Physical Review A

Level shifts of rubidium Rydberg states due to binary interactions

Aaron Reinhard, Tara Cubel Liebisch, Brenton Knuffman, Georg A. Raithel

Published Mar 14, 2007• 156 citations

Abstract

We use perturbation theory to directly calculate the van der Waals and dipole-dipole energy shifts of pairs of interacting Rb Rydberg atoms for different quantum numbers $n$, $\ensuremath{\ell}$, $j$, and ${m}_{j}$, taking into account a large number of perturbing states. Our results can be used to identify good experimental parameters and illuminate important considerations for applications of the ``Rydberg-excitation blockade.'' We also use the results of the calculation to explain features of previous experimental data on the Rydberg-excitation blockade. To explore control methods for the blockade, we discuss energy shifts due to atom-atom interaction in an external electric field.

DOI: 10.1103/physreva.75.032712

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Cold Rydberg-Atom Interactions

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Consequences of Zeeman degeneracy for the van der Waals blockade between Rydberg atoms

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Rydberg blockade with multivalent atoms: effect of Rydberg series perturbation on van der Waals interactions

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Van der Waals Interactions among Alkali Rydberg Atoms with Excitonic States

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Physical Review A

Level shifts of rubidium Rydberg states due to binary interactions

Aaron Reinhard, Tara Cubel Liebisch, Brenton Knuffman, Georg A. Raithel

Published Mar 14, 2007• 156 citations

Publisher

Abstract

We use perturbation theory to directly calculate the van der Waals and dipole-dipole energy shifts of pairs of interacting Rb Rydberg atoms for different quantum numbers

n

\ensuremath{\ell}

j

, and

{m}_{j}

, taking into account a large number of perturbing states. Our results can be used to identify good experimental parameters and illuminate important considerations for applications of the ``Rydberg-excitation blockade.'' We also use the results of the calculation to explain features of previous experimental data on the Rydberg-excitation blockade. To explore control methods for the blockade, we discuss energy shifts due to atom-atom interaction in an external electric field.

DOI: 10.1103/physreva.75.032712

Related papers

Cold Rydberg-Atom Interactions

Aaron Reinhard

Systems of cold, interacting Rydberg atoms are of interest because they exhibit a wide range of collective quantum phenomena. This thesis describes experimental and theoretical work related to these systems with an emphasis on two phenomena: Rydberg excitation blockades and quantum-state-changing collisions. I begin by presenting a detailed calculation of the interaction energies of two Rydberg atoms for a variety of orientations, quantum states, and applied electric fields. The calculated energies are used to interpret the experimental results that follow. I then describe measurements showing that the widths of the distributions of Rydberg excitation number are related to the effectiveness of a Rydberg excitation blockade. These distributions are investigated as a function of principal quantum number, n, and applied electric field. In the presence of a Forster resonant field, sub-Poissonian distributions are measured. I next present a spectroscopic measurement of the energy level shift of a system of atoms which collectively shares two Rydberg excitations. The qualitative nature of the shift depends sensitively on the type of interactions between the atoms (van der Waals or dipole-dipole) and may be changed by changing the quantum state or applied electric field. This measurement provides the first spectroscopic proof that Rydberg excitation blockades are operative. Finally, I describe measurements of the probability for quantum state-changing and Penning-ionizing collisions to provide evidence for intrinsic, electric field-free-interaction resonances and complex many-body interactions in systems of cold Rydberg atoms.Systems of cold, interacting Rydberg atoms are of interest because they exhibit a wide range of collective quantum phenomena. This thesis describes experimental and theoretical work related to these systems with an emphasis on two phenomena: Rydberg excitation blockades and quantum-state-changing collisions. I begin by presenting a detailed calculation of the interaction energies of two Rydberg atoms for a variety of orientations, quantum states, and applied electric fields. The calculated energies are used to interpret the experimental results that follow. I then describe measurements showing that the widths of the distributions of Rydberg excitation number are related to the effectiveness of a Rydberg excitation blockade. These distributions are investigated as a function of principal quantum number, n, and applied electric field. In the presence of a Forster resonant field, sub-Poissonian distributions are measured. I next present a spectroscopic measurement of the energy level shift of a system of atoms which collectively shares two Rydberg excitations. The qualitative nature of the shift depends sensitively on the type of interactions between the atoms (van der Waals or dipole-dipole) and may be changed by changing the quantum state or applied electric field. This measurement provides the first spectroscopic proof that Rydberg excitation blockades are operative. Finally, I describe measurements of the probability for quantum state-changing and Penning-ionizing collisions to provide evidence for intrinsic, electric field-free-interaction resonances and complex many-body interactions in systems of cold Rydberg atoms.

