Dipole-Dipole Frequency Shifts in Multilevel Atoms

A. Cidrim, A. Piñeiro Orioli, C. Sanner, R. B. Hutson, J. Ye, R. Bachelard, and A. M. Rey

Phys. Rev. Lett. 127, 013401 – Published 30 June 2021

Abstract

Dipole-dipole interactions lead to frequency shifts that are expected to limit the performance of next-generation atomic clocks. In this work, we compute dipolar frequency shifts accounting for the intrinsic atomic multilevel structure in standard Ramsey spectroscopy. When interrogating the transitions featuring the smallest Clebsch-Gordan coefficients, we find that a simplified two-level treatment becomes inappropriate, even in the presence of large Zeeman shifts. For these cases, we show a net suppression of dipolar frequency shifts and the emergence of dominant nonclassical effects for experimentally relevant parameters. Our findings are pertinent to current generations of optical lattice and optical tweezer clocks, opening a way to further increase their current accuracy, and thus their potential to probe fundamental and many-body physics.

Received 11 February 2021
Revised 25 April 2021
Accepted 19 May 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.013401

Physics Subject Headings (PhySH)

Atomic, optical & lattice clocks Cold gases in optical lattices Long-range interactions

Dipole approximation Spectroscopy

Atomic, Molecular & Optical

Authors & Affiliations

A. Cidrim ^1,2,3, A. Piñeiro Orioli^2,3, C. Sanner², R. B. Hutson², J. Ye ², R. Bachelard ¹, and A. M. Rey ^2,3

¹Departamento de Física, Universidade Federal de São Carlos, 13565-905 São Carlos, São Paulo, Brazil
²JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
³Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 127, Iss. 1 — 2 July 2021

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Ramsey spectroscopy for multilevel atoms with internal level structure $F_{g} = F_{e} = 9 / 2$ in an optical lattice. The atoms are prepared in a superposition of a particular ground and excited pair of states $g_{α}$ and $e_{β}$ by a laser with wave vector $k_{0}$ , polarization $ϵ$ , and pulse area $θ$ . During a dark time $t$ , the atoms interact via coherent and incoherent dipole-dipole processes, $Δ^{i j}$ and $Γ^{i j}$ , respectively. This induces a frequency shift $δ^{g_{α} e_{β}} \sim | C_{g_{α}}^{e_{β}} |^{2}$ controlled by the CGC of the interrogated transition. The schematic form of the dipolar shift corresponding to interrogating $π$ -polarized transitions (colored according to their CGC) is depicted here. CGCs squared for different $σ^{\pm}$ and $π$ transitions are displayed. (b) Shift from the Ramsey protocol addressing three different $π$ -polarized transitions for a 3D lattice of spacing $d = 7 λ / 12$ with $N = 10^{3}$ atoms and $θ = π / 2$ .
Reuse & Permissions
Figure 2
Local frequency shifts $δ_{i}$ for a 3D lattice with $N = 10^{3}$ atoms, interrogated by a laser with a pulse area of $π / 2$ and a dark time of $Γ t = 0.3$ as shown in the configuration labeled by a triangle for (a) a two-level system and transitions (b) $g_{- 9 / 2} \leftrightarrow e_{- 9 / 2}$ , (c) $g_{- 1 / 2} \leftrightarrow e_{- 1 / 2}$ , and (d) $g_{- 1 / 2} \leftrightarrow e_{- 1 / 2}$ in the presence of a large magnetic field $B$ . The shift is calculated using Eq. (6) and is averaged along $ε$ , with the resulting contribution at positions $(x_{i}, y_{i})$ . Shifts are rescaled by the corresponding CGC squared and by an overall $10^{- 2}$ factor. (e) Comparing the global shift of the multilevel model for transitions $α = - 9 / 2$ (top) and $α = - 1 / 2$ (bottom) (full and dotted lines, for zero and large magnetic fields, respectively) to a two-level model (dashed lines). (f) Absolute value of the difference between maximum and minimum of the local shift ( $δ_{i}^{\max}$ and $δ_{i}^{\min}$ ) versus magnitude of the global shift $| δ |$ for different geometries with $N \sim 10^{3}$ . Symbols represent configurations shown in the legend. The light-blue symbols correspond to the large- $| B |$ limit for $α = - 1 / 2$ .
Reuse & Permissions
Figure 3
Global shift for 2D arrays of atoms with laser configuration shown in (c). (a),(b) $N$ -scaling of the total shift from the short-time expansion (red/blue) and beyond-MF contribution (black) at $Γ t = 0.3$ : (a) $g_{- 9 / 2} \leftrightarrow e_{- 9 / 2}$ transition with $π / 2$ , and (b) $g_{- 1 / 2} \leftrightarrow e_{- 1 / 2}$ transition with $π / 4$ . The dotted, light-colored lines correspond to the large-magnetic-field limit. The inset of (a) shows the closeup region where beyond-MF corrections become comparable to the total shift. (c),(d) Dipolar shift $δ$ as a function of the dark time: cumulant (full lines) against MF (dashed lines) approximations for the $g_{- 9 / 2} \leftrightarrow e_{- 9 / 2}$ (red), $g_{- 5 / 2} \leftrightarrow e_{- 5 / 2}$ (yellow), and $g_{- 1 / 2} \leftrightarrow e_{- 1 / 2}$ (blue) transitions. Simulations performed for $N = 8^{2}$ atoms and using (c) a $π / 2$ and (d) $π / 4$ pulse.
Reuse & Permissions

Physical Review Letters