Consequences of Zeeman Degeneracy for van der Waals Blockade between Rydberg Atoms

By Thomas G. Walker, Mark Saffman. 2007

215 citations recorded by the source corpus.

We analyze the effects of Zeeman degeneracies on the long-range interactions between like Rydberg atoms, with particular emphasis on applications to quantum-information processing using the van der Waals blockade. We present a general analysis of how degeneracies affect the primary error sources in blockade experiments, emphasizing that blockade errors are sensitive primarily to the weakest possible atom-atom interactions between the degenerate states, not the mean interaction strength. We present explicit calculations of the van der Waals potentials in the limit where the fine-structure interaction is large compared to the atom-atom interactions. The results are presented for all potential angular momentum channels involving $\mathit{s}$, $\mathit{p}$, and $\mathit{d}$ states. For most channels there are one or more combinations of Zeeman levels that have extremely small dipole-dipole interactions and are therefore poor candidates for effective blockade experiments. Channels with promising properties are identified and discussed. We also present numerical calculations of Rb and Cs dipole matrix elements and relevant energy levels using quantum defect theory, allowing for convenient quantitative estimates of the van der Waals interactions to be made for principal quantum numbers up to 100. Finally, we combine the blockade and van der Waals results to quantitatively analyze the angular distribution of the blockade shift and its consequence for angular momentum channels and geometries of particular interest for blockade experiments with Rb.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/b89da4b961abe55db484cb82f8d9fd4bb34cdbd1

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Citations in the corpus

A Rydberg quantum simulator (2009, background): “Furthermore, corrections to a pure van der Waals interaction because of resonant dipole–dipole coupling”
Observation of Rydberg blockade between two atoms (2008, background): “87 Rb atoms excited to the 79 d 5/2 state experience a Forster interactio”
Observation of collective excitation of two individual atoms in the Rydberg blockade regime (2008, methodology): “The state 58 d 3/2 was chosen because of the existence of a quasi-degeneracy between the two-atom states (58 d 3/2 ,58 d 3/2 ) and (60 p 1/2 ,56 f 5/2 ) , also called a Forster resonanc”
Observation of coherent many-body Rabi oscillations (2012, background): “[25], while the reduced matrix element is approximated by 〈r〉 = 0.”
Experimental investigations of dipole–dipole interactions between a few Rydberg atoms (2016, background): “In the blockade regime, it is possible to define an effective van der Waals shift, given by a suitably weighted average of the eigenvalues of the effective Hamiltonian [29].”
Quantum computing with atomic qubits and Rydberg interactions: progress and challenges (2016, background): “The physics of the Rydberg interaction between individual atoms has been treated in detail elsewhere[36, 37, 38, 39, 40, 41], including a review in this special issue[27].”
Dipole blockade in a cold Rydberg atomic sample [Invited] (2010, methodology): “for reactions of the type nl+ nl↔ n1l1 + n2l2 which are listed for several atoms in reference [24].”