Strongly correlated gases of Rydberg-dressed atoms: quantum and classical dynamics G. Pupillo, 1 A. Micheli, 1 M. Boninsegni, 2, 1 I. Lesanovsky, 3 and P. Zoller 1 $^{1}$Institute for Theoretical Physics, University of Innsbruck, and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck, Austria $^{2}$Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2J1 $^{3}$School of Physics and Astronomy, University of Nottingham, Nottingham, UK We discuss techniques to generate long-range interactions in a gas of groundstate alkali atoms, by weakly admixing excited Rydberg states with laser light. This provides a tool to engineer strongly correlated phases with reduced decoherence from inelastic collisions and spontaneous emission. As an illustration, we discuss the quantum phases of dressed atoms with dipole-dipole interactions confined in a harmonic potential, as relevant to experiments. We show that residual spontaneous emission from the Rydberg state acts as a heating mechanism, leading to a quantum-classical crossover. PACS numbers: 32.80.Ee, 34.20.Cf, 03.75.-b arXiv:1001.0519v1 [cond-mat.quant-gas] 4 Jan 2010 There is currently significant interest in the physics of dipolar quantum degenerate gases [1]. Strong long- range dipole-dipole interactions promise the realization of novel many-body phases in neutral gases, such as self- assembled crystals [2], topological superfluids and quan- tum phases with hidden topological order [3]. The regime of strong dipolar couplings is easily accessible with inter- acting electric dipole moments, as realized in particu- lar in quantum gases with polar molecules prepared in their rovibrational ground state [4]. In contrast, quan- tum gases of ground state atoms typically interact via the much smaller magnetic interactions [5]. The question, therefore, is to what extent this regime of strong dipo- lar interactions can also be realized with present atomic gases experiments with alkali atoms. Here we propose and investigate a setup where the huge electric dipole moments d ∼ n 2 [6–8] of atomic Rydberg states with principal quantum number n are weakly admixed to the atomic ground state, thus providing an atomic gas of in- teracting effective electric dipoles comparable to the case of polar molecules. A central question, and the main dif- ference to the molecular case, is decoherence and heating mechanisms associated with spontaneous emission from Rydberg states, and possible inelastic collisions. Below we show that (i) dipolar crystals can be realized with Rydberg-dressed atoms confined to two dimensions, with negligible collisional losses, and (ii) spontaneous emission γ$_{r}$ provides an intrinsic heating mechanism, allowing the study of thermalization phenomena with full tunability of system parameters. We study the associated crystal melting with molecular dynamics calculations. The setup we have in mind is illustrated in Fig. 1: we propose to weakly couple with laser light the ground- state | g 〉 of each atom to a Stark-split Rydberg state | r 〉 with large dipole moment d$_{0}$ , in the kDebye. For large enough detuning Δ from resonance and interpar- ticle distances, interactions are of the dipole-dipole type V 3D int ∝ (Ω / Δ) $^{4}$d2 $_{0}$/r$^{3}$, with Ω the Rabi frequency. By confining the particles to a 2D plane using an optical field, the effective in-plane interactions V 2D int are then purely repulsive, with negligible collisional losses. This opens the way to the study of the many-body phases of 2D dipoles in these systems. As an illustration, we show the existence of mesoscopic supersolids and crystals with Rydberg-dressed atoms under realistic conditions of in-plane harmonic confinement, using exact quantum Monte-Carlo simulations. Residual spontaneous emis- sion γ$_{eff}$ ∼ (Ω / Δ) $^{2}$γ$_{r}$ from the Rydberg state introduces an intrinsic heating mechanism, driving the quantum phases into the classical regime. We study the quan- tum/classical crossover by means of molecular dynam- FIG. 1: (color online)(a) Sketch of the energy levels constitut- ing the Stark fan of an alkali metal atom exposed to an electric field. | g 〉 and | r 〉 are coupled by a laser with Rabi frequency Ω and (blue) detuning Δ. γ r is the spontaneous emission from | r 〉 , with momentum k R of the photon recoil. (b) BO poten- tials in the ( x − y )-plane in the dressed picture. R 0 is the resonant Condon point. The effective interaction potential V 3D int ( r ) is the higher-energy curve (red). Level crossings oc- cur for R n < R 0 . Inset: blow-up of V 3D int ( r ) (continuous line) compared to 1 /r 3 (dashed line). (c) Sketch of experimental setup: Rydberg-dressed atoms are confined to 2D by a strong confining laser beam, with dipoles polarized perpendicular to the plane. An effective spontaneous emission with rate γ eff provides for an intrinsic heating mechanism (see text). (a) (b) eF ΔE$_{n}$ ΔE$_{n}$ |r > |r > |r > |r' > |r >+ |r > |r' > |g > |g > |g > |r >+ |r > |g > |r' > |r'' > |g > n=19 GLYPH<endash.cap>10 0 1 2 2 4 6 3 r / R 0 10 GLYPH<endash.cap>4 GLYPH<endash.cap>5 0 Ω γ$_{r, }$k$_{R}$ Δ d$_{r}$ (c) R$_{n}$ / R 0 E /Δ 0 3 5 7 1 0 γ$_{eff, }$k$_{R}$