Letter | Published:

# A strongly interacting polaritonic quantum dot

## Abstract

Polaritons are promising constituents of both synthetic quantum matter1 and quantum information processors2, whose properties emerge from their components: from light, polaritons draw fast dynamics and ease of transport; from matter, they inherit the ability to collide with one another. Cavity polaritons are particularly promising as they may be confined and subjected to synthetic magnetic fields controlled by cavity geometry3, and furthermore they benefit from increased robustness due to the cavity enhancement in light–matter coupling. Nonetheless, until now, cavity polaritons have operated only in a weakly interacting mean-field regime4,5. Here we demonstrate strong interactions between individual cavity polaritons enabled by employing highly excited Rydberg atoms as the matter component of the polaritons. We assemble a quantum dot composed of approximately 150 strongly interacting Rydberg-dressed 87Rb atoms in a cavity, and observe blockaded transport of photons through it. We further observe coherent photon tunnelling oscillations, demonstrating that the dot is zero-dimensional. This work establishes the cavity Rydberg polariton as a candidate qubit in a photonic information processor and, by employing multiple resonator modes as the spatial degrees of freedom of a photonic particle, the primary ingredient to form photonic quantum matter6.

## Main

Recent years have seen a growing effort to create matter from light1,7. The speed of the photon may be employed to realize reduced-dimensional models with near-arbitrary single-particle dynamics, and recent breakthroughs have even enabled the creation of synthetic gauge fields that impose a Lorentz-like force on the photon8,9,10. While a number of groundbreaking experiments have probed the physics of photon condensation4,11, emergent crystallinity from long-range interactions12,13,14, and opto-mechanics15, the challenge of achieving strong interactions between individual photons for exploration of entangled photonic quantum matter persists. The demonstration of a single-photon nonlinearity mediated by a single atom coupled to a Fabry–Pérot cavity16 spurred an outpouring of theoretical work exploring Hubbard physics in coupled nonlinear resonators17,18, but the severe technical challenges associated with the deterministic preparation of individual atoms in resonator arrays remain.

Two major efforts have begun to address the technical challenges of mediating strong photonic interactions using atoms. In the first, researchers successfully demonstrated the loading of an individual atom into the near-field of a photonic crystal cavity19, and this capability was subsequently extended to the coupling of atomic ensembles to waveguides20. In the second, the challenges associated with trapping and cooling single atoms within optical resonators are eliminated by using Rydberg electromagnetically induced transparency (EIT)21. With Rydberg EIT, an entire thermal gas of atoms may act as a single ‘super atom’ that has the cross-section of the ensemble and the nonlinearity of a single atom22,23,24,25,26. Nonetheless, the propagation of these free-space excitations complicates their application to quantum information processors or materials compared to their cavity-confined counterparts.

Here, we present an approach combining Rydberg EIT and optical resonators27,28, which benefits from the best aspects of each previous approach: Rydberg EIT provides a robust atomic-ensemble-mediated single-photon nonlinearity, while the resonator enhances the light–matter coupling and allows us to work at substantially lower atomic densities while maintaining a high optical depth per blockade volume (ODB). This quantity is crucial, because ODB determines the number of collisions per polariton lifetime in a synthetic quantum material and the gate fidelity in a photonic quantum information processor29 (see Supplementary Information B). Perhaps most significantly, in the future, a quantum nonlinear resonator may be tuned near a mode-degeneracy point where interactions couple the transverse modes and the system behaves as a continuum-equivalent of an array of tunnel-coupled resonators. This approach would enable the creation of a strongly interacting quantum fluid within an individual, multi-mode cavity. Furthermore, the fluid can be trapped and subjected to strong magnetic fields3, providing access to the physics of photon crystals and Laughlin puddles6.

Here, we use this platform to demonstrate the first strongly interacting polaritonic quantum dot. We create a discrete mode spectrum by confinement of the photon in a cavity and strong interactions by tight confinement of the assembled atom cloud. In what follows, we describe the quantum dot in more detail and show that it exhibits the characteristic features of strong nonlinearity at the single-photon level, in contrast to related works exhibiting only weak nonlinearities5,30. First, we demonstrate strong light–matter coupling by measuring a well-resolved dark-polariton resonance in the transmission spectrum. We next explore transport via the statistics of photons tunnelling through the cavity, observing deep anti-bunching indicative of blockade due to strong interactions between individual polaritons. We further demonstrate that our polaritonic dot is zero-dimensional by detecting coherent Rabi oscillations between an empty dot and a dot containing a single polariton, as well as saturation of the intracavity dark polariton number at 0.47(3). We conclude with a discussion of applications in quantum information and strongly correlated, topological phases of matter.

