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Theoretical study of Photon-Assisted Tunneling of Ultracold Atoms in a Triple-well Potential

Pontificia Universidad Católica de Chile. Instituto de Física, E. Aguilera-Valdés

Published Jan 1, 2024• 0 citations
Publisher

Abstract

The thesis studies Photon-Assisted Tunneling (PAT) in a system of ultracold atoms in a triple-well potential, utilizing Bose-Hubbard and Gross-Pitaevskii models. Simulations reveal that an ac-driving field influence tunneling dynamics, enabling quantum self-trapping and PAT. The study extends to open quantum systems, analyzing PT-symmetric setups with balanced gain and loss, showcasing PAT’s role in quantum control and potential applications in ultracold atom systems and quantum optics.

DOI
10.7764/tesisuc/fis/102216

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The thesis studies Photon-Assisted Tunneling (PAT) in a system of ultracold atoms in a triple-well potential, utilizing Bose-Hubbard and Gross-Pitaevskii models. Simulations reveal that an ac-driving field influence tunneling dynamics, enabling quantum self-trapping and PAT. The study extends to open quantum systems, analyzing PT-symmetric setups with balanced gain and loss, showcasing PAT’s role in quantum control and potential applications in ultracold atom systems and quantum optics.
The correlated atoms in a tilted optical lattice driven by an ac field are studied within the Hubbard model. By making use of both photon-assisted tunneling and coherent destructive tunneling effects, we can move a pair of strongly correlated atoms in the lattice via manipulating the global amplitude of the driving field. We propose a scheme for creating entanglement between the particle pair and a single particle through interacting oscillations. Our model may provide a new building block for investigating quantum computing and quantum information processing with ultracold atoms in optical lattices.
We describe the coherent atomic tunneling between two Bose-Einstein condensates confined in a double-well potential, whose zero-point energies are modulated by a small oscillation of the barrier-laser position. The coupled-mode equations derived from the Gross-Pitaevskii equation describe the dynamics in terms of the population imbalance as a function of the modulation amplitude of the zero-point energies normalized by the modulation frequency. It is predicted that the modulation of the zero-point energies induces the laser-assisted tunneling (LAT) and the resonant peaks of the LATs are remarkably shifted in energy by the nonlinearity due to the many-body interactions. It is also shown that the threshold of the nonlinear self-interaction for the spontaneous symmetry breaking is modified by the potential modulations. These features are qualitatively explained by considering that the coupling (or tunneling) coefficient K is effectively given by $\stackrel{\ensuremath{\rightarrow}}{K}{K}_{n}^{\mathrm{eff}}{=J}_{n}{(E}_{\ensuremath{\omega}}/\ensuremath{\omega})K$ for the nthn\mathrm{th}nth LAT under the influence of the potential modulations, where ${E}_{\ensuremath{\omega}}$ and \ensuremath{\omega} are the modulation amplitude of the zero-point energies and the modulation frequency, respectively.
We review our theoretical advances in quantum tunneling of Bose-Einstein condensates in optical traps and in microcavities. By employing a real physical system, the frequencies of the pseudo Goldstone modes in different phases between two optical traps are studied respectively, which are the crucial feature of the non-Abelian Josephson effect. When the optical lattices are under gravity, we investigate the quantum tunneling in the “Wannier-Stark localization” regime and “Landau-Zener tunneling” regime. We finally get the total decay rate and the rate is valid over the entire range of temperatures. At high temperatures, we show how the decay rate reduces to the appropriate results for the classical thermal activation. At intermediate temperatures, the results of the total decay rate are consistent with the thermally assisted tunneling. At low temperatures, we obtain the pure quantum tunneling ultimately. And we study the alternating-current and direct-current (ac and dc) photonic Josephson effects in two weakly linked microcavities containing ultracold two-level atoms, which allows for direct observation of the effects. This enables new investigations of the effect of many-body physics in strongly coupled atom-cavity systems and provides a strategy for constructing novel interference devices of coherent photons. In addition, we propose the experimental protocols to observe these quantum tunneling of Bose-Einstein condensates.
In this thesis, I present experiments on making and probing strongly correlated gases of ultracold atoms in an optical lattice with engineered potentials and dynamics. The quantum gas microscope first developed in our lab enables single-site resolution imaging and manipulation of atoms in a two-dimensional lattice, offering an ideal platform for quantum simulation of condensed matter systems. Here we demonstrate our abilities to generate optical potential with high precision and high resolution, and engineer coherent dynamics using photon assisted tunneling. We also create a system of bilayer quantum gases that brings new imaging capabilities and extends the possible range of our quantum simulation.
