| Chiral Charge Density Waves - part II |
Our theoretical description of how electronic charge and orbitals can organise themselves into spiral patterns has been successfully tested by three independent recent experiments. Using the theory, we can now understand the emergence of chirality in a wide class of materials.
We recently proposed a theoretical model describing the way in which corkscrews of electronic charge can form in so-called transition-metal dichalcogenide materials. The unusual arrangement of electronic charge density (a scalar variable) into spiral shapes, was suggested to be stabilised by a simultaneous chiral arrangement of the orbitals in these materials. The theory thus explains the experimentally observed lack of inversion symmetry in the STM microscope images of the surfaces of materials like TiSe2 and TaS2.
The theoretical model also made the prediction that there must exist two separate phase transitions in the chiral material TiSe2, leading from the semi-metallic phase, into the usual type of charge density wave state, and then finally into the novel chiral charge and orbital ordered phase. The presence of this sequence of phase transitions in TiSe2 has now been experimentally confirmed. The chiral phase transition was found to sit just 7 K below the main charge density wave transition, and can be identified in independent X-ray diffraction, electric resistivity, and specific heat measurements.
Having identified the origin of the spiral charge patterns in a combined mechanism which incorporates the electronic orbitals as well as their charges, it is now possible to apply the theoretical description to related material classes as well. The elemental materials Te and Se for example are well known to have a chiral lattice structure, which can be understood as a consequence of the same type of simultaneous charge and orbital order as that observed in TiSe2. Similarly, Polonium was recently suggested to be susceptible to the formation of chiral charge and orbital order, although in this material the strong spin-orbit coupling prevents the onset of orbital order at low temperatures. This results in the unusual situation of a simple cubic lattice arrangement giving way to a less symmetric trigonal structure as temperature is increased.
Most recently, investigations of high-Tc superconductors have revealed both the presence of incommensurate charge density waves, and the absence of inversion symmetry in their crystal lattice. It was suggested that these observations may be explained by the presence of chiral charge order, similar to what is observed in TiSe2. Whether the chiral state in these cuprate superconductors also arises from the same mechanism, involving the simultaneous ordering of both orbital arrangements and electronic charge density, is the topic of ongoing investigations.
| University of Bristol |
This October, I will move to the University of Bristol to take up a position as lecturer. At Bristol I will continue my research on charge ordered phases, spontaneously broken unitarity, and other topics of condensed matter physics.
I will begin work at the University of Bristol in October 2012. As a lecturer, I will contribute to both the teaching and research of the School of Physics.
My research at the University of Bristol will initially focus on the exploration of recently discovered new types of charge order, and the effects their presence has on its host materials. Charge order arises when the electrons in a material form a spatial pattern that does not match the underlying atomic lattice. Recently, it was found that in certain materials, the charge order can cooperate with other degrees of freedom (such as orbitals or plasmons) to qualitatively alter the properties of the materials in which they exist. Besides the fundamental interest in the entirely new state of matter constituted in this way, the effects on specific materials may also be of interest because of their possible use in applications which rely on the ability to tune electronic properties.
Besides the work on electronically ordered materials, I will also continue to study the possible ways in which Einstein's theory of gravity may affect realizable quantum mechanical experiments. We recently suggested an experiment in which the interplay between these two seemingly distant realms of physics may become observable. Because Einstein's theory of gravity and the theory of quantum mechanics (the two most successful theories of physics ever known) contain mutually exclusive ingredients, they cannot be straightforwardly combined or reconciled which each other. Finding experimental evidence for which parts of these theories may survive, and which may not, in the regime where both play a role, is therefore an important step towards understanding the connection between the microscopic quantum world and the cosmic world of gravity.
| Chiral Charge Density Waves |
It was recently discovered that electrons in certain materials can conspire to make spiral patterns in their density distribution. We explain this new phenomenon as a consequence of the interactions between the different orbitals occupied by the electrons in these materials.
It is well known that chiral or helical patterns occur regularly in nature. The biological function of organic molecules for example often depends on their handedness, and certain types of magnets can have spiral shaped waves of local magnetization. Until recently however, no such chiral patterns were known in purely electronically ordered materials.
