Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Förster resonances

Abstract

Mapping the strong interaction between Rydberg atoms onto single photons via electromagnetically induced transparency enables manipulation of light at the single-photon level and few-photon devices such as all-optical switches and transistors operated by individual photons. Here we demonstrate experimentally that Stark-tuned Förster resonances can substantially increase this effective interaction between individual photons. This technique boosts the gain of a single-photon transistor to over 100, enhances the non-destructive detection of single Rydberg atoms to a fidelity beyond 0.8, and enables high-precision spectroscopy on Rydberg pair states. On top, we achieve a gain larger than 2 with gate photon read-out after the transistor operation. Theory models for Rydberg polariton propagation on Förster resonance and for the projection of the stored spin-wave yield excellent agreement to our data and successfully identify the main decoherence mechanism of the Rydberg transistor, paving the way towards photonic quantum gates.

ARTICLE

Received 15 Mar 2016 | Accepted 6 Jul 2016 | Published 12 Aug 2016

H. Gorniaczyk1, C. Tresp1, P. Bienias2, A. Paris-Mandoki1, W. Li3, I. Mirgorodskiy1, H.P. Bchler2, I. Lesanovsky3 &S. Hofferberth1

Mapping the strong interaction between Rydberg atoms onto single photons via electromagnetically induced transparency enables manipulation of light at the single-photon level and few-photon devices such as all-optical switches and transistors operated by individual photons. Here we demonstrate experimentally that Stark-tuned Frster resonances can substantially increase this effective interaction between individual photons. This technique boosts the gain of a single-photon transistor to over 100, enhances the non-destructive detection of single Rydberg atoms to a delity beyond 0.8, and enables high-precision spectroscopy on Rydberg pair states. On top, we achieve a gain larger than 2 with gate photon read-out after the transistor operation. Theory models for Rydberg polariton propagation on Frster resonance and for the projection of the stored spin-wave yield excellent agreement to our data and successfully identify the main decoherence mechanism of the Rydberg transistor, paving the way towards photonic quantum gates.

DOI: 10.1038/ncomms12480 OPEN

Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Frster resonances

1 5th Institute of Physics and Center for Integrated Quantum Science and Technology, Universitat Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.

2 Institute for Theoretical Physics III and Center for Integrated Quantum Science and Technology, Universitat Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany. 3 School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK. Correspondence and requests for materials should be addressed to H.G. (email: mailto:[email protected]

Web End [email protected] ) or to S.H. (email: mailto:[email protected]

Web End [email protected] ).

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12480

Rydberg excitations of ultracold atoms1 are currently attracting tremendous attention because of possible applications in quantum computing25 and simulation610.

One particular aspect is the realization of few-photon nonlinearities mediated by Rydberg interaction1114, enabling novel schemes for highly efcient single-photon generation15,16, entanglement creation between light and atomic excitations17, single-photon all-optical switches18 and transistors19,20, single-photon absorbers21 and interaction-induced photon phase shifts22,23. Interacting Rydberg polaritons also enable attractive forces between single photons24, crystallization of photons25 and photonic scattering resonances26. The above experiments and proposals make use of the long-range electric dipoledipole interaction between Rydberg atoms2731. A highly useful tool for controlling the interaction are Stark-tuned Frster resonances, where two dipole-coupled pair states are shifted into resonance by a dc32 or microwave33,34 electric eld. Frster resonances have been studied by observation of dipole blockade35, line shape analysis36, double-resonance spectroscopy37, excitation statistics38 and Ramsey spectroscopy39,40. Recently, resonant four-body interaction41 and the anisotropic blockade on Frster resonance42 and quasi-forbidden Frster resonances43 have been observed, and Frster resonances between different atomic species have been predicted44. For Rydberg-mediated single-photon transistors, the near-resonance in zero eld for specic pair states has been used to enhance the transistor gain20, while in experiments on Rydberg atom imaging45,46 an increase in Rydberg excitation hopping has been observed on resonance47.

