How Does the World Look Like Through a Rotating Window?

[Left to Right] Sonja Franke-Arnold, Graham Gibson, Robert W Boyd and Miles J Padgett

Authors:
Sonja Franke-Arnold¹, Graham Gibson¹, Robert W Boyd^2,3 and Miles J Padgett¹

Affiliation:
¹School of Physics and Astronomy, SUPA, University of Glasgow, UK
²Department of Physics, University of Ottawa, Canada
³The Institute of Optics and Department of Physics and Astronomy, University of Rochester, USA.

What do you expect to see if you look through a window spinning at faster and faster speeds? According to the theory by Augustin-Jean Fresnel the image is predicted to be dragged along with the window and should be rotated ever so slightly. Unfortunately under normal conditions the rotation angle is so minute that it cannot be observed by eye. At the Optics Group at Glasgow University we have slowed down light to around the speed of sound during its passage through a ruby window spinning at 30 Hz. This increases the dragging effect a million fold and we can rotate an image by 5 degrees [1].

Dragging light by a spinning medium

The speed of light is constant only in vacuum. Once it enters a material, its velocity decreases, and it can be dragged along with the material – a phenomenon first predicted by Fresnel in 1818 [2]. An experiment 50 years later investigated the longitudinal drag of light in an ingenious experiment shining light through tubes of water flowing along or against the propagation of the light [3]. Similarly, spinning a window as fast as possible should drag the light in the transverse direction and rotate the view ever so slightly [4]. The rotation angle is predicted to increase with the thickness of the material, with the spinning speed and with the refractive index. However, even if the window is spinning as fast as a dentist’s drill, this rotation is too small to be observed – in the order or a millionth of a degree. We overcame this problem by vastly increasing the refractive index, to slow the light down to that of the speed of sound.

In our experiment we used a ruby rod spinning at up to 30 Hz as our “window” and an elliptical light beam as “image.” This increased the refractive group index to around one million, or in other words, slowed down the light to roughly the speed of sound. Under these conditions, the light spent long enough within the rotating ruby so the transmitted image was dragged by up to 5 degrees.

Fig.1 An intense line of laser light at 532nm is transmitted through a 10cm long ruby rod, spinning at ±30 Hz. The false color images show the light for an anticlockwise (red) and clockwise (blue) spinning of the ruby rod, rotated by about ±5 degrees compared to the image seen through a stationary crystal.


Slow light

Ruby is a crystal with an extremely long upper-state lifetime of about 20 ms. (This long life-time of ruby was employed in the first laser, as it allows the build-up of population inversion and laser action.) We used the technique of “coherent population oscillations” pioneered by our co-worker Robert Boyd to produce slow light in ruby [5].

Because of the long lifetime, the absorption of ruby changes rapidly over a frequency range of around 36 Hz. The narrow absorption line is linked via Kramers-Kronig relations to a very rapid variation of the refractive index, and hence to a very large group index of the order of one million. In principle an intense pump laser could excite this transition, thereby generating a very narrow frequency hole, which could then be probed with a weak probe laser. Instead, we generate “pump” and “probe” with a single laser, using an intensity-modulated beam. The modulation components experience then an extremely high group index.

In our case, the elliptical intensity profile shining onto the ruby rod produced the required intensity modulation and is therefore slowed down. At the same time, the elliptical beam allowed us to define the orientation of our image and measure the rotation of its major axis as a function of how fast the ruby window was spinning. In a control experiment under better defined conditions we have studied the rotation of an elliptical light beam (aspect ratio of 2) through a 6mm thick ruby window and found good agreement of the image rotation with a model based on slow light under coherent population oscillations.











Fig.2 Transmitting an elliptical beam through a spinning rod produces locally a modulation in the light intensity which in turn modulates the number of atoms in the ruby crystal driven to the excited state. This generates a delay of the intensity transmitted through the crystal which depends on the rotation speed. The left image shows the calculated delay of the intensity modulation for an input beam power of 1W (blue curve) and 2W (red curve) respectively. The corresponding rotation of the orientation angle is the product of the time delay with the rotation speed, shown on the right.

Conclusions

Our experiments have shown that light can indeed be dragged along by a spinning window resulting in an image rotation – just as Fresnel predicted 200 years ago. This effect may also be useful to store and manipulate quantum images. The rotational drag applies not only for classical images, but also for single photons, keeping both intensity and phase profile intact. We are looking into the option to rotate a more complicated image by arbitrary angles in order to encode, store and manipulate quantum information.

