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arXiv:cond-mat/0205169 · Physical review. B, Condensed matter

Mott insulators in strong electric fields

Subir Sachdev A, K. Sengupta, S. M. Girvin

Published Aug 30, 2002• 214 citations
arXivHTMLPDF

Abstract

Recent experiments on ultracold atomic gases in an optical lattice potential have produced a Mott insulating state of ${}^{87}\mathrm{Rb}$ atoms. This state is stable to a small applied potential gradient (an ``electric'' field), but a resonant response was observed when the potential energy drop per lattice spacing $(E),$ was close to the repulsive interaction energy (U) between two atoms in the same lattice potential well. We identify all states which are resonantly coupled to the Mott insulator for $E\ensuremath{\approx}U$ via an infinitesimal tunneling amplitude between neighboring potential wells. The strong correlation between these states is described by an effective Hamiltonian for the resonant subspace. This Hamiltonian exhibits quantum phase transitions associated with an Ising density wave order and with the appearance of superfluidity in the directions transverse to the electric field. We suggest that the observed resonant response is related to these transitions and propose experiments to directly detect the order parameters. The generalizations to electric fields applied in different directions and to a variety of lattices should allow study of numerous other correlated quantum phases.

DOI
10.1103/physrevb.66.075128

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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.
In this thesis I report on experiments that enter a new regime in the many body physics of ultracold atomic gases. A Bose-Einstein condensate is loaded into a three-dimensional optical lattice potential formed by a standing wave laser light field. In this novel quantum system we have been able to both realize a quantum phase transition from a superfluid to a Mott insulator, and to observe the collapse and revival of a macroscopic matter wave field. Quantum phase transitions are driven by quantum fluctuations and occur, even at zero temperature, as the relative strength of two competing energy terms in the underlying Hamiltonian is varied across a critical value. In the first part of this work I report on the observation of such a quantum phase transition in a Bose-Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. In the superfluid ground state, each atom is spread-out over the entire lattice, whereas in the Mott insulating state, exact numbers of atoms are localized at individual lattice sites. We observed the reversible transition between those states and detected the gap in the excitation spectrum of the Mott insulator. A Bose-Einstein condensate is usually described by a macroscopic matter wave field. However, a quantized field underlies such a "classical" matter wave field of a Bose-Einstein condensate. The striking behavior of ultracold matter due to the field quantization and the nonlinear interactions between the atoms is the focus of the second part of this work. The matter wave field of a Bose-Einstein condensate is observed to undergo a series of collapses and revivals as time evolves. Furthermore, we show that the collisions between individual pairs of atoms lead to a fully coherent collisional phase shift in the corresponding many-particle state, which is a crucial cornerstone of proposed novel quantum computation schemes with neutral atoms. With these experiments we enter a new field of physics with ultracold quantum gases. In this strongly correlated regime, interactions between atoms dominate the behavior of the many-body system such that it can no longer be described by the usual theories for weakly interacting Bose gases. This novel quantum system offers the unique possibility to experimentally address fundamental questions of modern solid state physics, atomic physics, quantum optics, and quantum information.
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We study the phase diagram of ultracold bosons in an optical lattice near a Feshbach resonance. Depending on the boson density, the strength of the optical-lattice potential and the detuning from resonance, the ground state can be a Mott insulator, a superfluid phase with both an atomic and a molecular condensate, or a superfluid phase with only a molecular condensate. Mott insulator to superfluid transitions can be induced either by decreasing the strength of the optical-lattice potential or by varying the detuning from the Feshbach resonance. Quite generally, we find that for a commensurate density the ground state may undergo several insulator-superfluid or superfluid-insulator transitions as the magnetic field is varied through the resonance.