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Neuroscience and biology

Condensed matter physics

Neuroscience (experiments and theory) 

Whole-brain functional connectivity in C. elegans

During my postdoc at Princeton, I measured functional connectivity in the brain of the nematode C. elegans, using optogenetics and whole-brain imaging.

You can read the paper on the arXiv:

I've talked about my work at Cosyne, in Lisbon, in March 22.


Nonequilibrium Green's functions for functional connectivity in the brain

Read the article in Physical Review Letters

A theoretical framework describing the set of interactions between neurons in the brain, or functional connectivity, should include dynamical functions representing the propagation of signal from one neuron to another. Green’s functions and response functions are natural candidates for this but, while they are conceptually very useful, they are usually defined only for linear time-translationally invariant systems. The brain, instead, behaves nonlinearly and in a time-dependent way. I developed a theoretical framework to describe functional connectivity of a continuous-variable network of neurons based on nonequilibrium Green's functions, borrowing conceptual and mathematical tools from condensed matter physics. In this article, I showed how functional connectivity is related to the measurable response functions and illustrated the framework using two examples inspired by the brain of the C. elegans.

Rotifer neuro

As a Grass Fellow at MBL (Marine Biological Laboratory, Woods Hole MA) I am working on developing transgenic strains of the rotifer B. manjavacas to do whole-brain neural activity recordings. Right now I'm making and optimizing plasmids for pan-neuronal expression. More updates to come soon!


Nonequilibrium dynamics in solids (experiments and theory)

Summaries to come

Probing the fluctuations of optical properties in time-resolved spectroscopy

Read the article in Physical Review Letters

Phase separation in the non-equilibrium Verwey transition in magnetite

Read the article in Physical Review B

Bypassing the energy-time uncertainty in time-resolved photoemission

Read the article in Physical Review B

Anisotropic response of cuprate superconductors driven by mid-infrared pulses

Read the article in Physical Review Letters (and in my thesis)

A longer read: The introduction of my PhD thesis (pdf here)

Many macroscopic properties of solids are determined by the behaviour of the electrons they contain. In elemental crystals or in crystals containing elements solely from the first three periods of the periodic table, the electrons in the highest energy levels can easily hop from one atom to its neighbours. They are, therefore, (potentially) highly mobile and the atomic levels give rise to very dispersive bands. 
Given the crystalline structure of the solid, its electrical conductance is determined by the availability of empty states for the electrons to move through the crystal. In the cases in which the bands are sequentially filled and do not overlap, whether the solid is a metal or an insulator can, therefore, be determined by simple counting of the electrons in a unit cell.

The situation changes when the character of the highest energy states make the electrons less mobile. For example, the movement of electrons is difficult through alternating d- and p-orbitals, because the hopping integral between them is low. In this context, the correlation between the position of the electrons becomes, therefore, strongly relevant in the determination of the macroscopic properties of the system. On the most "basic" level, strong correlation may determine the insulating character of a system, even though the number of electrons per unit cell would suggest a metallic character. This is the case of the Mott insulator, which cannot be captured by the mean-field models which accurately describe the properties of s- and p-metals. 

More in general, strongly correlated materials display very rich phase diagrams, containing many phases in reach with small variations of the external parameters or of the chemical doping. The variety of phases encompasses superconducting states, antiferromagnets, insulators, Fermi liquid metals and strange (non-Fermi liquid) metals, charge density wave, nematic states, and others. Strong correlation is most famously realized in the oxides of the transition metals. 

The rich phase diagrams of strongly correlated materials provide deep intellectual problems, such as the emergence of collective phenomena in condensed matter, but also a wealth of possible technological application exploiting their phase transitions. For example, insulator-to-metal transitions in transition metal oxides are good candidates for new fast electronic switching.

In general, condensed matter can be studied both at and out of its equilibrium state. The first reason to perform out-of-equilibrium experiments is to gain a deeper insight on the interactions between degrees of freedom in the solid. They will, in fact, react to a strong perturbation with different relaxation timescales. If their interactions cannot be clearly identified from their equilibrium properties (e.g. their spectra), there is a higher chance to do it when they are out of equilibrium. Since the relevant timescales in condensed matter are of the order of the pico- and femtosecond, out-of-equilibrium experiments have to be perfomed using ultrashort light pulses in pump-probe experiments. An intense ultrashort light pulse, called pump, perturbs the system bringing it out of equilibrium and a second, delayed, and less intense pulse, called probe, probes its optical properties (e.g. its reflectivity) as a function of time after the excitation. 

Moreover, in many cases the technological exploitation of strongly correlated materials lies in the very fact that their phase transitions can be triggered on ultrashort timescales. Out-of-equilibrium pump-probe experiments allow therefore to study, characterize, and discover new ultrafast out-of-equilibrium phase transition. 

The case of magnetite (Fe3O4) is probably the most studied in this context, and one of the oldest. In 1939 E.J.W. Verwey identified a first-order transition at Tc=123 K between the high-temperature metallic phase of magnetite and a low-temperature insulating phase [1]. The crystalline structure of magnetite in the insulating phase has been particularly difficult to determine, and the exact nature of its refinement is still under debate [2]. In the system kept below the $T_c$ the insulator-to-metal transition can be triggered by light pulses and is complete within picoseconds [3], i.e. it is far quicker than anything that can be called quasistatic. What happens when first-order phase transitions occur too quickly? This question is addressed in part I of this thesis in the case of the photoinduced insulator-to-metal transition in magnetite. In particular, I will discuss the occurrence of phase separation in a specific regime, and its interesting effects on the out-of-equilibrium optical properties of the system.

