The production of strongly interacting many-body states in ultra-cold atoms experiments requires to reach very low temperatures. It is thus important to determine the possible sources of heating and quantify its effects on the quantum dynamics. We propose an implementation of a Matrix Product Operator (MPO) algorithm which simulates the time evolution of a system of cold atoms trapped in an optical lattice and subject to incoherent scattering of the laser light. We can quantify the loss of coherence through the study of several correlation functions and determine the time after which the system becomes essentially "classical". We study the evolution of the operator entanglement entropy which furnishes precious information on the feasibility of such simulations. We find that depending on the form and strength of the dissipation, such open quantum systems can be accurately simulated with reasonable numerical resources.
References
D. Charrier and A. Läuchli, in progress
Adiabaticity is a fundamental concept of quantum dynamics. When a system parameter is changed infinitely slowly (adiabatically), the quantum system stays in the ground state if it starts from the ground state. Of course, real-life parameter ramps can never be infinitely slow. Therefore, a natural question is how the system deviates from adiabatic behavior when the ramp takes place over a finite time.
This question is being addressed through analysis of slow ramps in several many-particle systems. The deviation from adiabaticity is quantified through the excess energy or heating of the system with respect to the final ground state after a ramp.
References
[1] T. Venumadhav, M. Haque, and R. Moessner; Phys. Rev. B 81, 054305 (2010). “Finite-rate quenches of site bias in the Bose-Hubbard dimer”.
[2] B. Dora, M. Haque, and G. Zarand, arXiv:1011.6655. “Crossover from adiabatic to sudden interaction quench in a Luttinger liquid”.
[3] F. E. Zimmer and M. Haque, arXiv:1012.4492. “Non-adiabatic interaction ramps in a trapped Bose condensate”.
Reversing the applied perpendicular electric field in half-filled BLG (left) at a finite rate 1/$\tau$ leads to excited states in the upper branch in accordance with the Kibble-Zurek theory (right).
When passing through a quantum critical point by changing the control parameter at a finite rate in time, the system leaves its ground state, and defects (e.g. excited states, vortices) are produced, accounted for by the Kibble-Zurek theory. When the relaxation time of the system, which encodes how much time it needs to adjust to new thermodynamic conditions, becomes comparable to the remaining ramping time to the critical point, the system crosses over from the adiabatic to the diabatic (impulse) regime. In the latter regime, its state is effectively frozen, so that it cannot follow the time-dependence of the instantaneous ground states — as a result, excitations are produced. We apply these ideas to mono- and bilayer graphene in the presence of strong in-plane or perpendicular electric fields, respectively. We predict that the non-linear electric conductivity of graphene grows with E1/2 (E the electric field), as corroborated by subsequent experiments. A time dependent gate voltage in bilayer graphene results in population inversion around the Dirac cone, which can in principle provide a coherent source of infra-red radiation with tunable spectral properties.
References
[1] Balázs Dóra, Eduardo V. Castro, Roderich Moessner, Phys. Rev. B 82, 125441 (2010)
[2] Balázs Dóra, Roderich Moessner, Phys. Rev. B 81, 165431 (2010); Phys. Rev. B 83, 073403 (2011)
Evolution of a non-equilibrium electron distribution in IQHE edge states as a function of distance from a QPC, calculated using our exact solution.
Recent progress in cold atoms and in condensed matter experiments allow one to study the time-evolution of many-particle quantum systems in an isolated setup. By applying an external perturbation such as, for example, a bias voltage in the case of quantum Hall edge states, one can look at a non-equilibrium situation, i.e. when the electron energy distribution is not described by a Fermi-function. In our group we study theoretically problems related to electron coherence and relaxation in out-of-equilibrium one-dimensional quantum systems. We also develop new nonperturbative techniques, such as nonequilibrium bosonization, which are necessary in order to understand surprising behavior observed in experiments.
A new non-equilibrium edge channel spectroscopy was recently developed in experiments by the group of F.Pierre in France and used to study relaxation of electrons in quantum Hall edge states. In these experiments a non-equilibrium electron distribution was generated by a quantum point contact (QPC) at finite bias voltage and measured at different distances from the QPC. It was found that the electrons cool down as they propagate along the edge and relax to an equilibrium (stationary) distribution far from the contact. In our recent papers we developed a theory, explaining experimental observations and found an exact solution, which gives a full quantitative description of the problem. One of the main results of our theory was a generalization of the Dzyaloshinskii-Larkin theorem in the non-equilibrium case.
References
[1] D. L. Kovrizhin, J. T. Chalker, “Equilibration of integer quantum Hall edge states”, arXiv:1009.4555
[2] D. L. Kovrizhin, J. T. Chalker, “Exactly solved model of edge-state equilibration”, paper in preparation
In several lattice systems, we have found that simple geometric features of the lattice like open edges can have dramatic non-equilibrium quantum effects, such as localizing few-particle clusters in itinerant systems or suppressing the propagation of multi-magnon composites in spin chains. Versions of the phenomenon appear in the Bose-Hubbard model, the spinless fermion model with nearest-neighbor interactions, and the anisotropic Heisenberg (XXZ) spin chain.
References [1] M. Haque, Phys. Rev. A 82, 012108 (2010). “Self-similar spectral structures and edge-locking hierarchy in open-boundary spin chains”. [2] R. Pinto, M. Haque, S. Flach, Phys. Rev. A 79, 052118 (2009). “Edge-localized states in quantum one-dimensional lattices”.
Bose-Einstein condensates realized in laser-cooled atoms display a remarkable range of observable non-equilibrium phenomena, reflected by the rich set of dynamical behaviors supported by the Gross-Pitaevskii equation, which describes mean-field dynamics of condensates.
MPI-PKS members have explored the dynamics of condensates with a few vortices. For example, a vortex-antivortex pair (vortex dipole) in a trapped condensate displays stationary configurations and characteristic trajectories due to the interplay between mutually driven and inhomogeneity-driven motion.
References
[1] W. Li, M. Haque and S. Komineas; Phys. Rev. A 77, 053610 (2008). “A vortex dipole in a trapped two-dimensional Bose condensate”.
[2] J. A. Seman, E. A. L. Henn, M. Haque, R. F. Shiozaki, E. R. F. Ramos, M. Caracanhas, P. Castilho, C. Castelo Branco, P. E. S. Tavares, F. J. Poveda Cuevas, G. Roati, K. Magalhaes, and V. S. Bagnato; Phys. Rev. A 82, 033616 (2010). “Three-vortex configurations in trapped Bose-Einstein condensates”.