Our quantum dot is formed from a sample of 2,600(500) atoms loaded into the 12 μm × 14 μm waist of a high-finesse single-mode optical resonator (Fig. 1a,c, and Supplementary Information D for details), at a peak density of $$1\times 1{0}^{11}$$ cm−3 (see Methods in Supplementary Information A). These atoms are distributed over a 35 μm r.m.s. axial length that may be reduced to 10 μm r.m.s. by spatially selective optical depumping, or ‘slicing’ (see Supplementary Information C). Due to strong light–matter coupling ($${{\rm{OD}}}_{{\rm{B}}}\approx 13$$), the modes of the system hybridize, forming polaritons (Fig. 1b): composite states of a resonator photon with an atomic excitation. Two of the hybridized modes are ‘bright’ polaritons, composed primarily of an admixture of a resonator photon and a short-lived P-state excitation; they are weakly interacting due to their small Rydberg component and short lifetime. The third polariton, called the ‘dark’ polariton, is composed of a coherent superposition of a Rydberg excitation and a resonator photon, with the mixing ratio set by θ, the dark-state rotation angle31. For our typical conditions, $${\rm{\tan }}\theta =\sqrt{N}g/\Omega =2.9(5)$$, where N, g and Ω are the atom number, single-atom Rabi frequency and control-field Rabi frquency, respectively. The Rydberg component of the dark polariton enables it to strongly repel other dark polaritons within a surrounding ‘blockade volume’, which scales with $${n}^{11/2}$$ (for van der Waals interactions), where n is the Rydberg level’s principal quantum number. It is for this reason that we typically employ the $$n=100$$ Rydberg state, as the atoms' extreme properties make this blockade volume comparable to the sample size. Confining the region of overlap between the resonator mode and the atomic gas to be smaller than the blockade volume gives rise to a zero-dimensional, strongly interacting polaritonic quantum dot; like its solid-state counterpart, the electronic quantum dot32, it is expected to exhibit blockaded transport (Fig. 1d).

To investigate the polaritonic excitations of our quantum dot, we first probe the transmission spectrum of the laser-dressed cavity–atom system. In Fig. 1b, we plot the quantum dot’s transmission spectrum on the $$\{5{S}_{1/2},\,F=2\}\to \{5{P}_{3/2},\,F=3\}\to \{100{S}_{1/2}\}$$ transition, without slicing the cloud. We observe two broad resonances that we identify as bright polaritons, whose spectral separation is an indication of strong light–matter coupling. The central feature is the spectrally narrow dark polariton. As we increase the probe power, the fractional transmission on the dark polariton resonance drops, as shown in Fig. 2, indicating that the repulsion between these polaritons suppresses their simultaneous injection into the dot.

To demonstrate that individual dark polaritons interact strongly with one another within the quantum dot, we explore transport dynamics. We test transport by injecting photons into the resonator at the energy of the dark polariton, such that most photons become dark polaritons on entering. The strong repulsion between polaritons shifts the energy and reduces the lifetime of a second polariton in the dot, thereby precluding its injection. In an electronic quantum dot, the analogous Coulomb-blockade physics is typically ascertained from the dependence of transport on bias voltage32; by contrast, we directly observe suppression of simultaneous polariton transit by detecting when photons tunnel through the dot. We characterize the tunnelling times via the temporal intensity autocorrelation function, $${g}_{2}(\tau )$$, where τ is the delay time, of the cavity transmission. This function compares the rate of photon pairs leaking out of the resonator separated by a time τ to a Poisson process with the same average rate. A reduction near zero delay ($$\tau =0$$) indicates interaction-driven suppression of double-occupancy of the dot, while the rise time back to steady state is dominated by the injection Rabi frequency.

After slicing the cloud so that it can hold only a single polariton at a time, we observe almost complete suppression ($${g}_{2}(0)=0.27(8)$$) of simultaneous tunnelling through the dot, indicative of transport blockade due to strong interactions (Fig. 3a). Indeed, strong anti-bunching at zero-time separation validates a model where a single intracavity polariton shifts and broadens the energy for the injection of the next polariton by more than the polariton linewidth, strongly suppressing its tunnelling into the resonator until the first polariton tunnels out. The observed $${g}_{2}(\tau )$$ is consistent with a master-equation effective theory bootstrapped by a full model of interacting three-level atoms coupled to a single resonator mode (see Supplementary Information J). Note that the linear growth of $${g}_{2}(\tau )$$ near zero delay, as opposed to the quadratic growth anticipated from a single-mode theory, arises from virtual excitation of bright polaritons.

We verify that the observed transport blockade results from strongly interacting polaritons by comparing the observations to transport with weaker interactions. First, we test the unsliced cloud (Fig. 3a), which exhibits only weak suppression of g2 near $$\tau =0$$ because the cloud is large enough to hold multiple polaritons along the resonator axis simultaneously. Similarly, a sliced sample with Rydberg atoms in the smaller 85S state can fit multiple excitations transversely and also exhibits weak suppression of g2 (Fig. 3b). Furthermore, we find that transport of bright polaritons is not blockaded at all (Fig. 3b), as these polaritons are essentially non-interacting33. The blockade of the dark polaritons can even be `reversed' by detuning from the atomic 5P state to make the polariton–polariton scattering more elastic and probing transport on the two-polariton resonance (Fig. 3c). In this case, we observe photon bunching, $${g}_{2} > 1$$, reflecting the preferential transit of photon pairs34.

