Superradiant and Subradiant Cavity Scattering by Atom Arrays

Zhenjie Yan, Jacquelyn Ho, Yue-Hui Lu, Stuart J. Masson, Ana Asenjo-Garcia, and Dan M. Stamper-Kurn

Phys. Rev. Lett. 131, 253603 – Published 21 December 2023

Abstract

We realize collective enhancement and suppression of light scattered by an array of tweezer-trapped ${}^{87}{Rb}$ atoms positioned within a strongly coupled Fabry-Pérot optical cavity. We illuminate the array with light directed transverse to the cavity axis, in the low saturation regime, and detect photons scattered into the cavity. For an array with integer-optical-wavelength spacing each atom scatters light into the cavity with nearly identical scattering amplitude, leading to an observed $N^{2}$ scaling of cavity photon number as the atom number increases stepwise from $N = 1$ to $N = 8$ . By contrast, for an array with half-integer-wavelength spacing, destructive interference of scattering amplitudes yields a nonmonotonic, subradiant cavity intensity versus $N$ . By analyzing the polarization of light emitted from the cavity, we find that Rayleigh scattering can be collectively enhanced or suppressed with respect to Raman scattering. We observe also that atom-induced shifts and broadenings of the cavity resonance are precisely tuned by varying the atom number and positions. Altogether, tweezer arrays provide exquisite control of atomic cavity QED spanning from the single- to the many-body regime.

Received 27 July 2023
Accepted 2 November 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.253603

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Collective effects in quantum optics Quantum optics

Trapped atoms

Optical tweezers

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Zhenjie Yan ^1,2, Jacquelyn Ho ^1,2, Yue-Hui Lu^1,2, Stuart J. Masson³, Ana Asenjo-Garcia³, and Dan M. Stamper-Kurn ^1,2,4,*

¹Department of Physics, University of California, Berkeley, California 94720, USA
²Challenge Institute for Quantum Computation, University of California, Berkeley, California 94720, USA
³Department of Physics, Columbia University, New York, New York 10027, USA
⁴Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

^*dmsk@berkeley.edu

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Vol. 131, Iss. 25 — 22 December 2023

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Images

Figure 1
Schematic of the experimental setup. (a) Atoms are driven by a pair of counter propagating side probe beams. The two-photon scattering amplitude $η (x, y)$ from the probe beam into the cavity, by an atom located at $(x, y)$ , exhibits a two-dimensional checkerboard pattern. (b) The probe light (orange) and the cavity photons (green) couple the $F = 2$ hyperfine states of the $5 S_{1 / 2}$ atomic ground state with the $5 P_{3 / 2}$ excited states. Three hyperfine manifolds $F^{'} = 3$ , 2, 1 of the excited states contribute to the probe-cavity scattering.
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Figure 2
(a) Cavity scattering by a two-atom array. One atom is placed at a cavity antinode, and scatters with steady-state cavity photon number $n_{1}$ on its own. Adding a second atom, at a distance $d$ from the first, changes the cavity photon number to $n_{2}$ . Expected ratios $n_{2} / n_{1}$ for perfectly localized atoms (dotted black line) and atoms with $σ = 100 (14) nm$ position fluctuations (dashed blue line, uncertainty in $σ$ indicated by shaded area). (b) Normalized cavity photon number $n_{N} / (N n_{1})$ generated by $N$ -atom arrays with fixed spacing, displaced by $Δ x$ from a cavity antinode. The array has $N = 1$ (gray), 2 (blue), 3 (yellow) atoms, and a spacing of $4 λ$ (circles) or $3.5 λ$ (squares). The dashed and dotted lines are cosinusoidal fits with a period of $λ / 2$ . All data are taken with $Δ_{pc} = 0$ .
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Figure 3
(a) Normalized cavity photon number ( $n_{N} / n_{1}$ ) for scattering by $N$ -atom arrays with either integer- (circles, $d = 5.0 λ$ ) or half-integer- (squares, $d = 5.5 λ$ ) wavelength spacing, using cavity-atom detuning at either $Δ_{ca} = - 2 π \times 507 MHz$ (red) or $- 2 π \times 38 MHz$ (green). Inset: close-up data from half-integer-wavelength arrays. The solid (dashed) black line corresponds to a quadratic $N^{2}$ (linear $N$ ) scaling. The red shaded area is calculated from Eqs. (2) and (3), while the green shaded area is the result of a Monte Carlo calculation assuming equal population among all $m_{F}$ states [34]. (b),(c) Polarization analysis of cavity emission. Relative transmission through a linear polarizer at an angle $θ$ with respect to the $z$ axis at (b) $Δ_{ca} = - 2 π \times 38 MHz$ and (c) $Δ_{ca} = - 2 π \times 507 MHz$ . Shown for scattering by a single atom (gray circles), or $N = 8$ atoms at the constructive (cyan circles) or the destructive interference condition (purple squares). The corresponding curves show results of the Monte Carlo calculation.
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Figure 4
Cavity spectra measured with arrays of $N = 1$ (black), 3 (yellow), and 8 (cyan) at (a) $Δ_{ca} = - 2 π \times 38 MHz$ and (b) $- 2 π \times 507 MHz$ . All atoms are aligned with cavity antinodes of the same phase. Lorentzian fits (dashed lines) are used to determine the peak positions and linewidths. The cavity resonance (c) shifts and (d) half widths at half maximum (HWHM) as a function of atom number, measured with all atoms aligned with cavity antinodes of the same phase (circles), at detunings of $Δ_{ca} = - 2 π \times 507 MHz$ (red), $- 2 π \times 38 MHz$ (green), $- 2 π \times 19 MHz$ (purple), and $2 π \times 19 MHz$ (blue). The corresponding shaded areas are predictions from a Monte Carlo calculation [34]. Results are also shown for an array with half-integer-wavelength spacing at the cavity antinodes (squares), and an array with integer-wavelength spacing at the cavity nodes (stars). For clarity, some symbols in (c) and (d) are slightly offset in $N$ .
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