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arXiv:1304.7802 · Physical Review A

Theoretical description of coherent doublon creation via lattice modulation spectroscopy

Andreas Dirks, Karlis Mikelsons, H. R. Krishnamurthy, James K. Freericks

Published Feb 10, 2014• 9 citations
arXivHTMLPDF

Abstract

Using a recently developed strong-coupling method, we present a comprehensive theory for doublon production processes in modulation spectroscopy of a three-dimensional system of ultracold fermionic atoms in an optical lattice with a trap. The theoretical predictions compare well to the experimental time traces of doublon production. For experimentally feasible conditions, we provide a quantitative prediction for the presence of a nonlinear ``two-photon'' excitation at strong modulation amplitudes.

DOI
10.1103/physreva.89.021602

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Using a recently developed strong-coupling method, we present a comprehensive theory for doublon production processes in modulation spectroscopy of a three-dimensional system of ultracold fermionic atoms in an optical lattice with a trap. The theoretical predictions compare well to the experimental time traces of doublon production. For experimentally feasible conditions, we provide a quantitative prediction for the presence of a nonlinear ``two-photon'' excitation at strong modulation amplitudes.
In the past fifteen years ultracold atoms confined to optical lattices, which are artificial crystals of light, have proven to be powerful tools in the study of strongly correlated many-body systems widely known from a condensed matter context. The detailed knowledge, high tunability and control of microscopic parameters has enabled the creation and control of highly non-trivial quantum systems for which a direct comparison of model calculations to experimental measurements is now possible. In order to gain precise information on the properties of ultracold gases in optical lattices, many powerful methods have been developed. In particular spectroscopic methods have enabled to probe different characteristic excitations. However, many fascinating properties of strongly interacting quantum many-body systems are not yet fully characterized. Therefore, this thesis explores further possibilities of lattice modulation spectroscopy which is a time-periodic modulation of the optical lattice amplitude. We theoretically investigate the response of different (mostly one-dimensional) cold atom systems to a lattice modulation by means of the time-dependent density matrix renormalization group method and different analytical approximations. In addition to the normal lattice modulation, we consider a superlattice modulation scheme where the lattice amplitude is modulated in a dimerized fashion, coupling to a certain class of excitations in the system. The lattice modulation spectroscopy is a versatile probe which we use to study different situations relevant for experimental applications. We show that a detection of signatures of the exotic bond order wave phase is feasible in a system of interacting fermions on a one-dimensional optical lattice with staggered energy offset. Moreover, we demonstrate that a temperature measurement of fermions confined to an optical lattice is possible as well as a determination of the interaction strength of bosonic atoms confined to a one-dimensional optical lattice. In addition, various excitations in all these systems are investigated in detail.
We theoretically study lattice modulation experiments with ultracold fermions in optical lattices. We focus on the regime relevant to current experiments when interaction strength is larger than the bandwidth and temperature is higher than magnetic superexchange energy. We obtain analytical expressions for the rate of doublon production as a function of modulation frequency, filling factor, and temperature. We use local density approximation to average over inhomogeneous density for atoms in a parabolic trap and find excellent agreement with experimentally measured values. Our results suggest that lattice modulation experiments can be used for thermometry of strongly interacting fermionic ensembles in optical lattices.
In the vicinity of a Feshbach resonance, a system of ultracold atoms in an optical lattice undergoes rich physical transformations which involve molecule formation and hopping of molecules on the lattice and thus goes beyond a single-band Hubbard model description. We explore theoretically the response of this system to a harmonic modulation of the magnetic field, and thus of the scattering length, across the Feshbach resonance. In the regime in which the single-band Hubbard model is still valid, we provide results for the doublon production as a function of the various parameters, such as frequency, amplitude, etc., that characterize the field modulation, as well as the lattice depth. The method may uncover a route towards the efficient creation of ultracold molecules and also provide an alternative to conventional lattice-depth-modulation spectroscopy.
We compute the integrated doublon production rate in response to a lattice modulation for two-component fermions in an optical lattice. We derive a general formula for the integrated intensity, valid in the presence of inhomogeneous potentials such as the trap, which gives the integrated intensity in terms of equal time correlation functions only. Such a formula is thus well suited for direct numerical calculations. We show that, in the limit of large repulsion for commensurate fillings, or for temperature ranges for which the hopping is incoherent, the integrated doublon spectrum is directly related to the nearest-neighbor spin-spin correlation function. We compute its temperature dependence in this regime using finite temperature quantum Monte Carlo calculation.
Motivated by the recent rapid development of the field of quantum gases in optical lattices, we present a comprehensive study of the spectrum of ultracold atoms in a one-dimensional optical lattice subjected to a periodic lattice modulation. Using the time-dependent density matrix renormalization group method, we study the dynamical response due to lattice modulations in different quantum phases of the system with varying density. For the Mott-insulating state, we identify several excitation processes, which provide important information about the density profile of the gases. For the superfluid, the dynamical response can be well described in a local density approximation. This simplification can be valuable in understanding the strong-correlated superfluid in a slow-varying harmonic potential. All these spectroscopic features of an inhomogeneous system can be used as a test for the validity of the Bose-Hubbard model in a parabolic trapping potential.
We theoretically consider noninteracting fermions confined to optical lattices and apply a lattice amplitude modulation that we choose to be either homogeneous or of superlattice geometry. We study the atom excitation rate to higher Bloch bands which can be measured by adiabatic band mapping. We find that the atom excitation rate shows a clear signature of the temperature-dependent Fermi distribution in the lowest band of the equilibrium lattice as excitations are quasimomentum resolved. Based on typical experimental parameters and incorporating a trapping potential, we find that thermometry of one- and two-dimensional systems is within the reach of present-day experiments. Our scheme is valid down to temperatures of a few percent of the hopping amplitude comparable to the N\'eel temperature in interacting systems.