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arXiv:2109.04917 · Physical Review A

Supersolid phases of ultracold bosons trapped in optical lattices dressed with Rydberg p states

Mathieu Barbier, Henrik Lütjeharms, Walter Hofstetter

Published Jan 31, 2022• 15 citations
arXivHTMLPDF

Abstract

Engineering quantum phases with spontaneously broken symmetries is a major goal of research in different fields. Trapped ultracold Rydberg-excited atoms in optical lattices are a promising platform for realizing quantum phases with broken lattice translational symmetry since they are interacting over distances larger than the lattice constant. Although numerous theoretical works on trapped Rydberg-excited gases have predicted such phases, in particular, density wave or supersolid phases, their experimental observation proves to be difficult due to challenges such as scattering processes and the limited experimentally achievable coupling strength. Most of these previous studies have focused on isotropically interacting gases dressed with Rydberg $s$ states, while the effect of anisotropic interactions due to Rydberg-excited $p$ states in trapped quantum gases remains much less investigated. Additionally, it was shown that the excitation scheme used to excite Rydberg $p$ states possesses advantages regarding achievable coupling strengths and limitation of scattering processes compared to its $s$-state counterpart, which makes the investigation of Rydberg $p$-state dressed quantum gases even more interesting. In the present work we study the extended two-component Bose-Hubbard model, realized with a bosonic quantum gas with Rydberg-excited $p$ states trapped in an optical lattice, within the Gutzwiller mean-field theory. We compute the ground-state phase diagram and investigate its different regimes. By comparison to the phase diagram of the isotropic case, we find the anisotropic interaction to be more advantageous for the observation of supersolid phases.

DOI
10.1103/physreva.105.013326

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Rydberg-dressed ground state atoms are atoms with an electron off-resonantly excited to a very high energy state, i.e., a state of high principal quantum number n ≫ 1. This thesis investigates the quantum dynamics of interacting Rydberg-dressed ground state atoms trapped in several multi-well potential traps. Rydberg atoms are atoms with exaggerated properties. One of their most interesting properties is that they exhibit a strong and long-ranged interaction that can be tuned leading to a variety of different quantum behaviours. My work focuses on studying the effects of these interacting atoms when loaded in multi-well potential traps. Generally, multi-well systems are considered as the simplest example of a finite optical lattice structure. For this reason, this thesis covers three research topics that examine the effects of long-range interaction on Rydberg-dressed atoms trapped in several potential confinements. I begin, in the introduction, by discussing the theoretical background of relevance to this work. It starts with presenting the physics of Bose-Einstein condensate. Then, the fundamentals of the interaction between two-level atom and light are analytically studied. This study has the purpose of understanding both; the dressed interacting atoms and optical lattices. The definition, characteristics, and the nature of the interaction between Rydberg atoms are analysed afterwards. The second chapter examines the dynamics of an ensemble of interacting Rydberg- dressed atoms trapped in static, i.e., time-independent, multi-well potentials using a mean-field theoretical approach. I choose one-dimensional double- and triple-well in addition to a two-dimensional quadruple-well potentials. The time-dependent non-linear Gross-Pitaevskii equation is used to numerically explore the ensemble’s quantum dynamics. Solving the dynamical differential equations along with tuning the strength of the applied long-range interaction shows that the behaviour of non-interacting Rydberg-dressed atoms does not differ conceptually according to the geometry of the trapping potential. However, this changes when the interactions are switched on where the shape of the confinement leads to interesting outcomes especially in the non-linear interacting limit, such as macroscopic quantum self-trapping. After investigating an ensemble of interacting Rydberg-dressed atoms in static multi-well potential traps, the second research topic examines the dynamical evolution of these atoms when loaded in a finite optical lattice using the extended Bose-Hubbard model. In this chapter, the atoms ensemble is assumed to be in a superfluid state where I investigate both, the order parameter when the Rydberg excitation laser is applied and the interference pattern of the condensates in different dimensions. The study shows the emerging long-range interactions lead to a rapid collapse of the superfluid order parameter and in general allow only for partial revivals. In addition, the interference experiments can directly reveal the interaction between Rydberg-dressed atoms. In the fourth chapter, the dynamics of Rydberg-dressed atoms trapped in a dynamical, i.e., time-dependent, potential confinement is presented. The dynamical trap is constructed such that it begins as a harmonic oscillator and ends as a double- well potential. The analysis investigates an ensemble of contact-interacting atoms via the time-dependent non-linear GP equation.

