The Largest Parity Violations Ever Measured in an Atom

Dmitry Budker [Photo courtesy: UC, Berkeley]

In a paper accepted for publication in Physical Review Letters, a team of scientists from Lawrence Berkeley National Laboratory and University of California, Berkeley reported the largest effects of parity violation in an atom ever observed. Their measurements with ytterbium-174, an isotope with 70 protons and 104 neutrons, have shown a hundred times larger effect than the most precise measurements made so far, with the element cesium.

“Parity” assumes that, on the atomic scale, nature behaves identically when left and right are reversed: interactions that are otherwise the same but whose spatial configurations are switched, as if seen in a mirror, ought to be indistinguishable.

“It’s the weak force that allows parity violation,” says Dmitry Budker, who led the research team. Of the four forces of nature – strong, electromagnetic, weak, and gravitational – the extremely short-range weak force was the last to be discovered. Neutrinos, having no electric charge, are immune to electromagnetism and only interact through the weak force. The weak force also has the startling ability to change the flavor of quarks, and to change protons into neutrons and vice versa.

Protons on their own last forever, apparently, but a free neutron falls apart in about 15 minutes; it turns into a proton by emitting an electron and an antineutrino, a process called beta decay. What makes beta decay possible is the weak force.

Scientists long assumed that nature, on the atomic scale, was symmetrical. It would look the same not only if left and right were reversed but also if the electrical charges of particles involved in an interaction were reversed, or even if the whole process ran backwards in time. Charge conjugation is written C, parity P, and time T; nature was thought to be C invariant, P invariant, and T invariant.

In 1957 researchers realized that the weak force didn’t play by the rules. When certain kinds of nuclei such as cobalt-60 are placed in a magnetic field to polarize them – line them up – and then allowed to undergo beta decay, they are more likely to emit electrons from their south poles than from their north poles.

This was the first demonstration of parity violation. Before the 1957 cobalt-60 experiment, renowned physicist Richard Feynman had said that if P violation were true – which he doubted – something long thought impossible would be possible after all: “There would be a way to distinguish right from left.”

It’s now apparent that many atoms exhibit parity violation, although it is not easy to detect. P violation has been measured with the greatest accuracy in cesium atoms, which have 55 protons and 78 neutrons in the nucleus, by using optical methods to observe the effect when atomic electrons are excited to higher energy levels.

An atomic beam of ytterbium is generated in the oven at left, then passed through a chamber with magnetic and electric fields arranged at right angles—the magnetic field colinear with the atomic beam, and the electric field colinear with a laser beam that excites a "forbidden" electron-energy transition. Weak interactions between electron and nucleus contribute to the forbidden transition. [image courtesy: LBNL]

The Berkeley researchers designed their own apparatus to detect the much larger parity violation predicted for ytterbium. In their experiment, ytterbium metal is heated to 500 degrees Celsius to produce a beam of atoms, which is sent through a chamber where magnetic and electric fields are oriented at right angles to each other. Inside the chamber the ytterbium atoms are hit by a laser beam, tuned to excite some of their electrons to higher energy states via a “forbidden” (highly unlikely) transition. The electrons then relax to lower energies along different pathways.

Weak interactions between the electron and the nucleus – plus weak interactions within the nucleus of the atom – act to mix some of the electron energy states together, making a small contribution to the forbidden transition. But other, more ordinary electromagnetic processes, which involve apparatus imperfections, also mix the states and blur the signal. The purpose of the chamber’s magnetic and electric fields is to amplify the parity-violation effect and to remove or identify these spurious electromagnetic effects.

Upon analyzing their data, the researchers found a clear signal for atomic parity violations, 100 times larger than the similar signal for cesium. With refinements to their experiment, the strength and clarity of the ytterbium signal promise significant advances in the study of weak forces in the nucleus.

The Budker group’s experiments are expected to expose how the weak charge changes in different isotopes of ytterbium, whose nuclei have the same number of protons but different numbers of neutrons, and will reveal how weak currents flow within these nuclei. The results will also help explain how the neutrons in the nuclei of heavy atoms are distributed, including whether a “skin” of neutrons surrounds the protons in the center, as suggested by many nuclear models.