The first chiral charge density wave was discovered in 2010 in the layered material TiSe2. In a viewpoint article, we compared its electronic chiral order to the well-known case of Tellurium, which has a helical lattice structure, but no charge order. In our most recent paper, the connection between these two types of chirality is further clarified by the discovery that both of them are due to the presence of so-called orbital order.
The electron clouds surrounding the nucleus of an atom can take on many different shapes, or orbitals. In an orbitally ordered material, the electrons do not occupy all possible states with equal probability, but rather pick out one particular orbital configuration which is then collectively occupied. In chiral charge ordered materials, the orbital occupation follows a corkscrew pattern, rotating as it progresses from one layer in the material to the next. The result is the formation of a chiral charge density wave or a helical lattice structure.
Because the chiral order involves orbitals as well as charge density modulations, we predicted that there will in fact be two charge ordered phases in TiSe2, one that is chiral, and one that is not. Recent X-ray, specific heat and transport experiments confirmed that a second phase indeed exists in TiSe2, in agreement with the theoretical predictions.
Understanding the origin of the chiral charge order allows us to now start thinking about the implications of its presence for the properties of its host material. Although it is too early to tell what will come out, the unique properties associated with a helical charge distribution make this novel type of order a promising candidate for many possible applications.
| Observing the Divergence of Quantum Critical Fluctuations |
Although it is well known that phase transition at zero temperature are accompanied by strong quantum fluctuations on all possible length scales, it is usually hard to directly observe these fluctuations in an experiment. We found that high resolution X-ray diffraction can be used to directly follow the divergence of the quantum critical fluctuations in the charge ordered material NbSe2.
Materials can be ordered in a variety of ways. The regular lattice structure of a crystal for example represents the translational and rotational order of its atoms. Likewise, a magnet is a material in which the magnetic moments of the individual atoms form an ordered array, and a superconductor has a macroscopically ordered phase. Charge order is the type of order that results when the electrons within a material arrange themselves in a regular pattern, that does not precisely match the underlying lattice.
Like all ordered states, the charge order can be destroyed in two distinct ways. If the material is heated to sufficiently high temperatures, thermal fluctuations in the electronic density will wash out the regularity of the ordered state, and the charge order melts. Alternatively, the charge order can be destroyed even at zero temperature, for example by the application of pressure. In this case, the order is destroyed by the quantum fluctuations which arise from the competition of the high pressure ground state with the electronically ordered phase. At the quantum critical point, where the order disappears completely, quantum fluctuations of all strengths and sizes occur in the material.
One particular material in which quantum fluctuations are expected to be able to destroy charge order, is NbSe2. This material is charge ordered at temperatures below 30 K, and the transition temperature into the charge ordered state can be made even lower by applying pressure to the material. At very high pressures, the charge order is absent even at the absolute zero of temperature. As in many other materials, the electronic quantum critical point at which the zero temperature charge order first disappears, is surrounded by a superconducting phase, making observations of the quantum critical fluctuations difficult. In a recent PNAS article, we show that it is possible to use X-ray scattering techniques under pressure to identify quantum critical charge fluctuations near the point where the charge order disappears. Because the scattered X-rays are insensitive to the superconducting order, it is possible to directly image the electronic order parameter even within the superconducting phase.
This measurement provides a very rare, direct look at the spatial divergence of quantum critical fluctuations. Most experiments studying quantum critical points focus on the time or energy domain, and cannot directly assess the typical size of the fluctuations. At best, an indirect measurement in terms of critical exponents can be used. In the X-ray experiment described here however, we directly image the spatial structure of the charge ordered state close to the quantum critical point, as well as the diverging range over which its quantum critical fluctuations stretch.
| A Nanoscale Experiment to Measure Gravity’s Influence on Quantum Mechanics |
We show that the conflict between the theories of quantum mechanics and gravity may well have consequences for nanoscale experiments in the very near future. An unexpected result of their interplay is the spontaneous reduction of quantum dynamics to classical physics.
Many approaches towards uniting the theories of gravity and quantum mechanics have traditionally focused on the description of physics at the Planck scale. At this scale the typical dimensions of the curvature of spacetime and the wavelength of quantum particles become comparable, and a theory of quantum gravity is definitely required to describe the prevailing physics. However, there is also a second length scale at which the theories of gravity and quantum mechanics meet. Rather than looking at the size of a single, localized object, this scale is determined by the maximum distance over which a massive object can be superposed before the associated curvature of spacetime begins to affect its time evolution.