This thesis summarizes the research work we did in the past years, which focuses on the theoretical study of quantum effects of ordered atomic structures interacting with the quantum electric field of an optical resonator. Within this work we investigated the quantum properties of the light at the cavity output, emitted by this kind of system, and the quantum state of the atoms confined by the light fields of the cavity mode. Following one possible partition, we have organized the thesis in two parts. The first part of the thesis is devoted to the quantum properties of the light at the output of optical cavities, in which atoms are confined. After a brief introduction on the basics of atom-photon interactions, we show theoretically, that two atomic dipoles in a resonator can behave as a quantum non-linear medium, whose response can be controlled through the interactomic distance of the atoms inside the resonator. We identify the parameter regime, for which the system operates as a parametric amplifier, based on the atoms' collective dipole cascade emission. Moreover we also determine the corresponding field squeezing spectrum at the cavity output. These dynamics could be observed as a result of self-organization processes of laser-cooled atoms in resonators. The second part of the thesis studies the quantum ground state of an ultracold atomic gas trapped inside an optical resonator by the mechanical effects of atom-photon interactions. Due to the strong coupling regime, the ultracold atomic gas feels a quantum potential, where the fluctuations at the single photon level may be relevant in determining the trapping conditions. This potential depends on the atomic distribution, which at the same time determines the intracavity field amplitude. Here, after a brief introduction on ultracold atoms in optical lattices, we study the low temperature physics of an ultracold atomic gas in the quantum potential formed inside a pumped cavity, by mapping the dynamics to an effective Bose-Hubbard model. We predict the existence of non-compressible states of the atomic gas, and determine a phase diagram as a function of the cavity parameters. Novel effects are encountered, such as the existence of overlapping stability regions corresponding to competing insulator-like states when the laser pumps the cavity, to provide one example out of many. At the end of the thesis a concluding chapter presents some general outlooks to this thesis work.
This thesis presents quantum simulation of strongly-correlated systems beyond standard Hubbard models, using ultracold fermionic potassium atoms in both static and periodically-driven optical superlattices. For this study, we utilize a three-dimensional optical lattice setup, controlling particle interactions via magnetic Feshbach resonances and tunneling between lattice sites through optical lattice intensity. High-resolution absorption imaging combined with radio-frequency spectroscopy distinguishes between singly and doubly occupied sites. To enhance our systems capabilities beyond the standard Hubbard model, we extend the apparatus with an in-plane optical superlattice, creating a bi-chromatic structure by superposition of two optical lattices with commensurate lattice spacings. Using a phase locked loop with an environmental feed forward, we create an excellent phase stability of the superlattice exceeding 3 mrad. This precision allows us to explore both static and periodically-driven one-dimensional tight-binding models with strong interactions. We characterize the static superlattice through radio-frequency spectroscopy and Rabi oscillations, and validate the experimental data against theoretical calculations. In a tilted superlattice configuration, we successfully prepare and detect repulsively bound atom pairs, representing a highly excited eigenstate of the system. Furthermore, we demonstrate control over pair tunneling dynamics in a double-well potential using Floquet engineering, employing a low-noise periodic modulation of the optical superlattice tilt. Using an adiabatic band mapping technique, we directly observe the tunneling dynamics in the driven superlattice. We realize dynamic localization in quarter-filled wells and density-assisted tunneling up to the third harmonic order in half-filled wells. We observe a crossover from density-assited tunneling to dominant pair tunneling by tuning the effective interactions. Remarkably, the pair tunneling is not only enhanced relative to the suppressed single-particle tunneling but also exceeds the superexchange rate of a static double-well by more than a factor of two. This opens the possibility to study many-body systems with dominant pair tunneling, that extend beyond the standard Hubbard model.