“The neutron skin is very hard to detect with charged probes, such as by electron scattering,” says Budker, “because the protons with their large electric charge dominate the interaction.” He adds, “At a small level, the measured atomic parity violation effect depends on how the neutrons are distributed within the nucleus – specifically, their mean square radius. The mean square radius of the protons is well known, but this will be the first evidence of its kind for neutron distribution.”

Measurements of parity violation in ytterbium may also reveal “anapole moments” in the outer shell of neutrons in the nucleus (valence neutrons). As predicted by the Russian physicist Yakov Zel’dovich, these electric currents are induced by the weak interaction and circulate within the nucleus like the currents inside the toroidal winding of a tokamak; they have been observed in the valence protons of cesium but not yet in valence neutrons.

Yacov Zel'dovich proposed that the weak force induces electrical currents in the nucleus, which flow like currents in a tokamak. This anapole moment has been detected in nuclear valence protons but not yet in valence neutrons.[image courtesy: LBNL]

Eventually the experiments will lead to sensitive tests of the Standard Model – the theory that, although known to be incomplete, still best describes the interactions of all the subatomic particles so far observed.

“So far, the most precise data about the Standard Model has come from high-energy colliders,” says Budker. “The carriers of the weak force, the W and Z bosons, were discovered at CERN by colliding protons and antiprotons, a ‘high-momentum-transfer’ regime. Atomic parity violation tests of the Standard Model are very different – they’re in the low-momentum-transfer regime and are complementary to high-energy tests.”

Since 1957, when Zel’dovich first suggested seeking atomic variation in atoms by optical means, researchers have come ever closer to learning how the weak force works in atoms. Parity violation has been detected in many atoms, and its predicted effects, such as anapole moments in the valence protons of cesium, have been seen with ever-increasing clarity. With their new experimental techniques and the observation of a large atomic parity violation in ytterbium, Dmitry Budker and his colleagues have achieved a new landmark, moving closer to fundamental revelations about our asymmetric universe on the atomic scale.

Reference
“Observation of a large atomic parity violation in ytterbium”,
K. Tsigutkin, D. Dounas-Frazer, A. Family, J. E. Stalnaker, V. V. Yashchuck, and D. Budker,
Accepted for publication in Physical Review Letters. arXiv:0906.3039

[We thank Lawrence Berkeley National Laboratory for materials used in this posting]

Topological Insulators : A New State of Quantum Matter

M. Zahid Hasan

[This is an invited article based on a series of recent works by the author and his collaborators -- 2Physics.com]

Author: M. Zahid Hasan

Affiliation: Joseph Henry Laboratories of Physics, Department of Physics,
Princeton University, USA

Most quantum states of condensed-matter systems or the fundamental forces are categorized by spontaneously broken symmetries. The remarkable discovery of quantum Hall effects (1980s) revealed that there exists an organizational principle of matter based not on the broken symmetry but only on the topological distinctions in the presence of time-reversal symmetry breaking [1,2]. In the past few years, theoretical developments suggest that new classes of topological states of quantum matter might exist in nature [3,4,5]. Such states are purely topological in nature in the sense that they do not break time-reversal symmetry, and hence can be realized without any applied magnetic field : "Quantum Hall-like effects without magnetic field".

Research Team at Princeton University: [L to R] David Hsieh, Dong Qian, L. Andrew Wray, YuQi Xia

This exotic phase of matter is a subject of intense research because it is predicted to give rise to dissipationless (energy saving) spin currents, quantum entanglements and novel macroscopic behavior that obeys axionic electrodynamics rather than Maxwell's equations [6]. Unlike ordinary quantum phases of matter such as superconductors, magnets or superfluids, topological insulators are not described by a local order parameter associated with a spontaneously broken symmetry but rather by a quantum entanglement of its wave function, dubbed topological order. In a topological insulator this quantum entanglement survives over the macroscopic dimensions of the crystal and leads to surface states that have unusual spin textures.

Topologically ordered phases of matter are extremely rare and are experimentally challenging to identify. The only known example was the quantum Hall effect discovered in the 1980s by von Klitzing (Nobel Prize 1985). It was identified by measuring a quantized magneto-transport in a two-dimensional electron system under a large external magnetic field at very low temperatures, which is characterized by robust conducting states localized along the one-dimensional edges of the sample. Two-dimensional topological insulators, on the other hand, are predicted to exhibit similar edge states even in the absence of a magnetic field because spin-orbit coupling can simulate its effect (Fig.1A) due to the relativistic terms added in a band insulator's Hamiltonian.

