A new version of Wheeler's set up

The particle-wave duality seem always under debate and ingenious experiments have been contrived from time to time to violate it. A famous example is the one proposed by John-Wheeler. It is called 'delayed-choice experiment'. In its existing version, a classical switch has been in use. Here comes a new design using quantum switches [http://physics.aps.org/articles/v4/102].

This so-called delayed-choice experiment was performed in 2007 using an interferometer [1]. In the normal setup, a beam splitter creates two separate light beams that later recombine in a second beam splitter. Detectors placed at the two outputs of this beam splitter both register an interference pattern. However, this wave detector can be turned into a particle detector by removing the second beam splitter, so that the two paths no longer interfere. In the experiment, the choice to add or remove the second beam splitter was made after an individual photon had already passed through the first beam splitter. The data showed that particle and wave behavior were unaffected by the delayed choice, as expected from standard quantum mechanics.

Radu Ionicioiu, now at the Institute for Quantum Computing in Waterloo, Canada, and Daniel Terno of Macquarie University in Sydney, Australia, wanted to see what happens in the thought experiment if the delayed choice is made through quantum means. They imagined that the interferometer contains a quantum device—perhaps an atom in a cavity or a micro-mirror placed on a cantilever—that can exist in two possible states. One state selects the particle experiment, and the other selects the wave experiment. This quantum control element can be placed in a combination, or superposition, of its two states, making the whole experiment participate in the wave-particle duality.

“We show you can do both wave and particle experiments at once,” Ionicioiu says. This means the choice of wave vs particle can be delayed indefinitely. The photon can be observed at one of the detectors and still not “know” if it is supposed to be a wave or a particle. It’s only when the observer decides to measure the state of the quantum control that the photon’s behavior can be identified as wavelike or particlelike.

How many neutrinos should exist ?

The SM assumes three types of neutrinos. However, these authors analyzed data to demonstrate the need of two more types [http://www.nature.com/nature/journal/v478/n7369/full/478328a.html?WT.ec_id=NATURE-20111020].

Neutrino oscillations, observed through the transmutation of neutrinos of one type into neutrinos of another type, occur if there is mixing between neutrino types and if individual neutrino types consist of a linear combination of different neutrino masses. (At present, the masses and mixings of the fundamental quarks and leptons can be measured but are not fully understood.) In the case of two-neutrino mixing — for example, mixing between the muon neutrino and the electron neutrino — the probability (P) that a muon neutrino (ν_μ) will oscillate into an electron neutrino (ν_e) is given by P(ν_μ ν_e) = sin²(2θ)sin²(1.27Δm²L/E). Here, θ, in radians, describes the mixing between the muon neutrino and electron neutrino; Δm² is the difference of the squares of the masses of the two neutrinos in square electronvolts; L is the distance travelled by the muon neutrino in kilometres; and E is the muon-neutrino energy in gigaelectronvolts.

In general, the number of different neutrino masses equals the number of neutrino types, so that three-neutrino mixing involves three neutrino masses and two independent Δm² values, whereas five-neutrino mixing involves five neutrino masses and four independent Δm² values. Neutrino oscillations have been observed at a Δm² of about 7 × 10⁻⁵ eV² by detectors that measure the flow of neutrinos from the Sun and experiments that detect neutrinos at a long distance from nuclear reactors. The oscillations have been detected at a Δm² of around 2 × 10⁻³ eV² by detectors that measure the flow of neutrinos from the atmosphere and by experiments in which neutrinos are measured at a long distance from particle accelerators. In addition to these confirmed observations of neutrino oscillations, there is also evidence for oscillations at a Δm² of about 1 eV² from short-distance accelerator and reactor neutrino experiments^{2, 3, 4}. However, it is not possible to explain this third Δm² value with only three neutrino masses. Therefore, additional neutrino masses are required.

In their study, Kopp et al.¹ tried fitting the world neutrino-oscillation data to theoretical models involving four different neutrino masses (three active neutrinos plus one sterile neutrino) and then five different neutrino masses (three active plus two sterile neutrinos; Fig. 1). They found that one sterile neutrino was insufficient to explain the world data, but two gave a satisfactory global fit. (Similar fits are discussed elsewhere^{5, 6, 7, 8, 9, 10}.) One other feature of the authors' two-sterile-neutrino fit is that it allows for violation in leptons of the charge–parity (CP) symmetry — according to which particles and antiparticles behave like mirror images of each other — or for a difference between neutrino oscillations and antineutrino oscillations. Such CP violation might help to explain the r-process, in which heavy elements are produced through nuclear reactions involving rapid neutron capture (hence the 'r'), and the production of heavy elements in neutrino bursts from stellar explosions known as supernovae. It might also help to explain why the Universe is dominated by matter and not by an equal amount of matter and antimatter.

Neutrino not that fast !!

I like this blog entry by Zz. He highlighted a recent article that did not see data indicating superfast!

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.

