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Super- and subradiant dynamics of quantum emitters mediated by atomic matter waves

Nature Physics (2024)Cite this article

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Abstract

The cooperative modification of spontaneous radiative decay exemplifies a many-emitter effect in quantum optics. So far, its experimental realizations have relied on interactions mediated by rapidly escaping photons, which do not play an active role in the emitter dynamics. Here we use a platform of ultracold atoms in a one-dimensional optical lattice geometry to explore cooperative non-Markovian dynamics of synthetic quantum emitters that decay by radiating slow atomic matter waves. By preparing and manipulating arrays of emitters hosting weakly and strongly interacting many-body phases of excitations, we demonstrate directional collective emission and study the interplay between retardation and super- and subradiant dynamics. Moreover, we directly observe the spontaneous buildup of coherence among emitters. Our results on collective radiative dynamics establish ultracold matter waves as a versatile tool for studying many-body quantum optics in spatially extended and ordered systems.

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Fig. 1: Schematic of the experiments.
Fig. 2: Phase control of emission characteristics in the SF regime.
Fig. 3: Super- and subradiant dynamics in the SF regime.
Fig. 4: Spontaneous coherence formation in the MI regime.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

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Acknowledgements

We thank J. Kwon and H. Huang for experimental assistance; M. G. Cohen for discussions; and J. Kwon, H. Huang and M. G. Cohen for a critical reading of the manuscript. This work was supported by the US National Science Foundation, through grants PHY-1912546 and PHY-2208050. Y.K. acknowledges additional partial support from Stony Brook University’s Center for Distributed Quantum Processing.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Stony Brook University, Stony Brook, USA

    Youngshin Kim, Alfonso Lanuza & Dominik Schneble

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Contributions

Y.K., A.L. and D.S. conceived the experiments. Y.K. took the measurements and analysed the data. Numerical simulations and analytical descriptions were developed by Y.K. and A.L., respectively. The results were discussed and interpreted by all authors. D.S. supervised the project. The manuscript was written by Y.K. and D.S. with critical contributions from A.L.

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Correspondence to Dominik Schneble.

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Extended data

Extended Data Fig. 1 Collective emission versus coherence.

a, Coherence of the initial array population characterized by the width σ of the phase distribution at various transverse lattice depths s⊥ as seen in ToF images. b, Excited fraction at a fixed decay time 300 μs as a function of s⊥ for two distinct excitation energies \(\hslash \Delta =4\hslash {\omega }_{{\mathsf{r}}},\hslash {\omega }_{{\mathsf{r}}}\) with coupling strength \(\Omega /{\omega }_{{\mathsf{r}}}=1.00(7),0.48(3)\). The z-lattice depth is fixed at sz = 15 throughout.

Extended Data Fig. 2 Numerical simulations of an M-well array containing a single excitation.

a,χ2 vs. M evaluated with respect to the data shown in Fig. 2d and Fig. 3a. In (i), the data at the phases \(\phi \in \left(0,2\uppi \right]\) and the coupling parameters \(\Delta /{\omega }_{{\mathsf{r}}}\in \{2,4\}\) are used (with \(\Omega /{\omega }_{{\mathsf{r}}}=0.6\) and t = 200 μs). In (ii), the data at the coupling times t ∈ [0, 0.25] ms for \((\Delta ,\Omega )/{\omega }_{{\mathsf{r}}}=(4,1)\) and at t ∈ [0, 0.5] ms for \((\Delta ,\Omega )/{\omega }_{{\mathsf{r}}}=(1,0.42)\) are used. The normalization \({\chi }_{0}^{2}\) is the value at which the cumulative χ2 distribution reaches 95%. The lines are guides to the eye. b, Simulated population versus time for \((\Delta ,\Omega )/{\omega }_{{\mathsf{r}}}=(4,1)\) and (1, 0.42) (with sz = 8, ϕ = 0) shown as solid and dashed lines, with M varying from one to five (lightest to darkest colors; red for M = 3, the case also shown in Fig. 3a).

Extended Data Fig. 3 Spectral contributions to the simulated dynamics of 3 emitters.

The domain coloring plots of \(\det {\mathcal{G}}\) (with a brightness of 1, a hue proportional to the argument of \(\det {\mathcal{G}}\), and a saturation inversely dependent on its absolute value) are represented on Riemann surfaces, along with their analytic continuations, for sz = 8 and \((\Delta ,\Omega )/{\omega }_{{\mathsf{r}}}=(0,0.6)\), (1,0.42) and (4,1) from left to right (the vertical bars represent the dispersion \(\bar{k}(\Delta )\), to which the origin of the imaginary axis for each Δ is aligned). The zeroes and branch cut of this function define the decay dynamics of the emitters, which are presented in the bottom panels. The black lines represent the simulated dynamics, while the red lines account for the various spectral contributions; with the main ones coming from superradiant (SR), subradiant (sR) and bound states (BS).