Remarkably, three-dimensional topological insulators, an entirely new state of matter with no charge quantum Hall analogue, are also postulated to exist. And its topological order or exotic quantum entanglement is predicted to give rise to unusual conducting two-dimensional surface states (Fig.1B) that have novel spin-selective energy-momentum dispersion relations. Utilizing state-of-the-art angle-resolved photoemission spectroscopy, an international collaboration led by scientists from Princeton University have studied the electronic structure of several bismuth based spin-orbit materials [7,8,9]. By systematic tuning of the incident photon energy, it was possible to isolate surface quantum states from the bulk states, which confirmed that these materials realized a three-dimensional topological insulator phase.

Figure 1. (A) Schematic of the 1D edge states in a 2D topological insulator. The red and blue curves represent the edge current with opposite spin character. (B) Schematic of the 2D surface states in a 3D topological insulator. (C) Most elemental topological Insulators exhibit odd number of Dirac cones on their surface unlike the even numbers observed in graphene. Topological insulator Dirac cones are spin polarized where as Dirac cones in graphene are not.

The remarkable property of the surface states of a 3D topological insulator is that its Fermi surface supports a geometrical quantum entanglement phase, which occurs when the spin-polarized Fermi surface encloses the Kramers' points and on the surface Brillouin zone an odd number of times in total (Fig.2B). ARPES intensity map of the (111) surface states of bulk insulating Bi1-xSbx (Fig.2A) shows that a single Fermi surface encloses . However, determination of the degeneracy of the additional Fermi surface around requires a detailed study of its energy-momentum dispersion. ARPES spectra along the - direction (Fig.2C) reveal that the Fermi surface enclosing is actually composed of two bands, therefore two Fermi surfaces enclose , leading to a total of seven and Fermi surface enclosures.

Figure 2. (A) ARPES surface state (SS) Fermi surface of insulating Bi1-xSbx showing spin polarization directions as indicated by red and blue arrows. (B) Schematic of the SS Fermi surface of a 3D topological insulator. (C) ARPES energy-momentum dispersion of the surface states. The shaded areas denote the bulk bands while the dashed white lines are guides to the eye for surface state dispersions. (D) A single Dirac cone is observed in Bi2Te3.

These results constitute the first direct experimental evidence of a topological insulator in nature which is fully quantum entangled. The observed spin-texture in BiSb is consistent with a magnetic monopole image field beneath the surface. It shows that spin-orbit materials are a new family in which exotic topological order quantum phenomena, such as dissipationless spin currents and axion-like electrodynamics, may be found without the need for an external magnetic field. The results presented in this study also demonstrate a general measurement algorithm of identifying and characterizing topological insulator materials for future research which can be utilized to discover, observe and study other forms of topological order and quantum entanglements in nature. A detailed study of topological order and quantum entanglement can potentially pave the way for fault-tolerant (topological) quantum computing [10].

Figure 3: A new type of quantum matter called a topological insulator contains only half an electron pair (represented by just one Dirac cone in schematic crystal structure at top left), which is observed in the form of a single ring (red) in the center of the electron-map (top right) with electron spin in only one direction. This highly unusual observation shows that if an electron is tagged "red" and then undergoes a full 360-degree revolution about the ring, it does not recover its initial face as an ordinary everyday object would, but instead acquires a different color "blue" (represented by the changing color of the arrows around the ring). This new quantum effect can be the basis for the realization of a rare quantum phase that had been a long-sought key ingredient for developing quantum computers that can be highly fault-tolerant.