Jan 1, 20082 citations

Consequences of Zeeman degeneracy for the van der Waals blockade between Rydberg atoms

Thad G Walker, Mark E. Saffman

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.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.

arXiv:0712.3438Physical Review AMar 26, 2008291 citations

Rydberg blockade with multivalent atoms: effect of Rydberg series perturbation on van der Waals interactions

Türker Topçu, Andrei Derevianko

We investigate the effect of series perturbation on the second order dipole-dipole interactions between strontium atoms in $5sns({^1}S_0)$ and $5snp({^1}P_1)$ Rydberg states as a means of engineering long-range interactions between atoms in a way that gives an exceptional level of control over the strength and the sign of the interaction by changing $n$ . We utilize experimentally available data to estimate the importance of perturber states at low $n$ , and find that van der Waals interaction between two strontium atoms in the $5snp({^1}P_1)$ states shows strong peaks outside the usual hydrogenic $n^{11}$ scaling. We identify this to be the result of the perturbation of $5snd({^1}D_2)$ intermediate states by the $4d^2({^1}D_2)$ and $4dn's({^1}D_2)$ states in the $n<20$ range. This demonstrates that divalent atoms in general present a unique advantage for creating substantially stronger or weaker interaction strengths than those can be achieved using alkali metal atoms due to their highly perturbed spectra that can persist up to high- $n$ .We investigate the effect of series perturbation on the second order dipole-dipole interactions between strontium atoms in $5sns({^1}S_0)$ and $5snp({^1}P_1)$ Rydberg states as a means of engineering long-range interactions between atoms in a way that gives an exceptional level of control over the strength and the sign of the interaction by changing $n$. We utilize experimentally available data to estimate the importance of perturber states at low $n$, and find that van der Waals interaction between two strontium atoms in the $5snp({^1}P_1)$ states shows strong peaks outside the usual hydrogenic $n^{11}$ scaling. We identify this to be the result of the perturbation of $5snd({^1}D_2)$ intermediate states by the $4d^2({^1}D_2)$ and $4dn's({^1}D_2)$ states in the $n<20$ range. This demonstrates that divalent atoms in general present a unique advantage for creating substantially stronger or weaker interaction strengths than those can be achieved using alkali metal atoms due to their highly perturbed spectra that can persist up to high-$n$.

May 26, 20150 citations

Van der Waals Interactions among Alkali Rydberg Atoms with Excitonic States

Zoubi, H.

We investigate the influence of the appearance of excitonic states on van der Waals interactions among two Rydberg atoms. The atoms are assumed to be in different Rydberg states, e.g., in the $|ns\\rangle$ and $|np\\rangle$ states. The resonant dipole-dipole interactions yield symmetric and antisymmetric excitons, with energy splitting that give rise to new resonances as the atoms approach each other. Only far from these resonances the van der Waals coefficients, $C_6^{sp}$ , can be defined. We calculate the $C_6$ coefficients for alkali atoms and present the results for lithium by applying perturbation theory. At short interatomic distances of several $\\mu m$ , we show that the widely used simple model of two-level systems for excitons in Rydberg atoms breaks down, and the correct representation implies multi-level atoms. Even though, at larger distances one can keep the two-level systems but in including van der Waals interactions among the atoms.We investigate the influence of the appearance of excitonic states on van der Waals interactions among two Rydberg atoms. The atoms are assumed to be in different Rydberg states, e.g., in the $|ns\\rangle$ and $|np\\rangle$ states. The resonant dipole-dipole interactions yield symmetric and antisymmetric excitons, with energy splitting that give rise to new resonances as the atoms approach each other. Only far from these resonances the van der Waals coefficients, $C_6^{sp}$, can be defined. We calculate the $C_6$ coefficients for alkali atoms and present the results for lithium by applying perturbation theory. At short interatomic distances of several $\\mu m$, we show that the widely used simple model of two-level systems for excitons in Rydberg atoms breaks down, and the correct representation implies multi-level atoms. Even though, at larger distances one can keep the two-level systems but in including van der Waals interactions among the atoms.