Extended Data Fig. 4 Collective dynamics at the continuum edge in the SF regime.

a, Excited fraction as a function of time for (sz, s⊥) = (8, 8), ϕ = 0 with strong coupling \(\Omega =0.60(4){\omega }_{{\mathsf{r}}}\) at Δ = 0 (red points). The solid line simulates a 3-well array with a coherently distributed excitation, as opposed to scenarios in which the excitation is located in an isolated well (dotted line) or in the central one of 3 wells (dashed-dotted). Shaded areas represent the uncertainty in Ω. The red dashed line is a fit to the beating of a dissipative and a bound state with the decay rate fixed by our analytic model. b, (i) Momentum distribution of the emitted matter waves versus time. The lineout plot shows the data at 0.3 ms (blue points) along with our simulation and bound-state contributions from our analytic model (gray solid and black dashed lines). (ii) Simulated position and momentum distributions of the matter waves versus time, with a lineout plot at 0.3 ms. The dashed vertical lines are the positions of the emitters. All data are averages of at least 3 measurements; the error bars show the standard error of the mean.

Extended Data Fig. 5 Supplementary data and simulation for Fig. 4.

a, Time evolution of the array populations (\(\left\vert r\right\rangle ,\left\vert g\right\rangle\)) initially prepared in a superposition \((\left\vert r\right\rangle +\left\vert g\right\rangle )/\sqrt{2}\) corresponding to the measurements shown in Fig. 4b,c. The solid and dashed lines are our two-well model without and with an additional empty well (scaled by 1.05). b, Time evolution of the visibility defined as c0 − c1 (c1 − c0) for \(\Delta =4{\omega }_{{\mathsf{r}}}({\omega }_{{\mathsf{r}}})\), where c0 and c1 are the integration of the change of the phase distributions (PD) over \(| q| \in [0,0.5{k}_{{\mathsf{r}}}]\) and \(| q| \in \left(0.5{k}_{{\mathsf{r}}},1.5{k}_{{\mathsf{r}}}\right]\) (cf. Fig. 4c). The solid and dashed lines are calculated from our model as in a.

Extended Data Fig. 6 Radiative decay of thermal excitations.

a, Excited fraction for \(\Delta =4{\omega }_{{\mathsf{r}}}\) and \({\omega }_{{\mathsf{r}}}\) (red points and circles), with coupling strength set to \(\Omega /{\omega }_{{\mathsf{r}}}=1.00(7)\) and 0.60(4). A thermal gas of \(\left\vert r\right\rangle\) atoms in the SF regime, (sz, s⊥) = (8, 8), is prepared by heating via periodic modulation of the lattice depths sz and s⊥ with an average amplitude ≈ 30% and a frequency 500 Hz for a duration of 40 ms. The solid and dashed lines are simulations of single-well decay for the corresponding parameters. We plot time in terms of Γ1 = 2π × 0.24 kHz (0.49 kHz) for \(\Delta =4{\omega }_{{\mathsf{r}}}({\omega }_{{\mathsf{r}}})\), phase distributions of the array population (\(\left\vert r\right\rangle\) atoms) are shown at t = 0 and 300 μs (150 μs). The top-right inset shows the same data including longer times. Also shown is the heating of the array population versus the lattice modulation time characterized by the momentum peak width54; the solid line is a sigmoidal fit. b, (i) Change in the normalized PD of the emitter array (\(\left\vert r\right\rangle\)) after 300 μs for \(\Delta =4{\omega }_{{\mathsf{r}}}\). (ii) Same but after 150 μs for \(\Delta ={\omega }_{{\mathsf{r}}}\). All data are averages of at least 3 measurements with the error bars from the standard error of the mean (gray points and circles are raw data).

Extended Data Table 1 Complex frequencies ωp (in units of ωr) and initial amplitudes \({\overrightarrow{\boldsymbol{A}}}_{{\boldsymbol{p}},{\bf{0}}}\) of the bound (BS), subradiant (sR), and superradiant (SR) states impacting the dynamics of 3 quantum emitters, for the parameters tested in the experiment (see Fig. 3 and Extended Data Fig. 4)
Full size table

Source data

Source Data Fig. 2

Numerical source data files (in .csv format).

Source Data Fig. 3

Numerical source data files (in .csv format).

Source Data Fig. 4

Numerical source data files (in .csv format).

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Kim, Y., Lanuza, A. & Schneble, D. Super- and subradiant dynamics of quantum emitters mediated by atomic matter waves. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02676-w

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