References
[1] S Franke-Arnold, G Gibson, R W Boyd, and M J Padgett, “Rotary Photon Drag Enhanced by a Slow Light Medium”, Science 333, 65-67 (2011). Abstract.
[2] A Fresnel, "Lettre d’Augustin Fresnel à François Arago sur l’influence du mouvement terrestre dans quelques phénomènes d’optique", Annales de chimie et de physique 9: 57 (1818).
[3] H. Fizeau, “On the effect of the motion of a body upon the velocity with which it is traversed by light”, Phil. Mag. 19 245 (1860).
[4] J Leach, A J Wright, J B Götte, J M Girkin, L Allen, S Franke-Arnold, S M Barnett, and M J Padgett, “‘Aether Drag’ and Moving Images”, Phys Rev Lett 100, 153902 (2008). Abstract.
[5] M S Bigelow, N N Lepeshkin and R W Boyd “Observation of Ultraslow Light Propagation in a Ruby Crystal at Room Temperature”, Phys Rev Lett 90, 113903 (2003). Abstract; M S Bigelow, N N Lepeshkin and R W Boyd “Superluminal and slow light propagation in a room-temperature solid”, Science 301, 200 (2003). Abstract.

Towards the Ideal Quantum Measurement

Juergen Volz

Author: Juergen Volz

Affiliation: Laboratoire Kastler Brossel de l'E.N.S., Paris, France

Measurement lies at the heart of quantum physics and gives rise to many of the counter-intuitive aspects of the theory. In a classical world, a measurement can in principle be performed with arbitrary precision without disturbing the system. In contrast, a quantum mechanical measurement inevitably projects the system into one of its basis states, although initially the system may have been in a superposition of these states. For example, it is possible to prepare an atom in a superposition of two internal states. However, a state measurement will always yield the result that the atom is either in one or the other state, which is typically referred to as 'collapse of the wave function'. This collapse during the measurement process constitutes the unavoidable back-action of the measurement on the measured system and gives rise to phenomena as for example Heisenberg's uncertainty relation[1].

While theoretically well described, experimental realizations typically fall short of these predictions, always causing a back-action on the system being measured -- with orders of magnitude larger than required for an ideal measurement. This additional back-action typically results in a energy transfer to the quantum system and heating which is a major drawback for many experiments.

The modern field of quantum optics and quantum information, relies on the accurate readout of quantum information stored in so-called quantum bits, i.e. single quantum objects that for example can be realized using the internal states of single atoms or ions. The most efficient detection method for internal atomic states is the fluorescence detection[2]. Here an atom with two stable ground states is subject to an incident light field resonant to a transition of one of the two ground states to an excited state. If the atom is in the resonant state, it will be repeatedly excited and - after spontaneously emitting a photon - decay back into the original state, while an atom in the off-resonant state is not affected by light field. The presence (or absence) of fluorescence photons then indicates the atomic state. However, this requires the atom to undergo a large amount of spontaneous emissions events, leading to an inevitable energy exchange between atom and light field.






















Fig 1: (a) Simplified level scheme of Rubidium. (b) Principle of the resonator measurement where the transmission properties of the resonator yield information on the atomic state (all light reflected: atom is in the resonant state, all light transmitted: atom is in the off-resonant state). (c) Schematic view of the experimental setup with the fiber-resonator implemented on an atomchip.

Theoretically, an ideal atomic state measurement only projects the atom onto its basis states and requires no spontaneous scattering. Therefore, our research team at the Ecole Normale Supérieure in Paris decided to investigate if we can reach a regime where we can perform a measurement with significantly less than one spontaneous emission event[3]. In our experiments we use as measurement device a so-called Fabry-Perot resonator which consists of two highly reflecting mirrors facing each other. This allows to keep light inside the resonator for approximately 38000 round trips before it is lost. With the help of a novel fiber-optical technology, the mirrors are directly imprinted on the tips of two optical fibers. In this way we can produce miniaturized resonators with a small enough volume so that a single atom placed between its mirrors is enough to shift the resonance frequency by a sizeable amount. As long as the atom is in the off resonant state it does not affect the resonator and a laser tuned to the empty cavity’s resonance is fully transmitted through the cavity. If, however, the atom is in the resonant state the resonance frequency changes and nearly all of the incident light is reflected without ever entering the resonator, thereby avoiding spontaneous scattering.






















