Coherent Population Trapping with Controlled Interparticle Interactions

Abstract

We investigate Coherent Population Trapping in a strongly interacting ultracold Rydberg gas. Despite the strong van der Waals interactions and interparticle correlations, we observe the persistence of a resonance with subnatural linewidth at the single-particle resonance frequency as we tune the interaction strength. This narrow resonance cannot be understood within a meanfield description of the strong Rydberg-Rydberg interactions. Instead, a many-body density matrix approach, accounting for the dynamics of interparticle correlations, is shown to reproduce the observed spectral features.PACS numbers: 42.50. Gy,42.50.Ct,32.80.Ee Coherent population trapping (CPT), i.e. the population of a quantum state decoupled from a resonant light field, serves as a paradigm for a quantum interference effect [1]. First observed in 1976 [2], CPT with its related phenomena electromagnetically induced transparency (EIT) [3,4] and stimulated Raman adiabatic passage (STIRAP) [5] has provided the basis for a large variety of effects and applications in many areas of physics, such as high-resolution spectroscopy, coherent control, metrology, quantum information and quantum gases. While CPT, EIT and STIRAP are generally described in terms of isolated single-atom interactions with coherent light fields, the situation becomes more involved when interactions between the particles need to be considered.To gain initial insights into the effects of interactions on the quantum interference in CPT, consider two atoms with a three-level ladder structure with states |1 , |2 and |3 as shown in Fig. 1(a). The atoms are exposed to two resonant coherent light fields and interact only if both of them are in the highly excited atomic state |3 . In the case of non-interacting atoms the population accumulates in the two-body product state of the single-particle dark state |d which is a coherent superposition of |1 and |3 [1]. This state is defined as the eigenstate of the total Hamiltonian with vanishing coupling to the coherent light field. When turning on the interparticle interaction this state is no longer a dark state as it is no longer an eigenstate of the total Hamiltonian. As pointed out in [6], the two interacting atoms, nevertheless, possess two dark states |d ± . These states are dissipative due to the admixture of the intermediate, decaying state |2 , but are significantly populated by optical pumping. While these states have dissipative character, they do not contain the state |33 and are, thus, immune to interactions.In a first approach to a many-particle system one could apply a meanfield model by replacing many-body opera- PSfrag replacementsFIG. 1: (a) Excitation scheme ( 87 Rb). Ω1 and Ω2 are the Rabi frequencies at 780 and 480 nm, respectively, δ is the detuning of the upper transition; (b) calculated Rydberg state population, produced by the two-step sequence described in the text. The upper panel shows the result of a meanfield calculation, which predicts a strong shift and broadening of the resonance line. On the contrary, the...

Antiferromagnetic long-range order in dissipative Rydberg lattices

“…Such three-level excitation schemes are utilised in numerous Rydberg atom experiments, either exploring interaction effects in the strong excitation regime (Ω 1 > Ω 2 ) [33][34][35][36] or quantum optics applications in the opposite limit [37][38][39][40]. As a specific example, laser excitation of Rb(35S 1/2 ) Rydberg states via the intermediate Rb(5P 1/2 ) state with Ω 1 = 0.5γ = 4Ω 2 yields p 0 ≈ 0.9, upon accounting for the small but nonnegligible Rydberg state decay.…”

Effective dynamics of strongly dissipative Rydberg gases

“…In this regime, which has been studied experimentally in Refs. [33,34,35,36,37,38,39], atoms are modelled by coherently driven and interacting three-level systems. Dissipation enters through a fast (radiative) decay of the middle level to the lower one.…”

An experimental approach for investigating many-body phenomena in Rydberg-interacting quantum systems

“…8 (a), with: |1 ≡ |5S 1/2 , F = 2 , |2 ≡ |5P 3/2 , F = 3 , and |3 ≡ |40S 1/2 . For simplicity we moreover restrict ourselves to a regime of experimental parameters in which Rydberg-Rydberg interaction effects on the EIT can be neglected [60][61][62]. We prepare a cigar shaped Gaussian cloud (σ radial = 75± 3 µm, σ axial = 280±10 µm) with N ≈ 2.4×10 5 atoms and a peak atomic density ρ = 2.2×10 9 cm −3 .…”