Jan 1, 20152 citations

Calculations of the van der Waals interaction strengths between two alkali Rydberg atoms

Noor M. Khan, Muhammad Sohail, Sapna Khan +5 more

We calculate the interaction strength of the van der Waals force between two Rydberg atoms by applying the applications of quantum information processing using for Rydberg blockade. The alkali metals (Cs and K) in states of principal quantum number n were used to calculate the interaction strength. We use some possible angular momentum channels involving s, p, and d states for measuring interaction strength. The obtained results were then generalized for all angular momentum channels which mostly have small interactions and therefore a poor candidate for blockade experiments. The interaction strength in the atoms of Cs and K dipole matrix elements was calculated first and then relevant energy levels were determined by using the quantum defects theory. The radial wave function was calculated numerically with the integration of the radial Schrodinger equation. Also, the interaction coefficients of van der Waals for various channels were calculated here.We calculate the interaction strength of the van der Waals force between two Rydberg atoms by applying the applications of quantum information processing using for Rydberg blockade. The alkali metals (Cs and K) in states of principal quantum number n were used to calculate the interaction strength. We use some possible angular momentum channels involving s, p, and d states for measuring interaction strength. The obtained results were then generalized for all angular momentum channels which mostly have small interactions and therefore a poor candidate for blockade experiments. The interaction strength in the atoms of Cs and K dipole matrix elements was calculated first and then relevant energy levels were determined by using the quantum defects theory. The radial wave function was calculated numerically with the integration of the radial Schrodinger equation. Also, the interaction coefficients of van der Waals for various channels were calculated here.

Chinese Journal of Chemical PhysicsJan 1, 20210 citations

Direct Measurement of the van der Waals Interaction between Two Rydberg Atoms

Lucas Béguin, Aline Vernier, Radu Chicireanu +2 more

We report the direct measurement of the van der Waals interaction between two isolated, single Rydberg atoms separated by a controlled distance of a few micrometers. Working in a regime where the single-atom Rabi frequency for excitation to the Rydberg state is comparable to the interaction, we observe partial Rydberg blockade, whereby the time-dependent populations of the various two-atom states exhibit coherent oscillations with several frequencies. Quantitative comparison of the data with a simple model based on the optical Bloch equations allows us to extract the van der Waals energy, and observe its characteristic C6/R6 dependence. The measured C6 coefficients agree well with ab initio calculations, and we observe their dramatic increase with the principal quantum number n of the Rydberg state.We report the direct measurement of the van der Waals interaction between two isolated, single Rydberg atoms separated by a controlled distance of a few micrometers. Working in a regime where the single-atom Rabi frequency for excitation to the Rydberg state is comparable to the interaction, we observe partial Rydberg blockade, whereby the time-dependent populations of the various two-atom states exhibit coherent oscillations with several frequencies. Quantitative comparison of the data with a simple model based on the optical Bloch equations allows us to extract the van der Waals energy, and observe its characteristic C6/R6 dependence. The measured C6 coefficients agree well with ab initio calculations, and we observe their dramatic increase with the principal quantum number n of the Rydberg state.

arXiv:1302.4262Physical Review LettersJun 24, 2013275 citations

We use perturbation theory to directly calculate the van der Waals and dipole-dipole energy shifts of pairs of interacting Rb Rydberg atoms for different quantum numbers

n

\ensuremath{\ell}

j

, and

{m}_{j}

\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.

We investigate the effect of series perturbation on the second order dipole-dipole interactions between strontium atoms in

5sns({^1}S_0)

and

5snp({^1}P_1)

Rydberg states as a means of engineering long-range interactions between atoms in a way that gives an exceptional level of control over the strength and the sign of the interaction by changing

n

. We utilize experimentally available data to estimate the importance of perturber states at low

n

, and find that van der Waals interaction between two strontium atoms in the

5snp({^1}P_1)

states shows strong peaks outside the usual hydrogenic

n^{11}

scaling. We identify this to be the result of the perturbation of

5snd({^1}D_2)

intermediate states by the

4d^2({^1}D_2)

and

4dn's({^1}D_2)

states in the

n<20

range. This demonstrates that divalent atoms in general present a unique advantage for creating substantially stronger or weaker interaction strengths than those can be achieved using alkali metal atoms due to their highly perturbed spectra that can persist up to high-

n

We investigate the influence of the appearance of excitonic states on van der Waals interactions among two Rydberg atoms. The atoms are assumed to be in different Rydberg states, e.g., in the

|ns\\rangle

and

|np\\rangle

states. The resonant dipole-dipole interactions yield symmetric and antisymmetric excitons, with energy splitting that give rise to new resonances as the atoms approach each other. Only far from these resonances the van der Waals coefficients,

C_6^{sp}

, can be defined. We calculate the

C_6

coefficients for alkali atoms and present the results for lithium by applying perturbation theory. At short interatomic distances of several

\\mu m

, we show that the widely used simple model of two-level systems for excitons in Rydberg atoms breaks down, and the correct representation implies multi-level atoms. Even though, at larger distances one can keep the two-level systems but in including van der Waals interactions among the atoms.