Electron induced rippling in graphene

Physicists are really blessed by nature in the sense that, they have all the time been offered some new objects that admit very rich phenomena to be explored. Latest examples include Graphene and Topological Insulators. Since its discovery, graphene never stops yielding surprising things for physicists. This time comes something that (again, considering Dirac physics) parallels particle physics: the strain field associated with the flexural phonon condenses in the same way as the Higgs field in the Standard Model [1]. Don't miss reading it !

[1]PRL, 106:045502(2011)

The proton size

In a previous entry, I posted a report on the measurement of the proton size that is based on muons. It gives a smaller size than had been accepted. There came a new measurement, which, nonetheless, disagrees with this smaller proton saying. This new one is based on electrons. [http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.105.242001]

The charge radius of the proton is one of nature’s fundamental parameters. Its currently accepted CODATA (Committee on Data for Science and Technology) value, 0.8768×10^-15 m, has been determined primarily by measurements of the hydrogen Lamb shift and, to lesser accuracy, by electron-proton scattering experiments. This value has recently been called into question by a research team at the Paul Scherrer Institut (PSI) in Villigen, Switzerland. By measuring the Lamb shift in muonic hydrogen, these researchers obtained a value of 0.8418×10^-15 m for the charge radius, five standard deviations below the CODATA value.

In a paper appearing in Physical Review Letters, the A1 Collaboration has determined the electric and magnetic form factors of the proton with higher statistics and precision than previously known, using the Mainz (Germany) electron accelerator MAMI (Mainz Microtron) to measure the electron-proton elastic-scattering cross section. Both form factors show structure at Q²≈ m_π² that may indicate the influence of the proton’s pion cloud. But, in addition, the collaboration’s extracted value for the charge radius agrees completely with the CODATA value. The discrepancy between “electron-based” measurements and the recent PSI “muon-based” measurement thus remains a puzzle. – Jerome Malenfant

Topological Insulators used to determine fundamental constants

Topological phenomena (TP) play crucial role in determining the precise values of fundamental constants such as elementary charge, Planck constant and speed of light. This is so because of the robustness of topological phenomena against local variation in samples and also weak disorder and interactions between particles. Some famous TP have already been in use to this end: the quanta of magnetic flux has been measured with circular superconducting devices; the electrical conductance has been measured with the help of quantum Hall effect. Recently, a new TP was discovered in materials now known as topological insulators (TI). These materials are characterized by their bulky band gap and gapless surface states that are topologically robust. Examples include Te-Bi type compounds. It is expected that, such TP may also be employed to improve the precision of measurement. This came to realization in a latest publication [PRL 105, 166803 (2010)]:

Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant topological insulator in three dimensions exhibits a topological magnetoelectric effect quantized in units of the fine structure constant ¼ e2=@c. In this Letter, we propose an optical experiment to directly measure this topological quantization phenomenon, independent of material details. Our proposal also provides a way to measure the half-quantized Hall conductances on the two surfaces of the topological insulator independently of each other.

Muonic hydrogen indicating a smaller proton

Muons are conceived as point-like elementary particles living a few microseconds (shall live longer when it moves fast) under lab conditions. They are heavier counterparts (200 times heavier) of electrons. When they are caught by a proton, a muonic hydrogen forms. Now they are used to investigate some fundamental questions concerning QED.

1. Muonic hydrogen is an exotic hydrogen atom, where a muon (instead of an electron) orbits the proton. Because the muon is 200 times heavier than the electron, the muon's orbit is 200 times closer to the proton in muonic hydrogen than that of the electron in regular hydrogen. This 200 times smaller orbit means that the muon "feels" the size of the proton: certain muon orbits are significantly perturbed by the size of the positive charge distribution of the proton. By measuring the perturbation of the muon orbit using a laser, it is possible to determine the size of the proton.
(https://muhy.web.psi.ch/wiki/index.php/Main/Introduction)
2. Our measurement of the muonic hydrogen Lamb shift has to be conceived as a progress in the investigation of the hydrogen atom. In fact, when combined with the the measured transition frequencies in hydrogen, the proton radius inferred from the measurement of the muonic hydrogen Lamb shift will provide the most precise test of bound-state QED in the hydrogen atom to this date. Our measurement is thus likely to spur additional investigations of the fundamental theory of the electromagnetic interaction (quantum electrodynamics), a theory that links charged particles and photons (and hence light), which are some of the most important building blocks of our universe. (https://muhy.web.psi.ch/wiki/index.php/Main/Introduction)
3. The μp Lamb shift, ΔE(2P-2S) ≈ 0.2 eV, is dominated by vacuum polarization which shifts the 2S binding energy towards more negative values (see figure). The μp fine- and hyperfine splittings are an order of magnitude smaller than the Lamb shift. The relative contribution of the proton size to ΔE(2P-2S) is as much as 1.8%, two orders of magnitude more than for normal hydrogen atoms. The muonic Lamb shift ΔE(2P-2S) was recalculated recently by several authors [6-8] considering all QED contributions on the ppm level, including three-loop vacuum polarization, hadronic vacuum polarization, light-by-light scattering, and recoil corrections to the order α6. The uncertainty in the calculated proton polarization shift will ultimately limit the calculated ΔE(2P-2S)-value to the 0.3 ppm precision level (disregarding terms which depend on the proton radius). The theoretical prediction of the muonic hydrogen Lamb shift is