To investigate the dimensionality of the polaritonic dot, we probe the cavity with pulses of substantially higher intensity and observe the transmitted light as the intracavity field rings up and then down. A zero-dimensional system may be coherently excited and then de-excited by the drive field, exhibiting Rabi oscillations, while in a one-dimensional system the excitation would propagate away before it can be removed. Figure 4a shows the detuning dependence of the ring-up process, exhibiting rapid, detuned Rabi oscillations away from the dark-polariton resonance, and slower oscillations on-resonance. Figure 4b shows the ring-up dynamics on the dark-polariton resonance for various probe intensities. We observe Rabi oscillations between zero and one dark polaritons at the highest intensities, indicative of a strongly blockaded, zero-dimensional dot interacting with many photons within the polariton lifetime. The dark-polariton oscillations exhibit a Rabi frequency of $${\Omega }_{{\rm{polariton}}}=2{\rm{\pi }}\times 245$$ kHz, in agreement with a first-principles calculation based on the probe power (see Supplementary Information G). Note that the fast ~100 ns oscillations arise from off-resonant excitation of non-interacting bright polaritons.

Strong interactions should cause the number of dark polaritons in the dot to saturate at large probe powers. However, the off-resonant excitation of bright polaritons does not saturate, resulting in a high steady-state leakage rate of bright polaritons that overwhelms the dark-polariton signal at high probe powers. To disentangle the bright and dark contributions to the cavity transmission, Fig. 4c shows the ring-down of the dot once the probe beam is turned off. At each probe intensity, the ring-down consists of slow and fast exponential decays; the slow feature (with a time constant of 730(40) ns) reflects the dynamics of the dark polariton, while the fast feature reflects the decay of the interfering bright polaritons. We isolate the steady-state dark-polariton number, shown in Fig. 4d, by extrapolating the slowly decaying tail of the ring-down to its zero-time population. The strong saturation of the dark-polariton number with drive power again indicates blockade, while the saturation value of $${n}_{{\rm{D}}}=0.47(3)$$ reflects the behaviour of a single zero-dimensional two-level emitter, as described by the optical Bloch equations. This stationary, strongly coupled, two-level emitter is an excellent candidate qubit for a photonic quantum information processor35. To verify saturation, we measure the g2 of the slowly decaying tail of the ring-down, after the bright polaritons have all decayed away. We find $${g}_{2}=0.31(7)$$, confirming that the dot rarely hosts multiple dark polaritons. Moving forward, blockade-enhanced detection of dark polaritons will directly boost the dark-polariton detection signal-to-noise above the bright-polariton background36, while enhanced control-field and light–matter coupling will suppress the background (see Supplementary Information H), enabling the dot to act as an on-demand single-photon source.

Cavity Rydberg polaritons are now ripe for applications in synthetic quantum materials; recent experiments have demonstrated synthetic magnetic fields for resonator photons3 and in conjunction with the present work, there is now a clear path to topological many-photon states6. More broadly, the numerous proposals to study synthetic quantum matter in cavity arrays and continua1 can now be explored in the modes of an individual, multi-mode optical cavity, employing Rydberg atoms to mediate strong photon–photon interactions. Achieving stronger light–matter coupling will require only additional atomic density, rather than increasingly challenging advances in optical super-mirror technology necessary for single-emitter approaches. Indeed, densities routinely achieved in free-space experiments ($$\rho \approx 1{0}^{12}$$ cm3)23 and finesses of single-atom experiments ($$F\approx 1{0}^{5}$$) would provide $${{\rm{OD}}}_{{\rm{B}}}\approx 88,000$$, more than sufficient for few-particle synthetic materials6. Therefore, upcoming challenges centre on harnessing these developments to answer questions about dissipative preparation of many-body quantum states37,38 and about the exploration of the resulting phase diagrams39 using the quasi-particle manipulation and detection tools unique to quantum optics40,41.

### Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

We would like to thank M. Fleischhauer and H. P. Buechler for fruitful conversations. This work was supported by DOE grant DE-SC0010267 for apparatus construction, DARPA grant W911NF-15-1-0620 for modelling, and MURI grant FA9550-16-1-0323 for data collection and analysis. A.G. acknowledges support from the UChicago MRSEC grant NSF-DMR-MRSEC 1420709. A.R. acknowledges support from the NDSEG Fellowship.

## Author information

### Author notes

• Albert Ryou

Present address: Department of Electrical Engineering, University of Washington, Seattle, WA, USA

• Ariel Sommer

Present address: Department of Physics, Lehigh University, Bethlehem, PA, USA

### Affiliations

1. #### Department of Physics and James Franck Institute, University of Chicago, Chicago, IL, USA

• Ningyuan Jia
• , Nathan Schine
• , Alexandros Georgakopoulos
• , Albert Ryou
• , Logan W. Clark
• , Ariel Sommer
•  & Jonathan Simon

### Contributions

The experiment was designed and built by all authors. J.N., N.S., L.W.C. and J.S. collected and analysed the data. All authors contributed to the manuscript.

### Competing interests

The authors declare no competing interests.

### Corresponding author

Correspondence to Jonathan Simon.

## Supplementary information

1. ### Supplementary Information

Supplementary notes, supplementary figures 1–9, supplementary references