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Physical Review Research

Collective photon emission of two correlated atoms in free space

Stefan Richter, Sebastian Wolf, Joachim von Zanthier, Ferdinand Schmidt‐Kaler

Published Mar 7, 2023• 12 citations
Publisher

Abstract

By preparing two distant emitters in entangled Dicke states via detection of a single photon, the subsequent spatiotemporal photon emission is investigated. Depending on the parity of the established quantum state, emission patterns for the second scattered photon are observed featuring spatial superradiance as well as subradiance. We employ ultrafast single-photon resolving cameras with high spatial resolution disclosing the spatiotemporal emission characteristics. By recording the first photon in one direction and the second photon in another, revealing the spatial two-photon cross-correlation function ${g}^{(2)}({\mathbf{r}}_{1},{\mathbf{r}}_{2})$, we characterize the collective spontaneous emission behavior of two ions in free space. We explain the observed contrast of ${g}^{(2)}({\mathbf{r}}_{1},{\mathbf{r}}_{2})$ considering independently derived experimental parameters. Our results show how the detection of a single photon can profoundly modify the collective spontaneous emission dynamics of an atomic ensemble.

DOI
10.1103/physrevresearch.5.013163

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By preparing two distant emitters in entangled Dicke states via detection of a single photon, the subsequent spatiotemporal photon emission is investigated. Depending on the parity of the established quantum state, emission patterns for the second scattered photon are observed featuring spatial superradiance as well as subradiance. We employ ultrafast single-photon resolving cameras with high spatial resolution disclosing the spatiotemporal emission characteristics. By recording the first photon in one direction and the second photon in another, revealing the spatial two-photon cross-correlation function g(2)(r1,r2){g}^{(2)}({\mathbf{r}}_{1},{\mathbf{r}}_{2})g(2)(r1​,r2​), we characterize the collective spontaneous emission behavior of two ions in free space. We explain the observed contrast of g(2)(r1,r2){g}^{(2)}({\mathbf{r}}_{1},{\mathbf{r}}_{2})g(2)(r1​,r2​) considering independently derived experimental parameters. Our results show how the detection of a single photon can profoundly modify the collective spontaneous emission dynamics of an atomic ensemble.
Modification of spontaneous decay in space and time is a central topic of quantum physics. It has been predominantly investigated in the context of cavity quantum electrodynamics (QED), gaining new interest recently in the domain of nano-optics. Beyond cavity-QED, spontaneous emission may be modified also in free space due to correlations among the photon emitters, a phenomenon known as super- and sub-radiance. Correlations may stem either from direct interactions between the particles, from long-range exchange of photons, or by measuring single photons in a common mode. Yet, the genuine spatial spontaneous emission pattern of an atomic ensemble in an entangled quantum state has not been observed so far, due to the lack of ultra-fast cameras with high spatial resolution suited for recording single photons from single atoms. Preparing two trapped ions in free space in entangled Dicke states via photon detection, we study the resulting collective spontaneous emission patterns. Depending on the symmetry of the Dicke states, associated with the direction of detection of the first state-determining photon, we observe fundamentally different emission patterns for the subsequently scattered photon, including super- and sub-radiance. Our results demonstrate that the detection of a single photon can profoundly modify the collective emission of an atomic array, here represented by its most elementary building block of two atoms in free space.
We study the collective spontaneous emission of three identical two-level atoms initially prepared in the excited states by measuring Glauber's third-order photon correlation function. Assuming two atoms at subwavelength distance from each other such that they are subject to the dipole-dipole interaction while the third one is located several wavelengths away, we observe super- and subradiant decay alike, depending on the direction of observation. Unlike the case where no remote atom is introduced or no conditional measurements are performed, the spontaneous emission behavior of the conditioned three-atom system is strongly modified, i.e., differing from the single-atom and the canonical two-atom configuration. The conditional measurements associated with the three-photon correlation function in combination with the dipole-dipole interaction between the adjacent atoms lead to quantum interference among the different decay channels allowing one to engineer the spontaneous emission in space and time.
We study the collective spontaneous emission of a linear atomic chain excited by a single photon. The interaction between the atoms and the common vacuum field can significantly change the eigenenergy and the spontaneous emission rate of the system. Due to the dipole-dipole interactions, the system prepared in a single-photon timed Dicke state is the superposition of superradiant and subradiant eigenstates that can have a nonexponential decay dynamics. We can tune the frequency and linewidth of the superradiant and subradiant emission from a timed Dicke state by changing the direction of the atomic dipole moment or the atomic separation. In addition, the emission direction of the superradiant and subradiant photons also depends on the polarization of the atoms.
The collective spontaneous emission of many atoms is significantly different from that of a single atom, depending on the geometry and the phase correlation of atomic ensembles. However, experimental observation of arbitrary superradiant and subradiant states of atoms remains challenging due to the difficulties in both preparation and detection of those states. Here we report the time-resolved observation of superradiance from a timed Dicke state in a momentum-space superradiance lattice of Bose-Einstein condensates, which enables an in situ measurement of the coherent lattice dynamics involving both superradiant and subradiant states. The long-lasting oscillation in the superradiant emission is contributed by population transport from the subradiant states in the superradiance lattice. This work paves the way to prepare and observe subradiant states, which has promising applications in quantum information processing.
The collective behavior of ensembles of atoms has been studied in-depth since the seminal paper of Dicke [R. H. Dicke, Phys. Rev. 93, 99 (1954)], where he demonstrated that a group of emitters in collective states is able to radiate with increased intensity and modified decay rates in particular directions, a phenomenon which he called superradiance. Here, we show that the fundamental setup of two atoms coupled to a single-mode cavity can be distinctly exceeding the free-space superradiant behavior, a phenomenon which we call hyperradiance. The effect is accompanied by strong quantum fluctuations and surprisingly arises for atoms radiating out-of-phase, an alleged non-ideal condition, where one expects subradiance. We are able to explain the onset of hyperradiance in a transparent way by a photon cascade taking place among manifolds of Dicke states with different photon numbers under particular out-of-phase coupling conditions. The theoretical results can be realized with current technology and thus should stimulate future experiments.
Recently a conditional quantum teleportation protocol has been proposed by Chen et al. [New J. Phys.7, 172 (2005)], which is based on the collective spontaneous emission of a photon from a pair of quantum dots. We formulate a similar protocol for collective emission from a pair of atoms, one of which is entangled with a single mode of an optical cavity. We focus on the performance of the protocol as characterized by the fidelity of the teleported state and the overall success probability. We consider a strategy employing spatially resolved photodetection of the emitted photon in order to distinguish superradiant from subradiant emission on the basis of a single detected photon. We find that fidelity approaches unity as the spacing of the atoms becomes much smaller than the emission wavelength with a success probability of 0.25. The fidelity remains above the classical limit of 2/3 for arbitrary atomic separations with the ultimate limit of performance coming from the spatial resolution of the detectors.