In this work, we use Stark-tuned Frster resonances to greatly increase the interaction between individual photons inside a Rydberg medium. We achieve this by tuning pair states |S(g),S(s)i

containing two different Rydberg S-states into resonance with |P(g),P(s)i pair states by an electric eld. We show that for gate

and source Rydberg states |50S1/2,48S1/2i, we can boost the

performance of a Rydberg single-photon transistor. When operated classically, we achieve G4100, enabling high-delity

detection of single Rydberg atoms. This improved transistor can be operated such that the gate photon is read out with nite efciency, reaching a gain G42. We develop theoretical models

for the dynamics of Rydberg polaritons in the presence of Frster resonances and the loss of coherence due to photon scattering. Excellent agreement with our experimental data is found. Finally, our all-optical probe represents a novel approach for the high-resolution study of the substructure of Frster resonances caused by ne structure and Stark/Zeeman splitting of the |P(g),P(s)i

pair states. We demonstrate this technique by resolving the multi-resonance structure of the |66S1/2,64S1/2i pair state.

ResultsExperimental set-up. Our experimental scheme13,19,20,45 is shown in Fig. 1a,b: by coupling the excited state |ei and the

Rydberg state |S(g)i with a strong light eld Og with detuning dg,

a gate photon Eg is converted into a Rydberg excitation inside a

cloud of ultracold 87Rb atoms. We then probe the presence of this gate excitation by monitoring the transmission of source photons

E coupled via electromagnetically induced transparency (EIT) to

the source Rydberg state S(s). Specically, we use (dg 40 MHz)

for efcient Raman absorption of the gate photon in the experiments without retrieval, while we use EIT-based slow light techniques (dg 0) for photon storage in experiments with

gate photon retrieval. At zero electric eld, the interaction between the |S(g),S(s)i pair is of van der Waals type. The

difference in electric polarizability between S- and P-states enables the shift of the initial pair state into degeneracy with specic |P(g),P(s)i pairs, resulting in resonant dipoledipole

interaction. We shift the Rydberg levels by applying a homogeneous electric eld along the direction of beam propagation. Active cancellation of stray electric elds is done with eight electric eld plates in Lw conguration48, while the homogeneous eld results from additional voltages V ,V to four electrodes (Fig. 1a).

Stark-tuned optical nonlinearities. We rst study the pair state |S(g),S(s)i |66S1/2,64S1/2i. Due to the ne structure splitting of

the Rydberg P-states, this pair is near resonant with two P-state pairs |65P1/2,64P3/2i and |65P3/2,64P1/2i20. Both |P(g),P(s)i pairs

can be tuned into resonance at electric elds Eo0:25 Vcm 1. The full pair state Stark map in the presence of a magnetic eld B 1 G (Fig. 1c, gray lines) reveals a large number of closely

spaced resonances arising from the non-degenerate mgj; msj

combinations. The strength of individual resonances depends on the angle y between the interatomic axis and the quantization axis dened by the external elds, resulting in a non-spherical blockade volume29. We explore these resonances by measuring the optical gain

G

Nnogates;out

Nwithgates;out

Ng;in; 1

that is, the mean number of source photons scattered by a single incident gate photon20, as a function of applied electric eld (Fig. 1c). Our high-resolution spectroscopy indeed reveals four resonances, matching with the calculated crossings of different pair state groups. In between resonances, the coupling of |S(g),S(s)i to multiple |P(g),P(s)i pair states with positive and

negative Frster defects results in smaller blockade than in the zero-eld case. This interplay between different resonances actually decreases the measured gain with respect to the eld-free value. This situation does not occur for the Frster resonance |50S1/2,48S1/2i2|49P1/2,48P1/2i at Eo0:710 Vcm 1 (Fig. 1d). For

this state combination there is one isolated resonance, resulting in the single peak in the optical gain.

Rydberg polaritons near Frster resonance. To quantitatively describe the observed resonances, we include in the microscopic description of polariton propagation13,14,26 the special character of the interaction close to Frster resonance, see Supplementary Note 1. For illustration, we consider the |50S1/2,48S1/2i pair

and angle y 0, which results in the selection rule

DM Dmgj Dmsj 0 for the magnetic quantum numbers

of the involved states. We then need to include four pair states: {|50S1/2,48S1/2i, |49P1/2,48P1/2i, |48P1/2,49P1/2i, |48S1/2,50S1/2i}

with mgj; msj

1

2; 12

.