Fig 2: Experimental results for the detection process. The blue data points are the residual error of the atomic state measurement, plotted as function of average number of scattered photons. The green curve is the minimum error possible for our resonator and the grey area corresponds to the regime accessible without resonator.

To investigate the exact amount of residual scattering in our experiment, we determine the state of the atom after each measurement from which we can deduce that our measurement allows us to infer the atomic state with a fidelity of more than 90% while scattering only 0.2 photons on average. The main limit of our measurement scheme is the small probability to finally detect the incident photons. In order to measure how our system would perform under ideal circumstances, we also directly analyzed the fundamental measurement back-action on the atom using the quantum Zeno effect[4]. This effect states that permanently measuring a physical system will stop its temporal evolution and freeze it in its current state. In our experiment, we apply a microwave pulse to transfer the atomic state to the other. At the same time we perform our state detection which permanently projects the atom into its initial state an thereby prevents the transfer. This allows us to directly measure the projection rate of the atom into its basis states, from which we conclude that three photons incident on the cavity are enough for a full collapse of the atomic state.

These results demonstrate that during the measurement (nearly) no spontaneous emission occurred and the back-action on the atom approaches the fundamental limit given by the uncertainty principle. Besides giving a compelling illustration of the quantum measurement process, these results have important consequences for quantum information applications with atoms or ions, allowing internal state readout without any heating, hereby allowing much higher cycling rates. In addition, this new detection scheme promises the development of efficient optical detectors for complex quantum systems as e.g. single molecules.

References:
[1] Maximilian Schlosshauer, "Decoherence, the measurement problem, and interpretations of quantum mechanics", Rev. Mod. Phys. 76, 1267 (2005). Abstract.
[2] A. H. Myerson, et al., "High-Fidelity Readout of Trapped-Ion Qubits", Phys. Rev. Lett 100, 200502 (2008). Abstract.
[3] Jürgen Volz, Roger Gehr, Guilhem Dubois, Jérôme Estève and Jakob Reichel, "Measurement of the internal state of a single atom without energy exchange", Nature 475, 210 (2011). Abstract.
[4] Wayne M. Itano, "Perspectives on the quantum Zeno paradox.", arXiv:quant-ph/0612187v1 (2006).

Three-Body Force in Nucleus

David Dean (left) and Hai Ah Nam (right)

The nucleus of an atom, like most everything else, is more complicated than we first thought. Just how much more complicated is the subject of a Petascale Early Science project led by Oak Ridge National Laboratory's David Dean.

According to findings outlined by Dean and his colleagues in a recent paper in the journal Physical Review Letters [1], researchers who want to understand how and why a nucleus hangs together as it does and disintegrates when and how it does have a very tough job ahead of them. Scientists from five institutes have contributed to this project: (from USA) Department of Physics and Astronomy, Iowa State University; Lawrence Livermore National Laboratory; Michigan State University; Oak Ridge National Laboratory; (from Canada) TRIUMF, Vancouver.

Specifically, they must take into account the complex nuclear interactions known as the three-body force.

Nuclear theory to this point has assumed that the two-body force is sufficient to explain the workings of a nucleus. In other words, the half-life or decay path of an unstable nucleus was to be understood through the combined interactions of pairs of protons and neutrons within.

An accurate picture of the carbon-14 nucleus must consider the interactions among protons and neutrons both in pairs (known as the two-body force, left) and in threes (known as the three-body force, right).

Dean's team, however, determined that the two-body force is not enough; researchers must also tackle the far more difficult challenge of calculating combinations of three particles at a time (three protons, three neutrons, or two of one and one of the other). This approach yields results that are both different from and more accurate than those of the two-body force.

Nuclei are held together by the strong force, one of four basic forces that govern the universe (The other three are gravity, which holds planets, solar systems, and galaxies together and pins us to the ground, the electromagnetic force, which holds matter together and keeps us from, for instance, falling through the ground, and the weak force, which drives nuclear decay). The strong force acts primarily to combine elementary particles known as quarks into protons and neutrons through the exchange of force carriers known as gluons. Each proton or neutron has three quarks. The strong force also holds neighboring protons and neutrons together into a nucleus.

