The phase diagram of equilibrium systems can change radically by introducing activity. Examples of this include motility induced phase separation, flocking induced by self propulsion and alignment interactions, and turbulent flows produced by extensile active liquid crystals, to name a few. I will describe a different process, complementary to MIPS, by which activity strongly suppresses phase separation in a binary mixture of active and passive particles. I will motivate the study experimentally with very recent experiments on mixtures of microtubules with DNA condensates, and introduce a continuum theory in which active turbulent flows produced by active liquid crystals provide a stirring force capable of mixing an immiscible mixture, shifting the critical point to a lower temperature. I will further explain how the phase separated regime, which is a highly dynamic form of micro phase separation, can be understood by looking at the linear dynamics of the interfaces between the active and passive species.
An overview of existing methods, which use trajectory guided grids of Coherent States, will be given and their technical details will be discussed. In chemistry the trajectory guided random grids of Gaussian Coherent States are routinely used to simulate quantum dynamics in ultrafast photochemistry in a manner similar to classical molecular dynamics, but with the difference that an ensemble of trajectories is used instead of a single trajectory1. With the right sampling techniques they can yield well converged results for molecules with tens of vibrations, treating all nuclear degrees of freedom on a fully quantum level2. Similar methods based on Gaussian Coherent States can be used in physics to simulate the dynamics of ensembles of Bose particles described by second quantisation Hamiltonians3 or to dynamics of electrons in strong field4, 5. Other types of Coherent States, such as Coherent States of two level systems can be used to describe fermions6 and to obtain Born-Oppenheimer electronic energies and coupled qubits. 1. Makhov, D. V.; Symonds, C.; Fernandez-Alberti, S.; Shalashilin, D. V., Ab initio quantum direct dynamics simulations of ultrafast photochemistry with Multiconfigurational Ehrenfest approach. Chemical Physics 2017, 493, 200-218. 2. Symonds, C.; Kattirtzi, J. A.; Shalashilin, D. V., The effect of sampling techniques used in the multiconfigurational Ehrenfest method. 2018, 148 (18), 184113. 3. Green, J. A.; Shalashilin, D. V., Simulation of the quantum dynamics of indistinguishable bosons with the method of coupled coherent states. Phys. Rev. A 2019, 100 (1), 013607. 4. Kirrander, A.; Shalashilin, D. V., Quantum dynamics with fermion coupled coherent states: Theory and application to electron dynamics in laser fields. Phys. Rev. A 2011, 84 (3), 13. 5. Symonds, C.; Wu, J.; Ronto, M.; Zagoya, C.; Figueira de Morisson Faria, C.; Shalashilin, D. V., Coupled-coherent-states approach for high-order harmonic generation. Phys. Rev. A 2015, 91 (2), 023427. 6. Shalashilin, D. V., Zombie states for description of structure and dynamics of multi-electron systems. Journal of Chemical Physics 2018, 148 (19), 194109.
We develop a computationally efficient way of employing Gaussian wave packets to study laser-induced electron dynamics in atomic and molecular systems by directly solving the time-dependent Schr\"odinger equation (TDSE). First, we investigate charge migration (treating the nuclei classically), high-order harmonic generation (HHG), and single-isolated attosecond pulse generation in the Hydrogen molecular ion subjected to intense laser fields in a different range of frequencies with a basis of static coherent states (SCS). Then, seeking a smarter way of constructing and guiding a minimal set of time-dependent basis functions, we introduce a fast and accurate approach for optimizing s-type Gaussian type orbitals (GTOs) and apply it to calculate electronic states of different 1D and 3D time-independent systems. Finally, we apply our optimization approach to time-dependent problems. With our approach, we obtain excellent agreement with the exact results for HHG spectra of the 1D Hydrogen atom and molecular ion exposed to intense laser fields, which is not possible even with a much larger basis of static s-type GTOs.
Floquet or periodically driven systems show topological phases that are qualitatively different from their static counterparts. In this talk I will first introduce the new kinds of topological phases that can be realized in free-fermion Floquet systems. I will then show that the edge modes encountered in certain free fermion Floquet systems are remarkably robust to adding interactions, even in disorder-free systems where generic bulk quantities can heat to infinite temperatures due to the periodic driving. This robustness of the edge modes to heating can be understood in the language of strong modes for free fermion chains, and almost strong modes for interacting chains. I will then outline a tunneling calculation for extracting the long lifetimes of these edge modes by mapping the Heisenberg time-evolution of the edge operator to dynamics of a single particle in Krylov subspace.
Computing a matrix permanent is known to be a classically intractable problem. This talk will present the first polynomial time quantum algorithm for computing permanents of arbitrary N-dimensional square matrices with multiplicative error or additive error protocols . We transformed the well-known classical algorithm, Ryser's formula, into sums of quantum overlap integrals to develop the quantum algorithm. This requires O(N) or O(N3) evaluations of the real part of the quantum overlap integrals for real and complex matrices, respectively, with polynomial depth quantum circuits of O(N) qubits.  J. Huh, A fast quantum algorithm for computing matrix permanent, arXiv:2205.01328
Quantum materials driven out-of-equilibrium by a laser pump offer new opportunities for exploring intriguing quantum phenomena, including electron-correlation behaviors and topological properties of excitations. After reviewing some recent motivating pump-probe experiments, I will turn to our theoretical studies of driven many-body quantum systems. I will place particular emphasis on the situation where the laser frequency is chosen to selectively excite particular phonon modes and describe the impact of the non-equilibrium lattice on the electron properties, such as magnetism and band topology. The layered van der Waals materials CrI3 and MnBi2Te4 serve as excellent examples of the broader phenomena one might expect. I will also describe how hybrid phonon-magnon excitations in insulating antiferromagnets can exhibit highly tunable topological transitions in the presence of an externally applied magnetic field. The talk will conclude with an outlook for the prospects of achieving other interesting many-body phenomena in driven materials.
Well-controlled synthetic quantum systems, such as ultracold atoms in optical lattices, offer intriguing possibilities to study complex many-body problems in regimes that are beyond reach using state-of-the-art classical computations. The basic idea is to construct and use a well-controlled quantum many-body system in order to study its in- and out-of-equilibrium properties and potentially use it to develop more efficient tailored numerical methods that can then be applied to other systems that are not directly accessible with the simulator. An important future quest concerns the development of novel experimental techniques that allow us to expand the range of models that can be accessed. I will demonstrate this using the example of topological lattice models, which in general do not naturally appear in cold-atom experiments. I will show how the technique of periodic driving, also known as Floquet engineering, facilitates their realization and show how charge-neutral atoms in lattices can mimic the behavior of charged particles in the presence of an external magnetic field. A key ingredient for quantum simulation is the degree of control one has over the individual particles and the microscopic parameters of the model. We have recently succeeded to not only use the technique of periodic driving to emulate physical systems that we know exist in nature, but to take this idea one step further and realize completely new topological regimes that do not have any static analog. Moreover, we are currently developing a novel hybrid optical lattice platform, where tightly focused optical tweezers are used to locally control the motion of the atoms in the lattice, paving the way towards quantum simulation of simplified lattice gauge theories, which play a fundamental role in a variety of research areas including high-energy physics and topological quantum computation.