The experiment on magnetite has been performed with two tacit assumptions, whose justifications and limitations are addressed in part II and III of this thesis. The first and probably most evident one concerns the photon energy (or wavelength) of the light pulses used to photoexcite the system. Technical reasons constrain commercial ultrafast pulsed lasers to very narrow spectral regions. In particular, titanium-doped sapphire lasers produce light with photon energies close to 1.5 eV. Pump-probe experiments have therefore been traditionally performed with such pulses, in the assumption that the excitations they create in the system are "right", in that they are either tuned to the relevant transitions or that the excitations they produce are sufficiently general in character.

This issue is of particular relevance for the excitation of degrees of freedom with energies of the order of 0.1 eV or below, which are far removed from the 1.5 eV photon energy of the Ti:Sapphire lasers. For example, in the high critical temperature cuprate superconductors the relevant energies of the superconducting state are of the order of tens or one hundred millielectronvolts. The mismatch between these energy scales and the available photon energies can be cured building pulsed light sources with tunable photon energy in the mid-infrared spectral range. These exploit nonlinear optical phenomena to produce light pulses at the desired photon energy using the pulses from the commercial laser source. In chapter II.I I will describe the optical set-up we have built for this purpose.

Bi2Sr2Ca0.92Y0.08Cu2O8 is a representative member of the familiy of the cuprates and is a superconductor at temperatures below 96 K. In chapter II.2 I will discuss how we were able, thanks to the tunable mid-infrared pulses, to identify a scattering channel for electronic excitations at room temperature and to study the response of the system along different directions both at room temperature and in the low-temperature phases of the system.

The second tacit assumption done in the experiment on magnetite is that the state of the system after the photoexcitation rapidly becomes an effectively thermal state. In many cases this is a safe assumption. For example, in simple metals, photoexcited electrons will quickly relax down to states close to the Fermi energy and thermalize. Their state will then display the standard features of thermal states, such as the fact that their occupation of electronic levels is described by the Fermi function.

There are more complicated situations in which this need not be the case. For example, when coherent dynamics are present in degrees of freedom with whom electrons are coupled, electrons may not be able to thermalize at all times. In part III, this situation is discussed for the case of coherent lattice vibrations in solids, with the aid of numerical calculations. For particular phases of the vibration, the electronic subsystem is indeed ``less thermal'' than for other phases, and I discuss how such kind of information can be retrieved from the out-of-equilibrium optical properties of the solid, comparing our calculations with experimental results obtained on bismuth single crystals.

Besides optical spectroscopy, a very important tool to study condensed matter is photoelectron spectroscopy, which allows to measure the single particle spectrum of the system. At equilibrium it gives access to the band structure of the occupied levels in the system. The spectroscopy of electrons photoemitted from a solid can be performed also in a time-resolved manner in a pump-probe scheme. A first pulse (usually with a photon energy of 1.5 eV) brings the system out of its equilibrium, and a subsequent ultraviolet pulse photoemits the electrons. In this way, the occupation of the bands can be studied as a function of time after the excitation. Moreover, changes in the band structure itself can be detected.

Time-resolved photoemission is affected by the so-called energy-time uncertainty relation. In fact, the light pulses employed to photoemit the electrons necessarily have a spectrum of finite width, which increases upon decreasing the temporal duration of the pulses. This is reflected in a spread in the kinetic energy of the photoemitted electrons. Therefore, a tradeoff must be made between the temporal and energetic resolution in time-resolved photoemission. Such limitation becomes extremely relevant in the study of the nonequilibrium dynamics of the emergent properties of strongly correlated materials. While these become manifest in very sharp spectral features, it is known that some of them can evolve on timescales shorter than the inverse width of their spectroscopic fingerprint [4]. This kind of dynamics beyond the spectral uncertainty limit cannot be resolved in standard time-resolved photoemission.

The energy-time uncertainty relation is often erroneously associated to the uncertainty relations stemming from the Heisenberg principle. Its consequences on time-resolved photoemission have been, therefore, always considered as an unavoidable limitation. However, the energy-time uncertainty is not of fundamental nature [5]. In part IV I discuss how time-resolved photoemission can be enhanced. In chapter IV.1 we theoretically propose an experimental scheme which allows to bypass the energy-time uncertainty in time-resolved photoemission using two photoemitting pulses. Moreover, in chapter IV.2, we theoretically study the features of time-resolved photoemission if it were performed with statistical and quantum light.

[1] E. J. W. Verwey. Electronic conduction of magnetite (Fe 3 O 4 ) and its transition point at low temperatures. Nature (London), 144:327–328, 1939.

[2] M. S. Senn, J. P. Wright, and J. P. Attfield. Charge order and three-site distortions in the Verwey structure of magnetite. Nature (London), 481:173–176, 2012.

[3] S. de Jong, R. Kukreja, C. Trabant, N. Pontius, C. F. CHang, T. Kachel, M. Beye, F. Sorgenfrei, B. Back, C. H. Bräuer, et al. Speed limit of the insulator-metal transition in magnetite. Nat. Mater., 12:882–886, 2013.

[4] B. Lechtenberg and F. B. Anders, “Spatial and temporal propagation of Kondo correlations”, Phys. Rev. B 90, 045117 (2014).[

[5] L. Landau and E. Lifschitz, “Quantum mechanics - Non-relativistic theory”, Course of theoretical physics 3, 157 (§44: The uncertainty relation for energy), Pergamon Press (1977).