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Engineering quantum phases with spontaneously broken symmetries is a major goal of research in different fields. Trapped ultracold Rydberg-excited atoms in optical lattices are a promising platform for realizing quantum phases with broken lattice translational symmetry since they are interacting over distances larger than the lattice constant. Although numerous theoretical works on trapped Rydberg-excited gases have predicted such phases, in particular, density wave or supersolid phases, their experimental observation proves to be difficult due to challenges such as scattering processes and the limited experimentally achievable coupling strength. Most of these previous studies have focused on isotropically interacting gases dressed with Rydberg sss states, while the effect of anisotropic interactions due to Rydberg-excited ppp states in trapped quantum gases remains much less investigated. Additionally, it was shown that the excitation scheme used to excite Rydberg ppp states possesses advantages regarding achievable coupling strengths and limitation of scattering processes compared to its sss-state counterpart, which makes the investigation of Rydberg ppp-state dressed quantum gases even more interesting. In the present work we study the extended two-component Bose-Hubbard model, realized with a bosonic quantum gas with Rydberg-excited ppp states trapped in an optical lattice, within the Gutzwiller mean-field theory. We compute the ground-state phase diagram and investigate its different regimes. By comparison to the phase diagram of the isotropic case, we find the anisotropic interaction to be more advantageous for the observation of supersolid phases.
Extended Hubbard models have proven to bear novel phases of matter, but their experimental realization remains challenging. In this work we propose to use bosonic quantum gases dressed with molecular bound states in Rydberg interaction potentials for the observation of these quantum states. We study the molecular Rabi coupling with respect to the effective principal quantum number and trapping frequency of the ground-state atoms for various molecular potentials of rubidium and potassium, and the hereby resulting dressed interaction strength. Additionally, we propose a two-color excitation scheme which significantly increases the dressed interaction and cancels otherwise-limiting ac Stark shifts. We study the various equilibrium phases of the corresponding extended Bose-Hubbard model by means of the cluster Gutzwiller approach and perform time evolution simulations via the Lindblad master equation. We find a supersolid phase by slowly ramping the molecular Rabi coupling of an initially prepared superfluid and discuss the role of dissipation.
Recent experiments with ultracold Rydberg-excited atoms have shown that long-range interactions can give rise to spatially ordered structures. Observation of crystalline phases in a system with Rydberg atoms loaded into an optical lattice seems also within reach. Here we investigate a bosonic model on a triangular lattice suitable for description of such experiments. Numerical simulations based on bosonic dynamical mean-field theory reveal a rich phase diagram with different supersolid phases. Comparison with the results obtained for a square lattice geometry shows qualitatively similar results in a wide range of parameters; however, on a triangular lattice we do not observe the checkerboard supersolid. Moreover, unlike on a square lattice, we did not find a phase transition from uniform superfluid to supersolid induced by increase of the hopping amplitude on a triangular lattice. Based on our results, we propose an intuitive interpretation of the nature of different supersolid phases. We also propose parameters for the experimental realization.
We investigate the possibility of realizing supersolid quantum phases in bosonic Rydberg-excited quantum lattice gases in the presence of nonunitary processes, by simulating the dynamical evolution starting from initial preparation in nondissipative equilibrium states. Within Gutzwiller theory, we first analyze the many-body ground state of a bosonic Rydberg-excited quantum gas in a two-dimensional optical lattice for variable atomic hopping rates and Rabi detunings. Furthermore, we perform time evolution of different supersolid phases using the Lindblad-master equation. With the inclusion of two different nonunitary processes, namely, spontaneous decay from a Rydberg state to the ground state and dephasing of the addressed Rydberg state, we study the effect of nonunitary processes on those quantum phases and observe long-lived states in the presence of decay and dephasing. We find that long-lived supersolid quantum phases are observable within a range of realistic decay and dephasing rates, while high rates cause any initial configuration to homogenize quickly, preventing possible supersolid formation.
Abstract The experimental realization of Rydberg dressing technology in ultracold atomic systems provides another superior platform for studying novel states of matter and macroscopic quantum phenomena. In this work, based on the mean-field theory, we have investigated the ground-state phases of a two-component Bose–Einstein condensate with Rydberg interaction and confined in a toroidal trap. The effects of the Rydberg interaction and external potential, especially the Rydberg blockade radius, on the ground-state structure of such a system have been investigated in full parameter space. Our results show that the Rydberg blockade radius, which can be regarded as another controllable parameter, can be used to obtain a variety of ground-state phases. More interestingly, it is found that for weak Rydberg interactions, the Rydberg blockade radius breaks the spontaneous rotational symmetry of the system, leading to the formation of a discrete unit cell structure. For strongly interacting cases, it can be used to realize different orders of discrete rotational symmetry breaking.