ΔE(2P^F=2 - 2S^F=1)=205.952 (3)(4)(137) meV

where the first error is the uncertainty of the calculated QED-terms, the second one the uncertainty from the proton polarization, and the third one the uncertainty given by the poor knowledge of the proton radius. A measurement of the muonic Lamb shift with 30 ppm precision will hence determine the proton radius with 0.1% precision.(https://muhy.web.psi.ch/wiki/index.php/Main/Motivation)

4. The aim of our laser spectroscopy experiment is to measure the Lamb shift in muonic hydrogen (μp):

ΔE(2P - 2S) (with 30 ppm precision)

and to deduce the rms proton charge radius r_p (with 1000 ppm, 10 times more precise than presently known):

ΔE(2P -2S) = 209.98 - 5.23 r_p² [meV]

where r_p is given in fm (r_p ≈ 0.9 fm).

The principle of the experiment is to irradiate μp atoms in the 2S state by a short pulse of infrared laser radiation whose wavelength (of about 6 micrometer) corresponds to the small energy difference of the binding energies of the 2S and 2P states. What can be measured is the number of 2P-1S transitions which occurs in time-coincidence with the laser pulse when its wavelength is tuned over the 2S-2P resonance.

• The PiE5 beam at the PSI proton accelerator provides 2 x 10⁸ s^-1 negative pions with a momentum of 100 MeV/c.
• Pions are injected into the cyclotron trap where they decay and produce negative muons of low kinetic energy.
• From the cyclotron trap the muons are axially extracted and transported to a solenoid with 5 T magnetic field where the hydrogen target is placed.
• Before entering the target, each muon is detected, and this is used to trigger the laser and the data acquisition system.
• About 500 s^-1 low energy muons (3 - 6 keV) enter the target and slow down in 1 mbar of hydrogen gas by ionization. When an electron from the hydrogen atom is replaced by the muon, a muonic atom μp is formed in a highly excited state (n ≈ 14).
• 99% of the muonic hydrogen atoms deexcite to the 1S state within 100 ns and produce "prompt" x-rays of 2 keV energy. The remaining 1% reach the metastable 2S state which has a lifetime of about ≈ 1 μs at 1 mbar.
• A laser pulse with a wavelength tunable around 6 μm is injected in the target and, when in resonance (hν = ΔE(2P - 2S)), induces a 2S to 2P transition.
• Atoms in the 2P state decay to the 1S ground state emitting 1.9 keV x-rays , which are delayed relative to the prompt x-rays, and occur in coincidence with the laser pulse.
• Detection of a delayed 1.9 keV x-ray followed by an electron (originated from the muon decay reaction) is a signature of the laser transition.
• By measuring the rate of delayed 1.9 keV x-rays as a function of the laser frequency, the resonance frequency (corresponding to ΔE(2P - 2S)), and hence the proton charge radius r_p can be determined.
  (https://muhy.web.psi.ch/wiki/index.php/Main/Experiment)

How does decoherence take place ?

This is a very fundamental and tantamount question. I remember, in a letter to Pauli, Einstein questioned the superposition principle of quantum mechanics, asking why a bullet is always there instead of everywhere. This is an old example of the question posed as the title. Although, it is now accepted by many authors that, the answer should be closely related to the concept of decoherence, it is not clear how this happens and if it is the case with every system.

I want to mention some other examples:

• In statistical mechanics, it is assumed that, the average of any observable should be taken over all thermodynamically accessible energy eigenstates with corresponding Boltzmann weights. This implies that, all the interferences that might occur during unitary evolution have been set aside. Usually, the physical system under interest is bulk and immersed in a heat bath, this assumption should work well. Nonetheless, violations may arise as long as the interference time becomes discernible. This situation is comparable to what is happening to light interference. For natural light, the polarization has no significant effect in interference experiments, which, however, is not so with a laser. It is quite evident that, such decoherence should be ascribed to interaction with heat bath, which represents a stochastic source. A general assertion regarding relations between system size, temperature and coherence time is lacking.
• The measurement theory has been debated since the discovery of quantum mechanics. How does a measurement lead to wave function collapse ? Does a measurement necessarily involve a classical object ? Or does a measurement actually involve decoherence ?
  
• The third is usually named 'Hund Paradox', which
  

  concerns how to explain from first principles why molecules often appear as enantiomers, i.e., either in a left-handed configuration or as in the right-handed image

  That is, the mixing of these two configurations disappears, contrary to one's expectation based on parity symmetry.

The last question was recently carefully addressed in Ref.[1], where the authors made use of molecular scattering theory and master equation to investigate the simplest molecule D2S2. They concluded that, the dominant collisional decoherence is due to a parity sensitive higher-order dispersive interaction term that is usually dropped in dealing with thermodynamic properties. They also made predictions on the conditions for experimental stabilization of enantiomers.

[1]PRL, 103:023202(2009)