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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Confined indirect excitons in one and two dimensional magnetic lattices: Bose-Hubbard model and beyond

Ahmed Abdelrahman, Byoung Seung HAM

Published Nov 29, 2012• 0 citations
Publisher

Abstract

Confined indirect excitons in a two-dimensional magnetic lattice are promoted to simulate condensed matter systems. Excitonic particles are magnetically trapped so that a sufficient cooling mechanism can allow the trapped clouds of indirect excitons to experience the Bose-Einstein condensation phase transition. Thus, a long­ range spatial coherence can be resolved causing an inherited phase-locked across all of the coupled sites (single traps). Using an external magnetic bias field a mutual tunneling can adiabatically be exchanged between sites in which case the underline physics of Bose-Hubbard model can be explored such as Mott-insulator and Josephson Effect.

DOI
10.1117/12.2000571

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Confined indirect excitons in a two-dimensional magnetic lattice are promoted to simulate condensed matter systems. Excitonic particles are magnetically trapped so that a sufficient cooling mechanism can allow the trapped clouds of indirect excitons to experience the Bose-Einstein condensation phase transition. Thus, a long­ range spatial coherence can be resolved causing an inherited phase-locked across all of the coupled sites (single traps). Using an external magnetic bias field a mutual tunneling can adiabatically be exchanged between sites in which case the underline physics of Bose-Hubbard model can be explored such as Mott-insulator and Josephson Effect.
Abstract The Hubbard model constitutes one of the most celebrated theoretical frameworks of condensed-matter physics. It describes strongly correlated phases of interacting quantum particles confined in a lattice potential. For bosons, in the last two decades the Hubbard Hamiltonian has been deeply scrutinised in the regime of short-range on-site interactions. On the other hand, extensions to longer-range off-site couplings between neighbouring lattice sites have remained mostly elusive experimentally. Entering this regime constitutes a well identified research frontier where quantum matter phases can spontaneously break the lattice symmetry. Here we unveil one of such phases, precisely the long-sought-after checkerboard solid. It is accessed by confining semiconductors dipolar excitons in a two-dimensional square lattice. The exciton checkerboard is signalled by a strongly minimised compressibility at half-filling of the lattice sites, in quantitative agreement with theoretical expectations. Our observations thus highlight that dipolar excitons enable controlled implementations of extended Bose-Hubbard Hamiltonians.
We propose a new method to create an asymmetric two-dimensional magnetic lattice which exhibits magnetic band gap structure similar to semiconductor devices. The quantum device is assumed to host bound states of collective excitations formed in a magnetically trapped quantum degenerate gas of ultracold atoms such as a Bose-Einstein condensate (BEC) or a degenerate Fermi gas. A theoretical framework is established to describe possible realization of the exciton-Mott to discharging Josephson states oscillations in which the adiabatically controlled oscillations induce ac and dc Josephson atomic currents where this effect can be used to transfer n Josephson qubits across the asymmetric two-dimensional magnetic lattice. We consider second-quantized Hamiltonians to describe the Mott insulator state and the coherence of multiple tunneling between adjacent magnetic lattice sites where we derive the self consistent non-linear Schrödinger equation with a proper field operator to describe the exciton Mott quantum phase transition via the induced Josephson atomic current across the n magnetic bands.
An asymmetric multi-quantum state magnetic lattice is proposed to host excitons formed in a quantum degenerate gas of ultracold fermionic atoms to simulate Bose-Einstein condensation (BEC) of excitons. A Quasi-two dimensional degenerate gas of excitons can be collected in the in-plane asymmetric magnetic bands created at the surface of the proposed magnetic lattice, where the ultracold fermions simulate separately direct and indirect confined electronhole pairs (spin up fermions-spin down fermions) rising to the statistically degenerate Bose gas and eventually through controlled tunnelling to BEC of excitons. The confinement of the coupled magnetic quantum well (CMQWs) system may significantly improve the condition for long lived exciton BEC. The exciton BEC, formed in CMQWs can be regarded as a suitable host for the multi-qubits (multipartite) systems to be used in quantum information processors.
In condensed-matter physics, electronic Mott insulators have triggered considerable research due to their intricate relation with high-temperature superconductors. However, unlike atomic systems for which Mott phases were recently shown for both bosonic and fermionic species, the fingerprint of a Mott phase implemented with bosons is yet to be found in the solid state. Here we unveil such signature by emulating the Bose-Hubbard hamiltonian with semiconductor excitons confined in a two-dimensional lattice. The exciton fluid is characterised by strong repulsive dipolar interactions. These mostly constrain the system to behave classically, but nevertheless allow for a very narrow parameter space where two Mott phases are formed, with either one or two excitons per lattice site. Our ability to program the lattice geometry explored by excitons then paves the way towards quantum simulations of long-sought many-body phases such as supersolids.
We derive an effective Bose-Hubbard model that predicts a phase transition from Bose-Einstein condensate to Mott insulator in two different systems subject to applied periodic potentials: microcavity exciton polaritons and indirect excitons. Starting from a microscopic Hamiltonian of electrons and holes, we derive an effective Bose-Hubbard model for both systems and evaluate the on-site Coulomb interaction UUU and hopping transition amplitudes ttt. Experimental parameters required for observing a phase transition between a Bose-Einstein condensate and a Mott insulator are discussed. Our results suggest that strong periodic potentials and polaritons with a very large excitonic component are required for observing the phase transition. The form of the indirect exciton interaction is derived including direct and exchange components of the Coulomb interaction. For indirect excitons, the system crosses over from a Bose-Hubbard model into a double layer Fermi-Hubbard model as a function of increasing bilayer separation. The Fermi-Hubbard model parameters are calculated, and the criteria for the location of this crossover are derived. We conjecture that a crossover between a Bose Mott insulator to a Fermi Mott insulator should occur with increasing bilayer separation.
Enriching condensed-matter systems with quantum optical phenomena currently drives intense research efforts, particularly to introduce collective quantum correlations. Here we access this paradigm, by confining dipolar excitons in a nanoscopic lattice where long-range hopping, and nearest-neighbour dipolar repulsions, dress the Bose-Hubbard Hamiltonian. Long-range hopping is evidenced by the spontaneous buildup of many-body sub-radiance, signalled by an algebraic slowdown of excitons radiative dissipation. In addition, we observe a threshold increase of temporal coherence for dipolar quantum solids only. It suggests that excitons condense in a single sub-radiant state for Mott-like phases. These combine then spatial order and collectively extended coherence, in a single degree of freedom. Our study unveils that nanoscopic exciton arrays provide a unique platform to design new frontiers of strongly-correlated lattice models with long-range correlations.