It does so imperfectly, however. Many nuclei are unstable and will eventually decay, emitting one or more particles and becoming a smaller nucleus. While we cannot say specifically when an individual nucleus will decay, we can determine the likelihood it will do so within a certain time. Thus an isotope's half-life is the time it takes half the nuclei in a sample to decay. Known half-lives range from an absurdly small fraction of a second for beryllium-8 to more than 2 trillion trillion years for tellurium-128.

One job of nuclear theory, then, is to determine why nuclei have different half-lives and predict what those half-lives are.

"For a long time, nuclear theory assumed that two-body forces were the most important and that higher-body forces were negligible," noted team member and ORNL computational physicist Hai Ah Nam. "You have to start with an assumption: How to capture the physics best with the least complexity?"

Two factors complicate the choice of approaches. First, two-body interactions do accurately describe some nuclei. Second, accurate calculations including three-body forces are very difficult and demand state-of-the-art supercomputers such as ORNL's Jaguar, the most powerful system in the United States. With the ability to churn through as many as 2.33 thousand trillion calculations each second, or 2.33 petaflops, Jaguar gave the team the computing muscle it needed to analyze the carbon-14 nucleus using the three-body force.

Carbon-14, with six protons and eight neutrons, is the isotope behind carbon dating, allowing researchers to determine the age of plant- or animal-based relics going back as far as 60,000 years. It was an ideal choice for this project because studies using only two-body forces dramatically underestimate the isotope's half-life, which is around 5,700 years.

"With Jaguar we are able to do ab initio calculations, using three-body forces, of the half-life for carbon-14," Nam said. "It's an observable that is sensitive to the three-body force. This is the first time that we've demonstrated at this large scale how the three-body force contributes."

The three-body force does not replace the two-body force in these calculations, she noted; rather, the two approaches are combined to present a more refined picture of the structure of the nucleus. In the carbon-14 calculation, the three-body force serves to correct a serious underestimation of the isotope's half-life produced by the two-body force alone.

Dean and his colleagues used an application known as Many Fermion Dynamics, nuclear, or MFDn, which was created by team member James Vary of Iowa State University. With it, they tackled the carbon-14 nucleus using an approach known as the nuclear shell model and performing ab initio calculations—or calculations based on the fundamental forces between protons and neutrons.

Analogous to the atomic shell model that explains how many electrons can be found at any given orbit, the nuclear shell model describes the number of protons and neutrons that can be found at a given energy level. Generally speaking, the nucleons gather at the lowest available energy level until the addition of any more would violate the Pauli exclusion principle, which states that no two particles can be in the same quantum state. At that point, some nucleons bump up to the next higher energy level, and so on. The force between nucleons complicates this picture and creates an enormous computational problem to solve.

The carbon-14 calculation, for instance, involved a billion-by-billion matrix containing a quintillion values. Fortunately, most of those values are zero, leaving about 30 trillion nonzero values to then be multiplied by a billion vector values. As Nam noted, just keeping the problem straight is a phenomenally complex task, even before the calculation is performed; those 30 trillion matrix elements take up 240 terabytes of memory.

"Jaguar is the only system in the world with the capability to store that much information for a single calculation," Nam said. "This is a huge, memory-intensive calculation."

The job is even more daunting with larger nuclei, and researchers will have a long wait for supercomputers powerful enough to compute the nature of the largest nuclei using the three-body force. Even so, if the three-body force gives more accurate results than the two-body force, should researchers be looking at four, five, or more nucleons at a time?

"Higher-body forces are still under investigation, but it will require more computational resources than we currently have available," Nam said.

Reference
[1] P. Maris, J. P. Vary, P. Navráti, W. E. Ormand, H. Nam, and D. J. Dean, "Origin of the Anomalous Long Lifetime of ¹⁴C", Physical Review Letters, 106, 202502 (2011). Abstract.

[The text is written by Leo Williams of Oak Ridge National Laboratory]

Chilling of Micromechanical Motion to the Quantum Ground State

NIST research affiliate John Teufel, who designed the micro drum, with a chip holder used to contain the drum during experiments in which the drum was cooled to its lowest possible energy level, the quantum ground state [photo credit: Burrus/National Institute of Standards and Technology].

Showcasing new tools for widespread development of quantum circuits made of mechanical parts, scientists from the National Institute of Standards and Technology (NIST) have demonstrated a flexible, broadly usable technique for steadily calming the vibrations of an engineered mechanical object down to the quantum "ground state," the lowest possible energy level.