=

In this basis, the interaction Hamiltonian reduces to

Hddr

1 r3

0

B

B

@

0 C3 C03 0 C3 0 0 C03

C03 0 0 C3 0 C03 C3 0

1

C

C

A

2

with two dipolar coupling parameters C3, C30. Since the interaction is dominated by the Frster resonance, we neglect any residual van der Waals interactions. In general, the Hamiltonian (2) gives rise to ip-op (hopping) processes of type |50S1/2,48S1/2i-{|49P1/2,48P1/2i, |48P1/2,49P1/2i}-|48S1/2,50S1/2i.

However, for this choice of Rydberg states the dipolar coupling parameters satisfy C3cC30, and therefore provide a strong suppression of hopping49. This behaviour is in contrast to the results in ref. 47, where hopping processes strongly inuenced the interaction-mediated imaging of Rydberg excitations. In the experimentally relevant regime with o, gs, gpooO, g, where o is the source photon detuning, while gs and gp describe the decoherence

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12480 ARTICLE

a

c

d

V

[afii9830]g

[afii9830]g [afii9828]

[afii9828]s

g

V +

16

12

Optical gain

E E 0(MHz)

Electric eld, (V cm1) Electric eld, (V cm1)

14

10

Optical gain

12

8

10

6

V

V +

8

4

6

2

b

4

0

U (r )

10

50 0.1 0.15 0.2 0.25

10

50 0.0 0.2 0.4 0.6 0.8 1.0

S (g) S (s)

0

0

E E 0(MHz)

10

10

g

20

20

30

30

[afii9829]g

40

40

e

g

[afii9830]

[afii9830]

Figure 1 | High-resolution spectroscopy of Frster resonances. (a) Tightly focussed source and gate beams (w0 6.2 mm) are overlapped with an

optically trapped cloud of 2 104 87Rb atoms at 3 mK (cylindrical 1/e dimensions L 40 mm, R 10 mm). For each transistor operation the optical trap is

shut off for 200 ms. We perform 23 individual experiments in a single cloud, recapturing the atoms in-between with minimal loss and heating. In-vacuum electrodes are used to apply the electric eld. (b) Level scheme for gate and source photons coupled to different Rydberg states, where 2O is the Rabi frequency of the control eld and 2g is the decay rate of |ei. (c,d) At certain electric elds (vertical dashed lines), the |S(g),S(s)i pair state is resonant to pair

states of type |P(g),P(s)i. The enhancement of interaction between |S(g)i and |S(s)i manifests in peaking of the transistor gain (blue dots). In c, the ne

structure of the involved P-states and the mJ-dependence of the Stark-shift result in the observed multi-resonance structure. The blue solid line is a

theoretical analysis of the full-polariton propagation in the presence of the gate excitation. The error bars are the s.e.m.

rates of |S(s)i and |P(s)i excitations, the equation describing a single

polariton Er; o and its interaction with the gate Rydberg

excitation |S(g)i at position rj simplies to

ic@r

g2 o igs

!E

r; o 0 3

O2

g2Vjefr O2 igVjefr

p is the

collective coupling strength with g0 being the single-atomphoton coupling strength and nat is the atomic density. The effective interaction Vjef simplies to

Vjefr

C23

DD o igp

as derived in our Supplementary Note 1. Here g g0

nat

1

r rj 6

4

where DD is the Frster defect. It is remarkable that, regardless of DD, our microscopic derivation provides an effective interaction always based on van der Waals type interaction.

For comparison with experiment, we generalize our calculation to nonzero angles y between the quantization and interatomic axis, as well as to the larger number of states involved for the |66S1/2, 64S1/2i pair. We then integrate equation (3) over the

cloud shape and average over the stored spin-wave. We also take into account the Poissonian statistics of the gate and source photons, the storage efciency, the fact that the blockade radius is comparable to the beam waist and the nite experimental resolution in electric eld DE 2 mVcm 1, see

Supplementary Note 1. The comparison, without any free parameters, with experimental results for the gain is shown in Fig. 1. We nd very good agreement for all electric elds except very close to the resonances. One reason for the discrepancy is the following: Close to the Frster resonance and for distances on the order of rb between gate and source, the atomic part of the polariton-excitation pair initially in |50S1/2,48S1/2i is converted

into the superposition of |49P1/2,48P1/2i and |50S1/2,48S1/2i.

This results in additional slowing down of the polariton, and, consequently, an accumulation of polaritons close to rb. Then, the assumption to study the propagation of individual polaritons breaks down as the interaction between the polaritons has to be included.

