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Optica Pura y Aplicada

Single molecular-excitation propagation in one-dimensional optical lattices

V. C. Olaya-Agudelo, Karen Rodríguez

Published Jun 26, 2019• 0 citations
Publisher

Abstract

We study a LiCs strongly-interacting molecular gas loaded on an one-dimensional optical lattice keeping one particle per site.The molecules are in the lowest electronic and vibrational (ν=0) state, Χ 1 Σ.Here, coherent transfers of rotational excitations (N={0,1}) along the lattice are shown for several lattice sizes and initial conditions.Due to the large intermolecular distance and low filling, the dipoledipole interaction in the nearest-neighbor approximation governs the dynamics of the rotational excitations.For low field strengths, the full set of internal rotational projections must be taken into account.The generated von Neumann entanglement entropy throughout the dynamics of the energy transfer are also presented.A monotonic growth for short times and a saturation towards the steady regime is observed, showing the potential of these molecular systems to be used in quantum information protocols.The numerical simulations are performed by means of the Time-Evolving Block Decimation algorithm based on the Matrix Product State formalism and the Susuki-Trotter decomposition.

DOI
10.7149/opa.52.2.50310

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We study a LiCs strongly-interacting molecular gas loaded on an one-dimensional optical lattice keeping one particle per site.The molecules are in the lowest electronic and vibrational (ν=0) state, Χ 1 Σ.Here, coherent transfers of rotational excitations (N={0,1}) along the lattice are shown for several lattice sizes and initial conditions.Due to the large intermolecular distance and low filling, the dipoledipole interaction in the nearest-neighbor approximation governs the dynamics of the rotational excitations.For low field strengths, the full set of internal rotational projections must be taken into account.The generated von Neumann entanglement entropy throughout the dynamics of the energy transfer are also presented.A monotonic growth for short times and a saturation towards the steady regime is observed, showing the potential of these molecular systems to be used in quantum information protocols.The numerical simulations are performed by means of the Time-Evolving Block Decimation algorithm based on the Matrix Product State formalism and the Susuki-Trotter decomposition.
We study a LiCs strongly-interacting molecular gas loaded into an one-dimensional optical lattice at quarter filling. The molecules are in the lowest electronic and vibrational state, X1ΣX^{1}ΣX1Σ (ν=0ν=0ν=0). Due to the large intermolecular distance and low filling, dipole-dipole interaction in the nearest-neighbor approximation governs the dynamics of the rotational excitations. For low DC electric field strengths, the full set of rotational levels N=0,1N=0,1N=0,1 must be taken into account, nevertheless, our calculations show that very weak fields act as field-selectors disclosing two- and three-level systems out of the original four-level one. The dynamics and the generated von Neumann entanglement entropy among the internal rotational states throughout the evolution are presented for low, moderate and strong fields . We observe a sharp and monotonous growth of the entanglement as the dynamics take place showing the potential of these molecular systems to be used in quantum information protocols. The numerical simulations are performed by means of the Time-Evolving Block Decimation algorithm based on the Matrix Product State formalism and the Susuki-Trotter decomposition.
Ultracold bosonic gases in optical lattices are strongly correlated quantum systems similar to solids. The strong correlation between the electrons in a solid on the one hand, and the bosonic atoms in optical lattice on the other, exhibit various quantum phenomena like insulation, conductivity, localization of electrons and atoms, respectively. Controlled by the intensity of the lattice laser, the ultracold bosonic gas can be transferred from a regime with superfluid character for shallow lattices into a regime of strong correlations, the Mott insulator. As an additional external parameter besides the lattice depth, one can generate spatial inhomogeneities by superimposing an additional standing wave (so-called two-color superlattices), which gives rise to localization effects or the formation of a Bose-glass phase. In the present work, numerical simulations are employed in order to investigate characteristic signatures of the quantum phases in the low-energy excitation spectrum of one-dimensional systems. We simulate temporal small amplitude modulations of the optical lattice in analogy to experiments, and evaluate the response of the system from the time-evolved initial state. The lattice systems are described in the framework of the Bose-Hubbard model. For the evaluation of the time-evolved state, we