Described in a Nature paper posted online July 6 [1], the NIST experiments nearly stop the beating motion of a microscopic aluminum drum made of about 1 trillion atoms, placing the drum in a realm governed by quantum mechanics with its energy below a single quantum, or one unit of energy. Like a plucked guitar string that plays the same tone while the sound dissipates, the drum continues to beat 11 million times per second, but its range of motion approaches zero. The cooling technique and drum device together promise new machinery for quantum computing and tests of quantum theory, and could help advance the field of quantum acoustics exploring the quantum nature of mechanical vibrations.

NIST scientists used the pressure of microwave radiation, or light, to calm the motion of the drum, which is embedded in a superconducting circuit [2]. The circuit is designed so that the drum motion can influence the microwaves inside an electromagnetic cavity. The cooling method takes advantage of the microwave light's tendency to change frequency, if necessary, to match the frequency, or tone, at which the cavity naturally resonates.

Multiple versions of NIST’s superconducting circuit containing a “micro drum” were fabricated on this sapphire chip, shown next to a penny for scale. NIST scientists cooled one such drum to its quantum ground state [image credit: Teufel/NIST]

"I put in the light at the wrong frequency, and it comes out at the right frequency, and it does that by stealing energy from the drum motion," says John Teufel, a NIST research affiliate who designed the drum. Teufel led the cooling experiments in NIST physicist and co-author Konrad Lehnert's lab at JILA, a joint institute of NIST and the University of Colorado Boulder.

Compared to the first engineered object to be coaxed into the quantum ground state, reported by California researchers last year, the NIST drum has a higher quality factor, so it can hold a beat longer, and it beats at a much slower rate, or lower frequency. As a result, individual packets of energy, or quanta, can be stored 10,000 times longer (about 100 microseconds)—long enough to serve as a temporary memory for a quantum computer and a platform for exploring complex mechanical and quantum states. In addition, the drum motion is 40 times greater per quantum, offering the possibility, for instance, of generating larger entangled "cat states"—objects that are in two places at once and also entangled, with properties that are linked even at a distance—for tests of theories such as quantum gravity. The NIST apparatus also allows researchers to measure the position of the drum directly, which is useful for force detection, with a precision closer than ever to the ultimate limit allowed by quantum mechanics.

To make engineered bulk objects obey the rules of quantum mechanics, typically observed only in atoms and smaller particles, scientists must lower an object's temperature beyond the reach of conventional refrigeration. The California researchers were able to use a passive cryogenic refrigeration technique to chill their high-frequency device enough to reach the ground state, avoiding the need for specialized techniques.

NIST's drum required the use of "sideband cooling" to reach much colder temperatures, taking advantage of strong interactions between the drum and the microwaves. This is the same idea as laser cooling of individual atoms, first demonstrated at NIST in 1978 [3], concurrently with another research group in Germany [4], opening a new field of research on ultracold atoms. Now a basic tool of atomic physics worldwide, laser cooling enabled many significant advances by allowing researchers to reduce the vibrational motion of trapped atoms to less than a single quantum. Sideband refers to a collection of light particles (photons) just above or below a specific target frequency. In the case of NIST's superconducting circuit, this stray radiation pressure, as it adjusts to the surrounding environment of the cavity, steadily removes energy from the drum motion in the same way that laser cooling slows atoms in a gas.

In the NIST experiments, the drum is first chilled in a cryogenic refrigerator using liquid helium. This lowers the drum energy to about 30 quanta. Sideband cooling then reduces the drum temperature from 20 milliKelvin (thousandths of a degree above absolute zero) to below 400 microKelvin (millionths of a degree above absolute zero), steadily lowering the drum energy to just one-third of 1 quantum.

Scientists begin the sideband cooling process by applying a drive tone to the circuit at a particular frequency below the cavity resonance. The drumbeats generate sideband photons, which naturally convert to the higher frequency of the cavity. These photons leak out of the cavity as it fills up. Each departing photon takes with it one mechanical unit of energy—one phonon—from the drum motion. At a drive intensity that corresponds to 4,000 photons in the cavity, the drum motion slows to less than 1 quantum. By detecting the scattered photons leaving the cavity, scientists can measure the mechanical motion near the lowest possible limits of uncertainty. Collectively, these steps proved that the mechanical drum entered the quantum regime.

The drum apparatus has applications in quantum computers, which could someday solve certain problems that are intractable today, even with the best supercomputers. Quantum information can be stored in the mechanical state for more than 100 microseconds before absorbing one phonon from the environment—much longer than conventional superconducting quantum bits can maintain information. The drum, thus, might serve as a short-term memory device in a superconducting quantum computer circuit, a technology under development by the same NIST research group. In addition, because mechanical oscillators can interact with light of any frequency, they could act as intermediaries for transferring quantum information between microwave and optical components.

References
[1] J.D. Teufel, T. Donner, Dale Li, J.W. Harlow, M.S. Allman, K. Cicak, A.J. Sirois, J.D. Whittaker, K.W. Lehnert and R.W. Simmonds, "Sideband cooling of micromechanical motion to the quantum ground state", Nature. Posted online July 6, 2011. doi:10.1038/nature10261. Abstract.
[2] J.D. Teufel, D. Li, M.S. Allman, K. Cicak, A.J. Sirois, J.D. Whittaker, and R.W. Simmonds, "Circuit cavity electromechanics in the strong coupling regime", Nature, 471, 204–208 (10 March 2011). Abstract.
[3] D. J. Wineland, R. E. Drullinger, and F. L. Walls, "Radiation-Pressure Cooling of Bound Resonant Absorbers", Physical Review Letters, 40, 1639–1642 (1978). Abstract.
[4] W. Neuhauser, M. Hohenstatt, P. Toschek, H. Dehmelt, "Optical-Sideband Cooling of Visible Atom Cloud Confined in Parabolic Well", Physical Review Letters, 41, 233–236 (1978). Abstract.

Phase Diagram of Quantum Chromodynamics

Nu Xu [Photo courtesy: Lawrence Berkeley National Laboratory]

In its infancy, when the universe was a few millionths of a second old, the elemental constituents of matter moved freely in a hot, dense soup of quarks and gluons. As the universe expanded, this quark–gluon plasma quickly cooled, and protons and neutrons and other forms of normal matter “froze out”: the quarks became bound together by the exchange of gluons, the carriers of the color force.

Nu Xu of the U.S. Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab), the spokesperson for the STAR experiment at the Relativistic Heavy Ion Collider (RHIC) at DOE’s Brookhaven National Laboratory says,“The theory that describes the color force is called quantum chromodynamics, or QCD, which has been extremely successful at explaining interactions of quarks and gluons at short distances, such as high-energy proton and antiproton collisions at Fermi National Accelerator Laboratory. But in bulk collections of matter – including the quark-gluon plasma – at longer distances or smaller momentum transfer, an approach called lattice gauge theory has to be used.”























Image 1: An ordinary proton or neutron (foreground) is formed of three quarks bound together by gluons, carriers of the color force. Above a critical temperature, protons and neutrons and other forms of hadronic matter “melt” into a hot, dense soup of free quarks and gluons (background), the quark-gluon plasma.

Until recently, lattice QCD calculations of hot, dense, bulk matter could not be tested against experiment. Beginning in 2000, however, RHIC was able to recreate the extreme conditions of the early universe in miniature, by colliding massive gold nuclei (heavy ions) at high energies.

Experimentalists at RHIC, working with theorist Sourendu Gupta of India’s Tata Institute of Fundamental Research, have recently compared lattice-theory predictions about the nature of the quark-gluon plasma with certain STAR experimental results for the first time. In so doing they have established the temperature boundary where ordinary matter and quark matter cross over and change phase. Their results appear in the journal `Science' [1].

The authors of the paper are: Sourendu Gupta of Tata Institute of Fundamental Research in Mumbai, India, where the theoretical calculations for this paper were carried out; Bedangadas Mohanty of the Variable Energy Cyclotron Centre in Kolkata, India (He was formerly a postdoctoral fellow at Berkeley Lab); Xiafeng Luo, Hans Georg Ritter, and Nu Xu of Berkeley Lab’s Nuclear Science Division (Luo is also with the University of Science and Technology of China in Hefei, and Xu is also with the Central China Normal University in Wuhan).