Resonant single-photon transistor. Next, we investigate to what extent these Frster resonances can be used to improve the Rydberg single-photon transistor19,20. We nd that for this application, the |50S1/2, 48S1/2i resonance is ideal. It enables large-

source photon input rates, because of the relatively weak van der Waals interaction between two source photons. On the other hand, the Frster resonance provides sufcient gatesource interaction to observe high transistor gain. For source photon rate Rin 35 ms 1, we reach a maximal gain of G 200. At

such high source rates, we observe small temporal changes in transmission, which we attribute to an accumulation of stationary Rydberg excitations in the medium caused by dephasing of single-source polaritons. This effect has been previously observed for Rydberg S-states14 and differs from the interaction-induced dephasing of D-state polariton pairs50. This accumulation sets an upper limit on the source photon rate for the non-destructive imaging of single Rydberg excitations45, since the creation of additional Rydberg atoms also destroys the original system. We thus restrict our analysis in Fig. 2 to non-destructive source input rates for which the maximum temporal change in source transmission remains o10%. In this regime, we observe a linear increase of the optical gain with Rin both at zero electric eld and on the Frster resonance (Fig. 2a). Exploiting the Frster resonance, we can improve the optical gain by a factor 42 on resonance (blue dots) compared with the zero-eld case (blue squares). The large number of source photons scattered from a single-gate excitation enables the single-shot detection of a stored gate photon with high delity18,19,51, see Methods. In Fig. 2, we show this delity as a function of the applied electric eld for two source photon rates. The Frster resonance enables a substantial increase of the delity to a maximal value of

F 0:8. This number is mainly limited by the fact that our beam

waist w0 is slightly larger than the gatesource blockade distance. For spatially resolved Rydberg detection45,46, even higher delities are possible using imaging systems with better optical resolution than our beam size w0 6.2 mm.

Single-photon transistor with gate photon read-out. The improved gatesource interaction on Frster resonance enables us for the rst time to operate our transistor with retrieval of the

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12480

a

b

a

Nin

[epsilon1] = 0.710 V cm1

[epsilon1] = 0 V cm1

0 13.6 13.6

Rin = 12.2 s1 Rin = 0.70 s1

2

r

1

Fidelity

Storage and retrieval effciency

0.8

0.0 0.2 0.4 0.6 0.8 1.0

101

100

Optical gain, G

1

2

Fp Fs

F

Detection delity, F

80

5

0.7

0.7

60

0

40

0.6

0.6

2

20

= 0 V cm1

F~0e N

in

F~0e N

r in

F~0e N

sc

= 0.71 V cm1

0.5

0.5

102

0 0 2 4 6 8 10 12 14

Rin (s1) Electric eld, [epsilon1] (V cm1)

Figure 2 | Transistor gain and single Rydberg detection. Performance of the single-photon transistor on the |50S1/2,48S1/2i2|49P1/2,48P1/2i

resonance. (a) Gain and single Rydberg detection delity increase linearly with the rate of incident source photons Rin in the non-destructive range, where the creation of stationary excitations from source photons is negligible. Both the optical gain (a) and the single Rydberg detection delity (a,b) are highly amplied on the Frster resonance at E 0:710 Vcm 1.

The solid curves are linear or Lorentzian ts to guide the eye. The error bars are the s.e.m.

5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 Scattered source photons

Figure 3 | Transistor operation with retrieval of the gate photon.(a) Efciency of storing and reading out one single gate photon versus the number of scattered source photons during the storage time of 4.2 ms.

When plotted as function of scattered photons, the observed retrieval efciencies on Frster resonance (red dots) and in zero eld (blue squares) are identical. (b) Calculated delity, that is, the overlap between the initial gate spin-wave state and the nal state after the propagation of a source photon through a one-dimensional Gaussian atomic cloud. The delity is the sum of contributions from scattered (short dashes) and transmitted (long dashes) source polaritons. The lines in a show the predicted decay of retrieval efciency using the full propagation model (solid blue line),as well as different limiting cases (see main text for details).

stored gate photon after the transistor operation51. To store the gate photon, we stop the polariton inside the medium by ramping down the control eld Og to zero for dg 0. Conversely, to read

out the gate photon, Og is turned on again. Without any source photon input between the storage and the read-out, we measure a lifetime of 3.6 ms for the atomic coherence of the stored gate spin-wave, mainly limited by the nite temperature of our atomic sample. Next, we apply a source pulse containing a mean number of photons

Nin and pulse length T 3.2 ms during a storage time

of 4.2 ms. On Frster resonance, we achieve a mean number of scattered source photons within this time of up to 2.7 photons for a single stored gate photon (Fig. 3a). This is the rst demonstration of a transistor with gain G42 and read-out,

a fundamental step towards quantum circuits employing feedback and gain or the non-destructive detection of the gate photon52.

