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| 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 the electronic chiral order to 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. 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. | ||||
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 | 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. | ||||
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| 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. | ||||
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 | 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. | ||||
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| 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. | ||||
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 | 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 Elitzur’s 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:
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| 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. | ||||
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 | 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. | ||||
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| 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:
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