Interacting ultracold atomic quantum gases provide an ideal test bed to study strongly correlated quantum matter. The interactions between atoms in such an ultracold quantum gas are typically short-ranged and well described by an effective contact potential. Introducing longer-range interactions promises the realization of novel quantum phases which are absent in systems with only short-range interactions. Trapped atoms, resonantly laser-coupled to highly excited, strongly interacting Rydberg states have been proposed as a versatile platform to realize such long-range interacting quantum matter. In a first experiment presented in this thesis, we combined the single-atom-sensitive local preparation and detection enabled by a quantum gas microscope to prepare and microscopically characterize an ensemble of rubidium-87 atoms trapped in an optical lattice in the regime of strong Rydberg blockade. There, we observe collectively enhanced optical coupling in an effective two-level system, the so-called “superatom”, and infer the presence of entanglement. Detuned optical coupling to Rydberg states, termed “Rydberg dressing”, has been proposed as an alternative approach to induce long-range interactions. Rather than directly exciting an atom to a Rydberg state, the properties of the latter are admixed to a ground state, which consequently acquires long-range interactions. In the context of this thesis, we have designed a laser system in the ultraviolet spectral range to admix Rydberg P-state character to the ground state of atoms in an optical lattice. In an emerging Ising quantum magnet, the presence of Rydberg-dressed interactions was demonstrated by an interferometric technique combined with spatially resolved spin correlation measurements. The theoretically predicted tunability of the isotropy and range of the interaction were confirmed experimentally. While these initial measurements exhibited unexpected dissipation, in a subsequent experiment in a one-dimensional spin chain this dissipation was overcome. We substantiated the improved coherence times by tracking the time evolution of the magnetization upon suddenly switching on interactions and observing coherent collapse and revival dynamics, one of the hallmarks of coherent quantum evolution. Our results establish Rydberg-dressed interactions in ultracold gases and pave the way to realize and study novel exotic quantum phases.
Rydberg-dressed ground state atoms are atoms with an electron off-resonantly excited to a very high energy state, i.e., a state of high principal quantum number n ≫ 1. This thesis investigates the quantum dynamics of interacting Rydberg-dressed ground state atoms trapped in several multi-well potential traps. Rydberg atoms are atoms with exaggerated properties. One of their most interesting properties is that they exhibit a strong and long-ranged interaction that can be tuned leading to a variety of different quantum behaviours. My work focuses on studying the effects of these interacting atoms when loaded in multi-well potential traps. Generally, multi-well systems are considered as the simplest example of a finite optical lattice structure. For this reason, this thesis covers three research topics that examine the effects of long-range interaction on Rydberg-dressed atoms trapped in several potential confinements. I begin, in the introduction, by discussing the theoretical background of relevance to this work. It starts with presenting the physics of Bose-Einstein condensate. Then, the fundamentals of the interaction between two-level atom and light are analytically studied. This study has the purpose of understanding both; the dressed interacting atoms and optical lattices. The definition, characteristics, and the nature of the interaction between Rydberg atoms are analysed afterwards. The second chapter examines the dynamics of an ensemble of interacting Rydberg- dressed atoms trapped in static, i.e., time-independent, multi-well potentials using a mean-field theoretical approach. I choose one-dimensional double- and triple-well in addition to a two-dimensional quadruple-well potentials. The time-dependent non-linear Gross-Pitaevskii equation is used to numerically explore the ensemble’s quantum dynamics. Solving the dynamical differential equations along with tuning the strength of the applied long-range interaction shows that the behaviour of non-interacting Rydberg-dressed atoms does not differ conceptually according to the geometry of the trapping potential. However, this changes when the interactions are switched on where the shape of the confinement leads to interesting outcomes especially in the non-linear interacting limit, such as macroscopic quantum self-trapping. After investigating an ensemble of interacting Rydberg-dressed atoms in static multi-well potential traps, the second research topic examines the dynamical evolution of these atoms when loaded in a finite optical lattice using the extended Bose-Hubbard model. In this chapter, the atoms ensemble is assumed to be in a superfluid state where I investigate both, the order parameter when the Rydberg excitation laser is applied and the interference pattern of the condensates in different dimensions. The study shows the emerging long-range interactions lead to a rapid collapse of the superfluid order parameter and in general allow only for partial revivals. In addition, the interference experiments can directly reveal the interaction between Rydberg-dressed atoms. In the fourth chapter, the dynamics of Rydberg-dressed atoms trapped in a dynamical, i.e., time-dependent, potential confinement is presented. The dynamical trap is constructed such that it begins as a harmonic oscillator and ends as a double- well potential. The analysis investigates an ensemble of contact-interacting atoms via the time-dependent non-linear GP equation.