The overall delity of the transistor is limited by projection and dephasing of the gate spin-wave due to scattered and transmitted source photons51,53. In Fig. 3a, we show the absolute retrieval efciency versus incident and scattered source photons at a mean number of

Ng;in 0:8 incident gate photons on and off the Frster

resonance. Interestingly, both cases collapse onto one exponential decay if plotted versus the number of scattered source photons. The black curve in Fig. 3a assumes zero retrieval delity for one or more scattered source photons. The dotted line and the dashed line, on the other hand, investigate the other hypothetic cases that the coherence of the gate spin-wave is destroyed by one photon of

Nin incident

mean photons (dashed) and by one photon of

Nrbin mean photons incident on the blockade sphere (dotted), respectively. By applying established theory to our data in the next section, we will show that both transmitted photons and scattered photons contribute to the coherence and thus to the retrieval efciency of the stored spin-wave.

Theory on coherent spin-waves. For more quantitative analysis we follow ref. 53, considering a one-dimensional (1D) model of the zero-eld case for a single-source photon passing through the atomic cloud with Gaussian density prole. The gate photon is stored in the initial spin-wave state ^

ri and interacts with source photons via the potential from equation (4). After the source photon has left the atomic cloud, the state of the atomic ensemble is ^

rf , and the quantum mechanical delity between the initial and nal state is given by F Tr

^

ri

p

^

rf

p

2

Fp Fs (ref. 54).

Here, Fp accounts for transmitted and Fs for scattered source polaritons. Both contributions are shown in Fig. 3b as a function of the blockade radius rb (gC6/O2)1/6 for our experimental

parameters. For large blockade radii, Fp becomes negligible because source photons are rarely transmitted through the blockaded region. To describe the experimental 3D situation, we average the delities from Fig. 3b over the spatial transversal distribution of gate and source photons. With this approach, we obtain the blue solid line in Fig. 3a, which is in very good agreement with our data, despite the simplications of our model. We consider this as evidence for the assumed mechanisms for the spin-wave decoherence to be correct. By identifying the decoherence mechanisms, we can isolate the required improvements for a high-delity coherent Rydberg transistor: the blockade volume of a single-gate excitation must be larger than the stored gate spin-wave to avoid the projection, while the optical depth ODB inside the blockaded region must be large to prevent the dephasing due to transmitted photons. Meeting both requirements simultaneously is challenging due to limits on the atomic density because of Rydberg-ground state interaction18,55.

DiscussionRydberg-mediated single-photon nonlinearities can be greatly enhanced by electrically tuning adjacent pair states to Frster resonance. By carefully choosing the employed Frster resonance, we have simultaneously improved the Rydberg transistor gain and the delity of single Rydberg atom detection. We identify the |50S1/2,48S1/2i2|49P1/2,48P1/2i resonance in 87Rb as ideal both

for the Rydberg single-photon transistor and non-destructive imaging of Rydberg atoms45,46. Exploiting this resonance, we have demonstrated the rst operation of the Rydberg transistor with read-out of the gate photon. Our quantitative analysis of the reduction of retrieval efciency caused by source photons points

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12480 ARTICLE

the way towards high-delity Rydberg-based photonic gates and transistors. Our polariton propagation theory correctly accounts for the enhanced sourcegate interaction and is in excellent agreement with the experiment. It also reveals unexpected and rich properties close to Frster resonances. This regime enables study of the transition from two- to many-body interaction and propagation with excitation hopping47,56. The complexity of the resonances due to the Rydberg-level structure provides a wide range of tuning options. The gatesource interaction can be reduced or even switched off between individual resonances. Similarly, by addressing different Zeeman pair state resonances with the external eld the angular dependence of the interaction can be greatly varied. This provides a rich set of new tools for tailoring the interaction of photons coupled to different Rydberg states inside the medium.

