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Spontaneous emission of matter waves from a tunable open quantum system


The decay of an excited atom undergoing spontaneous photon emission into the fluctuating quantum-electrodynamic vacuum is an emblematic  example of the dynamics of an open quantum system. Recent experiments have demonstrated that the gapped photon dispersion in periodic structures, which prevents photons in certain frequency ranges from propagating, can give rise to unusual spontaneous-decay behaviour, including the formation of dissipative bound states1,2,3. So far, these effects have been restricted to the optical domain. Here we demonstrate similar behaviour in a system of artificial emitters, realized using ultracold atoms in an optical lattice, which decay by emitting matter-wave, rather than optical, radiation into free space. By controlling vacuum coupling and the excitation energy, we directly observe exponential and partly reversible non-Markovian dynamics and detect a tunable bound state that contains evanescent matter waves. Our system provides a flexible platform for simulating open-system quantum electrodynamics and for studying dissipative many-body physics with ultracold atoms4,5,6.

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Fig. 1: Realization of matter-wave emitters.
Fig. 2: Markovian regime.
Fig. 3: Non-Markovian dynamics and bound-state formation.


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We thank M. G. Cohen for discussions and a critical reading of the manuscript. This work was supported by NSF PHY-1607633. M.S. was supported by a GAANN fellowship by the US Department of Education. A.P. acknowledges partial support from ESPOL-SENESCYT.

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Authors and Affiliations



D.S., L.K. and M.S. conceived the experiment. L.K. took the measurements with assistance from A.P. and J.K. L.K. analysed the data with contributions from M.S. Numerical simulations were performed by L.K. D.S. supervised the project. The results were discussed and interpreted by all authors. The manuscript was written by L.K. and D.S. with contributions from A.P., J.K. and M.S.

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Correspondence to Dominik Schneble.

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Extended data figures and tables

Extended Data Fig. 1 Average spectrum of coupling stationary atoms into the z lattice.

The spectrum was generated from a series of 17 spectra taken over a one-day period, whose fitted centres are shifted to zero. The coupling strength is Ω = 740(10) Hz and the pulse time is 400 μs, with the data points binned into 300-Hz-wide bins. The solid curve is a fit to the data with Ω as a free-fitting parameter and the dashed curve has no free parameters. The effective coupling strength was calculated using the wavefunction overlap between free and trapped species, γ0 = 0.72.

Extended Data Fig. 2 Raw momentum spectrum.

The spectrum shows a detuning-independent, diffuse background of roughly 103 atoms. The spectrum was acquired as described in the main text, Fig. 2 and Methods; colour scale is identical to Fig. 2c.

Extended Data Fig. 3 Raw data used to obtain the energy shift.

a, b, Second moment of k (a) and half-separation squared (b) both subtracted by Δ/(2π). The detuning Δ/(2π) is 1.0 kHz (black disks), 2.0 kHz (red triangles), 4.0 kHz (green squares) and 6.0 kHz (blue circles). Points in brackets correspond to the non-Markovian regime, Ω/Δ > 1.

Extended Data Fig. 4 Simulated decay dynamics for a 1-site and a 3-site model (with the central site initially populated).

a, Dynamics of the two models, as depicted in the insets, for Δ = 2π × 1.9 kHz and Ω = 2π × 0.74 kHz, with ωz = 2π × 0.1 kHz. b, Long-time decay dynamics of the 1-site (black) and 3-site (red) models for Ω = 2π × 0.74 kHz and Δ = 2π × 1.9 kHz, with ωz = 2π × 5 Hz. The dashed red line shows the population of the central, initially populated, site; the dotted red line shows the population of the neighbouring sites. c, Dynamics of the two models for Δ = −2π × 0.1 kHz and Ω = 2π × 3 kHz, with ωz = 2π × 0.1 kHz.

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Krinner, L., Stewart, M., Pazmiño, A. et al. Spontaneous emission of matter waves from a tunable open quantum system. Nature 559, 589–592 (2018).

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