We analyze the dynamics of two strongly interacting fermions moving in two-dimensional lattices under the action of a periodic electric field, both with and without a magnetic flux. Due to the interaction, these particles bind together forming a doublon. We derive an effective Hamiltonian that allows us to understand the interplay between the interaction and the driving, revealing surprising effects that constrain the movement of the doublons. We show that it is possible to confine doublons to just the edges of the lattice and to a particular sublattice if different sites in the unit cell have different coordination numbers. Contrary to what happens in one-dimensional systems, here we observe the coexistence of both topological and Shockley-like edge states when the system is in a nontrivial phase.
We analyze the dynamics of two strongly interacting fermions moving in two-dimensional lattices under the action of a periodic electric field, both with and without a magnetic flux. Due to the interaction, these particles bind together forming a doublon. We derive an effective Hamiltonian that allows us to understand the interplay between the interaction and the driving, revealing surprising effects that constrain the movement of the doublons. We show that it is possible to confine doublons to just the edges of the lattice and to a particular sublattice if different sites in the unit cell have different coordination numbers. Contrary to what happens in one-dimensional systems, here we observe the coexistence of both topological and Shockley-like edge states when the system is in a nontrivial phase.
The discovery of topological matter has revolutionized the field of condensed matter physics giving rise to many interesting phenomena, and fostering the development of new quantum technologies. In this thesis we study the quantum dynamics that take place in low dimensional topological systems, specifically 1D and 2D lattices that are instances of topological insulators. First, we study the dynamics of doublons, bound states of two fermions that appear in systems with strong Hubbard-like interactions. We also include the effect of periodic drivings and investigate how the interplay between interaction and driving produces novel phenomena. Prominent among these are the disappearance of topological edge states in the SSH-Hubbard model, the sublattice confinement of doublons in certain 2D lattices, and the long-range transfer of doublons between the edges of any finite lattice. Then, we apply our insights about topological insulators to a rather different setup: quantum emitters coupled to the photonic analogue of the SSH model. In this setup we compute the dynamics of the emitters, regarding the photonic SSH model as a collective structured bath. We find that the topological nature of the bath reflects itself in the photon bound states and the effective dipolar interactions between the emitters. Also, the topology of the bath affects the single-photon scattering properties. Finally, we peek into the possibility of using these kind of setups for the simulation of spin Hamiltonians and discuss the different ground states that the system supports.
The discovery of topological matter has revolutionized the field of condensed matter physics giving rise to many interesting phenomena, and fostering the development of new quantum technologies. In this thesis we study the quantum dynamics that take place in low dimensional topological systems, specifically 1D and 2D lattices that are instances of topological insulators. First, we study the dynamics of doublons, bound states of two fermions that appear in systems with strong Hubbard-like interactions. We also include the effect of periodic drivings and investigate how the interplay between interaction and driving produces novel phenomena. Prominent among these are the disappearance of topological edge states in the SSH-Hubbard model, the sublattice confinement of doublons in certain 2D lattices, and the long-range transfer of doublons between the edges of any finite lattice. Then, we apply our insights about topological insulators to a rather different setup: quantum emitters coupled to the photonic analogue of the SSH model. In this setup we compute the dynamics of the emitters, regarding the photonic SSH model as a collective structured bath. We find that the topological nature of the bath reflects itself in the photon bound states and the effective dipolar interactions between the emitters. Also, the topology of the bath affects the single-photon scattering properties. Finally, we peek into the possibility of using these kind of setups for the simulation of spin Hamiltonians and discuss the different ground states that the system supports.
The controlled transfer of particles from one site of a spatial lattice to another is essential for many tasks in quantum information processing and quantum communication. In this work we study how to induce long-range transfer between the two ends of a dimer chain, by coupling states that are localized just on the chain's end-points. This has the appealing feature that the transfer occurs only between the end-points - the particle does not pass through the intermediate sites-making the transfer less susceptible to decoherence. We first show how a repulsively bound-pair of fermions, known as a doublon, can be transferred from one end of the chain to the other via topological edge states. We then show how non-topological surface states of the familiar Shockley or Tamm type can be used to produce a similar form of transfer under the action of a periodic driving potential. Finally we show that combining these effects can produce transfer by means of more exotic topological effects, in which the driving field can be used to switch the topological character of the edge states, as measured by the Zak phase. Our results demonstrate how to induce long range transfer of strongly correlated particles by tuning both topology and driving.
The controlled transfer of particles from one site of a spatial lattice to another is essential for many tasks in quantum information processing and quantum communication. In this work we study how to induce long-range transfer between the two ends of a dimer chain, by coupling states that are localized just on the chain's end-points. This has the appealing feature that the transfer occurs only between the end-points - the particle does not pass through the intermediate sites-making the transfer less susceptible to decoherence. We first show how a repulsively bound-pair of fermions, known as a doublon, can be transferred from one end of the chain to the other via topological edge states. We then show how non-topological surface states of the familiar Shockley or Tamm type can be used to produce a similar form of transfer under the action of a periodic driving potential. Finally we show that combining these effects can produce transfer by means of more exotic topological effects, in which the driving field can be used to switch the topological character of the edge states, as measured by the Zak phase. Our results demonstrate how to induce long range transfer of strongly correlated particles by tuning both topology and driving.
We investigate theoretically the Bose-Hubbard version of the celebrated Su-Schrieffer-Heeger topological model, which essentially describes a one-dimensional dimerized array of coupled oscillators with on-site interactions. We study the physics arising from the whole gamut of possible dimerizations of the chain, including both the weakly and the strongly dimerized limiting cases. Focusing on two-excitation subspace, we systematically uncover and characterize the different types of states which may emerge due to the competition between the inter-oscillator couplings, the intrinsic topology of the lattice, and the strength of the on-site interactions. In particular, we discuss the formation of scattering bands full of extended states, bound bands full of two-particle pairs (including so-called 'doublons', when the pair occupies the same lattice site), and different flavors of topological edge states. The features we describe may be realized in a plethora of systems, including nanoscale architectures such as photonic cavities, optical lattices and qubits, and provide perspectives for topological two-particle and many-body physics.
While topological single-particle systems have been extensively studied [1], topologically protected entangled two-boson states [2] and many-boson states [3] have recently come into the focus of research. However, interacting particle pairs in these systems have yet to be studied experimentally. This work focuses on the topological center-of-mass motion of bound two-particle states - so-called doublons [4], arising in a 1D lattice for discrete potentials with repulsive interaction. The tight-binding dynamics of a repulsive interacting two-particle state on such a 1D chain can be mapped onto a single particle evolving in a 2D lattice (Fig. 1a), where the main diagonal sites experience an on-site potentialU[5]. For the 2D case, we choose a square lattice driven by a conventional anomalous Floquet protocol with a full wave packet transfer in each hopping and uniformly distributed couplingsc[6]. The driving scheme preserves the mapping and adds a long-range interaction between the two particles in the 1D lattice.