We show in a recent paper, that this second realm of quantum-gravity interactions can be reached in nano-scale experiments which employ masses that are only slightly greater than the masses involved in existing experiments.The tendency of modern experiments to produce ever heavier superpositions (going from single electrons, via Bucky balls, to nanomechanical resonators) thus forces us to take into account the combination of gravity and quantum mechanics.
In our article, we show that gravity will act as a “unitarity breaking field” in the presence of massive superpositions. This means that as a superposition becomes more and more massive, its dynamics will look less and less like that of a microscopic quantum particle. The most striking result of the altered dynamics is that for truly heavy objects (such as soccer balls, humans, tables and chairs), it will be impossible to form a quantum superposition state. The shear weight of the objects is enough to ensure that their dynamics will always be purely classical.
Moreover, in another (open access) review article, we show that the altered dynamics of heavy objects also implies that they can be used as quantum measurement machines. That is, by coupling a microscopic quantum particle to a heavy enough measuring device, the quantum superposition will be reduced to just one of its components. Born’s rule (which gives the probability for which component prevails) is automatically recovered from the interplay between gravity and quantum mechanics.
This way, the famous quantum paradoxes (such as Schrodinger’s cat, EPR, etc) can be resolved as consequences of the gravity-induced altered quantum dynamics of heavy objects. The line that separates “quantum weirdness” from everyday experience thus lies not in the consciousness of an observer, or even in any hidden variables describing elementary particles, but only in the shear size and weight of objects in our daily world.
| Aneesur Rahman Fellowship |
Argonne National Laboratory (Illinois, USA) has appointed me as their Aneesur Rahman Fellow. At Argonne I will continue my research on quantum critical phenomena, the loss of unitarity, and other topics of condensed matter physics.
Starting October 2010, I will be the Aneesur Rahman Fellow at Argonne National Laboratory in Illinois, USA. During the fellowship I will do research with prof. Mike Norman at the Materials Science Devision.
One of the main focusses of the research during the fellowship will be the search for observable experimental consequences of the interplay between Einstein’s theory of gravity and quantum mechanics. Although a lot of research on the quantum-gravity connection has been done in the realm of the so called Planck Scale, relatively little is known about the possible interactions between these theories in the more easily observable mesoscopic domain. Recently we proposed that the first consequences of the presence of gravity in mesoscopic quantum experiments may lead to the demise of the usual rules of quantum dynamics, and give rise to a process of quantum state reduction instead.
Apart from these projects, I will also continue doing research on the physics of materials near an electronic quantum critical point. In these materials, the interplay between electronic interactions (such as exciton formation) and structural effects (like charge density wave formation) may lead to unexpected physics like the enhancement of order or even the emergence of novel phases of matter.
Finally, I will continue various smaller research projects on (orbital) ordering phenomena in solid state materials; on the (de)coherence of different types of qubits and the associated quantum infomration theory; and on the consequences of driving different physical systems towards the dividing line between quantum and classical physics.
| Excitons, Superconductivity and Charge Order |
Going against the popular belief in condensed matter theory that excitons and charge order are always bad for superconductivity, we show that in some cases the presence of excitons can actually enhance the superconducting transition temperature.
It was pointed out decades ago by Ginzburg and Little that excitons (bound pairs of a particle and a hole) can act as mediators of superconductivity: just like the phonons in the standard theory of superconductivity they can bind together electrons to create a conductor with zero resistance. It was realised soon after this initial discovery that excitonic superconductors would not suffer from many of the limitations usually imposed by phonons. Dolgov and Maksimov even argued that room temperature superconductivity would be a real possibility.
To date however, no excitonic superconductors have been found. The reason is that in real materials excitons are never alone. Phonons are unavoidable, and when excitons interact with phonons this usually leads to the formation of a so-called charge density wave. This charge ordered state binds up all the available electrons in specific locations, and none are left to form the superconducting state.
In a recent article we show that this common theme of charge order precluding superconductivity is not the only possibility. Before the charge order sets in there is an opportunity for the excitons and phonons to work together in forming a superconducting state. What’s more, this superconducting state is more robust than it would have been without the influence of the excitons, and therefore has a higher transition temperature. There even turns out to be a material in which these effects may be seen experimentally. TiSe2 is normally charge ordered due to the interplay of excitons and phonons, but under pressure this charge order breaks down, and the new exciton-influenced type of superconductivity may have a chance to arise.
