Selection of recent research


§   Near-adiabatic ramps ("slow quenches") in quantum many-particle systems

An adiabatic change of system parameters is an essential notion of quantum mechanics.   Many experimental protocols involve adiabatically changing a parameter in order to reach a desired quantum state.   In addition, the idea of adiabatic quantum computation has recently attracted interest, as a path to computation via slow variation of a many-particle Hamiltonian.

Since a real-life ramp can never be infinitely slow, understanding non-adiabatic dynamics during ramps is vital. We are therefore studying the evolution of many-particle systems during and after a sudden change (quench) or gradual change (ramp) of parameter, e.g., changes of interaction strength or magnetic field, or (for cold-atom systems) trapping potential. Varying the rate of change, one can study the whole range between instantaneous and adiabatic limits.

A grand challenge is to understand deviations from adiabaticity in slow but finite ramps. I have explored this issue in a series of calculations, aiming to provide intuition about how this deviation is related to various system features, such as energy gap or gaplessness, inhomogeneity due to trapping potentials, and presence of phase transitions.

References:

[a]   M. Haque and F.E. Zimmer;    Phys. Rev. A 87, 033613 (2013)
Title: `Slow interaction ramps in trapped many-particle systems: universal deviations from adiabaticity.'

[b]   T. Venumadhav, M. Haque, and R. Moessner;    Phys. Rev. B 81, 054305 (2010).
Title: `Finite-rate quenches of site bias in the Bose-Hubbard dimer.'

[c]   B. Dorá, M. Haque, and G. Zaránd;    Phys. Rev. Lett. 106, 156406 (2011).
Title: ` Crossover from adiabatic to sudden interaction quench in a Luttinger liquid.'

[d]   F.E. Zimmer and M. Haque;    arXiv:1012.4492.
Title: `Non-adiabatic interaction ramps in a trapped Bose condensate.'

[e]   M. Haque and H.T.C. Stoof;    Phys. Rev. A 71, 063603 (2005).
Title: `Dynamics of a molecular Bose-Einstein condensate near a Feshbach resonance.'


§   Entanglement and topological order in quantum Hall states

Fractional quantum Hall states possess an unconventional ordering known as `topological order', characterized by fractionalized excitations and extra ground-state degeneracies depending on the topology of the space. Given the difficulty of describing topological order using the standard methods of condensed matter physics, newly discovered connections between topological order and entanglement measures are of significant interest. Recent and ongoing work has explored the use of entanglement entropy calculations in fractional quantum Hall states, with the aim of developing entanglement calculations as a tool for addressing physical questions concerning quantum Hall states.

References:

[a]   M. Haque, O. Zozulya, and K. Schoutens;    Phys. Rev. Lett. 98, 060401 (2007).
Entanglement entropy of fermionic Laughlin states.

[b]   O. Zozulya, M. Haque, K. Schoutens, and E. H. Rezayi;    Phys. Rev. B 76, 125310 (2007).
Bipartite entanglement entropy in fractional quantum Hall states.

[c]   O. Zozulya, M. Haque and N. Regnault;    Phys. Rev. B 79, 045409 (2009).
Entanglement signatures of Quantum Hall phase transitions.

[d]   A. M. Laeuchli, E. J. Bergholtz, J. Suorsa, and M. Haque;    Phys. Rev. Lett. 104, 156404 (2010).
Disentangling Entanglement Spectra of Fractional Quantum Hall States on Torus Geometries.

[e]   A. M. Laeuchli, E. J. Bergholtz, and M. Haque;    New Journal of Physics, 12, 075004 (2010).
Entanglement Scaling of Fractional Quantum Hall states through Geometric Deformations.
Also available as arXiv:1003.5656.


§   Edge-localized states in 1D quantum lattices

In one-dimensional quantum lattice models with open boundaries, examining few-particle dynamics led me to an edge-induced self-similar (`fractal') structure high up in the energy specturm, and associated out-of-equilibrium consequences.

The non-equilibrium consequences are a hierarchy of `edge-locking' or edge-localization effects. This is a collective rather than a single-particle effect, requiring at least three fermions or three bosons.

Till now, I found and examined versions of the phenomenon in three classic condensed-matter models:   (1) the Bose-Hubbard model;   (2) the spinless fermion model with nearest-neighbor repulsion;   (3) the XXZ spin chain.

References:

[a]   R. Pinto, M. Haque, S. Flach;    Phys. Rev. A 79, 052118 (2009).
Edge-localized states in quantum one-dimensional lattices.

[b]   M. Haque;    Phys. Rev. A 82, 012108 (2010).
Self-similar spectral structures and edge-locking hierarchy in open-boundary spin chains.


§   Few-vortex dynamics in Bose condensates

The nonlinear Schroedinger equation (Gross-Pitaevskii equation), describing mean-field dynamics of Bose-Einstein condensates, possesses a remarkable range of rich dynamical phenomena. We are exploring 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:

[a]   W. Li, M. Haque and S. Komineas;    Phys. Rev. A 77, 053610 (2008).
A vortex dipole in a trapped two-dimensional Bose condensate.

[b]   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.


§   Entanglement between unusual partitionings of many-particle systems

The standard usage of entanglement estimators in condensed matter theory is through the entanglement between a spatially connected block and the rest of the system. Clearly, it is possible to ask about the entanglement between other kinds of partitions of a many-particle state. Our work demonstrates that several alternate types of partitionings can be fruitful and instructive for characterizing correlations in many-particle states.

References:

[a]   O. Zozulya, M. Haque, and K. Schoutens;    Phys. Rev. A 78, 042326 (2008).
Particle partitioning entanglement in itinerant many-particle systems.

[b]   M. Haque, J.N. Bandyopadhyay and V. Ravi Chandra;    Phys. Rev. A 79, 042317 (2009).
Entanglement and level crossings in finite frustrated ferromagnetic chains.

[c]   (Review Article) M. Haque, O. Zozulya, and K. Schoutens;    J. Phys. A: Math. Theor. 42, 504012 (2009).
Entanglement between particle partitions in itinerant many-particle states.
Also available as arXiv:0905.4024

Personal home page: Masud Haque.

Email (replace ATT by @ and remove spaces): haque ATT pks.mpg.de