Rydberg Physics

The field of Rydberg physics has witnessed a revival in the last decades, followed more recently by a rapid expansion into new directions. A Rydberg atom is an atom excited into a high energy level. Studies of Rydberg atoms have a long history, starting over 80 years ago with investigations of pressure shifts and broadening of Na and K Rydberg levels by rare gases. Their detection in dilute interstellar region helped fuel the growing interest in Rydberg physics. In such dilute environment, highly excited atoms can live long enough to decay radiatively, and can be sensitive to weak magnetic fields of a few μG and thus act as magnetic probes of interstellar media.

alternate text A Rydberg atom resembles a hydrogen atom, the effect of the core electrons accounted for by the quantum defect δ For alkali atoms in a Rydberg state, the energy of the Rydberg level described by the principal quantum number n is given by

En = I - Ry / ν 2 where ν = n - δ.

While the ionization potential I and the Rydberg constant Ry depend on the atom, δ also depend on the Rydberg level considered: for example, for Rb, I = 33,690.798 cm-1 and Ry = 109,736.605 cm-1, while δ = 3.131 (ns 1/2), 2.655 (np 1/2), 2.641 (np 3/2), and 1.347 (nd 3/2,5/2)

Rydberg atoms posses exaggerated properties which scale rapidly with the principal quantum number n. For example, their size and dipole moment scale as n2, while their polarizability and radiative lifetime scale as n7 and n3, respectively. Together with the small spacing between Rydberg levels (scaling as n-3 ), these lead to large interactions between Rydberg atoms, scaling as n 4/ R3 and n11 /R6 for dipole-dipole and van der Waals types, respectively.

In our group, we study the effect of these strong interactions on the behavior of ultracold gases. For example, we predicted the so-called blockade mechanism; in an ensemble containing many atoms and under the right conditions, no more than one can be excited into a Rydberg state. We identified two types of blockade, namely the dipole blockade and the van der Waals (vdW) blockade. The underlying principle of both mechanisms is the same; strong Rydberg-Rydberg interactions shift the energy levels out of resonance (see Fig. beside). So, one atom can be resonantly excited into a Rydberg state, but additional Rydberg excitations are prevented by the large shifts.

alternate text The off-resonance condition depends on the laser bandwidth γ, and can serve to define a blockade or domain radius Rd (e.g., the smallest separation where the double-excitation can still take place). If the Rydberg-Rydberg interaction Δ shifts the energy of a pair by more than γ, atom pairs cannot be excited, and within this domain with R<R d, only one excitation can occur. As shown in the sketch beside, a laser illuminating a large atomic sample will generate several domains of radius Rd in which no more than one atom can be excited, and the number of Rydberg excitations is therefore suppressed by the blockade mechanism. Together with our UConn experimental collaborators, we have observed and explained such phenomena. Because a Rydberg atom excited near the edge of a domain has a larger probability of being closer to another Rydberg atom in a neighboring domain, the Rydberg-Rydberg energy shift ϵ becomes larger near the edge, leading to a decreasing excitation probability |ce|2. We proposed to use the strong Rydberg-Rydberg interactions as well as the blockade mechanism for quantum information processing (see Quantum Information Science for more details).

The strong interactions between Rydberg atoms have other consequences. In our group, we are also exploring how two Rydberg atoms could be bound and form extremely large molecules. We predicted the existence of molecules so extended (even in the μm range) that we call them macrodimers. They have been observed experimentally first by the group of Jim Shaffer at the University of Oklahoma. Since then, we have generalized our treatment and predicted the existence of bound states of three Rydberg atoms, now named macrotrimers.

Another interesting aspect of Rydberg physics is the possibility of using a laser detuned far enough from the Rydberg level as to have a very small probability of being excited. The state |g⟩ of the ground state atom is therefore dressed by the excited Rydberg state |r⟩, and can be written as

|ψ⟩ = a|g⟩ + b|r⟩ ,

where |a|2 + |b|2 = 1, with |b|2= |Ω|2 /2Δ2. Here, Ω is the Rabi frequency corresponding to the laser coupling between |g⟩ and |r⟩, and Δ is the detuning from |r⟩. We are exploring how a Rydberg-dressed atom interact with other atoms or molecules. For example, we showed that a Rydberg-dressed atom A approaching a molecule BC could be used to tune a chemical reaction: the little bit of Rydberg component |b|2 increases the polarizability of the atom, which in turn modifies the long-range van der Waals interaction between the atom and the molecule. By carefully tuning the value of b, once can modify the reaction rate A + BC → AB + C significantly.