Room temperature superconductivity is still a very long way off, but realising that excitons and phonons can cooperate as well as compete does open up new ways of thinking about the theme of high temperature superconductivity.
| Broken Unitarity and Quantum Measurement |
Unitarity, the guiding principle of quantum physics, can spontaneously break down in macroscopic objects. In addition to explaining their classical dynamics, this loss of unitarity may also help to better understand the ability of large objects to function as quantum measurement machines.
Time evolution in quantum physics is an inherently unitary process. One consequence of its unitarity is that quantum information can never be lost, nor copied. Extending this result to macroscopic objects leads to an apparent paradox: even though all the things in our everyday world are ultimately built out of microscopic quantum mechanical particles, the macroscopic objects we see around us (tables, chairs, etc.) don’t seem to behave very quantum mechanically. Tables for example do not usually seem to occur in a state of superposition.
Parts of the puzzle of how to connect the micro to the macro world have been understood during the past decades. Spontaneous symmetry breaking explains how a table can have a fixed position in the middle of the kitchen, even though it would really like to spread out in a quantum mist throughout the entire house. Decoherence on the other hand can be used to understand that the average effect of all the quantum particles that continuously bounce into the table, is just to make it seem more classical.
The piece of the puzzle that remains unaddressed by both spontaneous symmetry breaking and decoherence is the question of what happens when a macroscopic object like a table is subjected to a single experiment which according to the unitary rules of quantum mechanics should force it into a state of superposition. This situation of individual-state quantum dynamics was addressed in a recent paper, in which I showed that the same properties which allow everyday objects to undergo spontaneous symmetry breaking, also allow them to spontaneously break the unitarity of quantum physics.
This way of avoiding unitarity allows macroscopic objects like tables, chairs, etc. to interact with microscopic particles without having to absorb all their quantum information, and they can thus also avoid being forced into a state of superposition.
Besides explaining the lack of superpositions in our everyday experience, the process of spontaneous unitarity breaking may also help to better understand what happens during quantum measurement. Following the unitarity of quantum mechanics to the letter, any measurement machine that is used to measure a quantum property of a superposed microscopic particle should end up in a state of superposition itself. However, if macroscopic objects can spontaneously break unitarity, they can avoid the superposition, and display only a single measurement result.
In the paper, I show that the probability for finding a particular outcome in such a process coincides precisely with Born’s rule. That is, the probability of a particular result being displayed by the measurement machine is given by the (squared) amplitude of the corresponding component in the initial wave function.
The quantum measurement problem is thus reduced to the problem of defining which objects are large enough to undergo spontaneous unitarity breaking, and which are small enough to evolve quantum mechanically. This new problem may be addressed within the near future by experiments on mesoscopic superposition states, bringing the quantum-classical crossover back into the realm of experimental physics, and freeing it from any metaphysical connection to conscience observers, parallel worlds, or gambling deities.
| Thin Spectrum in Superconductors |
We have shown that finite-size superconductors have low-energy, in-gap states associated with their spontaneous breaking of a global phase symmetry. Because of this so-called thin spectrum of states, superconducting qubits can stay quantum coherent only for a limited time.
Solid state qubits in general are based on materials that have some broken symmetry. In the case of superconducting qubits (such as Cooper pair boxes and flux qubits) the relevant broken symmetry is a phase symmetry.
In a recent paper we have shown that the superconducting state corresponds to a state with a well defined global phase. The breaking of this global phase symmetry turns out to be precisely analogous to the breaking of a U(1) phase symmetry in a ‘cante” antiferromagnet (i.e. an antiferromagnet in a uniform magnetic field). This picture does not contradict Elitzurís theorem which states that the gauge symmetry associated with local phases cannot be broken. Indeed, the superconducting state is still fully gauge invariant even after obtaining a well defined global phase.