Phase diagrams

The aim of both the theoretical and experimental work is to explore and fix key points in the phase diagram for quantum chromodynamics. Phase diagrams are maps, showing, for example, how changes in pressure and temperature determine the phases of water, whether ice, liquid, or vapor. A phase diagram of QCD would map the distribution of ordinary matter (known as hadronic matter), the quark-gluon plasma, and other possible phases of QCD such as color superconductivity.

“Plotting a QCD phase diagram requires both theory calculations and experimental effort with heavy-ion collisions,” says Xu, who is a member of Berkeley Lab’s Nuclear Science Division and an author of the Science paper. Experimental studies require powerful accelerators like RHIC on Long Island or the Large Hadron Collider at CERN in Geneva, while calculations of QCD using lattice gauge theory require the world’s biggest and fastest supercomputers. Direct comparisons can achieve more than either approach alone.

One of the basic requirements of any phase diagram is to establish its scale. A phase diagram of water might be based on the Celsius temperature scale, defined by the boiling point of water under normal pressure (i.e., at sea level). Although the boiling point changes with pressure – at higher altitudes water boils at lower temperatures – these changes are measured against a fixed value.

The scale of the QCD phase diagram is defined by a transition temperature at the zero value of “baryon chemical potential.” Baryon chemical potential measures the imbalance between matter and antimatter, and zero indicates perfect balance.

Through extensive calculations and actual data from the STAR experiment, the team was indeed able to establish the QCD transition temperature. Before they could do so, however, they first had to realize an equally significant result, showing that the highly dynamical systems of RHIC’s gold-gold collisions, in which the quark-gluon plasma winks in and out of existence, in fact achieve thermal equilibrium. Here’s where theory and experiment worked hand in hand.

“The fireballs that result when gold nuclei collide are all different, highly dynamic, and last an extremely short time,” says Hans Georg Ritter, head of the Relativistic Nuclear Collisions program in Berkeley Lab’s Nuclear Science Division and an author of the Science paper. Yet because differences in values of the kind observed by STAR are related to fluctuations in thermodynamic values predicted by lattice gauge theory, says Ritter, “by comparing our results to the predictions of theory, we have shown that what we measure is in fact consistent with the fireballs reaching thermal equilibrium. This is an important achievement.”






















Image 2: The “current conjecture” for the QCD phase diagram. The boundary between the normal (hadronic) low-temperature phase and the high-temperature quark-gluon plasma phase is marked in black. The square box on the solid line indicates the yet-to-be-found critical point where phases can co-exist; RHIC is the only heavy-ion collider whose energy can be tuned across the region where it is likely to lie. Neutrons and protons and other ordinary matter particles (including antimatter particles) are detected after they “freeze out” of fireballs caused by heavy-ion collisions like those at RHIC, indicated by the dotted line. To the right is a possible region of “color superconductivity.”

The scientists were now able to proceed with confidence in establishing the scale of the QCD phase diagram. After a careful comparison between experimental data and the results from the lattice gauge theory calculations, the scientists concluded that the transition temperature (expressed in units of energy) is 175 MeV (175 million electron volts).

Thus the team could develop a “conjectural” phase diagram that showed the boundary between the low-temperature hadronic phase of ordinary matter and the high-temperature quark-gluon phase.

In search of the critical point

Lattice QCD also predicts the existence of a “critical point.” In a QCD phase diagram the critical point marks the end of a line showing where the two phases cross over, one into the other. By changing the energy, for example, the baryon chemical potential (balance of matter and antimatter) can be adjusted.

Among the world’s heavy-ion colliders, only RHIC can tune the energy of the collisions through the region of the QCD phase diagram where the critical point is most likely to be found – from an energy of 200 billion electron volts per pair of nucleons (protons or neutrons) down to 5 billion electron volts per nucleon pair.

Says Ritter, “Establishing the existence of a QCD critical point would be much more significant than setting the scale.” In 2010, RHIC started a program to search for the QCD critical point.

Xu says, “In this paper, we compared experimental data with lattice calculations directly, something never done before. This is a real step forward and allows us to establish the scale of the QCD phase diagram. Thus begins an era of precision measurements for heavy-ion physics.”

Reference
[1] Sourendu Gupta, Xiaofeng Luo, Bedangadas Mohanty, Hans Georg Ritter, Nu Xu, "Scale for the Phase Diagram of Quantum Chromodynamics", Science, vol. 332, pp. 1525-1528 (June 24, 2011). Abstract.

[The text is written by Paul Preuss of Lawrence Berkeley National Laboratory]