employ several numerical methods. We analyze systems of small size (6 particles on 6 sites) using an exact time-evolution by integration of the time-dependent Schrödinger equation. The formulation of an importance truncation scheme enables us to retain only the relevant components of the model space in the strongly correlated regime and, thus, allows for the investigation of systems with 10 particles on 10 sites using exact time-evolution. Based on this method, we present results of the Mott-insulating regime as well as for the Bose-glass phase. Furthermore, we employ particle-hole methods, which allow for the treatment of systems with experimental lattice sizes and particle numbers. Starting from the equation of motion method we adapt the Tamm-Dancoff approximation as well as the random-phase approximation for the occupation number representation of the Bose-Hubbard model. We present results of simulations of up to 50 particles on 50 sites and discuss the impact of the lattice depth on the low-energy excitations (U-resonance). Moreover, the impact of a two-color superlattice and the variation of its amplitude is investigated.
We derive a novel lattice Hamiltonian, the molecular Hubbard Hamiltonian , which describes the essential many-body physics of closed-shell ultracold heteronuclear molecules in their absolute ground state in a quasi-one-dimensional optical lattice. The molecular Hubbard Hamiltonian is explicitly time dependent, making a dynamic generalization of the concept of quantum phase transitions necessary. Using the time-evolving block decimation algorithm to study entangled dynamics, we demonstrate that, in the case of hard-core bosonic molecules at half-filling, the molecular Hubbard Hamiltonian exhibits emergent timescales over which spatial entanglement grows, crystalline order appears and oscillations between rotational states self-damp into an asymptotic superposition. We show that these timescales are non-monotonic functions of the physical parameters describing the lattice.
We consider the dynamics of rotational excitations placed on a single molecule in spatially disordered one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) ensembles of ultracold molecules trapped in optical lattices. The disorder arises from incomplete populations of optical lattices with molecules. This leads to a model corresponding to a quantum particle with long-range tunnelling amplitudes moving on a lattice with the same on-site energy but with forbidden access to random sites (vacancies). We examine the time and length scales of Anderson localization for this type of disorder with realistic experimental parameters in the Hamiltonian. We show that for an experimentally realized system of KRb molecules on an optical lattice this type of disorder leads to disorder-induced localization in 1D and 2D systems on a time scale t ∼ 1 s. For 3D lattices with 55 sites in each dimension and vacancy concentration 90%, the rotational excitations diffuse to the edges of the lattice and show no signature of Anderson localization. We examine the role of the long-range tunnelling amplitudes allowing for transfer of rotational excitations between distant lattice sites. Our results show that the long-range tunnelling has little impact on the dynamics in the diffusive regime but affects significantly the localization dynamics in lattices with large concentrations of vacancies, enhancing the width of the localized distributions in 2D lattices by more than a factor of 2.
Ultracold polar molecules, with their long-range electric dipolar interactions, offer a unique platform for studying correlated quantum many-body phenomena. However, realizing a highly degenerate quantum gas of molecules with a low entropy per particle is challenging. We report the synthesis of a low-entropy quantum gas of potassium-rubidium molecules (KRb) in a three-dimensional optical lattice. We simultaneously load into the optical lattice a Mott insulator of bosonic Rb atoms and a single-band insulator of fermionic K atoms. Then, using magnetoassociation and optical state transfer, we efficiently produce ground-state molecules in the lattice at those sites that contain one Rb and one K atom. The achieved filling fraction of 25% should enable future studies of transport and entanglement propagation in a many-body system with long-range dipolar interactions.
Optical lattices with one atom on each site and interacting via cold controlled collisions provide an efficient way to entangle a large number of qubits with high fidelity. It has already been demonstrated experimentally that this approach is especially suited for the generation of cluster states [O. Mandel et al., Nature 425, 937 (2003)] which reduce the resource requirement for quantum computing to the ability to perform single-qubit rotations and qubit read out. In this paper, we describe how to implement these rotations in one-dimensional and two-dimensional optical lattices without having to address the atoms individually with a laser field.