References:
[1] K. von Klitzing, G. Dorda, M. Pepper, "New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance", Phys. Rev. Lett. 45, 494-497 (1980). Abstract.
[2] D.C. Tsui, H. Stormer, A.C. Gossard, "Two-dimensional magnetotransport in the extreme quantum limit", Phys. Rev. Lett. 48, 1559-1562 (1982). Abstract.
[3] L. Fu, C. L. Kane and E. J. Mele, "Topological insulators in three dimensions", Physical Review Letters 98, 106803 (2007). Abstract.
[4] J. E. Moore and L. Balents, "Topological invariants of time-reversal-invariant band structures", Physical Review B 75, 121306(R) (2007). Abstract.
[5] S.-C. Zhang, "Topological states of quantum matter", Physics 1, 6 (2008). Abstract.
[6] M. Franz, "High energy physics in a new guise", Physics 1, 36 (2008). Abstract.
[7] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava and M. Z. Hasan, "A topological Dirac insulator in a quantum spin Hall phase", Nature 452, 970 (2008). Abstract.
[8] Y. Xia, D. Qian, L. Wray, D. Hsieh, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava and M. Z. Hasan, "Observation of a large-gap topological insulator class with single surface Dirac cone”, Nature Physics 5, 398 (2009). Abstract.
[9] D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava and M. Z. Hasan, "Observation of Unconventional Quantum Spin Textures in Topological Insulators", Science 323, 919 (2009). Abstract.
[10] A. Akhmerov, J. Nilsson, C. Beenakker, “Electrically detected interferometry of Majorana fermions in a topological insulator”, Phys. Rev. Lett. 102, 216404 (2009). Abstract.

Controlling Individual Qubits in Quantum Computers

Nathan Lundblad

In a paper published in 'Nature Physics', a team of physicists from the National Institute of Standards and Technology (NIST) reports a viable way of manipulating a single “bit” in a quantum processor without disturbing the information stored in its neighbors -- thus overcoming another hurdle in the development of quantum computer. The approach, which makes novel use of polarized light to create “effective” magnetic fields, could bring the long-sought computers a step closer to reality.

A great challenge in creating a working quantum computer is maintaining control over the carriers of information, the “switches” in a quantum processor while isolating them from the environment. These quantum bits, or “qubits,” have the uncanny ability to exist in both “on” and “off” positions simultaneously, giving quantum computers the power to solve problems conventional computers find intractable – such as breaking complex cryptographic codes.

One approach to quantum computer development aims to use a single isolated rubidium atom as a qubit. Each such rubidium atom can take on any of eight different energy states, so the design goal is to choose two of these energy states to represent the on and off positions. Ideally, these two states should be completely insensitive to stray magnetic fields that can destroy the qubit’s ability to be simultaneously on and off, ruining calculations. However, choosing such “field-insensitive” states also makes the qubits less sensitive to those magnetic fields used intentionally to select and manipulate them. “It’s a bit of a catch-22,” says NIST’s Nathan Lundblad. “The more sensitive to individual control you make the qubits, the more difficult it becomes to make them work properly.”

Optical lattices use lasers to separate rubidium atoms (red) for use as information “bits” in neutral-atom quantum processors -- prototype devices which designers are trying to develop into full-fledged quantum computers. The National Institute of Standards and Technology (NIST) physicists have managed to isolate and control pairs of the rubidium atoms with polarized light, an advance that may bring quantum computing a step closer to reality [image credit: NIST]

To solve the problem of using magnetic fields to control the individual atoms while keeping stray fields at bay, the NIST team used two pairs of energy states within the same atom. Each pair is best suited to a different task: One pair is used as a “memory” qubit for storing information, while the second “working” pair comprises a qubit to be used for computation. While each pair of states is field- insensitive, transitions between the memory and working states are sensitive, and amenable to field control. When a memory qubit needs to perform a computation, a magnetic field can make it change hats. And it can do this without disturbing nearby memory qubits.

The NIST team demonstrated this approach in an array of atoms grouped into pairs, using the technique to address one member of each pair individually. Grouping the atoms into pairs, Lundblad says, allows the team to simplify the problem from selecting one qubit out of many to selecting one out of two – which, as they show in their paper, can be done by creating an effective magnetic field, not with electric current as is ordinarily done, but with a beam of polarized light.

The polarized-light technique, which the NIST team developed, can be extended to select specific qubits out of a large group, making it useful for addressing individual qubits in a quantum processor without affecting those nearby. “If a working quantum computer is ever to be built,” Lundblad says, “these problems need to be addressed, and we think we’ve made a good case for how to do it.”

But, Lundblad adds, the long-term challenge to quantum computing remains: integrating all of the required ingredients into a single apparatus with many qubits.

Reference
"Field-sensitive addressing and control of field-insensitive neutral-atom qubits"
N. Lundblad, J.M. Obrecht, I.B. Spielman, and J.V. Porto,
Nature Physics, July 5, 2009 (doi:10.1038/nphys1330). Abstract.

[We thank NIST for materials used in this posting]