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arXiv:1806.08588 · Physical Review A

Decay-dephasing-induced steady states in bosonic Rydberg-excited quantum gases in an optical lattice

Mathieu Barbier, Andreas Geißler, Walter Hofstetter

Published Mar 5, 2019• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.99.033602

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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.
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.
We study the dynamics of bosonic atoms on a two-dimensional square lattice, where atomic interactions are long ranged with either a box or soft-core shape. The latter can be realized through laser dressing ground-state atoms to electronically excited Rydberg states. When the range of interactions is equal or larger than the lattice constant, the system is governed by an extended Bose-Hubbard model. We propose a quench process by varying the atomic hopping linearly across phase boundaries of the Mott insulator-supersolid and supersolid-superfluid phases. Starting from a Mott insulating state, the dynamical evolution of the superfluid order parameter exhibits a universal behavior at the early stage, largely independent of interactions. The dynamical evolution is significantly altered by strong, long-range interactions at later times. Particularly, we demonstrate that density wave excitation is important when the quench rate is small. Moreover, we show that the quench dynamics can be analyzed through time-of-flight images, i.e., measuring the momentum distribution and noise correlations.
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.
One of the major challenges in realizing a strongly interacting lattice gas using Rydberg states is the occurrence of avalanche loss processes. As these are directly proportional to the total Rydberg fraction, the commonly suggested solution is using far off-resonantly excited Rydberg states. We instead propose the realization of a correlated bosonic lattice gas at near-resonant excitation, where the total Rydberg fraction in the bulk is low due to the strong, interaction-driven effective detuning. Using real-space dynamical mean-field theory we show that its reduced effect at the boundary of a system can easily be compensated by considering a tailored beam waist of the driving Rabi laser. In this geometry we discuss the spectral properties at the crossover between the supersolid and the superfluid state and present the momentum-resolved spectral properties of the supersolid bulk. The latter results are obtained within an extended quasiparticle method which also yields a correction of the mean-field phase transition.
The work presented in this dissertation concerns dynamics of Rydberg atom lattices in the presence of noise and dissipation. Rydberg atoms possess a number of exaggerated properties, such as a strong van der Waals interaction. The interplay of that interaction, coherent driving and decoherence leads to intriguing non-equilibrium phenomena. Here, we study the non-equilibrium physics of driven atom lattices in the presence of decoherence caused by either laser phase noise or strong decay. In the first case, we compare between global and local noise and explore their effect on the number of excitations and the full counting statistics. We find that both types of noise give rise to a characteristic distribution of the Rydberg excitation number. The main method employed is the Langevin equation but for the sake of efficiency in certain regimes, we use a Markovian master equation and Monte Carlo rate equations, respectively. In the second case, we consider dissipative systems with more general power-law interactions. We determine the phase diagram in the steady state and analyse its generation dynamics using Monte Carlo rate equations. In contrast to nearest-neighbour models, there is no transition to long-range-ordered phases for realistic interactions and resonant driving. Yet, for finite laser detunings, we show that Rydberg atom lattices can undergo a dissipative phase transition to a long-range-ordered antiferromagnetic phase. We identify the advantages of Monte Carlo rate equations over mean field predictions. Having studied the dynamics of Rydberg atom lattices, we study an application of the strong interactions in such systems for quantum information processing. We investigate the coherent exchange of a single photon between a superconducting microwave cavity and a lattice of strongly interacting Rydberg atoms in the presence of local electric field fluctuations plaguing the cavity surface. We show that despite the increased sensitivity of Rydberg states to electric fields, as compared to ground state atoms, the Rydberg dipole-dipole interaction can be used to protect the system against the dephasing induced by the local noise. Using 1/f1/f1/f and laser phase noise models, we show that compared to the case with non-interacting atoms, our system exhibits longer coherence lifetimes and larger retrieval efficiency of the photon after storing into the atoms.
Abstract In the presence of strong dephasing noise the dynamics of Rydberg gases becomes effectively classical, due to the rapid decay of quantum superpositions between atomic levels. Recently a great deal of attention has been devoted to the stochastic dynamics that emerges in that limit, revealing several interesting features, including kinetically constrained glassy behaviour, self-similarity and aggregation effects. However, the non-equilibrium physics of these systems, in particular in the regime where coherent and dissipative processes contribute on equal footing, is yet far from being understood. To explore this we study the dynamics of a small one-dimensional Rydberg lattice gas subject to dephasing noise by numerically integrating the quantum master equation. We interpolate between the coherent and the strongly dephased regime by defining a generalised concept of a blockade length. We find indications that the main features observed in the strongly dissipative limit persist when the dissipation is not strong enough to annihilate quantum coherences at the dynamically relevant time scales. These features include the existence of a time-dependent Rydberg blockade radius, and a growth of the density of excitations which is compatible with the power-law behaviour expected in the classical limit.