues from the Institute of Theoretical Physics in Ulm, have come up with a way to produce states that, while still sensitive to the applied magnetic-field gradient, are far less vulnerable to noise and thus can be preserved more than 100 times longer. In a commentary accompanying the papers, Winfried Hensinger of the University of Sussex compares the group's scheme to a car's suspension system, which decouples the body from the wheels so that bumps in the road do not disturb the driver.

The NIST group, meanwhile, goes further and performs all of the essential quantum logical operations (albeit on only two qubits) using microwave radiation delivered via a waveguide integrated into a chip. "We've integrated the mechanism that does the entanglement between the two ions into the trapping structure," says Christian Ospelkaus, who built the experiment together with colleagues at NIST. "We no longer need to build a really complex and sophisticated laser system around the whole camp: we just send an electric current through the trap structure and that generates oscillating fields and it does all the other coherent quantum operations we need to do."[http://physicsworld.com/cws/article/news/46826]

The physics of how bubbles clean dusts

This is an interesting study published in PRL [PRL 107, 074503 (2011)], "It is now accepted that the physical forces in ultrasonic cleaning are due to strongly pulsating bubbles driven by the sound field. Here we have a detailed look at bubble induced cleaning flow by analyzing the transport of an individual particle near an expanding and collapsing bubble. The induced particulate transport is compared with a force balance model. We find two important properties of the flow which explain why bubbles are effectively cleaning: During bubble expansion a strong shear layer loosens the particle from the surface through particle spinning and secondly an unsteady boundary layer generates an attractive force, thus collecting the contamination in the bubble’s close proximity." The following is a review:

A team at the Nanyang Technological University in Singapore led by Claus-Dieter Ohl adapted a technique for creating a bubble where and when they wanted it. They focused a laser pulse up through a glass microscope slide into a strongly absorbing liquid dye. The laser heating caused the bottom layer of the dye to evaporate explosively, forming a hemispherical bubble at the glass surface that grew to tens of microns in radius and then collapsed, all within about 25 microseconds. The team stuck several-micron-diameter plastic beads on the slide surface and immersed them in the dye to mimic dirt particles adhering to a surface. They then recorded video of the beads' motion in response to the bubble.

BEC on an optical hexagonal lattice

The technology with lasers has incredibly enriched our understanding of a huge width of systems. The ability to prepare honeycomb lattice offers chances to study graphene-type physics and beyond. In this PRL paper, the authors addressed the issues of what would befall a Bose-Einstein condensate moving on a honeycomb lattice. They employed Gross-Pitaviskii equation, which is a mean-field theory for describing superfluids, to compute the band structure and found that, arbitrary interaction would drastically alter the structure around the Dirac points. Is it possible to observe similar stuff using graphene instead of an artificial lattice ? One needs to have superfluid to flow on graphene. The candidate is cooper pairs condensate, which may be created by placing a superconductor in contact with a layer of graphene.

The ability to prepare ultracold atoms in graphenelike hexagonal optical lattices is expanding the types of systems in which Dirac dynamics can be observed. In such cold-atom systems, one could, in principle, study the interplay between superfluidity and Dirac physics. In a paper appearing in Physical Review Letters, Zhu Chen at the Chinese Academy of Sciences and Biao Wu of Peking University use mean-field theory to calculate the Bloch bands of a Bose-Einstein condensate confined to a hexagonal optical lattice.

The Dirac point is a point in the Brillouin zone around which the energy-momentum relation is linear. Its existence in graphene is at the heart of this material’s unusual properties, in which electrons behave as massless particles. Chen and Wu’s study predicts, surprisingly, that in the analog cold-atom system, the topological structure of the Dirac point is drastically modified: intersecting tubelike bands appear around the original Dirac point, giving rise to a set of new Dirac points that form a closed curve. More importantly, this transformation should occur even with an arbitrarily small interaction between the atoms, upending the idea that such topological effects can only occur in the presence of a finite interaction between atoms.

The modified band structure prevents an adiabatic evolution of a state across the Dirac point, violating the usual quantum rule that a system remains in its instantaneous eigenstate if an external perturbation is sufficiently slow. This effect could be tested experimentally in a so-called triple-well structure, which is a combination of rectangular and triangular optical lattices. – Hari Dahal [http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.107.065301]

Physics about Guinness

This time we get to the physics of a kind of Irish beer, Guinness, which catches eyes for the bubbles and colors forming in it.

Look closely at a pint of Guinness and tell me: do the bubbles go up, or do the bubbles go down? Why is the head coloured the way it is? Is foam a gas, liquid or solid? An Irish physicist discusses.
....
The paper referenced in this discussion is "Waves in Guinness" by Marguerite Robinson, A. C. Fowler, A. J. Alexander, and S. B. G. O'Brien [DOI: 10.1063/1.2929369; free PDF]. And yes, it is rather intense reading, unless you are a fluid physicist or an astronomer. [http://www.guardian.co.uk/science/punctuated-equilibrium/2011/aug/02/1]