Methods

Preparation of the ultracold atomic sample. We load 87Rb from a constant Rubidium background pressure of 10 9 mbar atoms into a magneto-optical trap (MOT). Simultaneously, a crossed optical dipole trap (ODT) from a bre laser at a wavelength of 1,070 nm superimposes the MOT and attracts atoms of both 52S1/2 hyperne ground states (F 1,2). After 1 s of loading, the MOT is compressed by

ramping up the quadrupole magnetic eld by a factor of 8 during 40 ms followed by an optical molasses phase of 5 ms, to maximize the number of atoms loaded into the ODT. The intensity of the ODT laser is ramped down within 200 ms to perform forced evaporation yielding 2 104 atoms with a temperature 3 mK in a cigar shaped

trapping potential with a 1/e half length of L 40 mm and a radius of R 10 mm.

Finally, by shining in two pumping lasers, we transfer atoms from the F 1 state to

the F 2 state and optically pump the population to the stretched state mF 2.

Probing the optical nonlinearity. The gate excitation and the source EIT are realized with four independent laser systems, with the lower transition gate and source photons (near-)resonant to the MOT transition to achieve a maximum optical depth and thus highest efciency of single-photon absorption. The upper transition is at 480 nm. All four laser beams are overlapped on one axis with polarization optics and dichroic mirrors. Achromatic lenses are used from both sides to focus and collimate the laser beams. The transmitted source and gate photons are coupled through single-mode bres and detected on commercial avalanche photodiodes. Taking loss at optics and bre coupling into account, photons in the experiment are detected with an efciency of 30%.

Data acquisition. To reduce the statistical error, we average over multiple experiments. For instance, the data points in Fig. 1c are gathered during 23 transistor measurements per MOT cycle. We measure at 1 electric eld during 20 MOT cycles. The same procedure is repeated for the reference measurement which contains no gate photons. The elds are scanned in a triangular electric eld scan which was repeated 15 times. That way, systematic errors are suppressed. In addition, by monitoring the source transmission we make sure that electric eld drifts are negligible during the measurement. A similar procedure was done to measure the data in Fig. 2, but with yet another scan dimension, the source photon rate.

Single Rydberg detection. The attenuation of many source photons due to one gate photon (gain) is used to predict the single-shot existence of a gate Rydberg excitation via the number of detected source photons. If a low number of source photons is detected, probably a gate excitation was present which attenuated the source. Likewise, if a high number of source photons is detected, probably the gate excitation was absent. To quantify the minimum probability of the correct prediction (detection delity), we take two histograms of detected source photons, with and without incident gate photons, respectively. With the knowledge of the storage efciency (60%) and the Poissonian statistics of the coherent gate photons (mean value

Ng 1), it is possible to separate the histogram with this mean gate

photon input into two histograms, one corresponding to the events with no gate excitations present and one with gate excitations. With a discrimination line, we set a threshold value for the decision whether or not the excitation was present. Any overlap of both histograms through this line results in a delity Fo1.

Data availability. The data that support the ndings of this study are available from the corresponding author upon request.

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Acknowledgements

We thank Johannes Schmidt for construction of the electric eld control; Sebastian Weber for calculation of Rydberg potentials; and Christian Zimmer for contribution to the experiment. This work is funded by the German Research Foundation through Emmy-Noether-grant HO 4787/1-1 and within the SFB/TRR21. H.G. acknowledges support from the Carl-Zeiss Foundation. I.L. acknowledges funding from the European Research Council under the European Unions Seventh Framework Programme (FP/20072013)/ERC Grant Agreement No. 335266 (ESCQUMA), the EU-FET Grant No. 512862 (HAIRS), the H2020-FETPROACT-2014 Grant No. 640378 (RYSQ) and EPSRC Grant No. EP/M014266/1. W.L. is supported through the Nottingham Research Fellowship by the University of Nottingham and acknowledges access to the University of Nottingham HPC Facility.

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Author contributions

The experiment was conceived by H.G., C.T. and S.H. and carried out by H.G., C.T., A.P.-M., and I.M.; data analysis was done by H.G., A.P.-M. and C.T.; theory models and calculations were contributed by P.B., W.L., H.P.B., and I.L.; H.G. and S.H. wrote the manuscript with contributions from all authors.

Additional information

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How to cite this article: Gorniaczyk, H. et al. Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Frster resonances. Nat. Commun. 7:12480 doi: 10.1038/ncomms12480 (2016).

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