As a consequence of the spontaneous symmetry breaking in superconductors, there must exist a thin spectrum of states at very low energies within the superconducting gap. For finite-size superconducting qubits this thin spectrum of states gives rise to decoherence, and therefore to a finite lifetime of the qubits, in precisely the same way as in magnetic qubit systems (see our earlier PRL paper). In the case of superconducting Cooper pair box qubits the resulting limit to the lifetime of present-day setups is estimated to be of the order of 0.5 ms, which is still well beyond the limit set by the conventional sources of decoherence in these systems.
The paper was also selected to be featured in three virtual journals:
| Junior Research Fellowship |
Homerton College (Cambridge, UK) has appointed me in a Junior Research Fellowship position. At Homerton College I will continue my research on quantum coherence, symmetry breaking, and the connection between quantum mechanics and classical physics in general.
Starting October 2007, I will be a Junior Research Fellow at Homerton College in Cambridge (UK). During the fellowship I will do research with prof. Peter Littlewood at the theory of condensed matter group of the department of physics of Cambridge University.
One of the main focusses of the research during the fellowship will be the search for a dynamical connection between the quantum theory and classical mechanics. In equilibrium situations, the connection between these two realms of physcics is well understood in terms of the process of spontaneous symmetry breaking. A dynamical description on the other hand, is still missing.
Recently we have found a first consequence of the presence of spontaneous symmetry breaking on the dynamical process of decoherence: we have shown that there is a fundamental limit to the time that a (symmetry-broken) solid state qubit can stay quantum coherent.
Other ideas about the quantum-classical connection include the suggestion made recently by Sir Roger Penrose that gravity may have a deteriorating influence on the unitarity of quantum mechanical time evolution. Some first ideas of how this suggestion could be put to the test experimentally can already be found in my PhD thesis.
Apart from the projects aimed at findig a dynamical connection between quantum and classical physics, I will also continue doing research on (orbital) ordering phenomena in solid state materials; on the (de)coherence of different types of qubits and the associated quantum infomration theory; and on the realization and consequences of spontaneous symmetry breaking in different physical systems.
| Quantum Mechanics & The Big World |
I have completed my PhD thesis, and obtained my PhD degree (with honors). The thesis describes our work on orbital ordering, decoherence due to spontaneous symmetry breaking and a proposed experimental test of gravity’s influence on quantum mechanics.
On the 4th of April 2007 I have defended my PhD thesis ‘Quantum Mechanics & The Big World: order, broken symmetry and coherence in quantum many-body systems’. The thesis is available online. A hardcopy can be ordered through Leiden University Press, or at Amazon.com.
Three main topics are covered in the thesis. The first part shows how a novel orbital-assisted Peierls transition can occur in the one-dimensional spin chains of NaTiSi2O6. In this material a combined spin dimerization and orbital ordering transition has been observed. We use a tight-binding model to describe this transition. Based on the model we predict that the crystal field seen by the titanium ions in this material cannot be larger than the size of the super-exchange interaction.
In the second part our work on the relation between spontaneous symmetry breaking and decoherence in solid state qubits is described. In addition to the earlier results, we now also explicitly include a description of spontaneous symmetry breaking in superconducting qubits. The corresponding decoherence time of these qubits turns out to be only just out of reach for the experimental state of the art.
Finally, in the third part we propose an experimental test for a recent idea by Sir Roger Penrose about the possible influence of gravity on quantum mechanics. Penrose suggested that because of the incompatibility of general covariance and unitarity, gravity might be involved in quantum state reduction. Based only on this assumption, a timescale for the gravity-induced collapse process can be found. We propose to test these ideas by pushing the well-developed technology of superconducting flux qubits just a bit further.
| Decoherence due to Spontaneous Symmetry Breaking |
We have shown that there is a fundamental limit to the time that solid state qubits can stay quantum coherent. This limit is due to the decohering effect of the thin spectrum states associated with spontaneous symmetry breaking.
Solid state qubits are based on materials that have some broken symmetry; translation symmetry for example is broken in crystals, spin rotation symmetry in (molecular) magnets and (global) phase rotation symmetry in superconductors. Such a broken continuous symmetry implies the presence of a set of low-energy states called the thin spectrum states.
We have shown in a recent PRL paper that the presence of these thin spectrum states in solid state qubits will cause them to slowly loose coherence. The fundamental timescale associated with this decoherence process does not depend on the parameters of the underlying system, and scales with the system size.
The paper and the accompanying press releases (both in English and Dutch) attracted a great deal of media attention worldwide: